Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory

Marsalek, Ondrej; Markland, Thomas E.

doi:10.1063/1.4941093

Title: Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory

Abstract

Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the timemore »« less

Authors:

^[1]; Markland, Thomas E. ^[1]

Stanford Univ., Stanford, CA (United States)

Publication Date:: Fri Feb 05 00:00:00 EST 2016

Research Org.:: Univ. of California, Merced, CA (United States); Stanford Univ., CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division

OSTI Identifier:: 1469204

Alternate Identifier(s):: OSTI ID: 1236991; OSTI ID: 1526757

Grant/Contract Number:: SC0014437

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 144; Journal Issue: 5; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Path integral, quantum mechanics

Citation Formats


                    Marsalek, Ondrej, and Markland, Thomas E. Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory.  United States: N. p., 2016. 
Web.  doi:10.1063/1.4941093.

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                    Marsalek, Ondrej, & Markland, Thomas E. Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory.  United States.  https://doi.org/10.1063/1.4941093

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                    Marsalek, Ondrej, and Markland, Thomas E. Fri .  
"Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory".  United States.  https://doi.org/10.1063/1.4941093.  https://www.osti.gov/servlets/purl/1469204.

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@article{osti_1469204,

  title        = {Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory},

  author       = {Marsalek, Ondrej and Markland, Thomas E.},

  abstractNote = {Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost.},

  doi          = {10.1063/1.4941093},

  journal      = {Journal of Chemical Physics},

  number       = 5,

  volume       = 144,

  place        = {United States},

  year         = {Fri Feb 05 00:00:00 EST 2016},

  month        = {Fri Feb 05 00:00:00 EST 2016}

}

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The Journal of Chemical Physics, Vol. 148, Issue 10
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Accurate molecular dynamics and nuclear quantum effects at low cost by multiple steps in real and imaginary time: using density functional theory to accelerate wavefunction methods
text, January 2015

Kapil, Venkat; VandeVondele, Joost; Ceriotti, Michele
arXiv
DOI: 10.48550/arxiv.1512.00176

Structure and Dynamics of Water at the Water–Air Interface Using First-Principles Molecular Dynamics Simulations. II. NonLocal vs Empirical van der Waals Corrections
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Ryu, Won Hee; Han, Yining; Voth, Gregory A.
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Atomic shells according to ionization energies
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Napoli, Joseph A.; Marsalek, Ondrej; Markland, Thomas E.
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Proton transfer in guanine–cytosine base pair analogues studied by NMR spectroscopy and PIMD simulations
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Pohl, Radek; Socha, Ondřej; Slavíček, Petr
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DOI: 10.1039/c8fd00070k

Computational Methods for Ab Initio Molecular Dynamics
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Paquet, Eric; Viktor, Herna L.
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DOI: 10.1155/2018/9839641

Nuclear quantum effects enter the mainstream
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Nature Reviews Chemistry, Vol. 2, Issue 3
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Quantum Ring-Polymer Contraction Method: Including nuclear quantum effects at no additional computational cost in comparison to ab-initio molecular dynamics
text, January 2015

John, Chris; Spura, Thomas; Habershon, Scott
arXiv
DOI: 10.48550/arxiv.1512.08206

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Title: Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory

Abstract

Citation Formats

Generalized Gradient Approximation Made Simple journal, October 1996

Ab initio molecular dynamics study of water at constant pressure using converged basis sets and empirical dispersion corrections journal, July 2012

Calculation of heat capacities of light and heavy water by path-integral molecular dynamics journal, October 2005

Accurate molecular dynamics and nuclear quantum effects at low cost by multiple steps in real and imaginary time: using density functional theory to accelerate wavefunction methods text, January 2015

Quantum delocalization of protons in the hydrogen-bond network of an enzyme active site journal, December 2014

Quantum fluctuations and isotope effects in ab initio descriptions of water journal, September 2014

CP2K: Atomistic simulations of condensed matter systems text, January 2014

Density-functional tight-binding for beginners journal, November 2009

Quantum delocalization of protons in the hydrogen bond network of an enzyme active site text, January 2015

Quantum dynamical effects in liquid water: A semiclassical study on the diffusion and the infrared absorption spectrum journal, October 2009

Improving the convergence of closed and open path integral molecular dynamics via higher order Trotter factorization schemes journal, August 2011

Simulating Water with the Self-Consistent-Charge Density Functional Tight Binding Method: From Molecular Clusters to the Liquid State † journal, July 2007

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i-PI: A Python interface for ab initio path integral molecular dynamics simulations journal, March 2014

Everything You Wanted to Know About Data Analysis and Fitting but Were Afraid to Ask book, January 2015

Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach journal, April 2005

On the Quantum Nature of the Shared Proton in Hydrogen Bonds journal, February 1997

Probing the structural and dynamical properties of liquid water with models including non-local electron correlation text, January 2015

Ring-Polymer Molecular Dynamics: Quantum Effects in Chemical Dynamics from Classical Trajectories in an Extended Phase Space journal, April 2013

Efficient molecular dynamics and hybrid Monte Carlo algorithms for path integrals journal, August 1993

Theory and simulations of quantum glass forming liquids journal, February 2012

QUICKSTEP: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach text, January 2005

An efficient ring polymer contraction scheme for imaginary time path integral simulations journal, July 2008

A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu journal, April 2010

Ab initio path integral molecular dynamics: Basic ideas journal, March 1996

A fast path integral method for polarizable force fields journal, January 2009

Separable Dual Space Gaussian Pseudo-potentials text, January 1995

Efficient multiple time scale molecular dynamics: Using colored noise thermostats to stabilize resonances journal, January 2011

Self-consistent field theory based molecular dynamics with linear system-size scaling journal, April 2014

Efficient first-principles calculation of the quantum kinetic energy and momentum distribution of nuclei text, January 2014

Canonical sampling through velocity rescaling journal, January 2007

Ab initio path-integral molecular dynamics journal, June 1994

Nonergodicity in path integral molecular dynamics journal, October 1984

Quantum statistics and classical mechanics: Real time correlation functions from ring polymer molecular dynamics journal, August 2004

The formulation of quantum statistical mechanics based on the Feynman path centroid density. V. Quantum instantaneous normal mode theory of liquids journal, October 1994

Efficient and general algorithms for path integral Car–Parrinello molecular dynamics journal, April 1996

On path integral Monte Carlo simulations journal, May 1982

Probing the structural and dynamical properties of liquid water with models including non-local electron correlation journal, August 2015

Molecular Simulation of Water and Hydration Effects in Different Environments: Challenges and Developments for DFTB Based Models journal, September 2014

Efficient stochastic thermostatting of path integral molecular dynamics journal, September 2010

DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB) journal, March 2011

Competing quantum effects in the dynamics of a flexible water model text, January 2010

Ab initio molecular dynamics using hybrid density functionals journal, June 2008

How to remove the spurious resonances from ring polymer molecular dynamics journal, June 2014

The calculation of transport properties in quantum liquids using the maximum entropy numerical analytic continuation method: Application to liquid para-hydrogen journal, February 2002

A Self-Consistent Charge Density-Functional Based Tight-Binding Method for Predictive Materials Simulations in Physics, Chemistry and Biology journal, January 2000

How to remove the spurious resonances from ring polymer molecular dynamics text, January 2014

Ab initio molecular dynamics using hybrid density functionals text, January 2008

Study of an F center in molten KCl journal, January 1984

Efficient methods and practical guidelines for simulating isotope effects text, January 2012

cp2k: atomistic simulations of condensed matter systems journal, June 2013

Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface journal, February 2015

Efficient ab initio sampling methods in rate constant calculations for proton-transfer reactions journal, April 2001

Self-consistent field theory based molecular dynamics with linear system-size scaling text, January 2012

A comparative study of imaginary time path integral based methods for quantum dynamics journal, April 2006

Efficient mixed-force first-principles molecular dynamics journal, November 2003

Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids journal, April 1981

The Self-Consistent Charge Density Functional Tight Binding Method Applied to Liquid Water and the Hydrated Excess Proton: Benchmark Simulations journal, May 2010

i-PI: A Python interface for ab initio path integral molecular dynamics simulations text, January 2014

The inefficiency of re-weighted sampling and the curse of system size in high-order path integration journal, September 2011

Reversible multiple time scale molecular dynamics journal, August 1992

Quantum fluctuations can promote or inhibit glass formation text, January 2010

An efficient orbital transformation method for electronic structure calculations journal, March 2003

Accelerating the convergence of path integral dynamics with a generalized Langevin equation journal, February 2011

Efficient methods and practical guidelines for simulating isotope effects journal, January 2013

A hybrid Gaussian and plane wave density functional scheme journal, October 1997

An object-oriented scripting interface to a legacy electronic structure code journal, January 2002

Simulating Water with the Self-Consistent-Charge Density Functional Tight Binding Method: From Molecular Clusters to the Liquid State † text, January 2007

Multiple time step integrators in ab initio molecular dynamics journal, February 2014

Quantum mechanical correlation functions, maximum entropy analytic continuation, and ring polymer molecular dynamics journal, November 2007

Path Integral Coarse-Graining Replica Exchange Method for Enhanced Sampling journal, August 2014

Density‐functional thermochemistry. III. The role of exact exchange journal, April 1993

Efficient First-Principles Calculation of the Quantum Kinetic Energy and Momentum Distribution of Nuclei journal, September 2012

Ab initio phase diagram and nucleation of gallium journal, May 2020

Communication: Multiple-timestep ab initio molecular dynamics with electron correlation journal, July 2013

Error and timing analysis of multiple time-step integration methods for molecular dynamics journal, February 2007

Accurate molecular dynamics and nuclear quantum effects at low cost by multiple steps in real and imaginary time: Using density functional theory to accelerate wavefunction methods journal, February 2016

Generalized Gradient Approximation Made Simple
journal, October 1996

Ab initio molecular dynamics study of water at constant pressure using converged basis sets and empirical dispersion corrections
journal, July 2012

Calculation of heat capacities of light and heavy water by path-integral molecular dynamics
journal, October 2005

Accurate molecular dynamics and nuclear quantum effects at low cost by multiple steps in real and imaginary time: using density functional theory to accelerate wavefunction methods
text, January 2015

Quantum delocalization of protons in the hydrogen-bond network of an enzyme active site
journal, December 2014

Quantum fluctuations and isotope effects in ab initio descriptions of water
journal, September 2014

CP2K: Atomistic simulations of condensed matter systems
text, January 2014

Density-functional tight-binding for beginners
journal, November 2009

Quantum delocalization of protons in the hydrogen bond network of an enzyme active site
text, January 2015

Quantum dynamical effects in liquid water: A semiclassical study on the diffusion and the infrared absorption spectrum
journal, October 2009

Improving the convergence of closed and open path integral molecular dynamics via higher order Trotter factorization schemes
journal, August 2011

Simulating Water with the Self-Consistent-Charge Density Functional Tight Binding Method: From Molecular Clusters to the Liquid State ^†
journal, July 2007

Multiple-Time Step Ab Initio Molecular Dynamics Based on Two-Electron Integral Screening
journal, February 2015

i-PI: A Python interface for ab initio path integral molecular dynamics simulations
journal, March 2014

Everything You Wanted to Know About Data Analysis and Fitting but Were Afraid to Ask
book, January 2015

Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach
journal, April 2005

On the Quantum Nature of the Shared Proton in Hydrogen Bonds
journal, February 1997

Probing the structural and dynamical properties of liquid water with models including non-local electron correlation
text, January 2015

Ring-Polymer Molecular Dynamics: Quantum Effects in Chemical Dynamics from Classical Trajectories in an Extended Phase Space
journal, April 2013

Efficient molecular dynamics and hybrid Monte Carlo algorithms for path integrals
journal, August 1993

Theory and simulations of quantum glass forming liquids
journal, February 2012

QUICKSTEP: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach
text, January 2005

An efficient ring polymer contraction scheme for imaginary time path integral simulations
journal, July 2008

A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
journal, April 2010

Ab initio path integral molecular dynamics: Basic ideas
journal, March 1996

A fast path integral method for polarizable force fields
journal, January 2009

Separable Dual Space Gaussian Pseudo-potentials
text, January 1995

Efficient multiple time scale molecular dynamics: Using colored noise thermostats to stabilize resonances
journal, January 2011

Self-consistent field theory based molecular dynamics with linear system-size scaling
journal, April 2014

Efficient first-principles calculation of the quantum kinetic energy and momentum distribution of nuclei
text, January 2014

Canonical sampling through velocity rescaling
journal, January 2007

Ab initio path-integral molecular dynamics
journal, June 1994

Nonergodicity in path integral molecular dynamics
journal, October 1984

Quantum statistics and classical mechanics: Real time correlation functions from ring polymer molecular dynamics
journal, August 2004

The formulation of quantum statistical mechanics based on the Feynman path centroid density. V. Quantum instantaneous normal mode theory of liquids
journal, October 1994

Efficient and general algorithms for path integral Car–Parrinello molecular dynamics
journal, April 1996

On path integral Monte Carlo simulations
journal, May 1982

Probing the structural and dynamical properties of liquid water with models including non-local electron correlation
journal, August 2015

Molecular Simulation of Water and Hydration Effects in Different Environments: Challenges and Developments for DFTB Based Models
journal, September 2014

Efficient stochastic thermostatting of path integral molecular dynamics
journal, September 2010

DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB)
journal, March 2011

Competing quantum effects in the dynamics of a flexible water model
text, January 2010

Ab initio molecular dynamics using hybrid density functionals
journal, June 2008

How to remove the spurious resonances from ring polymer molecular dynamics
journal, June 2014

The calculation of transport properties in quantum liquids using the maximum entropy numerical analytic continuation method: Application to liquid para-hydrogen
journal, February 2002

A Self-Consistent Charge Density-Functional Based Tight-Binding Method for Predictive Materials Simulations in Physics, Chemistry and Biology
journal, January 2000

How to remove the spurious resonances from ring polymer molecular dynamics
text, January 2014

Ab initio molecular dynamics using hybrid density functionals
text, January 2008

Study of an F center in molten KCl
journal, January 1984

Efficient methods and practical guidelines for simulating isotope effects
text, January 2012

cp2k: atomistic simulations of condensed matter systems
journal, June 2013

Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface
journal, February 2015

Efficient ab initio sampling methods in rate constant calculations for proton-transfer reactions
journal, April 2001

Self-consistent field theory based molecular dynamics with linear system-size scaling
text, January 2012

A comparative study of imaginary time path integral based methods for quantum dynamics
journal, April 2006

Efficient mixed-force first-principles molecular dynamics
journal, November 2003

Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids
journal, April 1981

The Self-Consistent Charge Density Functional Tight Binding Method Applied to Liquid Water and the Hydrated Excess Proton: Benchmark Simulations
journal, May 2010

i-PI: A Python interface for ab initio path integral molecular dynamics simulations
text, January 2014

The inefficiency of re-weighted sampling and the curse of system size in high-order path integration
journal, September 2011

Reversible multiple time scale molecular dynamics
journal, August 1992

Quantum fluctuations can promote or inhibit glass formation
text, January 2010

An efficient orbital transformation method for electronic structure calculations
journal, March 2003

Accelerating the convergence of path integral dynamics with a generalized Langevin equation
journal, February 2011

Efficient methods and practical guidelines for simulating isotope effects
journal, January 2013

A hybrid Gaussian and plane wave density functional scheme
journal, October 1997

An object-oriented scripting interface to a legacy electronic structure code
journal, January 2002

Simulating Water with the Self-Consistent-Charge Density Functional Tight Binding Method: From Molecular Clusters to the Liquid State †
text, January 2007

Multiple time step integrators in ab initio molecular dynamics
journal, February 2014

Quantum mechanical correlation functions, maximum entropy analytic continuation, and ring polymer molecular dynamics
journal, November 2007

Path Integral Coarse-Graining Replica Exchange Method for Enhanced Sampling
journal, August 2014

Density‐functional thermochemistry. III. The role of exact exchange
journal, April 1993

Efficient First-Principles Calculation of the Quantum Kinetic Energy and Momentum Distribution of Nuclei
journal, September 2012

Ab initio phase diagram and nucleation of gallium
journal, May 2020

Communication: Multiple-timestep ab initio molecular dynamics with electron correlation
journal, July 2013

Error and timing analysis of multiple time-step integration methods for molecular dynamics
journal, February 2007

Accurate molecular dynamics and nuclear quantum effects at low cost by multiple steps in real and imaginary time: Using density functional theory to accelerate wavefunction methods
journal, February 2016

Unraveling quantum mechanical effects in water using isotopic fractionation
journal, May 2012

Competing quantum effects in the dynamics of a flexible water model
journal, July 2009

Quantum fluctuations can promote or inhibit glass formation
journal, January 2011