A Smolyak algorithm adapted to a system-bath separation: application to an encapsulated molecule with large amplitude motions

TL;DR

This paper introduces an adapted Smolyak algorithm for quantum simulations of complex molecules, enabling efficient convergence and overcoming traditional limitations, demonstrated on a molecule with large amplitude motions.

Contribution

The authors develop a novel Smolyak algorithm adapted for system-bath separation that efficiently simulates large, floppy molecules without Hamiltonian restrictions.

Findings

Successfully simulated H₂ in a clathrate hydrate cage

Achieved convergence of transition energies with increasing modes

Confirmed triplet splittings in translational and rotational transitions

Abstract

A Smolyak algorithm adapted to system-bath separation is proposed for rigorous quantum simulations. This technique combines a sparse grid method with the system-bath concept in a specific configuration without limitations on the form of the Hamiltonian, thus achieving a highly efficient convergence of the excitation transitions for the "system" part. Our approach provides a general way to overcome the perennial convergence problem for the standard Smolyak algorithm and enables the simulation of floppy molecules with more than a hundred degrees of freedom.The efficiency of the present method is illustrated on the simulation of H$_2$ caged in an sII clathrate hydrate including two kinds of cage modes. The transition energies are converged by increasing the number of normal modes of water molecules. Our results confirm the triplet splittings of both translational and rotational ($j=1$) transitions of the H$_2$ molecule. Furthermore, they show a slight increase of the translational transitions with respect to the ones in a rigid cage.