Gaussian-based multiconfiguration time-dependent Hartree: A two-layer approach. II. Application to vibrational energy transport in a molecular chain

Abstract

We report on first applications of the Two-Layer Gaussian-based Multi-Configuration Time-Dependent Hartree (2L-GMCTDH) method [Römer et al., J. Chem. Phys. 138, 064106 (2013)] for high-dimensional quantum propagation using variational Gaussian basis sets. This method circumvents the limitations of conventional variational Gaussian wavepacket (GWP) methods by introducing a hierarchical wavefunction representation with a fully flexible first layer composed of orthogonal single-particle functions, which are in turn expressed as superpositions of GWPs of fixed width. The method is applied to a model Hamiltonian describing vibrational energy transport through a molecular chain. The model combines bilinear site-to-site couplings with site-local couplings induced by cubic anharmonicities. We report on simulation results for realizations comprising 5 sites with 35 vibrational modes and 18 sites with 90 vibrational modes, which are shown to be in excellent agreement with reference calculations by the Multi-Layer MCTDH method.

Multi-layer Gaussian-based multi-configuration time-dependent Hartree (ML-GMCTDH) simulations of ultrafast charge separation in a donor–acceptor complex

“…52 Using 2L-GMCTDH, converged calculations could be performed up to 100 modes. 36 Here, we go significantly beyond these previous studies and demonstrate the application of the ML-GMCTDH approach for up to 300 modes. To obtain a series of realizations of the linear vibronic coupling Hamiltonian of Ref.…”

“…In Ref. [34], the approach was introduced as a natural extension of the two-layer 2L-GMCTDH method [34][35][36] to a larger number of layers. Alternatively, one can think of a modified ML-MCTDH approach, [29][30][31][32] where GWPs replace the single-particle functions (SPFs) of the last layer.…”

“…Since we will address coupled electronic states, we describe combined electronic-vibrational representations of the wavefunction. Specifically, we will employ the so-called single-set scheme, 28,36 where the GWP basis is taken to be state-independent, and the electronic states are treated as a set of additional electronic SPFs which are here assumed to be timeindependent. While several types of representations -single-set, multi-set, and a hybrid variant -were implemented in the 2L-GMCTDH framework, 36 we focus on the single-set variant in the present context since this is the approach chosen in the ML-MCTDH method (see also the discussion of this aspect below).…”

“…While we previously implemented the hierarchical two-layer version of the method (2L-GMCTDH) and presented applications to vibrational energy redistribution 35 and nonadiabatic dynamics 36 for up to 100 modes, the present paper presents the first application of a more general hierarchical ML-GMCTDH scheme with an arbitrary number of layers.…”

Non-adiabatic Matsubara Dynamics and Non-adiabatic Ring Polymer Molecular Dynamics

“…Directly performing exact quantum dynamics simulations is computationally demanding, despite exciting recent progress. [1][2][3][4][5][6][7][8][9][10][11] To accurately describe the non-adiabatic dynamics, a large number of these approaches are developed, including the popular trajectory surface-hopping method (mixed quantum-classical approach), [12][13][14][15] the linearized path-integral approaches, [16][17][18][19][20][21][22][23] and the mixed quantumclassical Liouville equation, [24][25][26][27][28] Despite providing accurate electronic non-adiabatic dynamics, these approaches often relies on the Wigner sampling of the initial nuclear distribution and a classical dynamics for propagation. Thus in generally, they do not preserve quantum Boltzmann distribution (QBD) 29,30 or zero point energy (ZPE) associated with the nuclear degrees of freedom (DOF).…”