Simulating Quantum Dynamics in Classical Nanoscale Environments

Hanna, Gabriel; Sergi, Alessandro

doi:10.1007/978-981-15-0006-0_14

Cited by 1 publication

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“…Over the years, a host of techniques have been developed based on approximate solutions of the QCLE [3,30]. The most accurate of these techniques are the stochastic surface-hopping solutions [6,[31][32][33][34][35][36], but they require extremely large ensembles of trajectories to obtain converged results and, as a result, will be computationally prohibitive for many systems. On the other hand, the Poisson Bracket Mapping Equation (PBME) approach provides a highly computationally efficient approximate solution of the QCLE, but its applicability is mainly restricted to systems with weak subsystem-bath couplings [8,[37][38][39].…”

Section: Introductionmentioning

confidence: 99%

DECIDE: A Deterministic Mixed Quantum-Classical Dynamics Approach

2022

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Mixed quantum-classical dynamics provides an efficient way of simulating the dynamics of quantum subsystems coupled to many-body environments. Many processes, including proton-transfer reactions, electron-transfer reactions, and vibrational energy transport, for example, take place in such open systems. The most accurate algorithms for performing mixed quantum-classical simulations require very large ensembles of trajectories to obtain converged expectation values, which is computationally prohibitive for quantum subsystems containing even a few degrees of freedom. The recently developed “Deterministic evolution of coordinates with initial decoupled equations” (DECIDE) method has demonstrated high accuracy and low computational cost for a host of model systems; however, these applications relied on representing the equations of motion in subsystem and adiabatic energy bases. While these representations are convenient for certain systems, the position representation is convenient for many other systems, including systems undergoing proton- and electron-transfer reactions. Thus, in this review, we provide a step-by-step derivation of the DECIDE approach and demonstrate how to cast the DECIDE equations in a quantum harmonic oscillator position basis for a simple one-dimensional (1D) hydrogen bond model. After integrating the DECIDE equations of motion on this basis, we show that the total energy of the system is conserved for this model and calculate various quantities of interest. Limitations of casting the equations in an incomplete basis are also discussed.

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