Regularizing the MCTDH equations of motion through an optimal choice on-the-fly (i.e., spawning) of unoccupied single-particle functions

Abstract

The multi-configuration time-dependent Hartree method is a general algorithm to solve the time-dependent Schrödinger equation, in which the wavefunction is expanded in a direct product of self-adapting time-dependent Single-Particle Functions (SPFs) that are propagated in time according to the Dirac-Frenkel variational principle. In the current version of this approach, the size of the SPF basis is fixed at the outset so that singularities in the working equations resulting from unoccupied functions have to be removed by a regularization procedure. Here, an alternative protocol is presented, in which we gradually increase the number of unoccupied SPFs on-the-fly (i.e., spawning) and optimize their shape by variationally minimizing the error made by the finite size of the basis. An initial estimate for the respective new expansion coefficients is also computed, thus avoiding the need to regularize the equations of motion. The advantages of employing the new algorithm are tested and discussed in some illustrative examples.