Gaussian-based multiconfiguration time-dependent Hartree: a two-layer approach. I. Theory.

We describe a novel two-layer variant of the Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH) approach which improves on the performance and convergence properties of quantum propagation based on variationally evolving frozen Gaussians (FGs). While the standard scheme uses factorizable multi-dimensional FGs, the present approach combines these into flexible, MCTDH-like single-particle functions. At the same time, the expensive variational evolution of the Gaussian parameters is reduced to low-dimensional subspaces. As a result, the novel scheme significantly alleviates the current bottleneck to accurate propagation in G-MCTDH and its variational multiconfigurational Gaussian (vMCG) variant. Since the first-layer single-particle functions are chosen to be orthogonal, the present approach can be straightforwardly combined with existing multi-layer MCTDH schemes.

[1]  E. Heller.  Time‐dependent approach to semiclassical dynamics , 1975 .

[2]  Victor S. Batista,et al.  Matching-pursuit for simulations of quantum processes , 2003 .

[3]  Todd J. Martínez,et al.  Ab Initio Quantum Molecular Dynamics , 2002 .

[4]  M. Beck,et al.  The multiconfiguration time-dependent Hartree (MCTDH) method: A highly efficient algorithm for propa , 1999 .

[5]  H. Metiu,et al.  A multiple trajectory theory for curve crossing problems obtained by using a Gaussian wave packet representation of the nuclear motion , 1986 .

[6]  E. Heller,et al.  Exact time‐dependent wave packet propagation: Application to the photodissociation of methyl iodide , 1982 .

[7]  G. Worth,et al.  Molecular dynamics of pyrazine after excitation to the S2 electronic state using a realistic 24-mode model Hamiltonian , 1999 .

[8]  D. Shalashilin,et al.  Description of tunneling with the help of coupled frozen Gaussians , 2001 .

[9]  Martin Karplus,et al.  Multidimensional variational Gaussian wave packet dynamics with application to photodissociation spectroscopy , 1990 .

[10]  M. Frisch,et al.  Nonequilibrium Fermi golden rule for electronic transitions through conical intersections. , 2011, The Journal of chemical physics.

[11]  A. D. McLachlan,et al.  A variational solution of the time-dependent Schrodinger equation , 1964 .

[12]  Lorenz S. Cederbaum,et al.  Approaches to the approximate treatment of complex molecular systems by the multiconfiguration time-dependent Hartree method , 1999 .

[13]  U. Manthe,et al.  Wave‐packet dynamics within the multiconfiguration Hartree framework: General aspects and application to NOCl , 1992 .

[14]  B. A. Lindquist,et al.  Photodynamics in complex environments: ab initio multiple spawning quantum mechanical/molecular mechanical dynamics. , 2009, The journal of physical chemistry. B.

[15]  Uwe Manthe,et al.  A multilayer multiconfigurational time-dependent Hartree approach for quantum dynamics on general potential energy surfaces. , 2008, The Journal of chemical physics.

[16]  I. Burghardt,et al.  Gaussian-based techniques for quantum propagation from the time-dependent variational principle: Formulation in terms of trajectories of coupled classical and quantum variables. , 2008, The Journal of chemical physics.

[17]  G. Worth,et al.  A novel algorithm for non-adiabatic direct dynamics using variational Gaussian wavepackets. , 2004, Faraday discussions.

[18]  V. Batista,et al.  Matching-pursuit/split-operator-Fourier-transform simulations of excited-state nonadiabatic quantum dynamics in pyrazine. , 2006, The Journal of chemical physics.

[19]  Lorenz S. Cederbaum,et al.  Using the MCTDH wavepacket propagation method to describe multimode non-adiabatic dynamics , 2008 .

[20]  Ian R. Craig,et al.  Proton transfer reactions in model condensed-phase environments: Accurate quantum dynamics using the multilayer multiconfiguration time-dependent Hartree approach. , 2007, The Journal of chemical physics.

[21]  U. Manthe,et al.  The multi-configurational time-dependent Hartree approach , 1990 .

[22]  Dajana Conte,et al.  Mathematical Modelling and Numerical Analysis an Error Analysis of the Multi-configuration Time-dependent Hartree Method of Quantum Dynamics , 2022 .

[23]  Michael A. Robb,et al.  Solving the time-dependent Schrödinger equation for nuclear motion in one step: direct dynamics of non-adiabatic systems , 2008 .

[24]  G. Worth,et al.  Relaxation of a system with a conical intersection coupled to a bath: A benchmark 24-dimensional wave packet study treating the environment explicitly , 1998 .

[25]  H. Metiu,et al.  A strategy for time dependent quantum mechanical calculations using a Gaussian wave packet representation of the wave function , 1985 .

[26]  P. Saalfrank,et al.  A local coherent-state approximation to system-bath quantum dynamics. , 2006, The Journal of chemical physics.

[27]  T. Carrington,et al.  A general discrete variable method to calculate vibrational energy levels of three‐ and four‐atom molecules , 1993 .

[28]  Scott Habershon,et al.  Linear dependence and energy conservation in Gaussian wavepacket basis sets. , 2012, The Journal of chemical physics.

[29]  G. Worth,et al.  Multiconfigurational system-bath dynamics using Gaussian wave packets: Energy relaxation and decoherence induced by a finite-dimensional bath , 2003 .

[30]  David J Rowe,et al.  Many-body quantum mechanics as a symplectic dynamical system , 1980 .

[31]  P. Dirac.  Note on Exchange Phenomena in the Thomas Atom , 1930, Mathematical Proceedings of the Cambridge Philosophical Society.

[32]  G. Worth,et al.  Multimode quantum dynamics using Gaussian wavepackets: The Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH) method applied to the absorption spectrum of pyrazine. , 2008, The Journal of chemical physics.

[33]  D. Shalashilin,et al.  The phase space CCS approach to quantum and semiclassical molecular dynamics for high-dimensional systems , 2004 .

[34]  H. Meyer,et al.  Multilayer multiconfiguration time-dependent Hartree method: implementation and applications to a Henon-Heiles hamiltonian and to pyrazine. , 2010, The Journal of chemical physics.

[35]  Irene Burghardt,et al.  Full quantum mechanical molecular dynamics using Gaussian wavepackets , 2003 .

[36]  Eric J. Heller,et al.  Frozen Gaussians: A very simple semiclassical approximation , 1981 .

[37]  Scott Habershon.  Trajectory-guided configuration interaction simulations of multidimensional quantum dynamics. , 2012, The Journal of chemical physics.

[38]  R. Levine,et al.  Multi-Electronic-State Molecular Dynamics: A Wave Function Approach with Applications , 1996 .

[39]  J. Broeckhove,et al.  On the equivalence of time-dependent variational-principles , 1988 .

[40]  Dmitrii V Shalashilin,et al.  Nonadiabatic dynamics with the help of multiconfigurational Ehrenfest method: Improved theory and fully quantum 24D simulation of pyrazine. , 2010, The Journal of chemical physics.

[41]  Haobin Wang,et al.  Multilayer formulation of the multiconfiguration time-dependent Hartree theory , 2003 .