# CMP Seminar-"The application of phase-space localized basis functions to the calculation of vibrational energies in polyspherical coordinates"

Ph.D. candidate James Brown who is supervised by Tucker Carrington.

Queen's Physics** **

Thursday, January 22nd, 2015

10:30 am @ Stirling 401

## Abstract:

Recently [1], it was shown that accurate energy levels can be computed using a pruned von Neumann (vN) basis whose functions are re-expanded in a sinc discrete variable representation (DVR) basis. This accuracy is not possible with the vN basis alone. Expanding the vN basis functions in a sinc DVR basis solved the long-standing convergence problem of phase-space localized vN functions. Equivalent accuracy was retained even after a substantial number of the initial basis functions were pruned, which is not the case when using the sinc DVR alone. We show that expanding the vN functions with any DVR produces a basis with similar properties, namely convergence and prunability. The ability to use any DVR with the vN basis permits the calculation of vibrational energies in polyspherical coordinates, whereas the vN basis alone introduces difficulties with, boundary conditions, and evaluating kinetic energy matrix elements in polyspherical coordinates. We also reformulate the method of Ref 1 to permit the use of iterative eigensolvers, and apply it to calculating the vibrational energies of H_2O (MJS: water not H_{20}.

[1] A. Shimshovitz and D. J. Tannor, Phys. Rev. Lett. 109, 070402 (2012).