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

## TL;DR

This paper introduces a new computational approach combining a numerical kinetic-energy operator and a Smolyak grid method to efficiently solve the (ro)vibrational Schrödinger equation for complex polyatomic molecules with multiple large-amplitude motions.

## Contribution

It presents a novel black-box variational method that reduces computational complexity for vibrational calculations of floppy, polyatomic molecules using combined advanced techniques.

## Key findings

- Successfully applied to CH₄·Ar complex in full 12D vibrational space.
- Achieved significant reduction in grid size while maintaining accuracy.
- Demonstrated feasibility of system-adapted coordinates and iterative eigensolvers.

## Abstract

Methodological progress is reported in the challenging direction of a black-box-type variational solution of the (ro)vibrational Schr\"odinger 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 [E. M\'atyus, G. Czak\'o, and A. G. Cs\'asz\'ar, J. Chem. Phys. 130, 134112 (2009)] and (ii) the Smolyak non-product grid method of [G. Avila and T. 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, multi-dimensional (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$_4\cdot$Ar complex treated in full (12D) vibrational dimensionality.