Smolyak Algorithm Adapted to a System–Bath Separation: Application to an Encapsulated Molecule with Large-Amplitude Motions

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.

Smolyak Scheme for solving the Schrödinger equation: Application to Malonaldehyde in Full Dimensionality

“…For spherical harmonic basis sets (with $${{{\bf Y}}_{{j}_{i}}^{{m}_{i}}}$$ as basis functions), we can define any increasing sequence between $${{{\cal{\ell}}}_{i}}$$ and $${{j}_{i}^{max}}$$ , where $${{j}_{i}^{max}}$$ is the largest value for $${{j}_{i}}$$ [29,58,59] …”

“…(iii) For spherical harmonic basis sets (with Y m i j i as basis functions), we can define any increasing sequence between ' i and j max i , where j max i is the largest value for j i . [29,58,59] Given the definitions of the nb i ' i sequences, the DB i ' i (Eqs (10) and (11)) and the constraint on the ' i (Eq. ( 9)), the Smolyak scheme applied to the corresponding multidimensional basis set (Eq (8)) allows the selection of an n-dimensional basis set, reduced in size with respect to the full direct-product basis set.…”

“…[21] Since then, several studies have been published by Avila and Carrington, [22][23][24] by the Matyus group [25,26] and by ourselves. [27][28][29] The main goal of the present study is to show that, with the Smolyak scheme, large realistic molecular systems with complex coordinates can be studied.…”

Quantum molecular dynamics simulations of the effect of secondary modes on the photoisomerization of a retinal chromophore model

“…Our quantum molecular dynamics simulations are performed by propagating vibronic wavepackets and classical-like trajectories. For the former, we will focus on the use of different ideas to define the time-independent grid, i.e., direct product versus Smolyak [22,23] grids, in order to be able to include efficiently at a reasonable computational cost the secondary modes representing the environment. The calculations are performed with the ElVibRot code [24].…”

High-dimensional neural network potentials for accurate vibrational frequencies: the formic acid dimer benchmark

“…An efficient quantum dynamics description of these types of systems is currently an active and challenging field for methodological developments. [70][71][72][73][74][75][76] These developments can be tested and validated with respect to precise spectroscopy data, assuming that a faithful and accurate PES representation for the molecular system is available.…”