Optimized unoccupied single-particle functions in the (multi-layer) multi-configurational time-dependent Hartree approach

Abstract

The multi-configurational time-dependent Hartree (MCTDH) approach and its multi layer-extension facilitate accurate high-dimensional quantum dynamics simulations. Its numerical efficiency results from the use of optimized basis sets consisting of self-adapting time-dependent single-particle functions (SPFs). While the propagation of occupied SPFs is determined by the MCTDH equations of motion derived from the Dirac-Frenkel variational principle, optimal choices for the unoccupied SPFs can not be obtained from a time-local variational principle. Equations defining optimal unoccupied SPFs have recently been derived by analyzing the time-dependence of the single-particle density matrices up to second order. However, this work has been restricted to analytical derivations and a simple numerical test. The present article continues this research and presents numerically efficient schemes for the calculation of optimal and approximately optimal unoccupied SPFs.