Toward breaking the curse of dimensionality in (ro)vibrational computations of molecular systems with multiple large-amplitude motions

Abstract

Methodological progress is reported in the challenging direction of a black-box-type variational solution of the (ro)vibrational Schrödinger equation applicable to floppy, polyatomic systems with multiple large-amplitude motions. This progress is achieved through the combination of (i) the numerical kinetic-energy operator (KEO) approach of Mátyus et al. [J. Chem. Phys. 130, 134112 (2009)] and (ii) the Smolyak nonproduct grid method of Avila and Carrington, Jr. [J. Chem. Phys. 131, 174103 (2009)]. The numerical representation of the KEO makes it possible to choose internal coordinates and a body-fixed frame best suited for the molecular system. The Smolyak scheme reduces the size of the direct-product grid representation by orders of magnitude, while retaining some of the useful features of it. As a result, multidimensional (ro)vibrational states are computed with system-adapted coordinates, a compact basis- and grid-representation, and an iterative eigensolver. Details of the methodological developments and the first numerical applications are presented for the CH 4 ·Ar complex treated in full (12D) vibrational dimensionality.