Compact MCTDH Wave Functions for High-Dimensional System-Bath Quantum Dynamics

Bonfanti, Matteo; Tantardini, Gian Franco; Hughes, Keith H.; Martinazzo, Rocco; Burghardt, Irène

doi:10.1021/jp3064504

Cited by 15 publications

(21 citation statements)

References 47 publications

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“…(7) can be quantized by applying standard quantization rules and represents the quantum problem that we tackle here at T = 0 K with a Multi Configuration Time-Dependent Hartree (MCTDH) expansion of the wavefunction [6,7], following previous works on similar model systems [10][11][12][13][14]. Further developments involving transformation of the bath Hamiltonian into linear chain form [15][16][17][18] and its application to similar problems have been discussed elsewhere [19].…”

Section: Theorymentioning

confidence: 99%

Vibrational relaxation and decoherence in structured environments: a numerical investigation

et al. 2015

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Vibrational relaxation is a key issue in chemical reaction dynamics in condensed phase and at the gas-surface interface, where the enviroment is typically highly structured and cannot be condensed in a simple friction coefficient. Rather, full knowledge of the coupling of the molecular oscillator to the environment is required, as typically subsumed in the so-called spectral density (of the environmental coupling). Here, we focus on harmonic Brownian motion and investigate the effectiveness of classical, canonical position autocorrelation functions to compute the spectral density of the coupling needed to describe vibrational relaxation in complex environments. Classical dynamics is performed on model systems, and several effects investigated in detail, e.g. the presence of anharmonicity, the role of a high-frequency "Debye" cutoff in the environment and the influence of the detailed structure of the latter. The spectral densities are then used in standard independent oscillator Hamiltonian models which are numerically solved at T=0 K to investigate quantum relaxation and decoherence.

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Section: Theorymentioning

confidence: 99%

Vibrational relaxation and decoherence in structured environments: a numerical investigation

et al. 2015

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“…While basis set techniques can approximate this continuous band, doing so typically results in algorithms that scale exponentially in time. 38 As the remaining environment modes are expected to be less strongly coupled to the electronic degrees of freedom, we can consider ways to integrate them out and arrive at a reduced description of the dynamics of the system. In this way, we will define the total Hamiltonian, H = H S + H SB + H B , as a partitioning between a system, bath and coupling terms.…”

Section: B System Bath Partitioningmentioning

confidence: 99%

Simulating conical intersection dynamics in the condensed phase with hybrid quantum master equations

Schile

Limmer

2019

The Journal of Chemical Physics

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We present a framework for simulating relaxation dynamics through a conical intersection of an open quantum system that combines methods to approximate the motion of degrees of freedom with disparate time and energy scales. In the vicinity of a conical intersection, a few degrees of freedom render the nuclear dynamics nonadiabatic with respect to the electronic degrees of freedom. We treat these strongly coupled modes by evolving their wavepacket dynamics in the absence of additional coupling exactly. The remaining weakly coupled nuclear degrees of freedom are partitioned into modes that are fast relative to the nonadiabatic coupling and those that are slow. The fast degrees of freedom can be traced out and treated with second-order perturbation theory in the form of the time-convolutionless master equation. The slow degrees of freedom are assumed to be frozen over the ultrafast relaxation, and treated as sources of static disorder. In this way, we adopt the recently developed frozenmode extension to second-order quantum master equations. We benchmark this approach to numerically exact results in models of pyrazine internal conversion and rhodopsin photoisomerization. We use this framework to study the dependence of the quantum yield on the reorganization energy and the characteristic timescale of the bath, in a two-mode model of photoisomerization. We find that the yield is monotonically increasing with reorganization energy for a Markovian bath, but monotonically decreasing with reorganization energy for a non-Markovian bath. This reflects the subtle interplay between dissipation and decoherence in conical intersection dynamics in the condensed phase. arXiv:1905.00029v2 [cond-mat.stat-mech]

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“…Still, the inherent exponential scaling with the number of degrees of freedom is a potential limitation, and several suggestions have been put forward to mitigate this, such as multilayer MCTDH, [10][11][12] or alternative approaches tailored to specific types of complex systems such as system-bath simulations. 13,14 Multi-configurational expansions have been combined with a time-dependent Gaussian basis or similar in various forms, such as the G-MCTDH 15 and variational multi-configurational Gaussian (vMCG) (see Ref. 16 for a review), and (two-layer) coupled-coherent states (CCS).…”

Section: Introductionmentioning

confidence: 99%

Exponential parameterization of wave functions for quantum dynamics: Time-dependent Hartree in second quantization

Madsen

Hansen

Zoccante

et al. 2018

The Journal of Chemical Physics

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Semiclassical transition state theory based on fourth order vibrational perturbation theory: Model system studies beyond symmetric Eckart barrier Perspective: Computational chemistry software and its advancement as illustrated through three grand challenge cases for molecular science Communication: The pole structure of the dynamical polarizability tensor in equation-of-motion coupledcluster theoryWe derive equations for describing the time evolution of variational wave functions in linear and exponential parameterization with a second-quantization (SQ) formulation. The SQ formalism covers time-dependent Hartree (TDH), while exact states and approximate vibrational configuration interaction wave functions are described using state-transfer operators. We present detailed expressions for efficient evaluation of TDH in linear (L-TDH) and exponential (X-TDH) parametrization and an efficient implementation supporting linear scaling with respect to the number of degrees of freedom M when the Hamiltonian operator contains a constant number of terms per mode independently of the size of the system. The computational cost of the X-TDH method is reduced significantly compared to the L-TDH method for systems with many operator terms per mode such as is typical for accurate molecular potential-energy surfaces. Numerical results for L-TDH and X-TDH are presented which confirm the theoretical reduction of the M scaling compared to standard first-quantization formulations. Calculations on Henon-Heiles potentials with more than 10 5 dimensions and polycyclic aromatic hydrocarbons with up to 264 modes have been performed. Thus, the SQ formulation and the X-TDH method pave the way for studying the time-resolved quantum dynamics of large molecules. Published by AIP Publishing. https://doi.

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Compact MCTDH Wave Functions for High-Dimensional System-Bath Quantum Dynamics

Cited by 15 publications

References 47 publications

Vibrational relaxation and decoherence in structured environments: a numerical investigation

Vibrational relaxation and decoherence in structured environments: a numerical investigation

Simulating conical intersection dynamics in the condensed phase with hybrid quantum master equations

Exponential parameterization of wave functions for quantum dynamics: Time-dependent Hartree in second quantization

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