title: Multidimensional Hamiltonian for tunneling with position-dependent mass.
abstract: A multidimensional Hamiltonian for tunneling is formulated, based on the mode with imaginary frequency of the transition state as a reaction coordinate. To prepare it for diagonalization, it is transformed into a lower-dimension Hamiltonian by incorporating modes that move faster than the tunneling into a coordinate-dependent kinetic energy operator, for which a Hermitian form is chosen and tested for stability of the eigenvalues. After transformation to a three-dimensional form, which includes two normal modes strongly coupled to the tunneling mode, this Hamiltonian is diagonalized in terms of a basis set of harmonic oscillator functions centered at the transition state. This involves a sparse matrix which is easily partially diagonalized to yield tunneling splittings for the zero-point level and the two fundamental levels of the coupled modes. The method is tested on the well-known benchmark molecule malonaldehyde and a deuterium isotopomer, for which these splittings have been measured. Satisfactory agreement with experiment results is obtained.
authors.affiliation: Department of Physical Chemistry and Center for Research in Biological Chemistry and Molecular Materials, University of Santiago de Compostela, 15706 Santiago de Compostela, Spain.
authors.forename: Antonio
authors.initials: A
authors.lastname: Fernández-Ramos
authors.affiliation: Department of Physical Chemistry and Center for Research in Biological Chemistry and Molecular Materials, University of Santiago de Compostela, 15706 Santiago de Compostela, Spain.
authors.forename: Zorka
authors.initials: Z
authors.lastname: Smedarchina
authors.affiliation: Department of Physical Chemistry and Center for Research in Biological Chemistry and Molecular Materials, University of Santiago de Compostela, 15706 Santiago de Compostela, Spain.
authors.forename: Willem
authors.initials: W
authors.lastname: Siebrand
mesh_terms: D003903:Deuterium / Q000737:chemistry; D004601:Elementary Particles; D008315:Malondialdehyde / Q000737:chemistry; D008962:Models, Theoretical
chemical_list: D008315:Malondialdehyde; D003903:Deuterium