Local density functional (LDF) theory has been used to calculate the geometry and vibrational frequencies of a set of transition-metal compounds in their molecular forms containing halogens, oxygens, alkyl groups, carbonyls, nitrosyls, and other substituents. The calculations were done with polarized double-zeta numerical and Gaussian basis sets, and the geometries were obtained by analytic gradient methods. The frequencies were evaluated by numerical differentiation of the analytic first derivatives. The results obtained with the numerical and the Gaussian basis sets were found to be in good agreement. The agreement with experiment for the geometries is quite good with an average mean deviation of 0.026 Á. The largest errors involve dative bonds with the LDF method predicting the bonds to be too short. Nonlocal corrections were applied to some of the methyl-carbonyl and metal-nitrosyl bond lengths, and this correction was found to lengthen the bonds to give better agreement with experiment. The frequencies are also predicted quite accurately. The LDF results are in much better agreement with experiment as compared to Hartree-Fock results.

A series of efficient split-valence basis sets for second-row transitions metals, termed 3-21G, has been constructed based on previously formulated minimal expansions of Huzinaga, and in a manner analogous to the previous development of 3-21G basis sets for first-row metals. The Huzinaga three Gaussian expansions for s-and p-type orbitals of given n quantum number have been fit by least squares to new three Gaussian combinations in which the two sets of functions share the same Gaussian exponents. The original three Gaussian expansions for Is, 3d, and 4d atomic orbitals have been employed as is. The valence description comprises 4d-5s-and 5p-type functions, each of which has been split into two and one Gaussian parts. 5p functions, while not populated in the ground state of the free atom, are believed to be important in the description of the bonding in molecules.The performance of the 3-21G basis sets is examined with regard to the calculation of equilibrium geometries and normal-mode vibrational frequencies for a variety of simple inorganic and organometallic compounds incorporating second-row transition metals.

Two new series of efficient basis sets for third-and fourth-row, main-group elements have been developed. Split-valence 3-21G basis sets have been formulated from the minimal expansions by Huzinaga, in which each atomic orbital has been represented by a sum of three Gaussians. The original expansions for s-and p-type orbitals (except those for 1s) have been replaced by new combinations in which the two sets of orbitals (of the same n quantum number) share Gaussian exponents. The Huzinaga expansions for Is, 3d and 4d (fourth-row elements only) have been employed without further alteration. The valence atomic functions 4s, 4p for third-row elements; 5s, 5p for fourth-row elements) have been split into two and one Gaussian parts. Supplemented 3-21G'*' representations have been formed from the 3-21G basis sets by the addition of a set of single d-type Gaussian functions. The performance of 3-21G and 3-21G'*' basis sets is examined with regard to the calculation of equilibrium geometries, normal mode vibrational frequencies, reaction energies, and electric dipole moments involving a variety of normal and hypervalent compounds containing third-and fourth-row, main-group elements. The supplementary functions incorporated into the 3-21G'*' basis sets are generally found to be important, especially for the proper description of equilibrium bond lengths and electric dipole moments. 3-21G'*' representations are recommended for general use in lieu of the unsupplemented 3-21G basis sets. INTRODUCTIONSingle-determinant Hartree-Fock molecular orbital theory has proven remarkably successful in the calculation of equilibrium geometries, vibrational frequencies, and relative energies of molecules containing firstand second-row e1ements.l Even minimal basis sets, such as the now widely employed STO-3G representation,2 are capable of reproducing a wide variety of experimental equilibrium structures to a reasonable degree of accuracy. More flexible split-valence basis sets, such as the 3-21G repre~entation,~ fare even better in the task of structure determination. In addition, theoretical treatments at this level are moderately successful in describing molecular vibrational frequencies, as well as relative isomer energies and electric dipole moments, properties which generally are not well handled at the minimal basis set level. Note, however, that molecules incor-*Dedicated to John Pople on the occasion of his 60th birthday.porating second-row elements with expanded valence octets, i.e., hypervalent molecules, do not appear to be properly described using either minimal or split-valence representations. Only when the basis sets for these elements are supplemented by d-type functions are their performances generally acceptable. Supplemented STO-3G and 3-21G basis sets for second-row atoms have appeared in the literature .4, 5 Larger atomic orbital representations, such as the 6-31G* full polarization basis set,' generally lead to further improvements in all calculated properties for both normal and hypervalent molecules. In addition, ...

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A series of efficient split‐valence basis sets for first‐row transition metals, termed 3‐21G, has been constructed based on previously‐formulated minimal expansions of Huzinaga, in which each atomic orbital has been represented by a sum of three gaussians. The original Huzinaga expansions for s‐ and p‐type orbitals (except those for 1s) have been fit by least squares to new three‐gaussian combinations in which the two sets of orbitals (of the same n quantum number) share gaussian exponents. The Huzinaga three‐gaussian expansions for ls and 3d atomic orbitals have been employed without alteration. The valence description of the 3‐21G basis sets comprises 3d‐, 4s‐ and 4p‐type functions, each of which has been split into two‐ and one‐gaussian parts. 4p functions, while not populated in the ground state of the free atoms, are believed to be important to the description of the bonding in molecules. The performance of the 3‐21G basis sets is examined with regard to the calculation of equilibrium geometries and normalmode vibrational frequencies for a variety of inorganic and organometallic compounds containing first‐row transition metals. Calculated equilibrium structures, while generally superior to those obtained at STO‐3G, are not as good as those for compounds containing main‐group elements only. The calculations generally underestimate the lengths of double bonds between transition metals and main‐group elements, and overestimate the lengths of single linkages. Calculated normal‐mode vibrational frequencies for metal‐containing systems are less uniform than in those for main‐group compounds.