Two extended basis sets (termed 5–31G and 6–31G) consisting of atomic orbitals expressed as fixed linear combinations of Gaussian functions are presented for the first row atoms carbon to fluorine. These basis functions are similar to the 4–31G set [J. Chem. Phys. 54, 724 (1971)] in that each valence shell is split into inner and outer parts described by three and one Gaussian function, respectively. Inner shells are represented by a single basis function taken as a sum of five (5–31G) or six (6–31G) Gaussians. Studies with a number of polyatomic molecules indicate a substantial lowering of calculated total energies over the 4–31G set. Calculated relative energies and equilibrium geometries do not appear to be altered significantly.

Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules

Polarization functions are added in two steps to a split-valence extended gaussian basis set: d-type gaussians on the first row atoms C. N, O and F and p-type gaussians on hydrogen. The same d-exponent of 0.8 is found to be satisfactory for these four atoms and the hydrogen p-exponent of 1.1 is adequate in their hydrides. The energy lowering due to d functions is found to depend on the local symmetry around the heavy atom. For the particular basis used, the energy lowerings due to d functions for various environments around the heavy atom are tabulated. These bases are then applied to a set of molecules containing up to two heavy atoms to obtain their LCAO-MO-SCF energies. The mean absolute deviation between theory and experiment (where available) for heats of hydrogenation of closed shell species with two non-hydrogen atoms is 4 kcal/mole for the basis set with full polarization. Estimates of hydrogenation energy errors at the Hartree-Fock limit, based on available calculations, are given.

The influence of polarization functions on molecular orbital hydrogenation energies

Various contracted Gaussian basis sets for atoms up to Kr are presented which have been determined by optimizing atomic self‐consistent field ground state energies with respect to all basis set parameters, i.e., orbital exponents and contraction coefficients.

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Fully optimized contracted Gaussian basis sets for atoms Li to Kr

A simple level of ab initio molecular orbital theory with a split-valence shell basis with d-type polarization functions (6–31G*) is used to predict equilibrium geometries for the ground and some low-lying excited states of AHn molecules and cations where A is carbon, nitrogen, oxygen or fluorine. The results are shown to be close to the limit for single determinant wave functions in cases where corresponding computations with more extensive bases are available. Comparison with experimental results also shows good agreement although a systematic underestimation of bond lengths up to 3 per cent is evident. For systems where no experimental data are available, the results provide predictions of equilibrium geometry.

Accuracy of AH n equilibrium geometries by single determinant molecular orbital theory

A new method is proposed for the analysis of components of molecular interaction energy within the Hartree-Fock approximation. The Hartree-Fock molecular orbitals of the isolated molecules are used as the basis for the construction of Fock matrix of the supermolecule. Then certain blocks of this matrix are set to zero subject to specify boundary conditions of the supermolecule molecular orbitals, and the resultant matrix is diagonalized iteratively to obtain the desired energy components. This method can be considered as an extension of our previous method, but has an advantage in the explicit definition of the charge transfer energy, placing it on an equal footing with the exchange and polarization terms. The new method is compared with existing perturbation methods, and is also applied to the energy and electron density decomposition of (H2O)2.

A new energy decomposition scheme for molecular interactions within the Hartree‐Fock approximation

Molecular orbital theory of the electronic structure of organic compounds. X. Systematic study of geometries and energies of AHn molecules and cations

Molecular orbital theory of the electronic structure of organic compounds. VIII. Geometries, energies, and polarities of C3 hydrocarbons

Molecular orbital theory of the electronic structure of organic compounds. XVII. Internal rotation in 1,2-disubstituted ethanes

Molecular orbital theory of the electronic structure of organic compounds. VI. Geometries and energies of small hydrocarbons

Ab initio calculation of equilibrium geometries and quadratic force constants for a large group of first‐row polyatomic molecules has been carried out, using the previously described [J. Chem. Phys. 51, 2657 (1969)] STO–3G approximation for STO basis functions. The average deviation of calculated and experimental bond lengths and angles is 0.035 A and 1.7°, respectively. Nearly all important experimental trends are reproduced. For a few cases involving bonds between electronegative atoms, significant discrepancies are found. Quadratic force constants are evaluated for symmetric stretching and bending modes and are found to be overestimated, typically by 20%–30%. Nearly all experimental trends are satisfactorily accounted for. It is concluded that a minimal STO basis with properly chosen orbital exponents offers a useful and computationally efficient model for potential surface studies.

William A. Lathan

Papers

Molecular orbital theory of the electronic structure of organic compounds. X. Systematic study of geometries and energies of AHn molecules and cations

Molecular orbital theory of the electronic structure of organic compounds. VIII. Geometries, energies, and polarities of C3 hydrocarbons

Molecular orbital theory of the electronic structure of organic compounds. XVII. Internal rotation in 1,2-disubstituted ethanes

Molecular orbital theory of the electronic structure of organic compounds. VI. Geometries and energies of small hydrocarbons

Self‐Consistent Molecular Orbital Methods. V. Ab Initio Calculation of Equilibrium Geometries and Quadratic Force Constants