Molecular bound state calculations as a test of arrangement channel quantum mechanics

Arrangement channel quantum mechanics (ACQM) is a nonrelativistic time-dependent many-body theory. Although originally formulated as a scattering theory, it is investigated in this thesis in its time independent form as a bound state formalism. The applications are to the calculations of the bound states of some simple molecules. The corresponding approximate or exact solutions of the Schroedinger equation are also determined. The following aspects of the ACQM theory are studied. First, the ACQM energy functional is not positive definite, so that the relevant variational principle is not a minimum principle. Second, the arrangement channel equations associated with the energy functional via the variational principle are non-Hermitian operator equations for which there is no Hylleraas-Undheim theorem. Extended calculations of the electronic energy of H2+ and the hydrogne molecule (H2) using a Hilbert space expansion in atomic orbitals are presented which demonstrate the difficulties of a non-Hermitian theory. Third, ACQM inherently describes many-body systems in terms of their constituent subsystems. The importance of this feature is demonstrated by the ground state calculations of H2 and the (HeH)+ ion and a calculation of the first excited H2 gerade state. Finally, to verify consistency with the Schroedinger equation the exact arrangement channel equations for H2+ are solved exactly using the finite element method. The ACQM energy surfaces and wave function of the gerade and ungerade states are found to be in excellent agreement with the known exact solutions of the Schroedinger equation for H2+