Mixed Quantum-Classical Liouville Approach for Calculating Proton-Coupled Electron-Transfer Rate Constants

Real-Time Dynamics and Detailed Balance in Ring Polymer Surface Hopping: The Impact of Frustrated Hops

Ring polymer surface hopping (RPSH) has been recently introduced as a well-tailored method for incorporating nuclear quantum effects, such as zero-point energy and tunneling, into nonadiabatic molecular dynamics simulations. The practical widespread usage of RPSH demands a comprehensive benchmarking of different reaction regimes and conditions with equal emphasis on demonstrating both the cons and the pros of the method. Here, we investigate the fundamental questions related to the conservation of energy and detailed balance in the context of RPSH. Using Tully's avoided crossing model as well as a 2-state quantum system coupled to a classical bath undergoing Langevin dynamics, we probe the critical problem of the proper treatment of the classically forbidden transitions stemming from the surface hopping algorithm. We show that proper treatment of these frustrated hops is key to the accurate description of real-time dynamics as well as reproducing the correct quantum Boltzmann populations.

DECIDE: A Deterministic Mixed Quantum-Classical Dynamics Approach

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.

Recent progress in approximate quantum dynamics methods for the study of proton-coupled electron transfer reactions

Proton-coupled electron transfer (PCET) reactions are ubiquitous natural processes at the heart of energy conversion reactions in photosynthesis and respiration, DNA repair, and diverse enzymatic reactions. Theoretical formulation and computational method developments have eyed modeling of thermal and photoinduced PCET for the last three decades. The accumulation of these studies, collected in dozens of reviews, accounts, and perspectives, has firmly established the influence of quantum effects, including non-adiabatic electronic transitions, vibrational relaxation, zero-point energy, and proton tunneling, on the rate and mechanism of PCET reactions. Here, we focus on some recently-developed methods, spanning the last eight years, that can quantitatively capture these effects in the PCET context and provide efficient means for their qualitative description in complex systems. The theoretical background of each method and their accuracy with respect to exact results are discussed and the results of relevant PCET simulations based on each method are presented.

Nonadiabatic Dynamics via the Symmetrical Quasi-Classical Method in the Presence of Anharmonicity

The symmetrical quasi-classical (SQC) method recently proposed by Miller and Cotton allows one to simulate nonadiabatic dynamics based on an algorithm with classical-like scaling with respect to system size. This is made possible by casting the electronic degrees of freedom in terms of mapping variables that can be propagated in a classical-like manner. While SQC was shown to be rather accurate when applied to benchmark models with harmonic electronic potential energy surfaces, it was also found to become inaccurate and to suffer numerical instabilities when applied to anharmonic systems. In this paper, we propose an extended SQC (E-SQC) methodology for overcoming those discrepancies by describing the anharmonic nuclear modes, which are coupled to the electronic degrees of freedom, in terms of classical-like mapping variables. The accuracy of E-SQC relative to standard SQC is demonstrated on benchmark models with quartic and Morse potential energy surfaces.