An effective model Hamiltonian for heteroatom-containing molecules reflecting the structures of both overlap and one-electron density matrices. The ammonia and water molecules

Abstract

Comparative analysis of the structures of both the one-electron density matrices ( P) and the overlap matrices ( S) of AOs has been carried out for the ammonia and water molecules and their hydrocarbon analogues (the - CH 3 and > CH 2 fragments, respectively). The matrices S and P for the hydrocarbon fragments are shown to be of similar structure. This serves to support the usual Huckel-type Hamiltonian matrix representing the structure of the overlap matrix only for these fragments and hydrocarbons in general. Again, additional non-zero off-diagonal elements between AOs of nitrogen and oxygen atoms originating from the intra-atomic exchange interactions are established to appear within the matrices P of the ammonia and water molecules, contrary to the relevant overlap matrices. Thus, the effective Hamiltonian matrices for ammonia and water molecules which reflect the structures of both S and P matrices have been suggested and diagonalized algebraically by means of successive passing into the bases of sp 3 hybrid AOs (HAOs), bond orbitals and symmetrized Orbitals. Lower one-electron energies of the HAOs which describe the lone electron pairs as compared with the remaining HAOs and the relevant occupation numbers equal to 2 and 1 respectively, follow from the solution of the secular problems for the proposed model Hamiltonian matrices. An analogous diagonalization of the P matrices provided the algebraic expressions for atomic charges and these proved to be related to the electronegativity of the respective atom.