In view of rapid progress of computer capability, it is very desirable to have a reliable assessment of the usefulness of Gaussian-type orbitals as basis functions for large-scale molecular calculations. In the present paper several attempts are made to answer this question mainly at the level of atomic Hartree—Fock calculations. The necessary number of terms of Gaussian-type basis functions in the analytical Hartree—Fock expansion calculation is apparently more than twice as much as the number of terms needed in the expansion with Slater-type basis functions. However, this fact does not necessarily suggest a definite choice of Slater-type orbitals. Discussions pertinent to this point are presented in the latter part of the present paper.

Atomic and molecular systems are often intuitively separated into almost independent subsystems as, for example, the core and valence parts of an atom. Consequently, if this separation provides a good approximation, one can obtain the states of the system from the states of the subsystems which best represent the entire system. In the light of the work of McWeeny, in which one assumes strong orthogonality among subsystem wavefunctions, we determine an effective Hamiltonian for a given subsystem which should properly describe the states of that subsystem. Previous work is shown to have dealt with an improper effective Hamiltonian.

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