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

2020 ◽  
Author(s):  
Sutirtha N. Chowdhury ◽  
Pengfei Huo
Keyword(s):  
Molecular Dynamics ◽  
Correlation Function ◽  
Quantum Dynamics ◽  
General Framework ◽  
Degrees Of Freedom ◽  
Normal Modes ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Ring Polymer ◽  
Ring Polymer Molecular Dynamics

We present the non-adiabatic Matsubara dynamics, a general framework for computing the time-correlation function (TCF) of electronically non-adiabatic systems. This new formalism is derived based on the generalized Kubo-transformed time-correlation function, using the Wigner representation for both the nuclear degrees of freedom (DOF) and the electronic mapping variables. By dropping the non-Matsubara nuclear normal modes in the quantum Liouvillian and explicitly integrate these modes out of the TCF, we derived the non-adiabatic Matsubara dynamics approach. Further making the approximation to drop the imaginary part of the Matsubara Liouvillian and enforce the nuclear momentum integral to be real, we arrived at the non-adiabatic ring-polymer molecular dynamics (NRPMD) approach. We have further justified the capability of NRPMD for simulating the non-equilibrium time-correlation function. This work provides the rigorous theoretical foundation for several recently proposed state-dependent RPMD approaches and offers a general framework for developing new non-adiabatic quantum dynamics approaches in the future.

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

2020 ◽  
Author(s):  
Sutirtha N. Chowdhury ◽  
Pengfei Huo
Keyword(s):  
Molecular Dynamics ◽  
Correlation Function ◽  
Quantum Dynamics ◽  
General Framework ◽  
Degrees Of Freedom ◽  
Normal Modes ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Ring Polymer ◽  
Ring Polymer Molecular Dynamics

We present the non-adiabatic Matsubara dynamics, a general framework for computing the time-correlation function (TCF) of electronically non-adiabatic systems. This new formalism is derived based on the generalized Kubo-transformed time-correlation function, using the Wigner representation for both the nuclear degrees of freedom (DOF) and the electronic mapping variables. By dropping the non-Matsubara nuclear normal modes in the quantum Liouvillian and explicitly integrate these modes out of the TCF, we derived the non-adiabatic Matsubara dynamics approach. Further making the approximation to drop the imaginary part of the Matsubara Liouvillian and enforce the nuclear momentum integral to be real, we arrived at the non-adiabatic ring-polymer molecular dynamics (NRPMD) approach. We have further justified the capability of NRPMD for simulating the non-equilibrium time-correlation function. This work provides the rigorous theoretical foundation for several recently proposed state-dependent RPMD approaches and offers a general framework for developing new non-adiabatic quantum dynamics approaches in the future.

scholarly journals Path-integral approximations to quantum dynamics

2021 ◽  
Vol 94 (7) ◽  
Author(s):  
Stuart C. Althorpe
Keyword(s):  
Molecular Dynamics ◽  
Correlation Function ◽  
Path Integral ◽  
Quantum Dynamics ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Imaginary Time ◽  
Integral Methods ◽  
Ring Polymer ◽  
Recent Extension

Abstract Imaginary-time path-integral or ‘ring-polymer’ methods have been used to simulate quantum (Boltzmann) statistical properties since the 1980s. This article reviews the more recent extension of such methods to simulate quantum dynamics, summarising the chain of approximations that links practical path-integral methods, such as centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD), to the exact quantum Kubo time-correlation function. We focus on single-surface Born–Oppenheimer dynamics, using the infrared spectrum of water as an illustrative example, but also survey other recent applications and practical techniques, as well as the limitations of current methods and their scope for future development. Graphic abstract

scholarly journals Kinetically-constrained ring-polymer molecular dynamics for non-adiabatic chemistries involving solvent and donor–acceptor dynamical effects

2016 ◽  
Vol 195 ◽  
pp. 191-214 ◽  
Author(s):  
Joshua S. Kretchmer ◽  
Thomas F. Miller III
Keyword(s):  
Molecular Dynamics ◽  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Golden Rule ◽  
Solvent Dynamics ◽  
Friction Regime ◽  
Donor Acceptor ◽  
Ring Polymer ◽  
Ring Polymer Molecular Dynamics ◽  
Kinetic Constraint

We investigate the performance of the recently developed kinetically-constrained ring polymer molecular dynamics (KC-RPMD) method for the description of model condensed-phase electron transfer (ET) reactions in which solvent and donor–acceptor dynamics play an important role. Comparison of KC-RPMD with results from Golden-Rule rate theories and numerically exact quantum dynamics calculations demonstrates that KC-RPMD accurately captures the combination of electronic- and nuclear-dynamical effects throughout the Marcus (intermediate solvent friction) and Zusman (large solvent friction) regimes of ET. It is also demonstrated that KC-RPMD accurately describes systems in which the magnitude of the diabatic coupling depends on the position of a dynamical donor–acceptor mode. In addition to these successes, however, we present an unsurprising failure of KC-RPMD to capture the enhancement of the ET rate in the low solvent friction regime associated with nuclear coherence effects. In this analysis, we re-visit several aspects of the original KC-RPMD formulation, including the form of the kinetic constraint and the choice of the mass of the auxiliary electronic variable. In particular, we introduce a Langevin bath for the auxiliary electronic variable to correct for its unphysically low coupling with the nuclear degrees of freedom. This work demonstrates that the KC-RPMD method is well suited for the direct simulation of non-adiabatic donor–acceptor chemistries associated with many complex systems, including those for which solvent dynamics plays an important role in the reaction mechanism.

Dynamics and kinetics of the Si(1D) + H2/D2 reactions on a new global ab initio potential energy surface

2021 ◽  
Vol 23 (10) ◽  
pp. 6141-6153
Author(s):  
Jianwei Cao ◽  
Yanan Wu ◽  
Haitao Ma ◽  
Zhitao Shen ◽  
Wensheng Bian
Keyword(s):  
Molecular Dynamics ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Ab Initio ◽  
Quantum Dynamics ◽  
Energy Surface ◽  
Molecular Dynamics Calculations ◽  
Ring Polymer ◽  
Ring Polymer Molecular Dynamics ◽  
Kinetics Of

Quantum dynamics and ring polymer molecular dynamics calculations reveal interesting dynamical and kinetic behaviors of an endothermic complex-forming reaction.

scholarly journals Investigating Tunneling Controlled Chemical Reactions Through Ab-Initio Ring Polymer Molecular Dynamics

2021 ◽  
Author(s):  
Xinyang Li ◽  
Pengfei Huo
Keyword(s):  
Molecular Dynamics ◽  
Ab Initio ◽  
Chemical Reaction ◽  
Quantum Tunneling ◽  
Quantum Dynamics ◽  
Density Functional ◽  
Molecular System ◽  
Ring Polymer ◽  
Ring Polymer Molecular Dynamics ◽  
Dynamics Simulations

<div>We use the ab-initio ring polymer molecular dynamics (RPMD) approach to investigate tunneling controlled reactions in methylhydroxycarbene. Nuclear tunneling effects enable molecules to overcome the barriers which can not be overcome classically. Under low-temperature conditions, intrinsic quantum tunneling effects canfacilitate the chemical reaction in a pathway that is neither favored thermodynamically nor kinetically. This</div><div>behavior is referred to as the tunneling controlled chemical reaction and regarded as the third paradigm of chemical</div><div>reaction controls. In this work, we use the ab-initio RPMD approach to incorporate the tunneling effects in our quantum dynamics simulations. The reaction kinetics of two competitive reaction pathways at various temperatures are investigated with the Kohn-Sham density functional theory (KS-DFT) on-the-fly molecular dynamics simulations and the ring polymer quantization of the nuclei. The reaction rate constants obtained here agree extremely well with the experimentally measured rates. We demonstrate the feasibility of using ab-initio RPMD rate calculations in a realistic molecular system, and provide an interesting and important example for future investigations on reaction mechanisms dominated by quantum tunneling effects.</div>

scholarly journals Communication: Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics

2015 ◽  
Vol 142 (19) ◽  
pp. 191101 ◽  
Author(s):  
Timothy J. H. Hele ◽  
Michael J. Willatt ◽  
Andrea Muolo ◽  
Stuart C. Althorpe
Keyword(s):  
Molecular Dynamics ◽  
Quantum Dynamics ◽  
Exact Quantum ◽  
Ring Polymer ◽  
Ring Polymer Molecular Dynamics
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