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 Title: A Sparse Linear Algebraic Approach To Arbitrary-order Vibrational Perturbation Theory Author(s): Boyer, Mark A. Contributor(s): McCoy, Anne B. Subject(s): Theory and Computation Abstract: Vibrational perturbation theory is a commonly-used method for obtaining anharmonic corrections to harmonic zero-order wave functions and energies. The method comes in two main variants, canonical Van Vleck perturbation theory, which has been used extensively by Sibert and coworkers\footnote{Sibert, E. L. J. Chem. Phys. 88, 4378-4390 (1987).} and Rayleigh-Schr\"{o}dinger perturbation theory, which was used by Nielsen to derive analytic corrections up through second-order.\footnote{Nielsen, H. H. Phys. Rev. 60, 794-810 (1941).}\footnote{Nielsen, H. H. Rev. Mod. Phys. 23, 90-136 (1951).} In this work, we introduce an adaption to the Rayleigh-Schr\"{o}dinger formalism. This approach, which is a generalization of approaches found in the physics literature,\footnote{Sakurai, J. J.; Liboff, R. L. Modern Quantum Mechanics. Am. J. Phys. (1986).} provides a simple route to obtain high-order corrections to the vibrational energies and wave functions for a system. The intensive symbolic algebra required in both the Van Vleck and Nielsen approaches is replaced by a sparse, numerical linear algebra for which efficient libraries already exist. This approach is formally equivalent to standard methods and admits a straight-forward approach to account for degeneracies. We apply this method to obtaining $4^{\mathrm{th}}$ and higher order corrections to the vibrational energies of a series of water clusters making use of curvilinear internal coordinates. Issue Date: 2021-06-23 Publisher: International Symposium on Molecular Spectroscopy Genre: Conference Paper / Presentation Type: Text Language: English URI: http://hdl.handle.net/2142/111205 Date Available in IDEALS: 2021-09-24
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