Nonclassical terms in the true effective valence shell Hamiltonian: A second quantized formalism

Abstract

A formulation is presented for the exact effective valence shell Hamiltonian M^v to enable the extraction of individual matrix elements of M^v within the valence orbital basis in a fashion where these matrix elements are independent of the remaining valence electrons so the same M^v applies to the neutral and ions of a given molecule. Particular attention is placed upon the isolation of nonclassical terms which are absent in traditional semiempirical theories, such as Pariser–Parr–Pople theory, MINDO, etc. These nonclassical terms include those that are neglected in zero differential overlap approximations as well as ones involving three, four,... electron operators. The latter are shown to correspond to dynamical variable electronegativity corrections, and particular experimental consequences are noted. A second quantization formalism is employed to enable the isolation of these terms, and the analysis utilizes a generalized perturbation expansion wherein the lowest order corresponds to an open‐shell sum‐of‐the‐pairs theory, obviating the cumbersome diagram summation procedures necessitated by the use of ordinary perturbation expansions. This work represents an advancement over previous theories of M^v in the use of generalized perturbation theory, the removal of all other valence orbital dependences, and the simplicity for extensions to nonorthogonal orbitals and pseudopotentials.