Accurate determination of normal stress differences via transient-time correlation function – non-equilibrium molecular dynamics (TTCF–NEMD) simulations

2009 ◽  
Vol 35 (5) ◽  
pp. 405-408 ◽  
Author(s):  
Caroline Desgranges ◽  
Jerome Delhommelle
Keyword(s):  
Molecular Dynamics ◽  
Correlation Function ◽  
Normal Stress ◽  
Accurate Determination ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Transient Time ◽  
Normal Stress Differences ◽  
Non Equilibrium Molecular Dynamics

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 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.

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