A Theory of Molecules in Molecules. I

Abstract

A theory of molecules in molecules is presented in which the wavefunction of a molecule is constructed from the wavefunctions of possible molecular fragments. In the formalism of the Hartree–Fock–Roothaan theory further approximations are introduced. In the formation of the new molecule from the molecular fragments the effects of the interaction on the charge distribution are regarded as important only in the molecular parts neighboring each other, but neglected in the other parts, which are regarded as unperturbed. The localized molecular orbitals constituting the wavefunctions of the fragments can therefore be transferred unaltered, if they lie outside the region of interaction, or are redetermined with the help of the variational principle. Our aim is to construct the wavefunction of a large molecule from the wavefunctions of two (or few) large fragments and in this way save in the computational time. No approximations in the Hamilton operator or in the integrals are made in the first formulation, but some approximations are required in the treatment of the orthogonality problem inherent in a theory of molecules in molecules. In a restricted form (calculation of only two modified orbitals) the theory is applied to determine the potential energy curve of two hydrogen fluoride molecules along the reaction coordinate FH–HF. A comparison with exact SCF–MO calculations demonstrates that good results are obtained for intermolecular distances larger than one atomic unit. On the basis of this justification the theory is generalized and reformulated. An arbitrary number of orbitals can be modified, where the orbitals are an expansion only over a subset of the total set of basis functions. This approach gives a high flexibility in the calculation of approximate wavefunctions.