How Inert, Perturbing, or Interacting Are Cryogenic Matrices? A Combined Spectroscopic (Infrared, Electronic, and X-ray Absorption) and DFT Investigation of Matrix-Isolated Iron, Cobalt, Nickel, and Zinc Dibromides

The interactions of FeBr2, CoBr2, NiBr2, and ZnBr2 with Ne, Ar, Kr, Xe, CH4, and N2 matrices have been investigated using IR, electronic absorption, and X-ray absorption spectroscopies as well as DFT calculations. ZnBr2 is linear in all of the matrices. NiBr2 is linear in all but N2 matrices, where it is severely bent. For FeBr2 and CoBr2 there is a more gradual change, with evidence of nonlinearity in Xe and CH4 matrices as well as N2. In the N2 matrices, the presence of νNN modes blue-shifted from the “free” N2 values indicates the presence of physisorbed species, and the magnitude of the blue shift correlates with the shift in the ν3 mode of the metal dibromide. In the case of NiCl2 and NiBr2, chemisorbed species are formed after photolysis, but only if deposition takes place below 10 K. There was no evidence for chemisorbed species for NiF2 and FeBr2, and in the case of CoBr2 the evidence was not strong.


■ INTRODUCTION
While the notion that the spectroscopic data obtained from species trapped in (noble) gas matrices are always directly comparable to those for their vapor-phase counterparts has been acknowledged as naïve, the need to identify and understand how matrices can affect the geometric and electronic structures of the trapped species remains. The matrix isolation literature is replete with asides and comments about site effects, matrix splittings, etc., usually invoked to explain some spectral artifact. For example PdCO is found in two sites in Ar, 1 as are CO 2 2 and SiH 4 . 3−6 In the case of PdCO, more recent calculations indicate the possible formation of Ar−PdCO. 7 However, in the related NiCO case, the computational work 8,9 indicated the possible presence of Ar−NiCO, but the experimentalists disputed this. 10,11 The ability of "inert" matrices to affect the structure of the trapped species has been demonstrated by Beattie and co-workers for both actinide tetrahalides and hexafluorometalates. ThCl 4 and UCl 4 are tetrahedral in neon but have a distorted C 2v geometry in argon. 12,13 The alkali metal hexafluorouranates are C 3v in solid argon but C 2v in nitrogen matrices. 14 The alkali metal hexafluoroniobates 15 have tridentate coordination in neon and argon matrices but a bidentate coordination mode in nitrogen and carbon monoxide matrices. Using CsClO 4 as a probe molecule, they showed that the order of host−guest interaction with the matrix was Ne < Ar < O 2 ≈ F 2 < Kr < Xe < N 2 < CO. 15 NiCl 2 is bent in nitrogen matrices but linear in argon matrices, 16,17 as is CoCl 2 . 17 SiH 4 adopts a D 2d geometry in argon but is C 3v in N 2 , 4−6 and GeH 4 is also C 3v in N 2 . 4,5 The absorption and excitation spectra of Mn atoms have been used to identify the different sites in which the Mn is trapped in Ar, Kr, and Xe matrices. 18 Fausto and co-workers have demonstrated how the choice of argon or xenon matrices can be used to control the photochemistry of 4-methoxybenzaldehyde. 19 Kofranek et al. 20 have carried out calculations on 1,3-butadiene embedded in an Ar 254 matrix, which confirmed that the argon matrix stabilizes the s-cis structure over the normally more stable gauche conformation.
It has normally been assumed that these matrix effects are due to different interactions between the trapped guest and the host rather than specific bond formation. However, there are a number of reports of noble gas (Ng) compound formation in matrices. Rasanen and co-workers 21−24 have beautifully demonstrated the formation of HArF when HF is photolyzed in argon. Their work also includes a wide range of other Kr and Xe compounds. 24 Perutz and co-workers showed that photolysis of matrix-isolated metal hexacarbonyls yielded metal pentacarbonyls with IR and UV−vis spectra that were dependent on the matrix material, indicating that the vacant site was occupied by a matrix atom with a weak metal−matrix bond, implying the formation of M(CO) 5 Ng complexes. 25−27 This work is often overlooked as one of the first reports of metal−noble gas bonding interactions. Later gas-phase measurements on M(CO) 5 Xe which the noble gas atoms act as electron donors into localized metal-based orbitals. 56 It was suggested that if the transition metal species trapped in the noble gas host has electrophilic character combined with low-lying empty or partially filled orbitals, then it will be able to coordinate with noble gas atoms, resulting in the formation of noble gas−transition metal complexes. An important observation was that while the coordination of the noble gas atom results in vibrational frequency shifts, there was no direct correlation between the matrix shifts and the strength of the noble gas coordination. 56 In the proceeding work, the evidence for interactions between the noble gas and the matrix-isolated species came from a combination of experimental (usually IR) data and calculations, as there are very few techniques that are able to directly yield bond distances from noble gas matrices. X-ray absorption spectroscopy is one of the few techniques that can yield direct structural information about both the matrix-isolated species and its interaction with the matrix host. The application of X-ray absorption spectroscopy to matrix-isolated species has recently been reviewed. 57 Gerry carried out extensive microwave studies of the gas-phase complexes between group 11 halides and noble gases (see ref 58 and references therein), and the complexes with xenon as a ligand are also important examples. 59−62 Therefore, there is considerable evidence that the noble gases, while providing an excellent medium for trapping reactive and unstable species, may actually exert a benign and often poorly characterized effect on the trapped species. While N 2 is often a very good matrix material, it is well-known that it can also have a considerable impact on the trapped species. For example, it can lift the degeneracy of degenerate modes, 63−65 and some 5d transition metal pentachlorides adopt a square-pyramidal geometry in N 2 but a variety of conformers in Ar. 66 N 2 matrices are also capable of exerting considerable influence on the structures of coordinatively unsaturated metal halides 16,17,67,68 and the formation of more formal complexes. 69−72 Therefore, it may be possible to identify two distinct aspects of interaction between the matrix and the trapped species, one that gives rise to compounds/complexes with significant bonding interactions and a second one that results in perturbation of the guest by the matrix. These could be compared to chemisorption and physisorption for surface species, especially for dinitrogen.
Photolysis was carried out with a LOT-Oriel 200 W Hg−Xe lamp equipped with a liquid light guide and appropriate filters.
The IR spectra were recorded using a Bruker IFS66 FTIR spectrometer equipped with a KBr beamsplitter for the mid-IR (MIR) and a 6 μm Mylar beamsplitter for the far-IR (FIR) along with DTGS detectors. The vacuum shroud used CsI windows and had a base pressure of ca. 2 × 10 −7 mbar before the APD DE204SL Displex closed-cycle helium cryostat (base temperature of ca. 9 K) was turned on. Temperature measurement and control were achieved via Si diodes and a Scientific Instruments 9650 controller. Depending on the experimental requirements, the deposition substrate was either a CsI polished window for transmission experiments (vacuum chamber within the spectrometer sample compartment) or a polished copper plate for reflectance experiments (vacuum chamber mounted externally).
Synchrotron radiation FIR (SR-FIR) spectra were collected using a Nicolet vacuum FIR bench on station 13.3 73 of the Daresbury Laboratory Synchrotron Radiation Source (SRS) operating in gapped beam mode at 2 GeV with circulating currents of ca. 180 mA. The deposition substrate was a polished copper block held at ca. 13 K with the incident and reflected beams at 135°to allow for in situ monitoring of the sample during both deposition and photolysis. The vacuum chamber was mounted between the optical bench and the He-cooled Ge bolometer, and the whole optical path was evacuated.
The UV−vis−NIR spectra were recorded using a Varian Cary 5E spectrometer with a similar vacuum and pumping regime as in the lab-based FTIR experiments, except that CaF 2 was used for the deposition substrate and the external windows on the vacuum chamber, which was mounted in the spectrometer sample compartment.
The X-ray absorption experiments utilized station 9.2 of the Daresbury Laboratory SRS, operating in either multibunch or gapped beam mode at 2 GeV with circulating currents of ca. 180 mA. A combined FTIR/XAFS facility 68,74 was used to collect simultaneous in situ IR and XAFS data from the same sample, which allowed for monitoring of the deposition as well as any subsequent annealing or photolysis. The metal and bromine K-edge XAFS spectra were collected in fluorescence mode (Tl/NaI scintillator) using a Si(220) double-crystal monochromator detuned by ca. 50% to remove harmonic contamination. Eight to 12 spectra were collected at each edge and then averaged. The 3d metal K-edges were calibrated using the first derivatives in the spectra of 5 or 10 μm metal foils (Fe, 7112.0 eV; Co, 7709.0 eV; Ni, 8333.0 eV; Zn, 9659.0 eV), and the Br K-edge was calibrated using the first derivative of the L 2 edge of a 5 μm Au foil (13 734.0 eV). 75 Background subtraction was carried out using PAXAS 76 by fitting the pre-edge region to a quadratic polynomial, subtracting this from the data, and approximating the atomic component of the postedge region with a high (typically sixth)-order polynomial. This approximation was optimized in order to minimize the low-r features in the Fourier transforms (FTs) by an iterative process, although it should be noted that atomic XAFS features may be expected in this part of the FT. 77,78 Fitting of the experimental data was carried out with EXCURV98, 79−81 making use of multiple-scattering curvedwave theory, a von Barth ground state, and a Hedin−Lundqvist exchange potential. For some samples, the metal K-edge and the Br K-edge were refined simultaneously. Although experiments utilizing Ne matrices are attractive, these were not conducted because complete isolation of the metal dibromide could not be guaranteed using the cryostat with a base temperature of 9 K under optimum conditions and data acquisition times of up to 24 h. The production of aggregates in these experiments would make the analysis of the data at best difficult and at worst meaningless. Experiments involving Ar are also intrinsically difficult for the 3d transition metals because of the short penetration depth of the matrix due to the high X-ray absorption cross-section of argon. For example, the attenuation length (1/e) for Ar at 8000 eV is ca. 50 μm. 82 The length of time for deposition is severely limited, as the increased thickness of the matrix soon cancels out any additional fluorescence due to the increase in deposited metal dihalide. For this reason, Kr and Xe experiments were also not possible, as these matrices have even higher X-ray absorption cross sections, with attenuation lengths of 40 and 10 μm, respectively, at 8 keV. In many ways CH 4 is an ideal matrix for XAFS work, as its X-ray absorption cross section is even lower than that of Ne. Therefore, in this work XAFS studies were conducted using CH 4 and N 2 matrices for FeBr 2 , CoBr 2 , and NiBr 2 and Ar matrices for FeBr 2 and CoBr 2 .
Force field calculations using the SVFF approach were carried out using the Wilson GF method within SOTONVIB. 83 DFT calculations were performed using the ADF program 84−86 at the BP86 level with triple-ζ (TZ2P) Slater-type orbital basis sets and relativistic effects at the ZORA level. 87 The excited states were calculated by changing the orbital configuration. Calculations were started from bent and linear starting points, and the vibrational frequencies were calculated to check that a minimum had been reached for that state. Time-dependent DFT (TD-DFT) calculations of the XANES spectra were carried out with ORCA 2.9.1 using the BP86 def2-TZVP(-f) def2-TZVP/J ZORA TightSCF methodology. 88−94 ■ SETTING THE SCENE Transition metal dihalides (MX 2 ) are ideal probes of matrix interactions, as they allow for variation in both hardness of the metal center as the halogen is changed and in the d-electron count as one goes across the series. While many matrix studies of the difluorides and dichlorides have been carried out, no complete sets of data are available for the related dibromides and diiodides. While data are available for CaBr 2 and CaI 2 in Ar and Kr 95 and ZnBr 2 and ZnI 2 in Ar and Kr, 96,97 there is much less data on the dibromides and diodes of the transition metals, with the only reports appearing to be on CrBr 2 in Ar and N 2 matrices 98 and NiBr 2 in Ar 68,99 and N 2 68 matrices. Infrared Spectroscopy. Linear MX 2 molecules have four vibrational degrees of freedom, whereas bent MX 2 molecules have three vibrational degrees of freedom. For the linear D ∞h molecules, the vibrational modes transform as Σ g + (ν 1 symmetric stretching mode), Π u (ν 2 bending mode), and Σ u + (ν 3 asymmetric stretching mode). Of these, only ν 2 and ν 3 are infraredactive, but in general the ν 2 mode is too low in energy to be observed on most spectrometers (<100 cm −1 ). The vibrational modes of the bent C 2v molecules span 2A 1 (ν 1 symmetric stretching mode and ν 2 bending mode) and B 2 (ν 3 asymmetric stretching mode), all of which are IR-active. As in the linear case, the low-frequency bending mode is expected to be beyond the range of most commercial spectrometers. Although the observation of the ν 1 mode in the IR spectrum is an obvious criterion for unambiguous evidence of a bent geometry in such molecules, its observation has been historically difficult, and assignment of both ν 3 and ν 1 has produced controversy even with such extensively studied systems as the alkaline-earth metal dihalides. 100 The intensity of the ν 1 mode is critically dependent on the bond angle and is expected to be observed only at fairly acute angles. Our DFT calculations indicate that the relative intensities of the ν 3 and ν 1 modes for bond angles of 155°and 130°i n metal dibromides (and dichlorides) are 50:1 and 10:1, respectively. Therefore, unless the molecule is severely bent, it will be almost impossible to identify the ν 1 mode with any certainty. Therefore, the absence of ν 1 is not unambiguous evidence for linearity in MX 2 compounds. While the chlorine isotope patterns for the 3d transition metal chlorides can be employed relatively routinely to obtain estimates of the bond angles, 16,17 the isotope splitting arising from bromine is much smaller and is often an experimental challenge to observe. Therefore, unless it is possible to identify the ν 1 mode unambiguously, the linearity or lack thereof cannot be determined from IR data alone unless either metal or bromine isotopic data are available. Although we have access to FT-Raman matrix facilities, which in principle allow for the identification of ν 1 directly, this is currently limited (because of the incident laser power) to chromophore:matrix ratios of about 1:200, which are too high for these type of experiments. As a result of these limitations, other spectroscopic techniques were employed in addition to IR spectroscopy.
Electronic Absorption Spectroscopy. UV−vis−NIR data on matrix-isolated transition metal dihalides in the literature are limited to the chlorides, although some vapor-phase data are available for the dibromides. For linear MX 2 species, the intensity of any d−d bands is expected to be very low because of the orbital and Laporte selection rules, but in the case of the nonlinear molecules, the Laporte selection rule is relaxed. Therefore, as noted previously, 101−103 the electronic absorption spectra will be dominated by charge transfer bands, with weak d−d bands observed only in some cases. As a result of this, the discussion of the spectra will be mainly based on assigning bands as either charge transfer or d−d bands and using the spectra as "fingerprints" indicative of a linear and nonlinear structure, rather than a detailed theoretical treatment.
X-ray Absorption Spectroscopy. In the past we have demonstrated that X-ray absorption fine structure spectroscopy (XAFS) is a powerful tool for determining interatomic distances of matrix-isolated species, 67,68,74,104−109 and this has recently been reviewed. 57 X-ray absorption spectroscopy is able to provide a detailed picture of both the local electronic and geometric structure of the matrix-isolated species. The electronic structure, which can also yield valuable information about the coordination geometry and oxidation state, is obtained from the X-ray absorption near edge structure (XANES) part of the spectrum located around the absorption edge. In contrast, bond length data are obtained from the oscillations in the absorption cross section after the absorption edge, which are known as extended X-ray absorption fine structure (EXAFS).
XANES. While metal K-edge XANES spectra are well-known to be diagnostic of the metal oxidation state, coordination number, and geometry for iron, 110 cobalt, 111 113 demonstrated that the intensity of the characteristic 1s → 4p edge feature in Cu(I) complexes is dependent on the copper coordination number. This has been widely used as a diagnostic probe of the electronic and geometric structure of copper metalloproteins. 114 Of more relevance to this work is that of Fulton 116 and on the basis of the work of Kau et al. 113 these were assigned to 1s → 4p transitions. With the use of TD-DFT calculations, 88−94 it is now possible to simulate the pre-edge and edge features in XANES spectra. Figure 1 presents the TD-DFT-calculated XANES spectra of NiBr 2 at 180°and 140°, showing both the individual transitions and also the molecular orbitals involved. The TD-DFT-calculated spectra do not look like conventional experimental XANES spectra, as they model only the electric dipole, electric quadrupole, and magnetic dipole transitions, which are superimposed on the 1s → continuum (edge) transition in the experimental spectra. In addition, there is an energy offset from the experimental values, and while empirical adjustments for this can be made, we have not done so. At 180°the spectrum is dominated by the dipole-allowed 1s → 4p transitions, in particular the intense transition at 8299.3 eV involving MOs with substantial Ni 4p x,y character and those at 8302.6 eV involving MOs with Ni 4p z character. The transitions at 8292.8 eV to MOs with substantial 3d xz,yz character are weak (one 400th of the main peak) and those at 8297.3 eV to MOs with 4s character are very, very weak (one 2300th), as they are dipole-forbidden but gain intensity from quadrupole and magnetic dipole transitions. Upon bending of the NiBr 2 molecule, the intensity of the transition from the 1s orbital to the 4p x,y orbitals is reduced because the two MOs are no longer degenerate, and as the bond angle becomes more acute, they resolve into two separate peaks. The most noticeable increase in intensity is for the 1s → 4s transition at 8296.5 eV, which is dipole-forbidden in the linear geometry but upon bending becomes dipole-allowed with a very small quadrupole The Journal of Physical Chemistry A Article contribution (∼0.3%). Of the two transitions at 8293 eV involving the 3d orbitals within 0.3 eV of each other, one is much more intense than the other by about an order of magnitude, but both are very much weaker than the 1s → 4s and 1s → 4p transitions. The lower-energy transition is essentially electric-dipole-forbidden and gains its intensity from magnetic dipole (36%) and electric quadrupole (64%) transitions, and this is an order of magnitude less intense than the second 1s → 3d transition, which has now become dipole-allowed (93%) with small magnetic dipole (2.5%) and electric quadrupole (4%) contributions. Figure 2 shows how the TD-DFT-calculated XANES spectra vary with bond angle for FeBr 2 , CoBr 2 , and NiBr 2 (the individual transitions and MOs are very similar to those for NiBr 2 shown in Figure 1). Therefore, the metal K-edge XANES spectra are expected to be very sensitive to changes in geometry. In particular, the presence of an intense edge feature in the experimental XANES spectra can be used diagnostically as an indicator of a linear geometry, and any reduction in its intensity can be attributed to nonlinearity. In addition, there is also expected to be an increase in the 1s → 3d based transitions as well the 1s → 4s transitions, but the latter may get masked by other changes in the edge structure.
EXAFS. In addition to the bond length information obtainable using EXAFS data, it is also possible to extract bond angle information. While this has been demonstrated previously from triangulation using the Br···Br and Br−M distances from the Br K-edge data, 68,105,118,119 multiple scattering paths through the central metal atom also yield valuable information from both the metal and bromine K-edges. The importance of these pathways as a diagnostic tool in determining the geometry at the metal center has been demonstrated in tetrahedral NiBr 2 (PPh 3 ) 2 , trans-NiBr 2 (PEt 3 ) 2 , and cis-NiBr 2 (dppe) (dppe = 1,2-bis-(diphenylphosphino)ethane) complexes. 120,121 The Fourier transforms of the Ni K-edge data of trans-NiBr 2 (PEt 3 ) 2 and cis-NiBr 2 (dppe) contained features at approximately twice the first shell distance that were absent in the Fourier transform of the Ni K-edge XAFS data of tetrahedral NiBr 2 (PPh 3 ) 2 . These features are due to multiple scattering involving pathways through the central absorbing atom (as shown in Figure 3 for CoBr 2 ) and can therefore be used as a diagnostic test of linearity for MBr 2 units.
To illustrate the sensitivity of these multiple scattering pathways with respect to the bond angles in the transition metal dihalides studied in this work, theoretical Fourier transforms of Co and Br K-edge data for CoBr 2 over a range of bond angles (180−90°) are shown in Figure 4. The model for the calculation of the spectra used a constant Co−Br bond length of 2.25 Å and constant Debye−Waller 2σ 2 terms of 0.010 and 0.015 Å 2 for the Co−Br and Br···Br shells, respectively. The angle of the Br−Co−Br unit was then defined and the theoretical spectrum calculated. The multiple scattering parameters used were also consistent for both K-edges and for every angle calculated. The Co K-edge theoretical Fourier transform for CoBr 2 calculated without multiple scattering has just the peak corresponding to the Co−Br distance at 2.25 Å for all bond angles.
However, when the multiple scattering contribution is included, a second peak at approximately twice the Co−Br bond distance is observed for near-linear geometries ( Figure 4a). As the bond angle is reduced, this feature diminishes very rapidly, particularly for bond angles less than 160°, and it completely disappears in the spectra calculated for bond angles of less than 155°, where the FTs are essentially identical to those calculated for no multiple scattering. It can therefore be concluded that in the analysis of good-quality metal K-edge XAFS data for the metal dibromides isolated in inert matrices, the presence of a multiplescattering feature at approximately twice the M−Br distance is indicative of a bond angle of 160°or greater. The effect of multiple scattering on the Br K-edge data is more complex, as there are no additional peaks solely due to multiple scattering. In this case, the multiple scattering events affect the intensity of the Br···Br shell, as the intervening metal atom in a linear arrangement acts as a lens, strongly forward-scattering the photoelectron, thus increasing the intensity of the backscattering Br shell. This is a much more well-known manifestation of multiple scattering than that involving the central absorbing element and is common in complexes containing CO, CN − , and imidazole ligands. Fourier transforms were calculated without multiple scattering theory, shown in Figure 4b, as well as with multiple scattering, shown in Figure 4c. Figure 4b shows a simple and expected increase in the intensity of the Br···Br peak as the distance is shortened as a result of the more acute bond angle due to the 1/r 2 effect. Figure 4c shows an altogether different effect due to multiple scattering. The data for 180°show an enhanced intensity of the Br···Br feature due to the multiple scattering. However, as the bond angle is decreased from 180°, the Br···Br peak shows a reduction in intensity, which is particularly evident between 165°and 155°, to such an extent that the Br···Br shell would not be observed above the noise level in the experiment. At smaller angles, the shape and size of the Br···Br peak corresponds closely to that of spectra calculated without multiple scattering theory. Thus, multiple scattering at the Br K-edge increases the intensity of the Br···Br peak at near linear geometries, reduces it around 160°, and then has little effect below 150°. Therefore, these calculations suggest that the absence of a Br···Br shell in the Br K-edge spectra is indicative of a bond angle between 155 and 165°and that peaks with intensities above what was expected when calculated without multiple scattering are indicative of a bond angle between 170 and 180°.
It is to be noted that the sensitivity of the XAFS multiplescattering effects is at a maximum where the trigonometric functions used for bond angle calculations with IR isotopic data are at their least sensitive, i.e., for nearly linear systems. The validity of the model was tested with the other metals employed in this study. As it has been shown previously 67 that the M−Hal bond length increases upon deviation from linearity, the calculations were carried out with slightly different bond lengths, and no appreciable differences in the trends shown in Figure 4 were detected.
DFT Calculations. In addition to the experimental results, DFT calculations on the ground and low-lying excited electronic states of the dibromides and diiodides have been carried out to support the interpretation of the experimental data.
Summary and Outline of Paper. This paper describes the results of the isolation of the 3d transition metal dibromides of Fe, Co, Ni, and Zn in matrices of noble gases (Ne, Ar, Kr, Xe) as well as CH 4 and N 2 , with O 2 also being employed in the NiBr 2 studies. While the difluorides and dichlorides of the 3d transition metals have been widely studied, the available data in the matrix isolation literature for the dibromides are much more scarce and are limited to NiBr 2 in Ar, 99 ZnBr 2 in Kr, 96,97,122,123 and CrBr 2 in Ar. 98 We have published two preliminary pieces of work on NiBr 2 in N 2 matrices. 68,69 The paucity of spectroscopic data for the transition metal dibromides has also been highlighted. 124 Therefore, the combination of the published data on the difluorides and dichlorides with the data presented herein will make it possible to compare the effect of changing the d-electron count as well as the hardness of the metal in going from the fluorides through the chlorides to the bromides. Previous electron diffraction work 124,125 on the molecular geometry of gas-phase metal halides has shown that all of the dihalides studied in this work are linear in the gas phase. Mass spectrometry indicates that for FeBr 2 126 and CoBr 2 127 the predominant vapor species is the monomer and that the dimer species only become significant close to the melting points. No dimeric species were observed for NiBr 2 . 127 In contrast, the vapor above ZnBr 2 can contain a considerable proportion of dimeric species. 128

■ RESULTS
This section is divided into subsections concerning each of the metals, and the metals are presented in the reverse order of their d-electron configurations. However, before the experimental data are considered, the DFT results on the ground and lowlying excited states are discussed.
DFT Calculations on the Ground and Low-Lying Excited States of MBr 2 and MI 2 . Density functional theory has been employed to calculate the geometries and spectroscopic properties of the ground and lowest-lying excited electronic states for the dibromides and diiodides. Wang and Schwarz 129 have carried out DFT calculations for the difluorides and dichlorides of the 3d transition elements. Although there have been many subsequent papers on chlorides and fluorides, there has not been a systematic study of all of the dibromides and diiodides, although individual reports detailing calculations on the dibromides and diiodides of manganese, 130 iron, 131,132 cobalt, 133 nickel, 132 and zinc 134,135 have been published, as well as a comparison of different DFT methods for calculating heats of formation and ionization potentials of third-row transition elements. 136 Therefore, we have carried out a comprehensive and consistent set of calculations on the ground and lowest-lying excited states for all of the 3d transition metal dibromides and diiodides as well as those of Ca. The optimized geometries, vibrational frequencies, and IR intensities are given in Tables 1 and 2 and are in good agreement with those of Wang and Schwarz 129 for the analogous dichlorides and difluorides. The numbers of low-lying excited states, both linear and bent, should be noted.
Zinc Dibromide. Vapor-phase electron diffraction studies on zinc dichloride, dibromide, and diiodide 137 showed them all to be linear with a Zn−Br bond length (r g ) of 2.204(5) Å in ZnBr 2 . XAFS studies 67 on matrix-isolated ZnCl 2 in argon and nitrogen matrices obtained bond distances that are in agreement with those obtained by vapor-phase electron diffraction (r g ). 137 Loewenschuss and co-workers conducted vibrational spectroscopy studies on all of the zinc dihalides isolated in krypton matrices, 96,97 with particular interest shown in the formation of mixed dihalides. 97,123 Infrared Spectroscopy. The IR spectra of ZnBr 2 isolated in neon, argon, krypton, xenon, methane, 14 N 2 , and 15 N 2 matrices are shown in Figure 5, and the observed frequencies of the ν 3 asymmetric ZnBr 2 stretching mode are given in Table 3. These data are in very good agreement with the Kr matrix data reported by Loewenschuss et al. 96,97 What is immediately clear is that all of the vibrational frequencies are very close to each other, indicating only a very small effect of the matrix on the vibrational energy levels of the trapped molecules.
At 2 cm −1 resolution, the Zn isotope pattern is clearly resolved with absorption intensities in line with the isotopic natural abundance ( 64 Zn, 48.6%; 66 Zn, 27.9%; 68 Zn, 18.8%). SVFF calculations (Table 3) using these data clearly indicate the linearity of ZnBr 2 in all of the matrices studied. ZnCl 2 vapor has been shown to contain a considerable concentration of dimer molecules, 128 and Loewenschuss and co-workers assigned a band at 326 cm −1 in the spectrum of ZnBr 2 isolated in krypton as belonging to the ZnBr 2 dimer. 96,97 None of the spectra recorded in this study showed any significant absorption bands in this region. The broad features at ca. 380 cm −1 in the spectrum of ZnBr 2 isolated in neon in Figure 5a are most likely to be associated with the problems of using Ne as a matrix with an 8−9 K cryostat. However, the 0.25 cm −1 resolution spectrum of ZnBr 2 isolated in neon shown in Figure 5b afforded both zinc and bromine isotopic fine structure (Table 3), both indicating a linear geometry and that the ZnBr 2 was well-isolated. This spectrum clearly shows the presence of multiple trapping sites in Ne, which are often observed. When ZnBr 2 was isolated in an 15  Photolysis studies of ZnBr 2 in 14 N 2 and 15 N 2 matrices produced no change in the absorption bands in the FIR and MIR. In addition to the usual H 2 O and CO 2 bands in the MIR, additional bands were observed in the 15 N 2 matrix at 2252.2 and 2250.0 cm −1 ( Figure 6 and Table 4). The latter of these (marked with *) has been previously assigned as an impurity-induced 15 N 2 mode. 138 In the 14 N 2 matrix, the impurity-induced N 2 mode was observed at 2327.8 cm −1 , 138 together with a new band at 2329.9 cm −1 .
The bands to high wavenumber of the impurity-induced ones are discussed in more detail in later sections, but their assignment was only possible once they had been clearly identified in the 15 N 2 matrices because of the problems with masking of this region for 14 N 2 by gas-and matrix-phase CO 2 . DFT calculations indicate that the reaction enthalpy for the formation of either a mono-or bis-dinitrogen ZnBr 2 complex is about −1 kJ mol −1 .
The isolation of a metal dihalide in a matrix can be viewed as being analogous to solvation in many ways. The small consistent matrix shift observed for ZnBr 2 is analogous to a solvent shift and indicated that there was no significant change in the geometry of ZnBr 2 among all of the matrices studied.
XAFS Spectroscopy. ZnBr 2 was isolated in a nitrogen matrix, and both the Zn and Br K-edge XAFS spectra were obtained. However, the data for this system were of such poor quality, particularly the Zn K-edge spectrum because of several large, unnormalized glitches of instrumental origin, that the data were essentially unanalyzable, except for an estimate of 2.19(2) Å for the Zn−Br bond length, which is in good agreement with the electron diffraction data previously obtained by Hargittai and co-workers (2.204(5) Å). 137 Therefore, no other matrices were studied using XAFS because of the instrumental origin of the glitches, and hence, no firm conclusions can be drawn from the XAFS data.
Conclusion. From the IR results, the consistent matrix shift observed for ZnBr 2 in all of the matrix hosts studied, combined with the bond angle calculations, suggest that ZnBr 2 has minimal interaction with the matrix and preserves its linear geometry in all cases. The order of interaction for ZnBr 2 is Ne < Ar < Kr < CH 4 < Xe < N 2 , which is in very good agreement with order proposed by Beattie and Millington. 15 There is no experimental evidence that ZnBr 2 is anything but linear in Ne, Ar, Kr, Xe, CH 4 , and N 2 matrices.
Nickel Dibromide. Nickel dihalides, and in particular NiCl 2 with its easily resolved nickel and chlorine isotope patterns, have received the most attention in the matrix isolation literature of all the dihalides investigated in this work. The IR spectra of NiF 2 isolated in neon and argon matrices 101,139 and also in argon matrices doped with N 2 and O 2 140,141 have been studied. A bond angle of 152°was calculated for NiF 2 isolated in Ne or Ar matrices by Margrave and co-workers, compared with 157°for ZnF 2 , 139 but as discussed below, these are at the margins of what could be considered as linear.
While NiF 2 ·N 2 and NiF 2 ·O 2 complexes were proposed by DeKock and Van Leirsburg using N 2 -doped Ar matrices, 140,141 no ν NN modes were observed for NiF 2 ·N 2 other than the impurityinduced mode, even in a pure N 2 matrix. NiCl 2 has been the subject of numerous studies in an argon matrix, with IR, 99,101,140−142 electronic absorption, 102,103 and fluorescence 143 spectra all indicating a linear or nearly linear structure. NiCl 2 has also been the subject of a number of very elegant molecular beam experiments with vibrational and rotational resolution on the 460 and 360 nm bands, which showed that it is linear in both the ground and excited states, with a 3 Σ g − ground state. 144−150 Green and co-workers 151 proposed that NiCl 2 isolated in an argon matrix has a nonlinear structure with a calculated bond angle of 161°. However, it has been shown 17,148 that a difference between the calculated isotope shifts of only ca. 0.1 cm −1 results in a change in bond angle from 180°to 160°. EXAFS data for NiCl 2 isolated in a methane matrix 67 indicated a linear structure, whereas in a N 2 matrix, NiCl 2 67 and NiBr 2 68 are strongly bent. N 2 and O 2 complexes of NiCl 2 analogous to those of NiF 2 have also been postulated by DeKock and Van Leirsburg. 140,141 Clearly, the nature of the geometry of nickel dihalides isolated in Ne, Ar, and N 2 matrices has been a contentious issue. The literature reports on matrix NiBr 2 concern its isolation in an argon matrix 99 and our more recent preliminary work. 68,69 Electron diffraction data indicate linearity in the vapor phase. 152 Infrared Spectroscopy. The IR spectra of NiBr 2 isolated in Ar, Kr, Xe, O 2 , and CH 4 matrices are shown in Figure 7, and  the observed frequencies of the ν 3 asymmetric Ni−Br stretching vibration are given in Table 5. There is reasonable agreement with the previous argon data. 99 The spectra obtained at 2 cm −1 resolution, shown in Figure 7, produced clear bands due to the 58 Ni and 60 Ni isotopes (natural abundances of 68.3% and 26.1%, respectively), with the 62 Ni isotope (natural abundance 3.6%) also observed after prolonged deposition. It is clear from the relative positions of the ν 3 modes in the spectra that a simple matrix shift is observed for NiBr 2 , analogous to the ZnBr 2 case. Bond angle determination from the 58 Ni and 60 Ni isotope   (Table 5). In line with the previous report on NiCl 2 isolated in an Ar/O 2 matrix, 140,141 no O−O stretches were seen for NiBr 2 isolated in an O 2 matrix or after broadband photolysis. This was perhaps not surprising, as the interaction between the guest molecule and the matrix seems to be weak since the gas-phase molecular geometry was preserved. Indeed, the broad absorption band observed for NiCl 2 in mixed Ar/O 2 matrices at 480.2 cm −1 (compared with 520.7 cm −1 for a pure Ar matrix) and assigned 140,141 as the asymmetric stretch of NiCl 2 O 2 may be simply due to the perturbed asymmetric stretch of NiCl 2 in a predominantly O 2 environment or mixed Ar/O 2 environment. The ν Ni−Br modes for NiBr 2 in nitrogen matrices are shifted by ca. 90 cm −1 (419.1 cm −1 in Ar to 331.8 cm −1 in N 2 ) (Figure 7f,g). As identified in our preliminary IR data, this indicates a very bent geometry for NiBr 2 in a nitrogen matrix, with a bond angle of ca. 125°. 68 IR studies by Beattie et al. 16,17 also found that NiCl 2 isolated in a N 2 matrix was also strongly bent, with a bond angle of ca. 130°. These observations are in contrast to what is seen for the other matrices described above, where bond angle calculations indicated linear geometries. When 15 N 2 was used instead of 14 N 2 (Figure 7g), the ν 3 mode shifted by 0.3 cm −1 to 331.5 cm −1 , indicating an enhanced interaction between the NiBr 2 guest and N 2 host compared with the 0.1 cm −1 shift observed for ZnBr 2 . The separation of the features due to the Ni isotopes was less defined in the N 2 matrices than previously seen for the other matrices and is a direct consequence of the change in bond angle, as the central-element isotope splitting decreases on bending, whereas the terminal-atom isotope splitting increases. The Br isotope splitting pattern could not be resolved in nitrogen matrices. The nature of the very weak bands centered around 315 cm −1 is uncertain, but they are probably not due to dimers, as these would be expected to be at lower energy 99 and their shape and intensity are also not consistent with dimer modes. These bands are more likely to be some sort of matrix site effect that is dependent on the experimental conditions. It is conceivable that they are the ν 1 modes, but our calculations show that for bond angles of ca. 130°the ν 3 −ν 1 separation is expected to be in excess of 100 cm −1 .
The low-energy bending mode of NiBr 2 in argon matrices has been reported previously to be 69 cm −1 . 99 This is below the range of most commercial spectrometers, so in order to determine how the bending mode was affected by varying the matrix gas, synchrotron radiation far-IR experiments were carried out. The SR-FIR spectra of NiBr 2 trapped in Ar, N 2 , and CH 4 matrices are shown in Figure 8. These experiments utilized heavy deposits because the DFT calculations indicated that the intensity of the ν 2 bending mode would be about 1−2% of that of the ν 3 mode. Unfortunately, it is clear from the SR-FIR argon matrix spectrum (Figure 8a) that the low-energy part of the spectrum (<100 cm −1 ), where the bending modes are expected to appear, is dominated by the Ar phonon bands (32.4 and 70.8 cm −1 ) and bands due to nearly freely rotating water molecules (<40 cm −1 ) and argon hydrates (40−100 cm −1 ). 153,154 While the water bands could be reduced by prolonged pumping and baking of the vacuum system, this was not feasible in the limited amount of SR-FIR time available, and water bands are essentially impossible to remove completely. In nitrogen matrices ( Figure 8b) the spectrum is also badly affected by the N 2 lattice modes at 49 and 71 cm −1 and the water libration bands at 147 and 225 cm −1 . 153,154 The 225 cm −1 bands are usually obscured when CsI optics are used down to 200 cm −1 . Therefore, it is not possible to identify the ν 2 mode with any certainty in Ar or N 2 matrices. However, in the spectrum of NiBr 2 isolated in CH 4 (Figure 8c) there is a band at 55 cm −1 , which is in reasonable agreement with the earlier Ar matrix value of 69 cm −1 . 99 If the molecule is severely bent in nitrogen, the ν 1 mode would be expected to gain some intensity, but there is no convincing evidence of this in any of the IR spectra. The DFT calculations indicate that the intensity of the ν 1 mode relative to the ν 3 mode is ca. 10% at 130°and ca. 2% at 155°. One explanation for the apparent absence of ν 1 is that it is masked by the broad libration modes of H 2 O in N 2 around 225 cm −1 , or it could possibly be the weak features at 315 cm −1 . The DFT calculations indicate that the separation of ν 1 and ν 3 decreases upon bending, and the separation is expected to be around 100 cm −1 for bond angles around 130°. Therefore, the most likely explanation is that the ν 1 mode is masked by the broad modes around 250−200 cm −1 in nitrogen matrices.
Experiments were also carried out on NiF 2 in nitrogen matrices ( Table 6) to provide a comparison with the NiCl 2 and NiBr 2 data. The Ni isotope pattern on ν 3 for 58 NiF 2 and 60 NiF 2 in 14 N 2 at 705.8 and 701.3 cm −1 gave a bond angle of 152°, and for 15 N 2 matrices the bands at 705.3 and 700.7 cm −1 yielded 162°(but these values reflect a difference of only 0.2 and 0.1 cm −1 from linearity, respectively). Previous work had calculated a bond angle of 152°for the ν 3 modes of NiF 2 in solid Ne ( 58 NiF 2 , 800.7 cm −1 ; 60 NiF 2 , 795.5 5 cm −1 ) and solid Ar ( 58 NiF 2 , 780.0 cm −1 ; 60 NiF 2 , 775.0 4 cm −1 ). 139,141 These values indicate a 10% reduction in wavenumber and an 18% drop in force constant (assuming linearity) between NiF 2 in Ar and NiF 2 in N 2 . The corresponding shifts in wavenumber for NiCl 2 and NiBr 2 between Ar and N 2 matrices are 17% and 21%, respectively, with a drop in force The Journal of Physical Chemistry A Article constant of 32% for NiCl 2 and 37% for NiBr 2 . This is a clear indication that the level of interaction between the nickel dihalide and the dinitrogen matrix decreases in the order Br > Cl > F. NiI 2 would be of obvious interest, as it would possibly coordinate to dinitrogen the most readily. Performing successful experiments with bulk NiI 2 was a challenge, as it decomposed upon heating to liberate I 2 , resulting in very poor throughput of the IR radiation, and no meaningful data were obtained.
Having identified that there is some form of interaction between the N 2 matrix and the trapped NiBr 2 and that the NiBr 2 unit is bent, the ν NN region was studied in some detail. A preliminary report of this has been published previously, 69 but the main findings are summarized below to put the rest of the data in context.
The ν NN region of NiBr 2 in an 15 N 2 matrix contained two bands at 2263.8 and 2259.4 cm −1 after deposition (Figures 6b  and 9a and Table 4) in addition to the perturbed ν NN mode of 15 N 2 at 2250.0 cm −1 . 138 In contrast, in the ZnBr 2 data (Figure 6a) the only additional bands were shoulders on the impurity-induced modes. The position of ν NN modes in the NiBr 2 spectra to high frequency of the "free" N 2 modes is unusual, and in comparison with the isoelectronic carbonyl species may be indicative of "nonclassical" bonding with very limited π back-bonding. 155 When this sample was photolyzed with broad-band Hg−Xe radiation, a radical change was observed ( Figure 9b) compared with the spectrum recorded after initial deposition (Figure 9a), with the appearance of two new bands at 2205.7 and 2186.4 cm −1 (these have low intensity, about 1−2% of the absorbance of the NiBr 2 ν 3 mode) together with a slight reduction in the intensity of the 2259.4 cm −1 band shown in the difference spectrum ( Figure 9c). When NiBr 2 was isolated in an 14 N 2 matrix, there were features at 2336.9 and 2342.8 cm −1 as well as the perturbed ν NN mode at 2327.8 cm −1 on deposition (Figure 6a), but because of the ubiquitous presence of matrix-isolated CO 2 features, these were only identifiable once the corresponding 15 N 2 features had been identified. After photolysis (Figure 9d),    156,157 were unsuccessful because of the very weak nature of the features. Failure to observe 14,15 N 2 species with weak ν NN modes was previously noted by Andrews and co-workers in their study of beryllium dinitrogen complexes. 138 No changes were observed in the NiBr 2 ν 3 region after photolysis. In all cases the intensity of the ν NN bands observed after photolysis was markedly reduced after annealing to 15 K, and the bands disappeared completely after the matrix was warmed to ca. 20 K but could be regenerated (with lower intensity) after further photolysis at ca. 8 K, but only three or four times. The intensity of the photoactive bands was greater when UV rather than visible irradiation was used and was also slightly enhanced if photolysis was carried out during deposition. The new bands after photolysis were only observed if the deposition (rather than photolysis) was carried out below 10 K.
To confirm that the ν NN bands observed in the NiBr 2 experiments were due to interaction of NiBr 2 with dinitrogen, a series of experiments involving NiCl 2 and NiF 2 were also carried out (Table 4 and 6). When NiCl 2 was isolated in nitrogen matrices, bands to high frequency of the impurity-induced modes ( 14 N 2 , 2327.8 cm −1 ; 15 N 2 , 2250.0 cm −1 ) were observed ( Figure 6 and Table 4 These features were weaker and also slightly shifted from those observed for NiBr 2 . For NiF 2 , no new bands were detectable after photolysis, but bands close to, and blue-shifted from, the perturbed ν NN mode were observed upon deposition at 2266.7 and 2262.5 cm −1 in an 15 N 2 matrix and at 2337.5 and 2340.5 cm −1 in an 14 N 2 matrix ( Figure 6).
From these experiments, it is clear that the bands observed between 2350 and 2150 cm −1 can be readily assigned to ν NN   The Journal of Physical Chemistry A Article modes on the basis of their 14 N/ 15 N isotopic shifts and that there are a variety of different X 2 Ni···(N 2 ) n and X 2 Ni−(N 2 ) n interactions occurring in nitrogen matrices. The fact that the position and intensity of the ν NN modes are halogen-dependent clearly indicates that they arise from interactions between the nitrogen matrix and the trapped metal dihalide rather than from N 2 ···H 2 O or N 2 ···HX complexes. 158,159 The isotopic behavior of the ν NN bands observed after photolysis is clearly indicative of the formation of a species containing two geminal N 2 units. They are at relatively high values compared with those for low-oxidation-state dinitrogen complexes but are similar to those observed for other complexes containing cationic metal centers such as [Ru II (N 2 ) 2 ] 2+ (2207 and 2173 cm −1 ) 160,161 and [Rh I (N 2 ) 2 ] + (2244 and 2218 cm −1 ). 162 Most significantly they are very similar to those observed for matrix-isolated Ni(N 2 ) 2 (O 2 ), which was shown via isotopic substitution to have a pseudotetrahedral geometry with two end-on-bonded dinitrogen ligands (η 1 -N 2 ) in a cis configuration and one side-on bonded dioxygen ligand (η 2 -O 2 ), with the dioxygen unit believed to be between peroxo and superoxo in character. 163,164 Our original DFT calculations 69 indicated that all of the sideon-bonded (η 2 -N 2 ) complexes were unbound with respect to NiX 2 (X = Cl, Br) and dinitrogen. Of the end-on-bonded species, pseudotetrahedral NiX 2 (η 1 -N 2 ) 2 were the most stable. The relatively small complexation enthalpies (Δ r H) of −43 kJ mol −1 (NiBr 2 ) and −37 kJ mol −1 (NiCl 2 ) for the reaction NiX 2 + 2N 2 → NiX 2 (η 1 -N 2 ) 2 indicated rather weak chemical bonding, consistent with complexes that are stable only at low temperatures. These calculations have been repeated for NiX 2 (η 1 -N 2 ) 2 using ADF, and the reaction enthalpies are very similar for NiBr 2 (−45 kJ mol −1 ) and slightly lower for NiCl 2 (−28 kJ mol −1 ), indicating that in the case of NiF 2 only one N 2 will bind end-on, but with a very low reaction enthalpy of ca. −11 kJ mol −1 . The original DFT-calculated values 69 for the ν NN modes of NiX 2 (η 1 -N 2 ) 2 were in excellent agreement with the experimental values, confirming the assignments. The relative intensities of the absorption bands observed after photolysis were used to determine a N−Ni−N bond angle of 98°± 5 for the (N 2 )Ni(N 2 ) fragment, with the principal NN force constant, k NN , and the interaction force constant, k NN·NN , having values of 21.268 and 0.192 mdyne Å −1 , respectively.
The NiX 2 (η 1 -N 2 ) 2 complexes reported in this work are very unstable, even under matrix isolation conditions, and provide an indication of the (in)stability of Ni(II) dinitrogen complexes as well as being an example of reversible binding of N 2 to Ni(II) The Journal of Physical Chemistry A Article centers. This work has also yielded a calibration value for ν NN attached to a Ni(II) center, thus confirming that the previous Ni(N 2 ) 2 (O 2 ) complexes 163,164 are best considered to contain Ni(II) and a peroxo ligand. The proportion of NiX 2 (η 1 -N 2 ) 2 formed upon photolysis is dependent on the deposition temperature and the photolysis wavelength but in all cases appears to remain fairly low. Upon warming to 20 K these chemisorbed species dissociate, as also found for Pd(N 2 ) 2 (O 2 ) 164 and Mo(N 2 ) x , 165 indicating their extremely reactive nature. The very low deposition temperatures required to observe the photoproducts may be related to the need for some preorganization of the nitrogen lattice that is only achieved by very rapid quenching of the NiX 2 in solid nitrogen below 10 K.
Electronic Absorption Spectroscopy. The electronic absorption spectra of gaseous NiCl 2 , NiBr 2 , and NiI 2 were studied previously in the range of 4000−20000 cm −1 , and assignments were made on the basis of axial ligand field calculations. 166 Gasphase spectra are often complicated by population of many rotational and vibrational levels as a consequence of the high temperatures required to obtain sufficient vapor pressure. The electronic absorption 101−103 and emission 101,143 spectra of NiCl 2 isolated in an argon matrix were also studied previously and found to be simpler. The most intense absorption for NiCl 2 in Ar at 28 400 cm −1 was found to have extensive vibrational structure. This progression with a spacing of ca. 260 cm −1 was believed to correspond to the symmetric ν 1 stretching mode in the excited state. 103 A splitting of approximately 80 cm −1 was also observed for some of the most prominent levels, possibly corresponding to the bending frequency, ν 2 , of the excited state or simply due to multiple sites in the matrix. The ligand field model applied to the gas-phase spectra by DeKock and Gruen 166 predicted a 3 II g ground state, which gave rise to four charge transfer transitions, and these were also observed for matrix-isolated NiCl 2 . 102 This approach predicted that the d orbitals would split into three levels with the relative energies d δ < d π < d σ , leading to a δ g 4 π g 3 σ g 1 configuration. Brown and co-workers studied gasphase NiCl 2 in a "cold" molecular beam using laser-induced fluorescence spectroscopy of the 360 and 460 nm bands. 144−150 They showed that NiCl 2 is linear in both the ground and excited states with a 3 Σ g − ground state, in contrast to 3 Π g as proposed by DeKock and Gruen. 102 This assignment has been debated further by computational chemists 129,167,168 and underlines the challenge that molecules of this type present. Local DFT calculations by Bridgeman 168 found NiCl 2 to be linear and    . This ground state could only arise from a δ g 4 σ g 2 π g 2 or π g 4 σ g 2 δ g 2 configuration. Cellular ligand field calculations, which explored the parameter values that would be required to generate such configurations, produced negative values for the π g 4 σ g 2 δ g 2 configuration, and this was therefore discounted. This led to the orbital occupation of δ g 4 σ g 2 π g 2 for the 3 Σ g − ground state with a reversal in the relative energy of the d σ and d π orbitals. While the d δ orbitals are nonbonding because of the lack of ligand orbitals of matching symmetry, both the d σ and d π orbitals are antibonding. As discussed in detail by Bridgeman for NiCl 2 , 168 the relative energy d σ < d π does not indicate that π bonding is stronger than σ bonding. Rather, the mixing between 3d and 4s is sufficient to lower the energy of the d σ orbital. Indeed, this interaction is enough to make the energy of d δ and d σ quite similar. These calculations were also found to concur with the experimentally observed bond length and vibrational frequency values from the molecular beam experiments. Our DFT calculations (see Table 1) indicate that the ground state of NiBr 2 also has a 3 Σ g − ground state with a δ g 4 σ g 2 π g 2 configuration. Between this and the first linear excited state, 3 Π g with a δ g 4 σ g 1 π g 3 configuration, there are two bent triplet states with bond angles of 155°a nd 130°. The UV−vis−NIR spectrum of NiBr 2 isolated in an Ar matrix is shown in Figure 10a, together with a spectrum of NiCl 2 in an argon matrix (Figure 10b), and the values are given in Table 7. The latter spectrum is in very good agreement with those previously reported for NiCl 2 , 101−103 where the bands at 28 500 cm −1 were assigned as ligand-to-metal charge-transfer bands. The intensities of any d−d bands are expected to be very low because of the linearity of the molecule and the low temperatures of the experiment. As expected, the features in the NiBr 2 spectrum are shifted by about 5500 cm −1 to lower energy compared with the NiCl 2 spectrum. The spectra for NiBr 2 isolated in Kr, Xe, and CH 4 matrices are very similar to those in Ar, and in all cases the most intense absorption displayed vibrational structure, as shown in Figure 11, with the values tabulated in Table 8. Although the vibrational fine structure is less well resolved for the CH 4 matrix data, it does highlight the fact that there are two absorption bands between 21 000 and 25 000 cm −1 . In the case of NiBr 2 , the vibrational progression on the first band has a separation of 188 cm −1 in Ar, Kr, and Xe and ca. 180 cm −1 in CH 4 . The progression separation for the second band in the Ar, Kr, and Xe data is also very similar to 188 cm −1 but suffers from overlap of the first progression. Therefore, it is possible to estimate a symmetric stretching frequency of 188 cm −1 for NiBr 2 in the excited state. In the case of NiCl 2 (Figure 10b), the poorly resolved vibrational fine structure (ca. 230 cm −1 ) was in good agreement with the previous values of 260 cm −1 . 102,103 The striking similarity between the spectra, with a simple matrix shift being observed, further underlines a consistent linear geometry for NiBr 2 isolated in argon, krypton, xenon, and methane matrices. The band system studied by Brown and coworkers 144−150 at ca. 22 000 cm −1 for NiCl 2 was not observed by DeKock and Gruen 102 and was seen only by Jacox and Milligan 103 after extensive deposition, and there is only the faintest hint of it in our spectra (Figure 10b). The only bands observed for NiBr 2 in this work at lower energy relative to the intense structured absorption band at ca. 23 000 cm −1 were very weak bands at 20 300 cm −1 in Ar, 20 030 cm −1 in Kr, 19 820 cm −1 in Xe, and 18 840 cm −1 in CH 4 .
The UV−vis−NIR spectrum of NiBr 2 isolated in an 14 N 2 matrix is shown in Figure 10c, with the observed absorption bands appearing at 24 800, 27 650, 29 870, 33 000, and 37 100 cm −1 . The inset (Figure 10d) shows the presence of weak features at 16 890 and 19 710 cm −1 and a very, very weak peak at 14 570 cm −1 that could be assigned as d−d transitions. The spectrum of NiCl 2 in a nitrogen matrix is given in Figure 10f and is similar to that of NiBr 2 but with all of the charge transfer bands (27 900, 30 410, 32 150, 34 790, and 37 940 cm −1 ) shifted by about 5000 cm −1 to higher wavenumber. There are some very weak features at 15 400 and 21 150 cm −1 . These spectra are both radically different compared with those obtained from argon matrices (Figure 10a,b). The most significant difference, aside from the extra transitions at high frequency, is the absence of the band centered around 22 600 cm −1 for NiBr 2 and 28 350 cm −1 for NiCl 2 , which provides further confirmation that a fundamental change in the geometric and electronic structures of both NiBr 2 and NiCl 2 occurs in going to a N 2 matrix. Broadband photolysis of NiBr 2 in solid N 2 also produced a subtle but significant change compared with the electronic absorption spectrum obtained after deposition. In the spectrum of the photolyzed sample, shown in Figure 10e, the absorption band at 33 000 cm −1 observed for the unphotolyzed sample disappeared. Annealing to 20 K brought about the return of this feature, with the rest the spectrum remaining unchanged. Further photolysis diminished this peak again, and the cycle of photolysis and annealing could be repeated two or three times before enhanced spectral noise and scattering intervened. A difference spectrum of before and after photolysis revealed that in addition to the reduction in intensity of the 33 000 cm −1 band after photolysis there were some more subtle changes after photolysis, including a reduction in intensity in the tail of the 27 650 cm −1 band and an enhancement in intensity of the band at 24 800 cm −1 . These changes mirror the formation of the dinitrogen complex observed in the IR spectra. However, they clearly indicate that only a small proportion of the trapped NiBr 2 molecules participate in the photochemistry, and it is intriguing The Journal of Physical Chemistry A Article that it is easier to identify the bands that disappear rather than those that appear upon photolysis. Therefore, it appears from the electronic absorption spectra that there may be at least two NiBr 2 species trapped in nitrogen and that only one of these (a minor component) is involved in the photochemistry.
XAFS Spectroscopy. As shown in Figures 1 and 2, features close to the edge in Ni(II) K-edge XANES spectra can be assigned to specific electronic transitions characteristic of different geometries. 112 The 1s → 3d transitions several electron volts below the edge are forbidden for centrosymmetric environments but are expected to gain intensity due to p−d mixing in noncentrosymmetric geometries. Therefore, relatively weak 1s → 3d peaks are expected for octahedral, square-planar, and linear geometries, with greater intensity expected for trigonalbipyramidal, square-pyramidal, and tetrahedral geometries as well as nonlinear triatomics. 57,112 A second pre-edge feature (peak or shoulder) about 1−3 eV below the edge that is found in the spectra of tetragonal complexes missing one or more axial ligands and in linear complexes has been assigned to 1s → 4p z transitions with shakedown contributions, 112 and this is confirmed by our calculations shown in Figures 1 and 2. Therefore, a sharp intense feature on the edge of the metal K-edge XANES spectrum can be used diagnostically to indicate linearity, and a reduction in the intensity of this feature and the appearance of weak pre-edge features are indicators of the onset of nonlinearity.
The Ni K-edge XANES spectra of NiBr 2 isolated in CH 4 and N 2 matrices are shown in Figure 12, and it is clear that the spectra of NiBr 2 in methane and nitrogen are very different, again confirming the significant change in geometry already indicated by the IR and UV−vis data. In the CH 4 matrix spectrum there is a very weak pre-edge 1s → 3d transition at 8334.0 eV, while in the N 2 matrix spectrum it is more defined and appears at 8329.5 eV. Analogous peaks are observed at 8332.9 eV for (solid) NiBr 2 and [(en) 2 NiBr 2 Ni(en) 2 ]Br 2 , 57 both of which have octahedral coordination, and at 8331.7 eV for tetrahedral NiBr 2 (PPh 3 ) 2 . 57 Although the intensity of the pre-edge feature in the Ni K-edge XANES spectrum of NiBr 2 in N 2 is more characteristic of a relatively high symmetry environment such as The Journal of Physical Chemistry A Article octahedral, its position and that of the edge itself are ca. 2 eV lower than in tetrahedral examples and ca. 3 eV lower than in octahedral examples. 57 In contrast, the intense edge feature at 8341.0 eV in the Ni K-edge XANES spectrum of NiBr 2 in solid CH 4 is associated with transitions from the 1s orbital to orbitals with significant p character, and as shown earlier this, is diagnostic of linearity. In the case of square-planar [Ni(CN) 4 ] 2− complexes these intense transitions involve the p π orbitals. 169−172 In the case of square-planar Ni(II) phosphine halide complexes, similar transitions were observed at 8334.7 eV for cis-[NiBr 2 (dppe)] and 8335.4 eV for trans-[NiBr 2 (PEt 3 ) 2 ]. 57 Therefore, as expected from both the IR and UV−vis−NIR data, the Ni K-edge XANES confirms that a significant change in electronic and geometric structure occurs in going from the methane matrix to the nitrogen matrix, consistent with a change from a linear to bent geometry. There was no significant difference between the Br K-edge XANES spectra of NiBr 2 in CH 4 and N 2 matrices.
The Ni K-edge and Br K-edge EXAFS and FTs for NiBr 2 isolated in CH 4 and N 2 matrices are shown in Figure 13. It is clear that there are significant differences between the CH 4 and N 2 data. Analysis of these data have been discussed in a preliminary report previously, 68 but full analysis was not possible at the time because of limitations in the analysis program (EXCURV92). As the implications of these experiments are significant and we now have substantial additional experimental data that have afforded considerable insight, the data have been reanalyzed using EXCURV98.
The Br K-edge data ( Figure 13) are straightforward to interpret and analyze with a Br−Ni shell and a Br···Br shell, and by simple triangulation the Br−Ni−Br bond angle can be determined. The greater intensity of the second shell in the FT of the NiBr 2 /CH 4 data compared with the NiBr 2 /N 2 data is due to the multiple scattering in the linear Br−Ni−Br unit (see Figure 4). With light matrix scatterers such as C and N there is, as expected, very little contribution from the matrix. The Ni K-edge data ( Figure 13) are not so straightforward. There is a feature at ca. 2 times the Ni−Br distance in the FT for the CH 4 matrix data that is absent in the N 2 data, but there is evidence of light scatterers in the low-k region of the N 2 matrix data. The first of these is due to multiple scattering through the central Ni atom, but this could not be modeled with the analysis programs available at the time of the initial publication 68 (EXCURV92). Subsequently these features were shown to be due to multiple scattering through the central atom, which is very diagnostic of linearity. 57,120,121 Therefore, the theoretical fits shown in Figure 13 for NiBr 2 in a CH 4 matrix are those derived using this approach with the more recent analysis suite (EXCURV98), and for consistency the other data in Figure 13 have also been reanalyzed.
The original Br K-edge EXAFS data for NiBr 2 in a CH 4 matrix gave r Br−Ni = 2.19(3) Å and r Br···Br = 4.36(6) Å, 68 and reanalysis gave essentially the same values (2.20(2) and 4.38(4) Å, respectively). Both of these sets of data imply a bond angle of 170°, which in view of the insensitivity of the sine function close to 90°can be taken as linear in both cases. These values are in good agreement with the r g value of 2.201 Å derived from electron diffraction experiments. 152 The reanalysis of the Ni K-edge data using the full multiple scattering (FMS) approach for NiBr 2 in a CH 4 matrix gave a Ni−Br bond length of 2.20(2) Å (compared to the original value of 2.19(2) Å) and a good fit to the feature at ca. 4.35 Å, indicating a linear geometry. This is in excellent agreement with the r g electron diffraction value of 2.201 Å. 152 While the reanalysis of these data made no significant difference to the overall picture, the reanalysis of the NiBr 2 /N 2 data does have more significant implications.
At the time of the original and very careful data analysis, the best model to fit both the XAFS and IR data was thought to be a bent NiBr 2 unit with a Br−Ni−Br bond angle of ca. 145°together with two nitrogen atoms ca. 2.6 Å from the Ni together with a second nitrogen shell at 3.4 Å. 68 This model gave a fit as good or better than that involving short Ni−N distances. In addition, the Ni−Br distance from the data including the short Ni−N interactions (2.30(3) Å) was in poorer agreement with the Br K-edge Br−N distance of 2.27(3) Å than that for the longer Ni···N distances (2.27(3) Å). The use of k 2 and k 1 weighting factors to enhance the low-z contribution also indicated against the inclusion of short Ni−N distances. Therefore, in conjunction with the absence of conventional ν NN modes in the IR spec-   20584  21810  21439  20881  21700  21999  21628  21075  21890  22190  21817  21262  22078  22380  22008  21459  22260  22569  22202  21658  22443  22761  22397  21842  22628  22960  22596  21985  22833  23178  22809  22077  23066  23388  23011  22259  23272  23575  23196  22444  23442  23757  23377  22622  23610  23936  23553  22794  23794  24113  23728  22964  24001  24281  23915  23134  24076 23309 23479 23649 The Journal of Physical Chemistry A Article tra (the 15 N 2 experiments had not been carried out at that time), we concluded that "there appears to be no convincing evidence for a short Ni−N interaction." 68 Having re-examined this original EXCURV92 data analysis in detail, we would almost certainly have come to the same conclusion, i.e., that there was no convincing evidence for Ni−N 2 formation when using EXCURV92 for analysis. For NiBr 2 in a N 2 matrix, the original analysis of the Br K-edge data gave r Br−Ni = 2.27(3) Å and r Br···Br = 4.34(6) Å, and the absence of a second relatively intense feature in the FT indicated a nonlinear geometry with a bond angle of 145°. 68 Reanalysis using the cluster multiple scattering (CMS) approach yielded similar values of r Br−Ni (2.29(3) Å) and r Br···Br (4.33(5) Å), indicating a bond angle of 142°. Although the change in the Br−Ni distance is small, it does have a considerable impact. The Br K-edge data are presented in Figure 13, and the refinement details are given in Table 9.
The analysis of the Ni K-edge data of NiBr 2 in solid nitrogen ( Figure 13) was less straightforward. From the relatively intense oscillations at low k in the Ni K-edge EXAFS, it is clear that there are low-z backscatterers in addition to bromine in the nickel coordination environment. The difficulty in analyzing these Ni K-edge data is in determining whether these oscillations are due to Ni−N or Ni···N type interactions. As in the previous EXCURV92 analysis, there are at least two different types of nickel−nitrogen interactions: one is at a similar distance to the Ni−Br interaction, with the other at ca. 3.2 Å. It was not possible to fit the data to just Ni−Br at ca. 2.3 Å and a Ni···N interaction at 3.2 Å. The 3.2 Å shell does not fit to a Ni···Ni interaction, as might be expected for a dimeric structure. The question therefore is whether the additional nickel−nitrogen interaction is at a short distance of ca. 2.1 Å, indicative of Ni−N, or at a longer distance of 2.6 Å, characteristic of Ni···N. The data can be modeled reasonably well by either a short Ni−N distance of ca. 2.12 Å together with a Ni···N distance of ca. 3.19 Å or a longer Ni···N distance of ca. 2.6 Å together with another Ni···N distance at ca. 3.2 Å. The Ni−Br bond length varies between the two different models, as does the E f parameter,  , and the E f value remains essentially the same as for just a Ni−Br refinement. In contrast, when a 2.6 Å Ni−N shell is included in the fit, the Ni−Br bond length decreases to 2.26 Å, and the E f parameter lies very close to its accepted boundaries (15 or −15 eV). The combination of a relatively large discrepancy between the Br and Ni K-edge data and the behavior of the E f parameter indicates that the model involving the longer Ni−N interaction at 2.6 Å is less physically reasonable than the model including the shorter Ni−N interaction at 2.1 Å. The goodness of fit (R) between the two models is small, but the model incorporating the shorter Ni−N distance has the best fit. For both of these models, the Ni−N occupation number was small, and the preferred number was 2 in each case, both in terms of R factor and also reasonableness of the Debye−Waller 2σ 2 terms. Therefore, we are forced to the conclusion that with more modern data analysis techniques, the only realistic interpretation of the Ni K-edge EXAFS data is that there is a Ni−N interaction at 2.12(2) Å with an occupation number of 2. The second Ni···N shell in this refinement at 3.19(4) Å implies the presence of linear Ni−NN units with a NN bond length of 1.07 Å. a The refinement standard deviation is given in parentheses. b The estimated systematic errors in EXAFS bond lengths are ±1.5% for well-defined coordination shells. c 2σ 2 is twice the mean square displacement term used in the Debye-Waller factor. d MS is multiple scattering approach used; FMS is full multiple scattering, CMS is cluster multiple scattering. e E f is a single refined parameter to reflect differences in the theoretical and experimental Fermi levels This should be compared to the solid-state value of 1.075 Å in α-N 2 . 173 Although it is possible to fit the EXAFS data properly only by including multiple scattering for this contribution, the Debye−Waller factor for this shell is a little larger than expected. If the Ni−NN bond angle is reduced to ca. 160−170°, the Debye−Waller factor becomes more reasonable, which may indicate that the Ni−NN units are not completely linear. The fit shown in Figure 13 and the data in the Table 9 are for linear Ni−NN units.
There are relatively few crystallographically characterized nickel dinitrogen complexes, and these are often stabilized by pincer ligands. Of the tetrahedral Ni(0) complexes with terminal N 2 ligands, Ni−N and NN distances and ν NN modes have been observed at 1.830 and 1.112 Å and 2072 cm −1 , respectively, 174 184 Therefore, the Ni−N distance of 2.12(3) Å determined in this work is considerably longer than that found for Ni(0), Ni(I), and Ni(II) complexes, which indicates the relative weakness of the Ni−N bond due to limited back-bonding from Ni(II). The EXAFS data relate to the "as deposited" material with ν NN modes in the IR spectrum to high frequency of ν NN for "free" N 2 (the XAFS experiments were carried out in the dark to avoid any unwanted photochemistry). Although XAFS studies of the NiBr 2 (N 2 ) 2 system after photolysis were seriously considered, they were not undertaken because of the highly reactive nature of the complex and, more importantly, because analysis of the data would be difficult or even impossible as a result of the partial conversion, and it was deemed that the limited amount of beam time could be used more effectively. Therefore, we believe that the best interpretation of the Ni K-edge XAFS and IR data is that the ν NN modes observed prior to photolysis are associated with the Ni−NN units with relatively weak bonding of the N 2 to the metal center, akin to physisorption.
Conclusions. Therefore, it is clear from all of the spectroscopic techniques that NiBr 2 behaves similarly in Ne, Ar, Kr, Xe, CH 4 , and O 2 matrices but that there is a severe change in structure of NiBr 2 in solid N 2 . The EXAFS data indicate a bond angle of ca. 140°, and both the IR and EXAFS data indicate that this is associated with weak physisorption-type coordination of N 2 to Ni. Upon photolysis, more traditional chemisorbed dinitrogen complexes are formed.
Cobalt Dibromide. Cobalt dibromide has received very little attention in the matrix isolation literature, with the emphasis of study residing on CoCl 2 , although CoF 2 has been studied by IR spectroscopy in Ne and Ar matrices. 139,185 The bias toward CoCl 2 is unsurprising from a vibrational spectroscopy viewpoint, with the 59 Co isotope being 100% naturally abundant and the bromine isotopes not easily resolved. CoCl 2 has been isolated in Ar and N 2 matrices and examined by IR 17,99,103,151 and UV−vis 102,103,186 spectroscopies, and the fluorescence spectrum has also been obtained in an Ar matrix. 186 To our knowledge there are no data concerning matrix-isolated CoBr 2 , although vapor-phase IR spectroscopy 187 yielded a value of 396 cm −1 for ν 3 . Electron diffraction suggested a linear structure for gaseous CoBr 2 with a Co−Br bond distance of 2.25 Å. 152,188 Infrared Spectroscopy. The IR spectra of CoBr 2 in a variety of matrices are shown in Figure 14, and the observed frequencies of the ν 3 asymmetric stretching vibration are given in Table 10. Two clear differences are observed when the spectra obtained for CoBr 2 are compared with those fof ZnBr 2 and NiBr 2 . The first is the number of extra absorption bands (in the form of secondary sites) in addition to the primary band. For CoCl 2 in argon, second, weaker features have also been observed 15 cm −1 below the most intense band in previous studies. 17,99,103,151 The second difference is the range of wavenumbers in which these bands occur. Taking the position of the most intense absorption as the reference, for ZnBr 2 , the total span of absorption frequencies upon change of matrix for the rare gases from neon to xenon is 16 cm −1 . Similarly, for NiBr 2 , the span in going from neon to xenon matrices is 18 cm −1 . For CoBr 2 , the span is 40 cm −1 in going from neon to xenon matrices.
The shifts in going from Ne to N 2 are 66 and 90 cm −1 for CoBr 2 and NiBr 2 , respectively. It is also clear that there is a gradual change between matrices with no clearly differentiated jumps, which is in stark contrast to NiBr 2 , where there was a dramatic change in going from a xenon matrix to a nitrogen matrix. A similar span of frequencies for the various matrices was seen previously for the principal ν 3 absorptions for 59 99 and 438.7 cm −1 in 14 N 2 . 17 Therefore, an intriguing problem is posed as to whether the linearity of the CoBr 2 unit is maintained for all of the matrices studied. If this is not the case, at which point in the matrix series does the CoBr 2 unit deviate significantly from linearity? Bond angle information for every system in the series would be invaluable in order to solve this problem. Unfortunately, Co is monoisotopic, and therefore, Br isotopic structure provides the only means of bond angle determination from the IR spectra. Resolving the Br isotope patterns was very difficult and was possible only in the case of Ne and  (Table 10) produced a 180°bond angle for CoBr 2 isolated in a neon matrix and a 164°b ond angle in a xenon matrix. While a 164°angle indicates a deviation from a linear structure, an increase in the difference of the two bands of 0.02 to 0.05 cm −1 would result in a linear geometry. Therefore, IR bond angle calculations alone cannot provide conclusive evidence that CoBr 2 is bent in a xenon matrix. What perhaps is more important is the actual frequencies and "matrix shifts" of the ν 3 mode observed for the dihalide in each matrix and their positions relative to each other in the series. The number of additional site absorptions for each system was consistent despite repeated experiments using different batches of CoBr 2 .
For CoBr 2 isolated in a CH 4 matrix, the relative intensities of the two bands at 375.8 and 369.8 cm −1 was dependent on the deposition temperature. The spectra shown in Figure 14g,h show an increase in the 375.8 cm −1 feature compared with that at 369.8 cm −1 when CoBr 2 was deposited at 20 K. After deposition, the relative intensities of the absorptions did not change when the sample deposited at 20 K was cooled to 9 K or when the sample deposited at 9 K was annealed to 20 K. Several experiments were conducted on CoBr 2 isolated in Xe matrices, as spectral noise levels were worse than usual and also to discover the nature of the weak bands at 350.9 and 343.2 cm −1 . Further purification of the sample and checks on the integrity of the matrix gas led to the assignment of these bands as additional sites, as they were reproducible in each experiment and considered too high in frequency to be bands due to a dimer. 99 Following the observation of ν NN modes to high frequency of the free N 2 value and also the photochemical formation of more conventional ν NN bands, CoBr 2 was isolated in both 14 N 2 and 15 N 2 matrices, and photolysis was conducted on both systems. The IR spectra shown in Figure 14i,j show a shift in the principal ν 3 absorption band of 0.5 cm −1 , which is on the same order as that observed for NiBr 2 (0.3 cm −1 ). Weak bands were observed ( Figure 6 and Table 4) upon deposition in the 15 N 2 matrix at 2261.9 cm −1 (with a shoulder at 2260.2 cm −1 ) and in 14 N 2 at 2340.0 and 2336.8 cm −1 , in addition to the impurityinduced modes ( 14 N 2 , 2327.8 cm −1 ; 15 N 2 , 2250.0 cm −1 ). These are similar to (but at different wavenumbers than) the bands observed in the NiBr 2 experiments, indicating that they arise from an interaction between the N 2 matrix and the metal dibromide. After broadband photolysis of CoBr 2 in nitrogen matrices, two new bands were seen at 2235.1 and 2229.7 cm −1 in 15 N 2 matrices. However, it should be noted that these bands were incredibly weak and were not always reproducibly observed, and therefore, the evidence for chemisorbed Co−N 2 species is not strong. DFT calculations indicate that the reaction enthalpy for the formation of end-on-bonded CoBr 2 (η 1 -N 2 ) is −26 kJ mol −1 and that for CoBr 2 (η 1 -N 2 ) 2 is −66 kJ mol −1 .
Electronic Absorption Spectroscopy. The electronic absorption spectra of gaseous CoCl 2 have been studied and interpreted using ligand field methodology, with vibrational structure being observed. 189−191 DeKock and Gruen 102 proposed a 4 Φ g ground state using the ligand field model, which gives five charge transfer transitions. The argon matrix isolation studies 102 produced a spectrum with at least eight transitions. Clifton and Gruen 186 noted that in the 4000−25000 cm −1 region it was only possible to observe a fluorescence spectrum for CoCl 2 in Ar and an absorption spectrum for CoCl 2 in N 2 . The assignment of the ground state by DeKock and Gruen 102 was contested by Lever and Hollebone,192 who predicted it to be 4 Σ g − on the basis of fitting suitable parameters within the orbital angular overlap model, which led to a predicted spectrum more compatible with the spectroscopic data available. The assignment of the 4 Σ g − ground state for CoCl 2 was more recently substantiated by Bridgeman 193 using density functional theory and a cellular ligand field approach, resulting from the relative The Journal of Physical Chemistry A Article energies of the d orbitals being in the order d δ < d σ < d π with a δ g 4 σ g 1 π g 2 configuration. These results are analogous to those obtained for NiCl 2 . 168 Wang and Schwarz 129 also predicted a 4 Σ g − ground state, but 4 Δ g was essentially equienergetic. The data in Table 1 show that the DFT-calculated ground state for CoBr 2 is 4 Δ g with a d orbital ordering and population of δ g 3 σ g 2 π g 2 , but this is only 0.33 eV below a 4 Σ g − state with an occupation of δ g 4 σ g 1 π g 2 , and the 4 Φ g state is 0.48 eV above 4 Δ g with a δ g 3 σ g 1 π g 3 occupation. Between the 4 Δ g and 4 Σ g − states there are two bent quartet excited states with bond angles of 155°and 130°. The closeness of the energies of the 4 Δ g and 4 Σ g − states highlights the similarity in energies of the d δ and d σ orbitals discussed above for NiBr 2 .
The UV−vis−NIR spectra of CoBr 2 isolated in Ar, Kr, Xe, CH 4 , and 14 N 2 matrices are shown in Figure 15. The observed absorption bands are given in Table 7. DeKock and Gruen 102 and Jacox and Milligan 103 observed a complex band for CoCl 2 isolated in a Ar matrix containing at least five transitions between 30 000 and 38 000 cm −1 , with the most intense band at 33 700 cm −1 showing a vibrational progression of 233 ± 4 cm −1 , which was reported to correspond to the symmetric stretch of the excited state. We have also collected the spectra of CoCl 2 in Ar and N 2 matrices using the same protocol and equipment as for CoBr 2 . Our CoCl 2 argon matrix spectra (Figure 15f) are in very good agreement with the literature spectra, with a poorly resolved complex band at ca. 34 000 cm −1 . For CoBr 2 isolated in an Ar matrix, shown in Figure 15a (Figure 15b) is very similar to that of CoBr 2 in Ar, with intense peaks at 27 380 and 31 000 cm −1 . However, there are some significant differences in the spectrum of CoBr 2 in Xe (Figure 15c), with some broadening of the main peak at 26 800 cm −1 and the appearance of weak features around 12 500 cm −1 (Figure 16b) that are not present in the spectrum of CoBr 2 in Ar (Figure 16a).
The UV−vis−NIR spectrum of CoBr 2 isolated in CH 4 is shown in Figure 15d. While it qualitatively looks similar to the argon matrix spectrum, there are some significant differences. Three strong bands are observed, with the most intense band at 27 325 cm −1 being very close to the corresponding absorption in an Ar matrix at 27 720 cm −1 . At higher energy, bands are observed at 30 050 and 33 070 cm −1 . The shape of the main peak is different, and there are also weaker bands at 12 475 and 12 675 cm −1 that are shown more clearly in Figure 16c. Figure 15e shows the very different spectrum obtained for CoBr 2 isolated in a N 2 matrix, with intense peaks at 26 470 and 37 750 cm −1 and weaker features at 28 260, 31 250, 35 070, and 41 100 cm −1 . An increase in intensity of the lowerenergy transitions at 12 235, 12 290, 15 910, and 17 610 cm −1 is shown in Figure 16d,f. Very similar transitions at very similar energies were observed for CoCl 2 isolated in a N 2 matrix by Clifton and Gruen 186 and also by us (Figures 15g and 16e,g). Clifton and Gruen assigned them to d 7 spin-flip transitions. 186 They based their assignments of the absorption spectrum obtained in a N 2 matrix and the fluorescence spectrum obtained in an Ar matrix on a linear CoCl 2 unit. 186 It was stated, however, that matrix site effects and deviation in the linearity of the molecule would affect their interpretation. Although they recorded the N 2 spectrum between 4000 and 50 000 cm −1 , only the absorption bands between 4000 and 25 000 cm −1 were shown and tabulated. 186 Charge transfer bands in the 25000− 30000 cm −1 region were reported to be the same as those observed in an Ar matrix. 102 Our data for CoCl 2 in argon and nitrogen matrices are shown in Figure 15f,g, and while there are some similarities, there are very marked differences, analogous to those for CoBr 2 in argon and nitrogen matrices. The spectra  The Journal of Physical Chemistry A Article shown in Figure 15 were obtained from very similar deposition rates and times, so the extra intensity in the d−d transitions compared with the charge transfer bands observed in a N 2 matrix are a consequence of a relaxation of the selection rules, which is indicative of a significant change in geometry compared with the linear CoBr 2 structure in an Ar matrix.
XAFS Spectroscopy. The Co K-edge XANES spectra of CoBr 2 isolated in Ar, CH 4 , and N 2 matrices are shown in Figure 12. The spectrum of CoBr 2 in argon is very similar to that of NiBr 2 in methane and displays the sharp, intense feature on the edge characteristic of transitions from the 1s orbital to orbitals with significant p character in linear molecules. This transition was less well-defined in the CH 4 matrix data and was observed only as a shoulder in the N 2 data. Conversely, a very weak pre-edge feature at 7709.4 eV in the Ar matrix data became slightly more intense at 7709.6 eV in a CH 4 matrix and grew in intensity and shifted to 7708.8 eV in a N 2 matrix. These pre-edge features are due to 1s → 3d transitions, and their intensities generally increase with a reduction in site symmetry; in the case of CoBr 2 in a nitrogen matrix, the position and intensity are very similar to those observed for [CoBr 2 (PPh 3 ) 2 ], 57,111 indicating that the linearity of the CoBr 2 unit in argon is being lost in a methane matrix and more markedly so in a nitrogen matrix, which correlates very well with both the IR and UV−vis data. This is further evidence that CoBr 2 is nonlinear in CH 4 and N 2 matrices.
XAFS experiments were carried out at the Co and Br K-edges for CoBr 2 in Ar, CH 4 , and N 2 matrices. The results are shown in Figure 17, and the refined parameters are given in Table 9. What is immediately clear from the Co K-edge data is that the feature at approximately twice the Co−Br distance in the argon matrix data is absent in both the methane and nitrogen matrix data. From comparison with Figure 4, this indicates that the bond angle in the CoBr 2 cannot be any greater than 155°in either a CH 4 or N 2 matrix. In the case of the nitrogen matrix data there is also evidence of additional shells in the Co K-edge data, both under the main peak at 2 Å and at ca. 3 Å. In addition, there is significantly enhanced intensity at low k in the EXAFS data, indicating the presence of low-z backscatterers around the Co in addition to the Br.
The Co K-edge and Br K-edge data for CoBr 2 isolated in an Ar matrix in Figure 17 both gave a Co−Br distance of 2.26(3) Å, which is in good agreement with the previous vapor-phase electron diffraction value 152,188 of 2.241(5) Å and the DFTcalculated value of 2.210 Å. The multiple-scattering feature observed at twice the Co−Br distance in the Co K-edge data confirms linearity, and the Br···Br distance of 4.51(5) Å from the Br K-edge data gives a bond angle of 172°.
Therefore, all of the experimental data point to a linear geometry for CoBr 2 in an argon matrix. Between the Br−Co and Br···Br features in the FT of the Br K-edge data of CoBr 2 in Ar there is a Br···Ar interaction at 3.80(4) Å, in excellent agreement with the sum of the van der Waals radii for Br and Ar and as observed previously for CH 2 Br 2 in an argon matrix. 105 Although the refinement surface is fairly shallow for this shell, the best fit was obtained for an occupation number of nine Ar atoms. Therefore, in combination with the Br···Ar distance, this The Journal of Physical Chemistry A Article indicates that the Br atoms of CoBr 2 are located within a substitutional site in the argon lattice. There was no evidence for a Co···Ar shell in the Co K-edge EXAFS data, although we have observed Hg···Ar distances of 3.86 and 3.90 Å for Hg atoms and HgF 2 in argon matrices, respectively. 194 The Co K-edge XAFS spectrum and FT for CoBr 2 isolated in a CH 4 matrix are also shown in Figure 17. While Br K-edge experiments were also performed for this system, unfortunately the data suffered from a large step in the absorption cross section that made fitting of the data impossible, and there was insufficient beam time available to repeat the experiment. The highquality data from the Co K-edge show an increase of 0.05 Å in the Co−Br distance from 2.26(3) Å in an argon matrix to 2.31(3) Å in a CH 4 matrix. The Debye−Waller 2σ 2 term for the Co−Br shell is larger than that observed for the other systems, and this reflects the fact that two distinct trapping sites were observed in the IR spectra for CoBr 2 in methane, presumably giving rise to two slightly different Co−Br distances. The IR spectra of CoBr 2 in solid methane recorded simultaneously with the EXAFS 74 indicated that there were equal proportions of the two sites in this case. There is no evidence of a multiplescattering feature at approximately twice the Co−Br bond distance, and when the bond angle is refined, the maximum value that it would adopt was 158°. This is correlated with a relatively large shift of ca. 25 cm −1 in the ν 3 stretching frequencies between the Ar and CH 4 matrices.
Data were obtained at both the Co and Br K-edges for CoBr 2 isolated in N 2 . The EXAFS spectra and corresponding Fourier transforms are shown in Figure 17, and the refined parameters are collected in Table 9. The Co K-edge data gave a Co−Br distance of 2.29(3) Å, while that from the Br K-edge data was 2.31(3) Å. The Co−Br bond length is similar in the CH 4 and N 2 matrices. This degree of bond lengthening is less than that observed for NiBr 2 (0.09 Å) isolated in N 2 compared with NiBr 2 isolated in CH 4 , where a change in bond angle from 180°t o 145°was observed. Taken together with a smaller shift in ν 3 , this indicates that a smaller perturbation is at work in the CoBr 2 /CH 4 and CoBr 2 /N 2 systems than in NiBr 2 /N 2 . While at first glance there does not appear to be a distinguishable feature due to a Br···Br interaction in the Br K-edge FT, it will be recalled from Figure 4 that this in fact is indicative of a bond angle of ca. 160°, and when the model was refined using full multiple scattering, a Br···Br distance of 4.55(5) Å was obtained, which gives a bond angle of ca. 160°. The lack of a multiple-scattering feature in the FT of the Co K-edge EXAFS data also indicates that the bond angle must be less than 160°. There were no other shells that could be fit to the Br K-edge data, indicating that there must be a spread of Br···N interactions. However, in the Co K-edge data it is clear that there is a low-z backscattering contribution, and this manifests itself in the EXAFS as both enhanced intensity at low k and a shoulder on the main peak and a second peak in the FT. As in the case of NiBr 2 in a nitrogen matrix, it was not possible to fit the 3 Å shell without including a shorter Co−N interaction, and the only sensible fit was to two dinitrogen ligands attached endon to the Co. These have Co−N and Co···N distances of 2.13(3) and 3.22(4) Å, respectively, giving a NN distance of 1.09 Å assuming linearity. The corresponding values for NiBr 2 were 2.12(3) and 3.19(4) Å with a NN distance of 1.07 Å.
There has been a recent surge in the number of crystallographically characterized cobalt dinitrogen complexes. For example, S = 1 / 2 complexes with terminal N 2 ligands typically have Co−N distances of 1.8−1.9 Å. 195,196 Upon reduction, the Co−N distance decreases from 1.865 to 1.792 Å, 196 whereas upon oxidation it increases from 1.814 to 1.886 Å. 196 These Co−N values are all substantially shorter than those observed in our data, indicating the weakness of the bonding of N 2 to CoBr 2 .
Conclusions. When the results produced by all three spectroscopic techniques are collated, a more complex variation in the level of interaction between the matrix hosts and CoBr 2 is observed compared with that for NiBr 2 and certainly ZnBr 2 . The IR spectra showed a shift in frequency of ν 3 for each matrix gas in the series that was far greater than those observed for ZnBr 2 and NiBr 2 , where a linear geometry was preserved in all cases with the exception of NiBr 2 in a N 2 matrix. IR isotopic bond angle determinations revealed a linear structure for CoBr 2 isolated in Ne and a 164°bond angle for CoBr 2 isolated in Xe, but the inaccuracy of bond angle determinations close to linearity should be remembered. The electronic absorption data indicate that Ar and Kr are similar, but that there are more significant changes in going to Xe, CH 4 , and especially N 2 . Co K-edge XANES data have shown a gradual change in electronic structure and hence geometric structure in going from Ar to CH 4 to N 2 . A combination of Co and Br K-edge EXAFS has shown that CoBr 2 is linear in Ar and has a bond angle of about 160°in both CH 4 and N 2 matrices. As the ν 3 stretching frequency for CoBr 2 isolated in CH 4 is blue-shifted by only 2 cm −1 from that in Xe, a similar bond angle could be assumed. UV−vis−NIR experiments, although difficult to interpret, produced radically different spectra for CoBr 2 isolated in Ar compared with CoBr 2 isolated in N 2 . The spectrum obtained for a CH 4 matrix was more similar to that obtained for Ar, which suggested that a less significant deviation from linearity was probable for this system. Co K-edge XANES confirmed these observations. Combined FTIR/XAFS experiments further complemented these results. An average Co−Br bond distance of 2.26(1) Å for CoBr 2 isolated in an Ar matrix is in good agreement with the bond length of 2.24(1) Å obtained by vaporphase electron diffraction. 152,188 The presence of a multiplescattering feature at twice the Co−Br bond length in the Co K-edge spectrum and a Br···Br distance of 4.51(2) Å obtained from the Br K-edge spectrum confirmed a linear structure. A lengthening of the Co−Br bond distance to 2.31(1) Å for CoBr 2 isolated in a CH 4 matrix with no multiple-scattering feature being evident was indicative of a nonlinear structure. Without Br K-edge data it was difficult to ascertain an accurate bond angle, but from theoretical calculations the absence of multiple scattering had clearly shown that a bond angle of around 155−160°is reasonable. Co K-edge and Br K-edge data for CoBr 2 isolated in N 2 , although complicated by matrix interactions, gave bond distance and bond angle information similar to that provided by CoBr 2 isolated in CH 4 . As the ν 3 stretching frequency for the N 2 system occurred nearly 30 cm −1 below that seen for the CH 4 system and a very different UV−vis−NIR spectrum was obtained, a more significant interaction with the N 2 matrix and greater perturbation from a linear structure are probable.
Iron Dibromide. In common with CoBr 2 , FeBr 2 has received little attention in the matrix isolation literature, with nearly all of the iron dihalide studies being concentrated on FeCl 2 . FeBr 2 has a slight advantage over CoBr 2 in determining bond angle information, as the spectral features from the 54 Fe isotope, with a natural abundance of 5.8%, in addition to those from the dominant 56 Fe isotope can be observed after prolonged deposition. Matrix-isolated FeCl 2 has been studied The Journal of Physical Chemistry A Article as part of several systematic investigations of the 3d transition metal dichlorides using IR, 17,99,103,142,151,197 UV−vis, 102,103 Raman, 198 and nuclear γ ray (Mossbauer) spectroscopies. 199,200,201 The Fe−Cl bond length in CH 4 and N 2 matrices was obtained by XAFS spectroscopy, 67 with the bond length of 2.16(3) Å in a CH 4 matrix being in good agreement with the value of 2.151 Å determined by vapor-phase electron diffraction. 152 An increase in the bond length of 0.05 Å was seen in a N 2 matrix. There are also reports of 57 Fe Mossbauer investigations of FeBr 2 matrix-isolated in argon and xenon, 200,201 together with calculations. 199 FeBr 2 was also studied by vaporphase electron diffraction, which gave an Fe−Br r g value of 2.294(7) Å. 152 Although experimental data are limited for FeBr 3 in matrices, the DFT-calculated value for the IR-active E′ mode has been reported as 363.1 cm −1 . 202 For the analogous FeCl 3 case, the DFT-calculated value 202 of 473.0 cm −1 was ca. 13 cm −1 higher than the Kr matrix value 198,203 of 460.2 cm −1 and ca. 8 cm −1 higher than the argon matrix value 197 of 464.8 cm −1 . The calculated value for the IR-active terminal ν Fe−Br mode in Fe 2 Br 6 was found to be 354.4 cm −1 . 202 Infrared Spectroscopy. The IR spectra for FeBr 2 isolated in a variety of matrices are shown in Figure 18, and the observed wavenumbers of the ν 3 asymmetric FeBr 2 stretching vibration for all of the matrices employed are shown in Table 11. As for CoBr 2 , a wide range of frequencies was observed, above what would be expected from simple matrix shifts, and these are also more similar to those of CoBr 2 than those of NiBr 2 . The shift in ν 3 in going from an Ar matrix to a N 2 matrix in this case is 39 cm −1 , compared with 51 cm −1 for CoBr 2 and 87 cm −1 for NiBr 2 . The shift of 0.4 cm −1 in ν 3 in going from an 14 N 2 matrix to an 15 N 2 matrix is similar to that observed for NiBr 2 and CoBr 2 but larger than that for ZnBr 2 . The question therefore arises again, for which matrices does the Br−Fe−Br unit suffer significant perturbation from linearity? It has been generally agreed 17,99,103,142,151,197 that FeCl 2 isolated in an Ar matrix is linear, while isolation in 14 N 2 has previously yielded a bond angle of 150°. 17 FeBr 2 exhibited extra absorption bands due to matrix effects for all of the matrices except CH 4 , as shown in Figure 18. The degree of splitting and the intensity of these extra bands varied for each matrix, but as Br isotopic structure was resolved for Kr, Xe, and N 2 matrices, this indicates that excellent isolation was achieved. In the krypton matrix experiments, the deposition was carried out at 25 K, and upon cooling to 9 K (Figure 18b), the most intense peak shifted slightly from 391.7 to 392.3 cm −1 with no marked change in intensity, and this was also reflected in the weaker peak at 376.3 cm −1 . The inset clearly shows the presence of bromine isotopic structure, and the values are given in Table 11. The xenon matrix experiments were carried out using a deposition temperature of 50 K, and when the sample was cooled to 9 K (Figure 18c), the band at 365.3 cm −1 grew in intensity slightly, while that at 373.2 cm −1 displayed a much more marked increase in intensity and shifted from to 374.4 to 373.2 cm −1 . At higher resolution (see the inset), both of these peaks displayed Br isotopic structure consistent with the presence of two bromines. In contrast to CoBr 2 ( Figure 14), only one feature was observed in the Fe−Br stretching region for FeBr 2 in methane matrices.
In 14 N 2 matrices (Figure 18e), two peaks were observed at 356.7 and 330.7 cm −1 , and upon annealing to 20 K a feature at 336 cm −1 grew in. In the 15 N 2 experiments (Figure 18f), the deposition was carried out at 15 K, and in this case the additional peak at 336 cm −1 was observed upon deposition before annealing. The Br isotopic structure on the band at 356.7 cm −1 (shown in the inset) is clearly indicative of a dibromide, and while Br isotopic structure on the 330.7 cm −1 band was not so well resolved, it is also consistent with the presence of two bromines. 57 Fe Mossbauer experiments on FeCl 2 indicated two sites in Xe matrices, one of which could be removed by annealing to 42 K. 199 Therefore, it is reasonable to assign the second peaks in these data to matrix or site effects.
In addition to confirming the presence of two bromine atoms, the Br isotopic structure observed for Kr, Xe, and 14 N 2 matrices (shown in the insets in Figure 18) can be used for bond angle determination (Table 11). This indicated linear FeBr 2 in the case of Kr and Xe matrices and a 150°bond angle for an 14 N 2 matrix using the higher-quality 56 Fe data. An FeBr 2 bond angle of 150°is essentially identical to that previously obtained for FeCl 2 in N 2 . 17 The position of the ν 3 stretching vibration for FeBr 2 isolated in Xe midway between the Ar and N 2 values might have been expected to indicate some deviation from linearity. However, the insensitivity of bond angle determination using IR data must be highlighted, as the difference between the calculated values of 180°and 160°for FeBr 2 is only 0.06 cm −1 (Table 11). These very small shifts in frequency are clearly within the experimental error, leading to great uncertainty in the true bond angle for each of these systems using this technique alone. While there appears to be isotopic structure associated with 54 FeBr 2 and 56 FeBr 2 in the lower-resolution Ar, Xe, and N 2 matrix spectra, using it is problematic given the large effect on bond angle calculations produced by small errors in the measurement of the positions of weak bands. For example, the separation is too large for linear molecules in the case of Xe and N 2 but indicates a bond angle of ca. 135°for the argon matrix data. Therefore, other In nitrogen matrices, bands were observed ( Figure 6 and Table 4) in the ν NN region at 2332.3 cm −1 ( 14 N 2 ) and 2254.9 cm −1 ( 15 N 2 ) in addition to the impurity-induced modes ( 14 N 2 , 2327.8 cm −1 ; 15 N 2 , 2250.0 cm −1 ). These are closer to the "free" N 2 value than for either NiBr 2 or CoBr 2 and therefore indicate a lower level of interaction between FeBr 2 and the N 2 host, consistent with the smaller shift of ν 3 between Ar and N 2 matrices as well as between 14 N 2 and 15 N 2 matrices. Photolysis of FeBr 2 in 14 N 2 and 15 N 2 matrices yielded no new bands assignable to ν NN stretches and no change in the bands close to the impurity-induced modes. The DFT calculations indicated that the reaction enthalpies for the formation of end-on-bonded FeBr 2 (η 1 -N 2 ) and FeBr 2 (η 1 -N 2 ) 2 are −38 and −72 kJ mol −1 , respectively, and that the reaction enthalpy for one side-onbonded N 2 is −5 kJ mol −1 .
Electronic Absorption Spectroscopy. The electronic absorption spectrum of FeCl 2 isolated in an Ar matrix was previously studied by DeKock and Gruen 102 and Jacox and Milligan. 103 A 5 Δ g ground state was proposed, 102 predicting five charge transfer transitions, all of which were observed. The assignment of the ground state was more recently confirmed by Bridgeman,193 although the assignments of the transitions was contested. As in the cases of NiCl 2 and CoCl 2 the ordering of the σ g and π g orbitals was found to be the reverse of what is predicted by simple ligand field theory arguments. Bridgeman agreed with the assignment of the ground state proposed by previous workers, but only because the 5 Δ g ground state is independent of the order of σ g and π g , giving the configuration δ g 3 σ g 1 π g 2 . Our DFT calculations on FeBr 2 also predict a 5 Δ g ground state with a d-orbital configuration of δ g 3 σ g 1 π g 2 , but it should be noted that there is a second quintet state, 5 Σ g − with a δ g 2 σ g 2 π g 2 configuration, at almost the same energy. There are no low-lying bent states.
The UV−vis−NIR spectra of FeBr 2 isolated in Ar, CH 4 , and 14 N 2 matrices are shown in Figure 19, and the observed bands are given in Table 7. The spectrum of FeBr 2 in an argon matrix ( Figure 19a) is qualitatively similar to that reported previously for Ar-matrix-isolated FeCl 2 in the 32000−38000 cm −1 region, 102 except that the features are ca. 6000 cm −1 lower. In addition to the most intense peak at 35 570 cm −1 , additional peaks for FeBr 2 in argon were seen at 31 260, 32 950, 33 650, 37 060, 39 615, 41 180, and 43 850 cm −1 . It is not surprising that some of these higher-energy transitions were not seen for FeCl 2 in argon, as they would have probably occurred beyond 50 000 cm −1 , outside the spectral range of the experiment. When FeBr 2 was isolated in a CH 4 matrix (Figure 19b), a reduction in the number of bands compared with the Ar matrix was observed. The peaks observed in the Ar matrix centered at 31 260, 32 950, 33 650, and 37 060 cm −1 were essentially lost, leaving peaks at 35550, 39780, 41930 cm −1 , together with a shoulder at 33870 cm −1 and a weak peak at 44130 cm −1 .
Relatively little change in energy was seen for the remaining peaks in the CH 4 matrix spectrum compared with the Ar matrix spectrum. Even further simplification of the spectrum was seen when FeBr 2 was isolated in a N 2 matrix (Figure 19c). While the most intense peak was still observed at 35 300 cm −1 , only The Journal of Physical Chemistry A Article one intense band at higher energy remained, at 45 190 cm −1 , which was blue-shifted in excess of 1000 cm −1 relative to those bands seen in the Ar and CH 4 matrices. This reduction in the number of observed bands upon changing from Ar to CH 4 and N 2 matrices was in direct contrast to what was seen for NiBr 2 and CoBr 2 , where the complexity of the spectra increased in going from the Ar matrix to the N 2 matrix. All of the observed bands in these spectra are assigned as charge transfer transitions, with no bands occurring at lower energy assignable to d−d transitions. The simple observation that the spectra of FeBr 2 isolated in Ar and N 2 matrices appear to have little in common is an indication of a significant difference in the electronic and hence geometric structures of FeBr 2 in these two matrix environments. Moreover, the spectrum of FeBr 2 isolated in a CH 4 matrix seems to show an FeBr 2 environment intermediate between the extreme cases, which coincides with the evidence provided by the IR studies.
XAFS Spectroscopy. The Fe K-edge XANES of FeBr 2 in an argon matrix ( Figure 12) is qualitatively similar to that for CoBr 2 in argon and NiBr 2 in methane and displays an intense edge feature at 7119.3 eV together with a very weak pre-edge feature at 7112.7 eV. The feature on the edge is most intense in FeBr 2 and decreases as one goes to linear CoBr 2 and NiBr 2 . In a methane matrix, the sharp edge feature at 7119.3 eV has lower relative intensity and the weak pre-edge band at 7112.3 eV has greater intensity, both of which are indicative of a drop in symmetry from linearity. This continued for FeBr 2 in a nitrogen matrix, where the edge peak has disappeared into the edge structure and the pre-edge feature at 7112.3 eV is slightly more intense. The behavior of the XANES spectra is consistent with that of the other spectra, indicating a less substantial change in the geometry of FeBr 2 in going from the Ar matrix to the CH 4 matrix but a more significant change for N 2 matrices.
Fe K-edge XAFS studies were conducted on FeBr 2 isolated in Ar, CH 4 , and N 2 matrices. The results are shown in Table 9 and the spectra in Figure 20. Unfortunately, there was insufficient synchrotron time available to collect the Br K-edge as well. As for CoBr 2 , there is a consistent change in the FTs, with the argon data having a multiple-scattering feature at approximately twice the first shell distance, indicating linearity, the methane data containing only the Fe−Br shell, indicating a maximum bond angle of ca. 160°, and the N 2 data exhibiting a weak feature at ca. 3 Å. Although the peak at ca. 4.5 Å in the FT of the N 2 data looks like a multiple-scattering feature indicating linearity, it was not possible to fit this using the full multiple-scattering approach and is more likely due to some of the high-frequency noise in the spectrum. The argon data are very noisy because of the short X-ray attenuation length (1/e) of ca. 34 μm for Ar at 7 keV. 82 The Fe−Br bond length of 2.27(3) Å determined for FeBr 2 in solid argon is in good agreement with the electron diffraction 152 value (r g ) of 2.294(7) Å. In a methane matrix and a nitrogen matrix, the Fe−Br bond length increased by 0.02 Å to 2.29(3) Å. Full multiple scattering refinement of the methane data indicated a maximum bond angle of ca. 160°. As was the case for both NiBr 2 131 Conclusions. The IR data collected for FeBr 2 showed a decrease in the ν 3 stretching frequency in going from Ne to Xe matrices, but this covered a far greater range than that seen for ZnBr 2 and NiBr 2 for Ne to Xe matrices, where a linear geometry was preserved. This was also seen for CoBr 2 , where there was good evidence that CoBr 2 is bent in CH 4 , Xe, and N 2 matrices. Bond angle information from the IR data suggested that FeBr 2 is linear in all of the matrices except N 2 , where a bond angle of 150°was obtained. While this angle was  The Journal of Physical Chemistry A Article consistent with that obtained for FeCl 2 in N 2 , 17 some deviation from linearity might have been expected in a Xe matrix. The UV−vis−NIR data showed a progression in the number of observed transitions and their frequency in going from Ar to CH 4 to N 2 . This provides good evidence of a steady change in the nature of the Br−Fe−Br unit from linear to increasingly bent when isolated in these matrices, with FeBr 2 isolated in Ar being in reasonable agreement with the comparable spectrum observed for FeCl 2 . 102 The Fe K-edge XANES data indicate a small change between the Ar matrix and the CH 4 matrix, with a more substantial change for N 2 . The EXAFS data were consistent with linear FeBr 2 in solid argon, but the absence of a feature in the Fourier transform at twice the Fe−Br distance combined with a lengthening of the Fe−Br bond in solid methane is consistent with a reduction in bond angle. Therefore, it is concluded that the bond angles for FeBr 2 isolated in CH 4 and Xe matrices are probably between 150°a nd 160°. The Fe K-edge EXAFS data of FeBr 2 isolated in solid nitrogen is also consistent with a nonlinear geometry (around 150°), together with two weakly bound dinitrogen units in the first coordination sphere. Figure 21 shows all of the observed ν 3 frequencies for different matrix gases plotted against the metal dibromides and also includes all of the related data of which we are aware for the difluorides and dichlorides of Fe, Co, Ni, and Zn. (Copper has not been included, as there are only limited matrix data for CuF 2 , 46,207 CuCl 2 , 208,209 and CuBr 2 . 210 ) For the difluorides the only complete sets of data are for Ar and Ne matrices, but the pattern observed is characteristic of a general increase in Z eff across the row, with a ligand field stabilization energy (LFSE)type effect superimposed on this. For the dichlorides, the only complete sets of data are for argon and nitrogen matrices. As expected, the trends for argon matrices mirror those for the difluorides, but there is a very marked difference in the nitrogen matrix data. The most complete set of data is for the dibromides presented in this work, which in addition to confirming the trend observed for nitrogen matrices highlights some other more subtle effects with Xe and CH 4 matrices. The most dramatic features in Figure 21 are the behavior of the metal halides in nitrogen matrices and the change in the spread of the ν 3 modes. For the zinc halides there is very little difference between the values of ν 3 in argon and nitrogen matrices. In going from iron to cobalt there is a larger-than-expected drop in the value of ν 3 for nitrogen compared with argon, and this is associated with bond angles of ca. 150°in FeBr 2 and 150−160°i n CoBr 2 . In the case of nickel, the change in going from argon to nitrogen becomes very marked. For NiF 2 a drop in ν 3 of 9.5% is observed in going from an argon matrix to a nitrogen matrix. In contrast, reductions of 18% and 21% are observed for NiCl 2 and NiBr 2 , respectively, on going from an argon matrix to a nitrogen matrix. These are much larger than usually encountered for "matrix shifts" and are associated with a structural perturbation of the nickel dihalide. For nitrogen matrices the calculated NiF 2 bond angle is 152°, which is similar to that in argon matrices, but this decreases much more markedly to ca. 140°for both NiCl 2 and NiBr 2 , which are essentially linear in argon. This significant structural perturbation is also confirmed by both electronic absorption spectroscopy and X-ray absorption spectroscopy. Therefore, the hardness of the metal center has a profound effect on the propensity for the triatomic molecule to be bent via the interaction with the nitrogen matrix.

■ DISCUSSION
While nitrogen may be expected to be a "non-innocent" matrix, the data for the dibromides isolated in noble gas matrices and methane indicate that some more subtle structural perturbation may occur for these molecules in different matrices, although the variation is much less than that observed for the nitrogen matrices. In particular, it is clear from Figure 21c that for ZnBr 2 there is very little difference in the value of ν 3 among all the matrix gases. A similar position is observed for NiBr 2 for all but N 2 matrices. In contrast, for both CoBr 2 and FeBr 2 there is a much greater spread of values observed for ν 3 , indicating a variation in the extent of interaction of the guest with the host, which is in good agreement with the order proposed by Beattie and Millington 15 and has also been observed for diatomic molecules. 211 The electronic absorption spectra for CoBr 2 indicate that there is very little difference between argon and krypton matrices but that there are differences between these and xenon and methane matrices, which is mirrored in the value of ν 3 for these matrix gases. Likewise, the Co K-edge XANES indicates that there is increasing nonlinearity in going from argon through methane to nitrogen matrices, and both the Co and Br K-edge EXAFS data confirm this. The best estimate is that the bond angle of CoBr 2 in a methane matrix cannot be greater than 160°. In view of the similarity of the positions of ν 3 and the electronic absorption spectra of CoBr 2 in Xe and CH 4 , it seems sensible to suggest that CoBr 2 is also probably slightly bent in xenon. A similar case exists for FeBr 2 , but in this case the extent of perturbation is more similar for CH 4 , Xe, and N 2 matrices.

Article
There is a subtle interplay of geometric and electronic effects, both intrinsic to the metal dihalide and between the metal dihalide and the matrix host, that are responsible for this complex behavior. For example, the different populations of the metal-based σ g , π g , and δ g orbitals (Table 1) and the presence of low-lying linear and bent excited states are intrinsic properties of the metal dihalides that affect the way they can interact with the matrix host as well as the relative ease with which the dihalides can bend. The soft-bending modes in CuCl 2 have been studied previously. 212 Hastie et al. 139,185 estimated the frequencies of ν 2 for CoF 2 (151 cm −1 ), NiF 2 (142 cm −1 ), and ZnF 2 (157 cm −1 ) using gas-phase data with an uncertainty of ±30 cm −1 . Thompson and Carlson 99 observed ν 2 for MnCl 2 (83 cm −1 ), FeCl 2 (88 cm −1 ), CoCl 2 (94.5 cm −1 ), NiCl 2 (85 cm −1 ), and NiBr 2 (69 cm −1 ). We attempted to determine the values of ν 2 for the dibromides using SR-FIR spectroscopy but were unable to identify them in the presence of the various phonon and hindered rotational modes, apart from a possible value of 55 cm −1 for NiBr 2 in CH 4 . The DFT-calculated ν 2 bending modes for these molecules are in given in Table 1 and increase from 53 cm −1 for FeBr 2 through 63 cm −1 for CoBr 2 and 68 cm −1 for NiBr 2 to 80 cm −1 for ZnBr 2 . These data, even with the uncertainty of the difluorides, establish a trend in the frequencies of the ν 2 bending modes to be MF 2 > MCl 2 > MBr 2 , implying that the dibromides will be easier to bend than the dichlorides and difluorides, and the order of flexibility decreases from FeX 2 to ZnX 2 . It is also reasonable to expect the diiodides to have even lower ν 2 bending mode frequencies. The ease of bending is also expected to decrease as the metal−halogen bond length becomes shorter in going from the iron dihalides to the zinc dihalides. This is borne out in the data in Figure 21, where (excluding N 2 matrices; see below) the spread of ν 3 wavenumbers decreases in going from FeX 2 through to ZnX 2 .
In the previous cases where there was evidence for the metal dihalide being bent in a matrix, the primary interaction between the dihalide and the surrounding host was thought to be electrostatic. 17 Polarization of the host atom or molecule by the positively charged metal ion leads to an ion−induced-dipole interaction. Therefore, the polarizability of the host is an important consideration. Of those studied in this work, xenon is by far the easiest matrix atom to polarize, followed by methane, which is consistent with the stronger interactions seen with FeBr 2 and CoBr 2 . Neon and argon are the hardest atoms to polarize, and this too was evident, as linear geometries were observed in all cases for the metal dibromides in these matrices. In addition to electrostatic interactions, the physical sizes of the halide and the substitutional sites within the matrix as well as how tightly the metal dihalide is held within in them will also have an effect on the geometry adopted, 213 especially if the molecule is easily bent and/or there are low-lying excited bent states. Which of these various effects is dominant in any particular case is not straightforward to unravel.
In addition to the structural changes in different matrices, the other key observation is the presence of bands blue-shifted from the impurity-induced N 2 modes at 2327.8 cm −1 ( 14 N 2 ) and 2250.0 cm −1 ( 15 N 2 ) for the metal dihalides in N 2 matrices. Table 4 summarizes the observed frequencies of these bands for a variety of metals in both 14 N 2 and 15 N 2 matrices, and Figure 6 shows the corresponding spectra in the ν NN stretching region, with the N 2 impurity-induced modes marked with * labels. The 14 N 2 data in Figure 6 have been truncated to exclude the CO 2 bands, e.g., the band due to CO 2 occurred very close to the 2342.8 cm −1 absorption band for NiBr 2 in 14 N 2 . It is clear from Table 4 and Figure 6 that these bands occurred at different frequencies for each metal and also for each halide, clearly indicating that they arise from an interaction between the metal halide and N 2 . The largest blue shift was observed for nickel, which also had the largest shift in ν 3 .
For N 2 absorbed onto surfaces studied either with highresolution electron energy loss spectroscopy (HREELS) or IR reflection−absorption spectroscopy (IRAS), bands near the gas-phase value are characteristic of physisorbed species, whereas those at lower frequency arise from chemisorbed N 2 moieties. 214 For example from IRAS experiments the ν NN mode for N 2 physisorbed on Pt(111) occurs at 2322 cm −1 , whereas that for chemisorbed N 2 appear at 2265 cm −1 (terrace sites) and 2232 cm −1 (defect/step sites). 215,216 For physisorbed N 2 on Rh/Al 2 O 3 and Al 2 O 3 , ν NN was observed at 2331 cm −1 , 217 and for chemisorbed 14 N 2 on Rh, ν NN was measured as 2257 cm −1 . 214,217 More recently, ν NN for physisorbed N 2 on Rh/Al 2 O 3 and Rh/TiO 2 was observed at 2331 cm −1 , with ν NN for chemisorbed N 2 at 2248 cm −1 . 218,219 The 2258 cm −1 band observed previously 214,217 was due to interaction of N 2 with a surface treated with H 2 . 218,219 On H-ZSM-5, the ν NN mode for physisorbed 14 N 2 was observed at 2332 cm −1 and that for physisorbed 15 N 2 at 2253 cm −1 . 220 For chemisorbed N 2 on Ni(110), ν NN was observed at 2196 cm −1 . 221 From HREELS experiments, ν NN for physisorbed N 2 on NbO(110) at 20 K was observed at 2339 cm −1 , whereas for chemisorbed N 2 , ν NN was observed at 2194 cm −1 at 80 K and 2162 cm −1 at 20 K. 222 For N 2 on Ru(001), the physisorbed ν NN peak was at 2331 cm −1 , while for the chemisorbed species ν NN was at 2194 cm −1 . 223 ν NN for N 2 physisorbed on Al (111) was observed at 2339 cm −1 . 224 For N 2 on Pd(111), ν NN was observed at 2331 cm −1 for the physisorbed species and at 2258 cm −1 for the chemisorbed species. 225 Surface EXAFS (SEXAFS) indicates a Ni−N bond length of 1.86 Å for N 2 chemisorbed on Ni (110). 226 These ν NN modes clearly show the difference in the spectroscopic properties of physisorbed and chemisorbed species.
Kinematic effects will result in an increase in ν NN for physisorbed N 2 even with the same force constant. As for carbonyl complexes, there is also the possibility that bands to high frequency of the free N 2 value may indicate nonclassical bonding, with predominantly σ bonding. Lubezky et al. 227,228 observed bands at 2344 and 2334 cm −1 for 14 N 2 on LiCl and at 2341 and 2332 cm −1 for 14 N 2 on LiF, with calculated adsorption potentials of 18.0 and 6.3 kJ mol −1 , respectively. Lesiecki and Nibler 100 observed bands in 14 N 2 matrices that were blue-shifted from the gas-phase values by 18 cm −1 for MgF 2 (Raman) and 14 cm −1 for MgCl 2 (Raman and IR). Boganov et al. 229 calculated that in SnF 2 (N 2 ) and SnF 2 (N 2 ) 2 the Sn−N bond lengths should be ca. 2.9 Å, with the ν NN modes 14 and 13 cm −1 higher than "free" N 2 value, but they were unable to observe any such features in their spectra. For NiCl 2 and NiF 2 isolated in solid 14 N 2 at ca. 14 K, bands at 2327 cm −1 were reported by DeKock and Van Leirsburg 140,141 that were not assigned with any certainty at the time but are almost certainly due to 14 N 2 -impurity-perturbed ν NN modes 138 rather than N 2 complexes.
Therefore, the IR bands to high frequency of the perturbed ν NN modes of free N 2 in FeBr 2 , CoBr 2 , and NiBr 2 are best considered as X 2 M···(N 2 ) n species akin to physisorption on a surface, indicative of N 2 coordinated to the metal with a relatively weak interaction. The positions of these bands with respect to the perturbed ν NN mode are mirrored in the differences of the MX 2 ν 3 modes between Ar and N 2 matrices.

Article
The relatively small change (0.3 cm −1 ) in the position of the NiBr 2 ν 3 mode between 14 N 2 and 15 N 2 matrices indicates a weak level of interaction, as a shift of 7.7 cm −1 has been observed in ν Cu−Cl for CuCl(N 2 ) between 14 N 2 and 15 N 2 matrices. 70 The metal K-edge EXAFS data indicate M−N and M···N distances of 2.15(3) and 3.19(4) Å for FeBr 2 , 2.13(3) and 3.22(4) Å for CoBr 2 , and 2.12(2) and 3.19(4) Å for NiBr 2 . All of the M−N distances are significantly longer than those observed for complexes or chemisorbed species. The ν NN bands observed for ZnBr 2 in 14 N 2 and 15 N 2 matrices before and after photolysis are very close to the free N 2 impurity-induced modes and appear as shouldered absorption bands. This underlines the fact that a minimal interaction between ZnBr 2 and N 2 was observed, consistent with the molecule retaining its linear structure.
In the case of NiBr 2 and NiCl 2 in nitrogen matrices, photolysis brings about the appearance of new ν NN bands at lower wavenumber than for free N 2 that are more consistent with conventional chemisorbed dinitrogen coordinated to the metal center or conventional complexes. For CoBr 2 these features were very weak, and none were observed for FeBr 2 or NiF 2 . The isotopic behavior of the ν NN bands observed after photolysis clearly indicates the formation of a species containing two geminal N 2 units in [NiX 2 (η 1 -N 2 ) 2 ]. They are at relatively high values compared with those for low-oxidationstate dinitrogen complexes but are similar to those observed for other complexes containing cationic metal centers. Most significantly, they are very similar to those observed for matrix-isolated Ni(N 2 ) 2 (O 2 ), which was shown via isotopic substitution to have a pseudotetrahedral geometry with two end-on-bonded dinitrogen ligands (η 1 -N 2 ) in a cis configuration and one side-on-bonded dioxygen ligand (η 2 -O 2 ), with the dioxygen unit believed to be between peroxo and superoxo in character. 163,164 The NiX 2 (η 1 -N 2 ) 2 complexes reported in this work are very unstable, even under matrix isolation conditions, and provide an indication of the stability of Ni(II) dinitrogen complexes as well as being an example of reversible binding of N 2 to Ni(II) centers. This work also indicates a calibration value for ν NN attached to a Ni(II) center, thus confirming that the Ni(N 2 ) 2 (O 2 ) complexes are best considered as containing Ni(II) and a peroxo ligand. The proportion of NiX 2 (η 1 -N 2 ) 2 formed upon photolysis is dependent on the deposition temperature (which needs to be less than 10 K) and the photolysis wavelength, but in all cases it appears to remain fairly low. These chemisorbed species dissociate upon warming to 20 K, as found for Pd(N 2 ) 2 (O 2 ) 164 and Mo(N 2 ) x , 165 indicating their extremely reactive nature. The very low deposition temperatures required to observe the photoproducts may be related to the need for some preorganization of the nitrogen lattice that is only achieved by very rapid quenching of the NiX 2 in solid nitrogen below 10 K.

■ CONCLUSIONS
The combination of IR, UV−vis−NIR, and XAFS spectroscopies has produced good evidence that there are different and varying interactions between metal dihalides and a wide range of matrix hosts. For zinc there is little perturbation of the spectroscopic signatures, and for nickel this is also the case, except for N 2 , where there is a significant change associated with a change from a linear geometry to a bent geometry. In the case of cobalt and iron there is a more gradual change, where in addition to N 2 matrices the CH 4 and Xe matrices also have interactions leading to nonlinear geometries. The extents of interaction between the metal halide and host increased in the order Ne < Ar < O 2 < Kr < CH 4 < Xe. In N 2 matrices there is evidence for the formation of physisorbed-type species, and the extent of the blue shift of the ν NN mode correlates strongly with the shift in the MBr 2 ν 3 mode. Photolysis of NiBr 2 and NiCl 2 in N 2 matrices results in the formation of chemisorbed NiX 2 (η 1 -N 2 ) 2 -type species, with ν NN modes red-shifted from that for free N 2 .
Therefore, this work has demonstrated that the term "inert" must be viewed with caution when dealing with species that possess geometries that are easily perturbed.

■ ACKNOWLEDGMENTS
The EPSRC are thanked for financial support of this work through grants for the provision of equipment (GR/H29117, GR/K17513, GR/T09651) and Ph.D. studentships to O.M.W., N.H., E.L.D., and J.F.R. and also for access to the Chemical Database Service at Daresbury Laboratory. 230 The STFC are acknowledged for access to synchrotron and computing facilities. The staff at Daresbury Laboratory are thanked for their assistance with the X-ray absorption and far-IR experiments.