Studying molecular quantum dynamics with the multiconfiguration time‐dependent Hartree method

Abstract

This review covers the multiconfiguration time‐dependent Hartree (MCTDH) method, which is a powerful and general algorithm for solving the time‐dependent Schrödinger equation. The formal derivation is discussed as well as applications of the method. Recent extensions of MCTDH are treated in brief, namely, MCTDHB and MCTDHF, for treating identical particles (bosons and fermions), and the very powerful multilayer (ML‐MCTDH) formalism. Compact representations of potential energy surfaces (PESs) are also discussed, as the representation of a PES becomes a major bottleneck when going to larger systems (nine or more dimensions) while employing a full‐dimensional, complicated, and nonseparable PES. As applications of MCTDH, we discuss the calculation of photoionization and photoexcitation spectra of the vibronically coupled systems butatriene and pyrazine, respectively, and the infra‐red spectrum of the Zundel cation (protonated water dimer) H5O+2. © 2011 John Wiley & Sons, Ltd.This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics

Quantum breathing dynamics of ultracold bosons in one-dimensional harmonic traps: Unraveling the pathway from few- to many-body systems

“…Such a scheme is employed by the family of Multi-Configuration Time-Dependent Hartree (MCTDH) methods [24,25]. With Multi Layer-MCTDHB, a powerful generalization has been developed very recently for applications to the quantum dynamics of ultracold bosonic pure and multi-species systems [22,23].…”

Vibrational dynamics of the ${\rm H}_5^+$H5+ and its isotopologues from multiconfiguration time-dependent Hartree calculations

“…The MCTDH method (see Ref. 38 and references therein) expands the wavefunction in a sum of products, namely, singleparticle functions (SPFs), which in principle allow the treatment of more degrees of freedom, maintaining the correlation between them. The SPFs are one-or multidimensional functions of the system coordinates, and are represented by linear combinations of time-dependent primitive basis functions of discrete variable representation (DVR) grids.…”

Neural network‐based approaches for building high dimensional and quantum dynamics‐friendly potential energy surfaces

“…Transformed coordinates and dimensionality reduction were used to produce the first ab initio-based PES for the reaction of a triatomic molecule with a surface including all molecular DOF: dissociative adsorption of N 2 O on Cu (111). [29] The PES was sampled by placing N and O atoms randomly in the simulation cell and only imposing an "inverse potential" pdf on the NAN bond length (which does not dissociate).…”

“…This form is advantageous for some high-dimensional quantum dynamics calculations [36,[109][110][111] that use product basis functions because it obviates the need to do multidimensional quadrature.…”