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

Manthe U. Optimized unoccupied single-particle functions in the (multi-layer) multi-configurational time-dependent Hartree approach. CHEMICAL PHYSICS. 2018;515:279-286.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. (C) 2018 Elsevier B.V. All rights reserved