Fernández Ramos, AntonioSmedarchina, ZorkaSiebrand, Willem2018-06-202018-06-202014-09-15Fernández-Ramos, A., Smedarchina, Z., & Siebrand, W. (2014). Multidimensional Hamiltonian for tunneling with position-dependent mass. Physical Review E, 90(3). doi: 10.1103/physreve.90.0333062470-0045http://hdl.handle.net/10347/16855A 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 obtainedeng©2014 American Physical Societyjournal article10.1103/PhysRevE.90.0333062470-0053open access