First Bond Dissociation Energy of M(CO)6 (M = Cr, Mo, W ) Revisited

Prediction of the Bond Lengths, Vibrational Frequencies, and Bond Dissociation Energy of Octahedral Seaborgium Hexacarbonyl, Sg(CO)6. Clinton S. Nash ...
1 downloads 0 Views 559KB Size
Download PDF
J . Phys. Chem. 1994,98, 48384841

4838

First Bond Dissociation Energy of M(CO)a (M = Cr, Mo, W) Revisited: The Performance of Density Functional Theory and the Influence of Relativistic Effects Jian Li, Georg Schreckenbach, and Tom Ziegler’ Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N I N4 Received: December 28, 1993; In Final Form: February 21, 1994’

Density functional (DF) calculations have been carried out on the M-CO bond lengths as well as the first bond dissociation energy (FBDE) for the M(CO)a hexacarbonyls with M = Cr, Mo, and W. The main objective of the investigation has been to examine how well D F theory can predict the observed bond dissociation energies and M-CO bond distances. It is shown that the calculated M-CO bond lengths are within 0.01 A of experiment after the inclusion of nonlocal corrections and relativistic effects, NL-SCF+QR. Relativity contracts the W-CO bond by 0.07 A, and bond distances calculated without nonlocal corrections are too short by 0.04 A. The FBDEs calculated by the NL-SCF+QR scheme were 46.2 kcal/mol (Cr), 39.7 kcal/mol (Mo), and 43.7 kcal/mol (W), whereas the corresponding experimental values are given by 36.8 f 2 kcal/mol (Cr), 40.5 f 2 kcal/mol (Mo), and 46.0 f 2 kcal/mol (W). The agreement with experiment is good for M = Mo and W, where relativity increase the bond strength with 1.5 and 4.9 kcal/mol, respectively. The origin of the relativistic effects are analyzed by an energy decomposition scheme. The NL-SCF+QR value of 46.2 kcal/mol for M = C r agrees well with recent ab initio estimates. However, it is a t variance with the experimental value of 36.8 f 2 kcal/mol. It is suggested that the experimental value should be adjusted upward. Nonlocal corrections are essential for a quantitative estimate of the FBDEs.

Introduction The first bond dissociation energy (FBDE) for transition-metal compoundsis an important parameter in studieson organometallic kinetics.1 However, an accurate estimate of FBDE by theoretical or experimental techniques still presents a challenge, even for simple binary compounds such as M(CO)6 with M = Cr, Mo, W. Earlier experimental data for M(CO)6 (M = Cr, Mo, W) were obtained in solution, based on kinetic measurements and photoacoustic calorimetry.2J The only set of data in the gas phase was determined by Lewis et al. by using pulsed laser pyrolysis technique^.^ On the theoretical side, Sherwood and Hall5, Moncrieff et a1.6, Barnes et al.7 calculated the FBDE for Cr(CO)6 at the Hartree-Fock (HF) and post-HF levels. Similar all electron calculations have not been presented for the 4d and 5d homologues due to the large number of core electrons. However, Ehlers and Frenking have recently published a comprehensive study on structures and FBDEs of M(CO)6 for all three members of the chromium triad by the aid of effective core potentials using second-order Maller-Plesset theory (MP2) as well as coupled cluster schemes (CCSD(T)).8 Their calculated results are in excellent agreement with experimental values for M = Mo and W. Density functional theory (DFT) has also been employed in calculations on FBDEs of organometallic compounds. Six years ago, Ziegler et ~ 1reported . ~ a DFT calculation on M(C0)d (M = Ni, Pd, Pt), M(CO)5 (M = Fe, Ru, Os) and M(CO)6 (M = Cr, Mo, W), based on experimental geometries and the local density approximation (LDA)lO with Becke’s” and Stoll’s12 corrections added as a perturbation. Since the publication of this work, great advances have been achieved in DFT.13 First, it is now possible to optimize molecular geometries by methods based on analytical energy gradients14 and to calculate vibrational frequencies15 as well as intensities16 by numerical second derivatives. Further, new nonlocal correction terms to the LDA method have been introduced by Becke and Perdew” for exchange and correlation, respectively, and these correctionshave been included self-consistently,14bNL-SCF. Finally, relativistic effects can now be taken into account in the geometry optimization procedure via ______

0

~

~~

~~

~

Abstract published in Advance ACS Abstracts. April 1, 1994.

a quasi-relativistic Hamiltionian.Is Therefore, it seems timely to reexamine the FBDEs for M(CO)6 (M = Cr, Mo, W) by the current DFT techniques. This study has been prompted by the recent work by Ehlers and Frenking.8

Computational Method All calculations were based on the density functional package AMOL, developed by Baerends et al.19 and vectorized by RavenekeZ0The numerical integration scheme applied for the calculations was developed by te Velde et al.zl Uncontracted triple-{STO basis sets were used for ns, np, nd, (n 1)s and (n l ) p orbitals of chromium, molybdenum, and tungsten.22 For the 2s and 2p orbitals of carbon and oxygen, double-{ basis sets were used and augmented by an extra d polarization function. The inner cores of chromium (ls2s2p), molybdenum (ls2s2p3s3p3d), and tungsten (ls2~2p3~3p3d4~4p4f) as well as carbon and oxygen (1s) were treated by the frozen-core approximation. To fit the molecular density and to present Coulomb and exchange potentials accurately, a set of auxiliary s, p, d, f, and g STO functions, centered on all nuclei, was introduced.23 The molecular geometries were optimized based on the method implemented by Versluis and Ziegler at the LDA level and by Fan and Ziegler at the NL-SCF 1 e ~ e l . l ~ Relativistic effects play an important role in the structural chemistry and energetics of molecules containing heavy atoms such as tungsten.24 Two approaches, first-order perturbation theory (FO)25 and the quasi-relativistic method (QR),26 were employed to account for relativistic effects. In the FO method, terms up to order a2, where a is the fine structure constant, are retained in the Hamiltionian. In the QR method changes in the density induced by the first-order Hamiltonian are considered to all orders in az, Furthermore, the QR scheme was extended to include geometry optimization.18

+

+

Results and Discussion Geometries of M(C0)6 and M(CO),. The geometries of the hexacarbonyls were optimized within Oh symmetry constraints. Table 1 displays M-C and C-0 bond lengths obtained by DFT and correlated ab initio methods, together with the experimental

0022-3654/94/2Q98-4838s04.5Q/Q 0 1994 American Chemical Society

The Journal of Physical Chemistry, Vol. 98, No. 18, 1994 4839

Bond Dissociation Energy of M(CO)6

TABLE 1: Calculated and Experimental Bond Lengths (annstroms) for M(CO)s Cr(CO)s M0(c0 6 W(COI6 method M-C C-O M-C C-O M-C C-O LDA 1.866 1.145 2.035 1.144 2.060 1.144 1.910 1.153 2.077 1.152 2.116 1.154 NL-SCF NL-SCF+QR 1.910 1.153 2.076 1.153 2.049 1.155 MP2a 1.883 1.168 2.066 1.164 2.054 1.166 CCSD(T)b 1.939 1.178 expe 1.918 1.141 2.063 1.145 2.058 1.148 a Reference 8. Reference 7. Reference 27. ~~

values.27 The Cr-C bond length at the LDA level is calculated to be too short, by 0.05 A. This error is diminished by the NLS C F scheme to 0.01 A. The NL-SCF Cr-C bond length provides a better fit to experiment than the distances obtained by the CCSD(T)' and MP28 methods. The NL-SCF method is also seen to improve the calculated M-CO bond length for molybdenum to within 0.01 A of experiment. The MP2 value is in even better agreement with experiment. The influence of nonlocal corrections on the metalligand bond lengths in Cr(CO)6, Mo(C0)6, and other transitionmetal compounds have been studied extensively by Fan and Ziegler.14b The impact of relativity is quite apparent in the DFT calculations on W(CO)6. The W-CO distance calculated at the nonrelativistic NL-SCF level as 2.1 16 A is too long by 0.06 A. The inclusion of relativistic effects in the NL-SCF+QR scheme affords a contraction of the W-CO bond by 0.07 A to 2.049 A, which is 0.01 A shorter than experiment. The MP2 calculations do not allow for a separate study of relativistic effects since these are included implicitly in the effective core potential. However, the W-CO distance calculated by the MP2 method is in excellent agreement with experiment. The C-0 distances obtained by the NL-SCF scheme for the three carbonyls are in better agreement with experiment than the MP2 and CCSD(T) values (Table 1). It is interesting to note that the experimental M-CO bond distance is longer for molybdenum than tungsten. This trend is reproduced by the MP2 calculations with relativistic core potentials as well as the DFT scheme, after relativistic effects have been included. Previous experimental28and theoretical29 studies have shown that the M(CO)5 species with M = Cr, Mo, and W possess a square-pyramidal structure of C4"symmetry, and this conformation has also been adopted in the present study. Experimental I R studies reveal that the axial M-CO distance should be shorter than the equatorial M-CO bonds.28 Thi is born out by all the theoretical calculations, Table 2. There is in general a good accord between the MP2 and NL-SCF+QR distances for M = Mo, W, and we note again the relativistic M-CO bond contraction for M = W. The Cr-CO distances calculated by the DFT and ab initio schemes differ considerably. It is likely that the ab initio estimates are subject to errors of the same magnitude8 as in Cr(CO)6 (Table 1). All the M-C-O 0 bond angles optimized a t the MP2 level are smaller than 90°, in contradiction to lowtemperature matrix IR spectroscopic studies28 which suggest that the M-C-0 0 bond angles in pentacarbonyls of Cr, Mo, and W are between 90 and 95'. Our calculated M-C-0 0-bond angles are slightly smaller than 90° at the LDA level, and slightly larger than 90° a t the NL-SCFlevel. First Bond DissociationEnergies. The first bond dissociation energy (FBDE) is defined as the reaction enthalpy corresponding to the process M(CO),

-

M(CO),

+ CO

(1)

Table 3 collects calculated FBDE values based on DFT and ab initio calculations, together with the experimental values for M = Cr, Mo, W.

Calculated Geometries for M(C0)S. method NLNLLDA SCF SCF+QR MPZb CCSD(T)c Cr(C0)S M-C, 1.800 1.848 1.848 1.774 1.811 M-Cq 1.865 1.923 1.923 1.891 1.942 C-O, 1.155 1.162 1.162 1.193 1.175 C-O, 1.149 1.154 1.154 1.166 1.175 a(Cax-M-C,) 89.5 90.9 90.9 86.0 92.5 @(M-C,-O,) 178.9 179.6 179.6 173.4 179.4 Mo(CO)S M-Cax 1.924 1.968 1.965 1.935 2.031 2.085 2.083 2.063 M-C, 1.154 1.162 1.163 1.178 C-O, 1.146 1.155 1.156 1.165 C-O, a(C,-M-Cq) 89.1 90.3 90.2 86.9 @(M-C,-O,) 179.3 179.0 179.0 175.0 W(CO)S M-C, 1.969 2.003 1.915 1.935 2.065 2.129 2.045 2.049 M-C, 1.156 1.160 1.168 1.179 C-O, 1.148 1.153 1.157 1.168 C-O, a(C,-M-Cq) 89.8 91.2 91.2 86.8 @(M-C,-O,) 179.6 179.3 179.6 175.3 a Bond lengths in angstroms and bond angles in degrees. b Reference 8. Reference 7. Partially optimized. TABLE 2

TABLE 3: Calculated and Experimental First Bond Dissociation Energies (kcal/mol) for M(COh

c ~ ( c o ) ~ MO(CO)~

W(CO)~ 48.4 33.5 41.8 38.8 47.2 43.7 54.9 48.0 47.8

LDA 62.1 52.7 LDA/NLa 44.6 37.4 LDA/NL+FOb 45.1 39.8 NL-SCF 45.9 38.2 NL-SCFIFOC 46.8 40.6 NL-SCF+QRd 46.2 39.7 MPZC 58.0 46.1 CCSD(T)C 45.8 40.4 CCSD(TY 45.3 40.3 CCSD(T)g 42.7 exph 38.7 30.1 39.7 exd 37 f 5 34f5 38 f 5 exd 36.8 2 40.5 f 2 46.0 f 2 a LDA geometry and density, with nonlocal corrections17included as a perturbation. LDA geometry and density, including nonlocal correction~'~ and first-order relativisticcorrections(FO)Z'as a perturbation. NL-SCF geometry and density," including relativistic effects to first order:' FO. d NL-SCF+QR geometry and densitye26e AEvalues without ZPE and thermal corrections.8f AZP9*values including ZPE and thermal correction.8g Reference 7. Reference 2. Reference 3. Reference 4.

*

f

The DFT estimates represent the electronic contribution to the reaction enthalpy of eq 1. Thus, thermal corrections and contributions due to the vibrational zero-point energy correction, ZPE, are not included. However, it is possible to provide an estimate of these corrections. Roughly, the vibrational degrees of freedom lost in reaction 1 are one M-C stretching vibration and two M-C-O bending vibrations. Taking Cr(C0)6 as an example, the frequencies of these three vibrations are about 380,360, and 650 cm-1, respectively,30 corresponding to a ZPE correction of -2.0 kcal/mol. This estimate is close to the ZPE values of -1.8 and -2.6 kcal/mol reported in refs 7 and 8, respectively, based on Hartree-Fock frequency calculations. The thermal corrections from the PV work term as well as the translational and rotational degrees of freedom gained in reaction 1 amount to 7/2RT= 2.1 kcal/mol. According to this estimate, the net correction is less than 0.5 kcal/mol. Our calculated FBDE values should be comparable to the experimental m9* estimate if the ZPE and thermal contributions cancel out for all three species. Ehlers and Frenkings find in fact this to be the case in their ab initio study. It follows from Table 3 that the FBDEs obtained by the nonrelativistic LDA scheme are too high in comparison with the best experimental data.4 The inclusion of nonlocal corrections as a perturbation, LDA/NL, improves the agreement, and an even better fit is obtained by adding relativistic effects to first

4840

Li et al.

The Journal of Physical Chemistry, Vol. 98, No. 18, 1994

order,25 LDA/NL+FO, in particular for M = W. We have also carried out nonrelativistic calculations in which nonlocal terms are included self-consistently, NL-SCF,l4b and combined this approach with first-order relativistic correction^,^^ NL-SCF/ FO, as well as a full QR treatment, NL-SCF+QR.18q26The NLSCF+QR approach provides the best agreement with experiment4 when both bond energies and M-CO bond lengths are considered. The NL-SCF+QR and LDA/NL+FO methods afford bond energies of nearly the same accuracy (Table 3). Wenote, with regard to theabinitioresults,8 that the relativistic MP2 calculations overestimate the bond energies, in particularly for Cr(C0)6 and Mo(CO)6. The relativistic CCSD(T) approach affords on the other hand estimates of the same accuracy as the NL-SCF+QR method. There are three sets of experimental data available for the FBDEs of M(CO)6 (M = Cr, Mo, W).24 However, only the gas-phase data obtained by Lewis et alS4can be compared directly to the calculated values. The other experimental estimates2s3 refer to solution. As already mentioned, CCSD(T) and NL-SCF+QR provide bond energies in excellent agreement with experiment4 for Mo(CO)6 and W(CO)6. In fact, the deviation is close to the experimental errorrange for both methods. The situation is quite different for Cr(C0)6 were the CCSD(T) and NL-SCF+QR schemes overestimate the FBDE by nearly the same amount (Table 3). Ehlers and Frenking attributed their large FBDE value to the poor MP2 geomtry2 for the Cr(C0)6. Using experimental Cr-C bond lengths for c r ( c o ) 6 and estimated Cr-C bond distances for Cr(C0)5, they were able to reduce the calculated FBDE to 33 kcal/mol at the CCSD(T) level, in much better agreement with the experimental value. However, in another CCSD(T) study, Barnes et al.’ still obtained a FBDE of 43 kcal/mol for Cr(C0)6, by using the Cr-C bond distance optimized at the CCSD(T) level. Their Cr-CO distanceobtained at the CCSD(T) level was 0.03 A longer than the experimental value (Table 1). The experimental4 gas-phase FBDE of Cr(C0)6 is based on an estimated log A value for the preexponential factor A in the Arrhenius equation. The observed log A value was considered to be too large and a value obtained from studies on Mo(CO)~, W(CO)6, and Fe(C0)S was adopted instead. Nevertheless, if the measured log A value is used for the estimate of AfPg8,the corresponding FBDE would be about 47 kcal/mol (Table 1 of ref 4), which is considered to be too large, but is in better agreement with the CCSD(T) and NL-SCF+QR results (Table 3). It is also interesting to note that the gas-phase values for the FBDE of Mo(CO)6 and W(CO)6 are about 6-8 kcal/mol larger than the bond energies obtained in solution for the same systems. However, for Cr(C0)6, the gas-phase FBDE of 36.8 kcal/mo14 is seen to be slightly smaller than the value obtained in solution.2 A gas-phase FBDE of 44 kcal/mol for Cr(C0)6 would give rise to the same uniform shift between solution and gas phase for all three systems. The rates for the substitution reaction M(CO),

+L

-

-

M(CO),L

+ CO

(2)

with M = Cr, Mo and W are observed2Jl to follow the order of Mo(C0)6 > Cr(C0)6 W(co)6. This order is consistent with the trend in the calculated FBDEs if we assume that CO dissociation is the rate-determining step. However, it is possible that the mechanism for the substitution reaction in eq 2 changes gradually from dissociative to associative along the triad M = Cr, Mo, and W. Thus, there might not be a direct relation between the rates in eq 2, and the FBDEs for the three hexacarbonyls. This point deserves to be investigated further by theoretical calculations. The order for the FBDEs obtained here is in agreement with that found in the earlier DFT study.9 However, the absolute

TABLE 4 Decomposition of FBDE’ for W(CO)6 at Nonrelativistic (NL-SCF) and Relativistic (NGSCF+QR) Levels E(al)d E(e)d E(orb) E,,, FBDEC NL-SCF 39.5 -29.2 -44.2 -73.4 0.3‘ 34.2‘ NL-SCF+ 35.0 -19.6 -60.1 -79.7 1.0 43.7 QR Energies in kcal/mol. The geometry used in the ETS calculations is the one obtained at NL-SCF+QR level in both cases. The NL-SCF bond energy is increased by 4.6 kcal/mol at the NL-SCF geometry. ‘Total bond energy is given as FBDE = -(Esk”, E(orb) EplCp). dE(al) and E(e) contributes to E(orb).

+

+

values from the earlier DFT study are smaller than those reported in Table 3. The deviation is due to the use of different correction terms to the LDA approximation. Also, the geometries in the earlier study were assumed rather than optimized. The present study based on the NL-SCF+QR scheme represents the most accurate set of DFT based calculation presented to date on the M(CO)6 systems (M = Cr, Mo, W). Relativistic Effects. Relativistic effects are seen to play a key role in reproducing the periodic trends among the M-CO dissociation energies and bond distances. We calculate a relativisticcontractionof0.067Afor the W-CObondin W(CO)6 (Table 1). In W(CO)5, the contractions for the W-CO,, and W-CO, bonds are 0.088 and 0.084 A, respectively (Table 2). Much smaller contractions are observed in the case of Mo(CO)~ and Mo(CO)s, whereas the contraction is negligible for the chromium systems. The origin of the relativistic bond contraction has been discussed previ0usly.3~ Relativistic effects are further seen to strengthen the M-CO bonds. For Cr(C0)6, Mo(CO)6, and W(CO)6, the relativistic effects increase the FBDEs by 0.9, 2.4, and 8.4 kcal/mol, respectively, at the NL-SCF/FO level of theory, whereas the more accurate NL-SCF+QR method provides an increase of 0.3, 1.5, and 4.9 kcal/mol, respectively. We might gain further insight into the influence of relativistic effects on the W-CO bond strength by decomposing the corresponding FBDE according to the extended transition state (ETS) method33 as

Here Estehc r e p r e s e n t ~the ~ , ~steric ~ interaction energy between COand the W(CO)5fragment in thecombinedcomplex W(CO)6. The term Estericis made up of the stabilizing electrostatic interaction between W(CO)5 and CO as well as the repulsive destabilizing two orbital four electron interactions between occupied orbitals on the two fragments in the combined complex W(CO)6. The destabilizing contribution is also refered to as Pauli repulsion. The term Embstems9J4from thestabilizing interactions between occupied and virtual orbitals of the two separate fragments after they are brought together in W(CO)6. This term can be decomposed into contributions from the different symmetry representations of the C, point group preserved during the formation of W(CO)6 from W(CO), and CO. The contribution from theal representation, E(al), is due to thedonation of charge from the occupied ~JCOorbital to thevacant doorbital on W(CO)5, whereas E(e) represents the back-donation from the occupied d, orbitals on W(CO)5 to the empty T*CO orbitals. The last term, Eprcp, comes from the energy required to relax the structure of the free fragments to the geometries they take up in W(CO)6. Calculated values for the terms in eq 2 are shown in Table 4 for W(CO)6, with and without relativistic effects included. The analysis was carried out at the geometry optimized by the NLSCF+QR scheme.

Bond Dissociation Energy of M(CO)6

As expected, relativistic effects diminish Encric.This is a direct result of a reduction in the electronic kinetic energy due to the relativistic mass-velocity correction. This reduction will in turn diminish the Pauli repulsion as explained in details by Ziegler et aI.32 Relativistic effects are also of important for the u-donation term, E(al), as well as the r-back-donation contribution, E(e) (Table 4). We note that -E(al) is reduced and -E(e) increased by relativity. Both trends can be explained by observing that relativistic effects will raise metal-based d-orbitals.35 The increase amounts of 1.4 eV for the 5d orbitals of tungsten. The higher energy of d, will reduce the d,-rco* gap and thus enhance the tungsten to CO r-back-donation as well as -E(e). The higher energy of d, will on the other hand increase the d,-uco gap and thus reduce the CO to tungsten a-donation, as well as -,??(al). Conclusion We have carried out calculations on the homologous series of hexacarbonyls Cr(C0)6, Mo(CO)6, and W(CO)6. The calculations were based on the NL-SCF+QR method in which nonlocal corrections and relativistic effects are included self-consistently. The NL-SCF+QR scheme provides a better fit to the observed Cr-CO bond distance than estimates from the most involved ab initio calculations and affords Mo-CO and W-CO distances of the same accuracy as the MP2 scheme. Nonlocal corrections are essential for accurate calculations of all three M-CO bond lengths. Relativistic corrections contract the W-CO bond by 0.07 A and are essential for a description of the 5d homologues. M o ( C O ) ~ is calculated to have the longest M-CO bond, in agreement with experiment. Calculation based on the MP2 and CCSD(T) schemes as well as the NL-SCF+QR method find the FBDE in M(CO)6 to follow the order Mo < Cr W. This ordering is in line with kinetic observations, but contradicts the order Cr > Mo > W established in the gas phase by Lewis et al.4 We have provided a possible explanation for the difference between theory and experiment. Relativistic effects enhance the M-CO bond strength by 0.3 kcal/mol (Cr), 1.5 kcal/mol (Mo), and 4.9 kcal/mol (W), respectively. It is shown that relativistic effects increase the metal to CO r-back-donation and decrease the CO to metal u-donation as a result of a general destabilization of the 5d orbitals. However, the C O r-back-donation is the prevailing factor, and the W-CO bond as a whole is strengthened. A further stabilizing factor is the reduction in the Pauli repulsion between the W(C0)s and CO fragments due to the relativistic mass-velocity term.

-

Acknowledgment. This investigation was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). We are grateful to Professor Frenking for a preprint prior to publication. J.L. thanks NSERC for an International Fellowship and Professor P. Pyykkij for correspondence. The University of Calgary is acknowledged for access to the IBM6000/RISC facilities. This work was supported in part by the donors of the Petroleum Research Fund, administered by the American Chemical Society (ACS-PRF 27023-AC3). References and Notes (1) Marks, T. J. Bonding energetics in organometallic compunds; ACS symposium series 248; Americal Chemical Society: Washington DC, 1990. (2) (a) Angelici, R. J. Organomet. Chem. Rev. A3 1968,173. (b) Covey, W. D.; Brown, T. L. Inorg. Chem. 1973,12,2820. (c) Centinis, G.; Gambino,

The Journal of Physical Chemistry, Vol. 98, No. 18, 1994 4841 0.Atti. Acad. Sci. Torino 1 1963,97,1197. (d) Werner, H. Angew. Chem., Int. Ed. Engl. 1968, 7,930. (e) Graham, J. R.; Angelici, R. J. Inorg. Chem. 1967, 6, 2082. (f) Werner, H.; Prinz, R. Chem. Ber. 1960, 99, 3582. (g) Werner, H.; Prinz, R. J. Organomet. Chem. 1966, 5, 79. (3) Bernstein, M.; Smith, J. D.; Peters, G. D. Chem. Phys. Lett. 1983, 100, 241. (4) Lewis, K. E.; Golden, D. M.; Smith, G. P. J . Am. Chem. SOC.1984, 106, 3905. ( 5 ) Sherwood, D. E.; Hall, M. B. Inorg. Chem. 1983, 22, 93. (6) Moncrieff, D.; Ford, P. C.; Hillier, I. H.; Saunders, V. R. J . Chem. SOC.,Chem. Commun. 1983, 1108. (7) (a) Barnes, L. A.; Rosi, M.;Bauschlicher, Jr., C. W. J . Chem. Phys. 1991, 94, 2031. (b) Barnes, L. A.; Liu, B.; Lindh, R. J. Chem. Phys. 1993, 98, 3978. (8) (a) Ehlers, A. W.; Frenking, G. J . Chem. SOC.,Chem. Commun. 1993, 1709. (b) Ehlers, A. W.; Frenking, G. J . Am. Chem. SOC.1994, 116, 1514. (9) Ziegler, T.; Tschinke, V.; Ursenbach, C. J . Am. Chem. SOC.1987, 109,4825. (10) Vosko, S.J.; Wilk, L.; Nusair, M.Can. J . Phys. 1980, 58, 1200. (11) Becke, A. J . Chem. Phys. 1986,84,4524. (12) Stoll, H.; Golka, E.; Preuss, H. Theor. Chim. Acta 1980, 55, 29. (13) (a) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University Press: New York, 1988. (b) Labanowski, J.; Andzelm, J. Density Functional Methods in Chemistry, Springer-Verlag: Heidelberg, 1991. (c) Ziegler, T. Chem. Rev. 1991, 91, 651. (14) (a) Versluis, L.; Ziegler, T. J . Chem. Phys. 1988,88,322. (b) Fan, L.; Ziegler, T. J . Chem. Phys. 1991, 95, 7401. (15) Fan, L.; Versluis, L.; Ziegler, T.; Baerends, E. J.; Ravenek, W. Int. J . Quantum Chem. 1988, S22, 173. (16) Fan, L.; Ziegler, T. J . Phys. Chem. 1992, 96, 6937. (17) (a) Perdew, J. P. Phys. Rev. 1986,833,8822. Erratum: Ibid. 1986, 834, 7406. (b) Becke, A. Phys. Rev. 1988, A38, 3098. (18) Schreckenbach, G.; Ziegler, T., unpublished work. (19) Baerends, E. J.; Ellis, D. E.; Ros, P. Chem. Phys. 1973, 2, 41. (20) Ravenek, W. In Algorithms and applications on vector andparallel computes; te Riele, H. J. J., Dekker, Th. J., van de Vorst, H. A., Us.Elsevier: ; Amsterdam, 1987. (21) (a) Boerrigter, P. M.;te Velde, G.; Baerends, E. J. Inr. J . Quantum Chem. 1988,33,87. (b) te Velde, G.; Baerends, E. J. J . Comput. Phys. 1992, 99, 84. (22) (a) Snijders, J. G.; Baerends, E. J.; Vernooijs, P. At. Nucl. Data Tables 1982,26,483. (b) Vernooijs, P.; Snijders, J. G.; Baerends, E. J. Slater type basis functions for the whole periodic system; Internal report; Free University of Amsterdam, The Netherland, 1981. (23) Krijn, J.; Baerends, E. J. Fit functions in the HFS-method; Internal report (in Dutch); Free University of Amsterdam, The Netherland, 1984. (24) (a) Pyykk6, P. Chem. Reu. 1988,88,563. (b) Ziegler, T.; Snijders, G. J.; Baerends, E. J. In The challenge of d and f electrons, Theory and computation; ACS Symposium Series 349; Salahub, D. R., Zerner, M.C., Eds.; Americal Chemical Society: Washington DC, 1989. (25) (a) Snijders, J. G.; Baerends, E. J. Mol. Phys. 1978, 36, 1789. (b) Snijders, J. G.; Baerends, E. J.; Ros, P. Mol. Phys. 1979, 38, 1909. (26) Ziegler, T.; Tschinke, V.; Baerends, E. J.; Snijders, J. G.; Ravenek, W. J . Phys. Chem. 1989, 93, 3050. (27) Jost, A.; Rees, B. Acta Crystallogr. 1975, 831, 2649. (28) (a) Graham, M. A.; Poliakoff, M.; Turner, J. J. J . Chem. SOC.A 1977,2939. (b) Perutz, R. N.; Turner, J. J. Inorg. Chem. 1975,14,262. (c) Perutz, R. N.; Turner, J. J. J. Am. Chem. SOC.1975, 97,4791. (d) Perutz, R.N.; Turner, J. J. Inorg. Chem. 1975, 14,262. (e) Perutz, R. N.; Turner, J. J. J . Am. Chem. SOC.1975, 97,4791. (29) (a) Hay, P. J. J . Am. Chem. Soc. 1978,100,241 1. (b) Demuynck, J.; Kochanski, E.; Veillard, A. J . Am. Chem. SOC.1979, 101, 3467. (30) Jones, L. H.; McDowell, R. S.;Goldblatt, M. Inorg. Chem. 1969,8, 2349. (31) Wieland, S.; van Eldik, R. Organometallics 1991, I O , 3110. (32) (a) Ziegler, T.; Snijders, G. J.; Baerends, E. J. Chem. Phys. Lett. 1980,75, 1. (b) Ziegler, T.; Snijders, G. J.; Baerends, E. J.; Ros, P. J . Chem. Phys. 1981, 74, 1271. (33) Ziegler, T.; Rauk, A. Theor. Chim. Acta 1977, 46, 1. (34) (a) Baerends, E. J.; Rozendaal, A. In Quantum Chemistry, The Challenge of Transition Metals and Coordination Chemistry; Veillard, A,, Ed.; Kluwer: Dordrecht, 1986. (b) Kraatz, H. B.; Jacobsen, H.; Ziegler, T.; Boorman, P. M. Organometallics 1993, 12, 76. (35) (a) Pyykkb, P.; Declaux, J.-P. Acc. Chem. Res. 1979,12, 276. (b) Schwarz, W. H. E.; van Wezenbeek, E. M.; Baerends, E. J.; Snijders, G. J. J. Phys. B 1989, 22, 1515.