All-particle Hamiltonians for polyatomic molecules. I. Body-fixed frames and coordinates. Classical treatment

Abstract

With a view to quantization, exact classical expressions of Hamiltonians are derived for a molecular system made up of ν electrons and N nuclei, by applying a body-fixed (BF) matrix procedure recently introduced. Two cases are considered, depending on whether the BF frame origin is at the centre of mass of the nuclei or at the total centre of mass. The arrangement of the nuclei is described by 3 N — 6 internal coordinates, and the 3ν electron BF Cartesian coordinates are used. All terms which contribute to the total energy are identified. The similarities and the differences between the two cases are emphasized, particularly with regard to the consequences of (i) neglecting the electron/total system mass ratio, (ii) the assumption of infinitely slow nuclear motion and the fact that (iii) there can be either no distinction between the body-fixed and the space-fixed frames, i.e. no overall rotation, or not, i.e. no total angular momentum is considered. The separability of the Hamiltonians is discussed.