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.

An extended basis set of atomic functions expressed as fixed linear combinations of Gaussian functions is presented for hydrogen and the first-row atoms carbon to fluorine. In this set, described as 4–31 G, each inner shell is represented by a single basis function taken as a sum of four Gaussians and each valence orbital is split into inner and outer parts described by three and one Gaussian function, respectively. The expansion coefficients and Gaussian exponents are determined by minimizing the total calculated energy of the atomic ground state. This basis set is then used in single-determinant molecular-orbital studies of a group of small polyatomic molecules. Optimization of valence-shell scaling factors shows that considerable rescaling of atomic functions occurs in molecules, the largest effects being observed for hydrogen and carbon. However, the range of optimum scale factors for each atom is small enough to allow the selection of a standard molecular set. The use of this standard basis gives theoretical equilibrium geometries in reasonable agreement with experiment.

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The complete hydrogenation of an organic molecule is separated into two processes. In the first, termed bond separation, the molecule is separated into its simplest parents containing the same component bonds.The energy associated with such a reaction is then the heat of bond separation. The second step consists of full hydrogenation of the products of bond separation. To study these two processes, we have performed ab initio molecular orbital calculations on a variety of polyatomic molecules. Both minimal and extended basis sets, taken as linear combinations of Gaussian-type functions, are shown to give heats of bond separation in good agreement with experiment. In contrast, only the extended basis is successful in reproducing the heats of hydrogenation of the parents. An important objective of quantum chemistry is .

Hartree-Fock perturbation theory of magnetic susceptibility and magnetic shielding is developed using a basis set of gauge invariant atomic orbitals. The theory is used to calculate magnetic shielding and spin-rotation constants associated with the nuclei in LiH and HF giving results in good agreement with experimental values.