Quantum simulations

2017 ◽  
Author(s):  
Michael P. Allen ◽  
Dominic J. Tildesley
Keyword(s):  
Ab Initio ◽  
Quantum Monte Carlo ◽  
Degrees Of Freedom ◽  
Small Region ◽  
Time Correlation ◽  
Ab Initio Molecular Dynamics ◽  
Classical Dynamics ◽  
Integral Methods ◽  
Quantum Time ◽  
Low Mass

This chapter covers the introduction of quantum mechanics into computer simulation methods. The chapter begins by explaining how electronic degrees of freedom may be handled in an ab initio fashion and how the resulting forces are included in the classical dynamics of the nuclei. The technique for combining the ab initio molecular dynamics of a small region, with classical dynamics or molecular mechanics applied to the surrounding environment, is explained. There is a section on handling quantum degrees of freedom, such as low-mass nuclei, by discretized path integral methods, complete with practical code examples. The problem of calculating quantum time correlation functions is addressed. Ground-state quantum Monte Carlo methods are explained, and the chapter concludes with a forward look to the future development of such techniques particularly to systems that include excited electronic states.

scholarly journals Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo

2015 ◽  
Vol 142 (14) ◽  
pp. 144111 ◽  
Author(s):  
Andrea Zen ◽  
Ye Luo ◽  
Guglielmo Mazzola ◽  
Leonardo Guidoni ◽  
Sandro Sorella
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Molecular Dynamics Simulation ◽  
Ab Initio ◽  
Liquid Water ◽  
Quantum Monte Carlo ◽  
Dynamics Simulation ◽  
Ab Initio Molecular Dynamics

scholarly journals Optical Spectra in the Condensed Phase: Capturing Anharmonic and Vibronic Features Using Dynamic and Static Approaches

2019 ◽  
Author(s):  
Tim Zuehlsdorff ◽  
Andres Montoya-Castillo ◽  
Joseph Anthony Napoli ◽  
Thomas E. Markland ◽  
Christine Isborn
Keyword(s):  
Condensed Phase ◽  
Potential Energy Surfaces ◽  
Energy Gap ◽  
Time Correlation ◽  
Optical Spectra ◽  
Ab Initio Molecular Dynamics ◽  
Classical Dynamics ◽  
Dynamics Simulations ◽  
Energy Surfaces ◽  
Franck Condon

<p>Simulating optical spectra in the condensed phase remains a challenge for theory due to the need to capture spectral signatures arising from anharmonicity and dynamical effects, such as vibronic progressions and their induced asymmetry. As such, numerous simulation methods have been developed that invoke different approximations and vary in their ability to capture different physical regimes. Here we use several models of chromophores in the condensed phase and ab initio molecular dynamics simulations to rigorously assess the applicability of methods to simulate optical absorption spectra. Specifically, we focus on the ensemble scheme, which can address anharmonic potential energy surfaces but relies on the applicability of extreme nuclear-electronic timescale separation; the Franck-Condon method, which includes dynamical effects but only at the harmonic level; as well as the recently introduced ensemble zero-temperature Franck-Condon approach, which straddles these limits. We also devote particular attention to the performance of methods derived from a cumulant expansion of the energy gap fluctuations and test the ability to approximate the requisite time correlation functions using classical dynamics with quantum correction factors. These results provide insights as to when these methods are applicable and able to capture the features of condensed phase spectra qualitatively and, in some cases, quantitatively across a range of regimes.<br></p>

scholarly journals Deriving the exact nonadiabatic quantum propagator in the mapping variable representation

2016 ◽  
Vol 195 ◽  
pp. 269-289 ◽  
Author(s):  
Timothy J. H. Hele ◽  
Nandini Ananth
Keyword(s):  
Degrees Of Freedom ◽  
Reaction Rates ◽  
Time Correlation ◽  
Electron Transfer Reaction ◽  
Classical Dynamics ◽  
Nonadiabatic Dynamics ◽  
Path Integral Representation ◽  
Quantum Propagator ◽  
Large Systems ◽  
Variable Representation

We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and discrete electronic states. The resulting Liouvillian is a Moyal series that, when suitably approximated, can allow for the use of classical dynamics to efficiently model large systems. We demonstrate that different truncations of the exact Liouvillian lead to existing approximate semiclassical and mixed quantum–classical methods and we derive an associated error term for each method. Furthermore, by combining the imaginary-time path-integral representation of the Boltzmann operator with the exact Liouvillian, we obtain an analytic expression for thermal quantum real-time correlation functions. These results provide a rigorous theoretical foundation for the development of accurate and efficient classical-like dynamics to compute observables such as electron transfer reaction rates in complex quantized systems.

scholarly journals Boltzmann-conserving classical dynamics in quantum time-correlation functions: “Matsubara dynamics”

2015 ◽  
Vol 142 (13) ◽  
pp. 134103 ◽  
Author(s):  
Timothy J. H. Hele ◽  
Michael J. Willatt ◽  
Andrea Muolo ◽  
Stuart C. Althorpe
Keyword(s):  
Correlation Functions ◽  
Time Correlation ◽  
Time Correlation Functions ◽  
Classical Dynamics ◽  
Quantum Time

scholarly journals Optical Spectra in the Condensed Phase: Capturing Anharmonic and Vibronic Features Using Dynamic and Static Approaches

2019 ◽  
Author(s):  
Tim Zuehlsdorff ◽  
Andres Montoya-Castillo ◽  
Joseph Anthony Napoli ◽  
Thomas E. Markland ◽  
Christine Isborn
Keyword(s):  
Condensed Phase ◽  
Potential Energy Surfaces ◽  
Energy Gap ◽  
Time Correlation ◽  
Optical Spectra ◽  
Ab Initio Molecular Dynamics ◽  
Classical Dynamics ◽  
Dynamics Simulations ◽  
Energy Surfaces ◽  
Franck Condon

<p>Simulating optical spectra in the condensed phase remains a challenge for theory due to the need to capture spectral signatures arising from anharmonicity and dynamical effects, such as vibronic progressions and their induced asymmetry. As such, numerous simulation methods have been developed that invoke different approximations and vary in their ability to capture different physical regimes. Here we use several models of chromophores in the condensed phase and ab initio molecular dynamics simulations to rigorously assess the applicability of methods to simulate optical absorption spectra. Specifically, we focus on the ensemble scheme, which can address anharmonic potential energy surfaces but relies on the applicability of extreme nuclear-electronic timescale separation; the Franck-Condon method, which includes dynamical effects but only at the harmonic level; as well as the recently introduced ensemble zero-temperature Franck-Condon approach, which straddles these limits. We also devote particular attention to the performance of methods derived from a cumulant expansion of the energy gap fluctuations and test the ability to approximate the requisite time correlation functions using classical dynamics with quantum correction factors. These results provide insights as to when these methods are applicable and able to capture the features of condensed phase spectra qualitatively and, in some cases, quantitatively across a range of regimes.<br></p>

Combustion Driven by Fragment-based Ab Initio Molecular Dynamics Simulation

2019 ◽  
Author(s):  
Liqun Cao ◽  
Jinzhe Zeng ◽  
Mingyuan Xu ◽  
Chih-Hao Chin ◽  
Tong Zhu ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Ab Initio ◽  
Large Scale ◽  
Methane Combustion ◽  
Combustion Method ◽  
Dynamics Simulation ◽  
Ab Initio Molecular Dynamics ◽  
Computational Time ◽  
Combustion Mechanism ◽  
Daily Lives

Combustion is a kind of important reaction that affects people's daily lives and the development of aerospace. Exploring the reaction mechanism contributes to the understanding of combustion and the more efficient use of fuels. Ab initio quantum mechanical (QM) calculation is precise but limited by its computational time for large-scale systems. In order to carry out reactive molecular dynamics (MD) simulation for combustion accurately and quickly, we develop the MFCC-combustion method in this study, which calculates the interaction between atoms using QM method at the level of MN15/6-31G(d). Each molecule in systems is treated as a fragment, and when the distance between any two atoms in different molecules is greater than 3.5 Å, a new fragment involved two molecules is produced in order to consider the two-body interaction. The deviations of MFCC-combustion from full system calculations are within a few kcal/mol, and the result clearly shows that the calculated energies of the different systems using MFCC-combustion are close to converging after the distance thresholds are larger than 3.5 Å for the two-body QM interactions. The methane combustion was studied with the MFCC-combustion method to explore the combustion mechanism of the methane-oxygen system.

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