Tangent space formulation of the Multi-Configuration Time-Dependent Hartree equations of motion: The projector-splitting algorithm revisited

TL;DR

This paper revisits the derivation of MCTDH equations using tangent space projection methods and introduces an improved integrator that avoids direct inversion of reduced density matrices by using non-orthogonal functions.

Contribution

It formulates a new tangent space-based algorithm for MCTDH that enhances numerical stability and efficiency by employing auxiliary non-orthogonal functions.

Findings

The new integrator avoids direct inversion of reduced density matrices.

The formulation is presented in conventional chemical physics notation.

Key features of the integration scheme are highlighted.

Abstract

The derivation of the time-dependent variational equations of the Multi-Configuration Time-Dependent Hartree (MCTDH) method for high-dimensional quantum propagation is revisited from the perspective of tangent space projection methods. In this context, we focus on a recently introduced algorithm [C. Lubich, Appl. Math. Res. eXpress 2015, 311 (2015), B. Kloss et al., J. Chem. Phys. 146, 174107 (2017)] for the integration of the MCTDH equations, which relies on a suitable splitting of the tangent space projection. The new integrator circumvents the direct inversion of reduced density matrices that appears in the standard method, by employing an auxiliary set of non-orthogonal single-particle functions. Here, we formulate the new algorithm and the underlying alternative form of the MCTDH equations in conventional chemical physics notation, in a complementary fashion to the tensor formalism used in the original work. Further, key features of the integration scheme are highlighted.