The generator coordinate method for molecular wavefunctions: A moment method and a simple intrinsic function

An extension of the generator coordinate method to the description of the electronic structure of molecules is presented. An exact formal solution to the Hill-Wheeler equation is obtained for a certain class of intrinsic functions, namely, those whose Hamiltonian and overlap kernels are of degenerate form. Since the exact kernels are used in the Hill-Wheeler equation, the variational principle is retained. The formal solution is represented by the set of moments of the generator coordinate with respect to the weighting function. The features of the method are illustrated by application to the hydrogen molecule. A simple trial intrinsic function and a PPP Hamiltonian are used to describe the π-electron structure of three linear conjugated polyenes (1,3-butadiene; 1,3,5-hexatriene; and 1,3,5,7-octatetraene). A significant part of the apparent ground state correlation energy is recovered for each molecule and π-electron excited state energies are also calculated. These results are compared with PPP CI calculations and the limitations of this simple trial intrinsic function are discussed.