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Using Contracted Basis Functions and the Lanczos Algorithm to Compute Spectra of Flexible Van der Waals Dimers

Banff International Research Station for Mathematical Innovation and Discovery

We have developed a new method to compute numerically exact ro--vibrational levels of Van der Waals dimers with fexible monomers and applied it to water dimer, 12 vibrational coordinates, and $Cl^-$--$H_2O$, 6 vibrational coordinates. The method uses vibrational basis functions that are products of an inter-monomer function and intra-monomer functions. The inter-monomer function is a product of Wigner functions and an inter-monomer stretch function. The intra-monomer functions are monomer vibrational wavefunctions. When the coupling between inter- and intra-monomer coordinates is weak, this new basis is very efficient and only a few monomer vibrational wavefunctions are necessary. The product structure of the basis makes it efficient to use the Lanczos algorithm to calculate eigenvalues and eigenfunctions of the Hamiltonian matrix. For water dimer, it is necessary to do (12-D) integrals by quadrature, but crucial to obviate the need to keep values of the potential on the full direct product quadrature grid in memory (if there were 10 quadrature points per coordinate, the full grid would have 1012 points (~8000 GB)). This is done by storing an intermediate matrix (X.-G. Wang and T. Carrington Jr., J.~Chem.~Phys. {\bf 119} 101 (2003) and {\bf 129} 234102 (2008)). It represents the potential at a set of values of the 6 intermolecular coordinates in the intra-monomer basis. For water dimer, we have obtained numerically exact inter-monomer energy levels on the CCpol-8sf {\it ab initio} potential energy surface and compare them with results obtained using the 6D + 6D adiabatic approach of C. Leforestier, K. Szalewicz, and A. van der Avoid, J. Chem. Phys. {\bf 137} 014305 (2012).

Mathematics; Quantum theory; Partial differential equations; Applied computer science

video/mp4

Author affiliation: Queen's University

2016-07-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58555

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/