A quantum-mechanical study of the water molecule

Abstract

Non-empirical calculations of the electronic structure of the water molecule (treated as a full ten-electron system) are carried out for various types of wave function. These include a ‘bond orbital’ function, a ‘modified electron-pair’ function, and various Roothaan-type self-consistent field (s. c. f.) functions. These approximations are refined by admitting interaction with up to twelve configurational functions of ground-state symmetry. Three bond angles are considered. The results show that the modified electron pair function, which has not hitherto been used in non-empirical calculations, provides the most satisfactory first approximation. This function is constructed from orthonormalized hybrid orbitals in order to overcome non-orthogonality difficulties; and the inclusion of configuration interaction in this particular basis is found to be simple, effective and physically meaningful. The concept of a ‘core’, comprising the oxygen inner shell and lone pairs and providing an effective field for the bond pairs, is found to be remarkably satisfactory. Provided the effective field is properly defined, it is then possible to treat the molecule formally as a four-electron system and to obtain, nevertheless, a total energy 0⋅3 eV better than that given by the best of the s. c. f. calculations. This suggests that the ‘core approximation’ is not a real obstacle to progress. The one-electron density matrices are calculated from the various wave functions and the corresponding dipole moments are evaluated.