A transformed hamiltonian theory for HD+

Sadler, Ian Anthony (1988) A transformed hamiltonian theory for HD+. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

By performing a unitary transformation on the hamiltonian for HD⁺ the symmetry breaking term in the kinetic energy operator (arising from the different nuclear masses) is eliminated. In the transformed hamiltonian the symmetry breaking appears in the potential energy operator and is interpreted largely in terms of effective nuclear charges. With this transformed Schrodinger equation the symmetry breaking is included and the properties of the dissociation products are correctly given in an adiabatic approximation. Consequently, greatly improved adiabatic energies of vibration-rotation levels and Fermi contact parameters for HD⁺ near dissociation are obtained, compared with those from the untransformed equation. A second unitary transformation is applied to the hamiltonian, that eliminates cross-derivatives between electronic and nuclear coordinates in the kinetic energy operator, which arise from the use of prolate spheroidal coordinates. The transformed hamiltonian has a nuclear kinetic energy operator, which is simply proportional to ∂²/∂R^2. It is thought that a full inclusion of nuclear motion effects will be possible in a relatively straightforward approach for high vibrational levels of HD^+ using the transformed Schrodinger equation. The electric quadrupole moments of one-electron atoms are calculated from the Schrodinger and the Dirac equations. The energy of interaction between the electric field gradient at the nucleus (due to the electronic charge distribution) and the nuclear quadrupole moment is calculated for the deuterium atom. (D 82538)

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