The computation of the structure of transition metal complexes has been an area of long standing interest, with clear problems not present in the corresponding studies of 1st and 2nd row species . Much of the growing acceptance by the chemistry community of Density Functional Theory (DFT) is due to its success in treating transition metal complexes, in stark contrast to the failure of the Hartree Fock method.
Accurate Hartree Fock geometry optimisations on main group molecules typically yield bond distances too short by some 0.01 - 0.03 A . There is now a wealth of data that points to far greater errors in the HF geometry of transition metal compounds [2,4-16], with bond distances involving the metal atom frequently much longer than experimental values or those obtained in extensive CI treatments. The case of ferrocene and Fe(CO)5 provide examples of this effect. The calculated HF metal-ligand distance in ferrocene is 0.23 A longer than the experimental value [6,7], while in iron pentacarbonyl the axial carbonyl - iron distance is calculated to be 0.24 A longer than experiment . Calculations by Almlof and co-workers on Ni(CO)4  and a series of sandwich compounds  suggest the need for extensive basis sets to achieve stable results which may, nevertheless, remain in poor agreement with experiment. Such evidence casts considerable doubt on the value of 'small' basis sets in such studies [10-11]. The undoubted role of electron correlation in the above systems has been elegantly demonstrated by Siegbahn and co-workers .
In contrast to Hartree Fock, both coupled cluster CCSD and CCSD(T) have been shown to achieve a high degree of accuracy. The structure of Cr(CO)6 and Cr(CO)5 optimized at the MCPF, CCSD and CCSD(T) levels suggests that the CCSD(T) method provides the optimum structure . The role of the less computationally demanding MP2 method is less well chronicled, at least on complexes with 1st row transition metal species; an ECP study of the binary carbonyls M(CO)6 and M(CO)5 (M = Cr, Mo, W) using HF and MP2  finds that the Cr-CO bond in Cr(CO)6 is too short at MP2 (1.883 vs 1.918 A).Perhaps the most compelling demonstration of the success of DFT is provided by C.Sasa et al , who applied LDF (DMOL and DGauss) to some 45 complexes, revealing a RMS deviation of 0.026 A with expt., the largest errors occurring for dative bonds which lengthen with non-local corrections. The use of various gradient correction functionals (VWN vs. B88-VWN, B88-LYP) on the binary transition metal carbonyls of Cr, Fe, Ni, Mo, Ru and Pd  matches the quality of CCSD(T) and pair functional methods, with VWN underestimating M-L bonds by 0.03-0.05 A, B88-VWN overestimating by similar amounts, while use of the B88-LYP functional reduced these overestimates by 50%. The application of HF, LDA and B-LYP to the ionic d^0 complexes ScF3, TiF4, VF5 and CrF6  suggests that HF and LDA provide excellent agreement with expt., while use of the B-LYP functional gives bond lengths too long by 0.04-0.05 A, with improved distances given by the hybrid HF/DFT scheme of Becke.
In the present work we have extended these previous findings through a systematic study of the equilibrium ground state geometries of some 45 transition metal complexes at the HF, MP2 and DFT levels of theory using a variety of basis sets. The transition metal compounds investigated include those containing oxygens, halogens, alkyl and aryl groups, carbonyls, nitrosyls etc. The SCF and MP2 calculations were performed using parallel implementations of the GAMESS-UK code, while the DFT calculations used the NWChem code , with both the LDA and gradient corrected B-LYP functional, and with both exact and charge fitting basis treatments of the coulomb term. All calculations were performed using the IBM-SP2 at Daresbury, the Cray T3Ds at Edinburgh and NERSC, and the Kendall Square KSR-2 at PNL.
A variety of basis sets were employed. Basis I is essentially of DZ quality, with an (11s8p5d/8s6p2d) basis for the metal and a DZ basis on the ligands -- (9s5p/4s2p) for 1st row atoms and an (11s7p/6s4p) for 2nd row atoms . A more extended basis set (Basis II) was also employed, incorporating polarization functions. In the SCF and MP2 calculations, a Wachters (14s11p6d/10s8p3d) was used on the metal and a DZP basis on the ligands (9s5p1d/4s2p1d for C-F, and 11s7p1d/6s4p1d for Cl). In the DFT calculations we used an (14s11p6d3f/10s8p3d1f) metal basis, and the correlation consistent cc-PVDZ basis of Dunning on the ligands .
To summarize the results, we show in the Table the RMS deviation between calculated and experimental bond lengths as a function of method of treatment and class of complex. Satisfactory agreement between each level of theory and experiment is evident in the transition metal fluorides, chlorides and oxides. RMS Deviation of Calculated Metal-Ligand Bond Lengths from Experiment Transition & Metal-Ligand SCF MP2 DFT Metal Ligand (A) (A) (A) ----------------------------- S-VWN B-LYP B-P86 B3LYP Oxide M-O 0.075 0.061 0.022 0.011 0.008 0.022 Fluoride M-F 0.036 0.038 0.037 0.028 0.025 0.024 Chloride M-Cl 0.069 0.037 0.026 0.045 0.023 0.027 Carbonyl M-C 0.190 0.092 0.048 0.034 0.022 0.027 Hydride M-H 0.095 0.127 0.046 0.036 0.039 0.043 Organometallic M-C 0.136 0.101 0.051 0.047 0.014 0.029
Far greater discrepancies are found, however, in the series of carbonyl, hydride and organometallic complexes. Hartree Fock exhibits unacceptable errors, with the metal-carbon distance significantly overestimated, compared to experiment, in all carbonyl and organometallic complexes. While not apparent from the RMS values above, MP2 typically over compensates for this effect, leading to bond lengths shorter than experiment. This effect is particularly pronounced in those complexes containing M-H bonds, with MP2 leading to bonds lengths too short by some 0.17 A. In contrast, DFT provides a far more systematic tool in structural predictions; regardless of ligand, the methods consistently overestimates experiment by some 0.03-0.05 A, an effect that would appear attributable to the B-LYP functional employed in the present study. In agreement with previous results , we find that improved distances are given by use of the hybrid HF/DFT scheme due to Becke.
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