A contracted Gaussian basis set (6-311G**) is developed by optimizing exponents and coefficients at the Mo/ller–Plesset (MP) second-order level for the ground states of first-row atoms. This has a triple split in the valence s and p shells together with a single set of uncontracted polarization functions on each atom. The basis is tested by computing structures and energies for some simple molecules at various levels of MP theory and comparing with experiment.

Some methods of describing electron correlation are compared from the point of view of requirements for theoretical chemical models. The perturbation approach originally introduced by Mgller and Plesset, terminated at finite order, is found to satisfy most of these requirements. It is size consistent, that is, applicable to an ensemble of isolated systems in an additive manner. On the other hand, it does not provide an upper bound for the electronic energy. The independent electron-pair approximation is accurate to second order in a MgllerPlesset expansion, but inaccurate in third order. A series of variational methods is discussed which gives upper bounds for the energy, but which lacks size consistency. Finally, calculations on some small molecules using a moderately large Gaussian basis are presented to illustrate these points. Equilibrium geometries, dissociation energies, and energy separations between electronic states of different spin multiplicities are described substantially better by Moller-Plesset theory to second or third order than by Hartree-Fock theory.

Constraints that may be applied to the spin orbitals used in Hartree–Fock theory are classified and discussed. Once a constrained stationary wavefunction has been obtained by a self-consistent procedure, it may be tested for stability both internally (with constraints remaining) and externally (with some constraints removed). Methods for carrying out these tests are presented. In addition, a general technique is described for further energy minimization following detection of an instability.

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A configuration interaction (CI) procedure which includes all single and double substitutions from an unrestricted Hartree-Fock single determinant is described. This has the feature that Mvller-Plesset perturbation results to second and third order are obtained in the first C1 iterative cycle. The procedure also avoids the necessity of a full two-electron integral transformation. A simple expression for correcting the final C I energy for lack of size consistency is proposed. Finally, calculations on a series of small molecules are presented to compare these CI methods with perturbation theory.