Next generation extended Lagrangian first principles molecular dynamics

Niklasson, Anders M.  N.

doi:10.1063/1.4985893

Title: Next generation extended Lagrangian first principles molecular dynamics

Abstract

Extended Lagrangian Born-Oppenheimer molecular dynamics [Phys. Rev. Lett., 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density functional theory and compared to the extended Lagrangian framework of rst principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended Lagrangian Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended Lagrangian Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended Lagrangian Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Materials systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born- Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground state optimization prior to themore »« less

Authors:

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: 2017-08-04

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1463545

Alternate Identifier(s):: OSTI ID: 1373986

Report Number(s):: LA-UR-17-23007
Journal ID: ISSN 0021-9606

Grant/Contract Number:: AC52-06NA25396; LANL2014E8AN

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 147; Journal Issue: 5; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 74 ATOMIC AND MOLECULAR PHYSICS; Mathematics; Molecular dynamics, electronic structure theory

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                    Niklasson, Anders M.  N. Next generation extended Lagrangian first principles molecular dynamics.  United States: N. p., 2017. 
Web.  doi:10.1063/1.4985893.

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                    Niklasson, Anders M.  N. Next generation extended Lagrangian first principles molecular dynamics.  United States.  https://doi.org/10.1063/1.4985893

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                    Niklasson, Anders M.  N. Fri .  
"Next generation extended Lagrangian first principles molecular dynamics".  United States.  https://doi.org/10.1063/1.4985893.  https://www.osti.gov/servlets/purl/1463545.

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@article{osti_1463545,

  title        = {Next generation extended Lagrangian first principles molecular dynamics},

  author       = {Niklasson, Anders M.  N.},

  abstractNote = {Extended Lagrangian Born-Oppenheimer molecular dynamics [Phys. Rev. Lett., 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density functional theory and compared to the extended Lagrangian framework of rst principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended Lagrangian Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended Lagrangian Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended Lagrangian Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Materials systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born- Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on-the- y updates of the kernel, this formulation provides an efficient and general framework for quantum based Born-Oppenheimer molecular dynamics simulations.},

  doi          = {10.1063/1.4985893},

  journal      = {Journal of Chemical Physics},

  number       = 5,

  volume       = 147,

  place        = {United States},

  year         = {2017},

  month        = {8}

}

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Extended Lagrangian Born–Oppenheimer molecular dynamics [ Phys. Rev. Lett. 2008, 100, 123004] is presented for Hartree–Fock theory, where the extended electronic degrees of freedom are represented by a density matrix, including fractional occupation numbers at elevated electronic temperatures. In contrast to regular direct Born–Oppenheimer molecular dynamics simulations, no iterative self-consistent field optimization is required prior to the force evaluations. To sample regions of the potential energy landscape where the gap is small or vanishing, which leads to particular convergence problems in regular direct Born–Oppenheimer molecular dynamics simulations, an adaptive integration scheme for the extended electronic degrees of freedom is presented.more »« less
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Title: Next generation extended Lagrangian first principles molecular dynamics

Abstract

Citation Formats

Energy conserving, linear scaling Born-Oppenheimer molecular dynamics journal, October 2012

Curvy-steps approach to constraint-free extended-Lagrangian ab initio molecular dynamics, using atom-centered basis functions: Convergence toward Born–Oppenheimer trajectories journal, December 2004

Graph-based linear scaling electronic structure theory journal, June 2016

Linear-scaling density-functional theory with tens of thousands of atoms: Expanding the scope and scale of calculations with ONETEP journal, July 2009

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Hybrid Extended Lagrangian, Post-Hartree–Fock Born–Oppenheimer ab Initio Molecular Dynamics Using Fragment-Based Electronic Structure journal, May 2016

Parallel sparse matrix multiplication for linear scaling electronic structure calculations journal, June 2001

Understanding Modern Molecular Dynamics: Techniques and Applications journal, January 2000

Fock matrix dynamics journal, March 2004

Modified Broyden’s method for accelerating convergence in self-consistent calculations journal, December 1988

Efficient iteration scheme for self-consistent pseudopotential calculations journal, March 1981

Dyanmics of organic reactions journal, November 1973

Generalized extended Lagrangian Born-Oppenheimer molecular dynamics journal, October 2014

Extended Lagrangian Born-Oppenheimer molecular dynamics in the limit of vanishing self-consistent field optimization journal, December 2013

Geometric integration in Born-Oppenheimer molecular dynamics journal, December 2011

Synchronization of chaotic systems journal, September 2015

Electronic structure calculations on workstation computers: The program system turbomole journal, October 1989

Stable and Efficient Linear Scaling First-Principles Molecular Dynamics for 10000+ Atoms journal, November 2014

Large-Scale Electronic-Structure Calculations Based on the Adaptive Finite-Element Method journal, November 1998

Classical trajectories using the full a b i n i t i o potential energy surface H − +CH 4 →CH 4 +H − journal, May 1978

Accurate Classical Polarization Solution with No Self-Consistent Field Iterations journal, April 2017

HONPAS: A linear scaling open-source solution for large system simulations journal, December 2014

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

Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics journal, April 2015

Analysis of Time Reversible Born-Oppenheimer Molecular Dynamics journal, December 2013

Thermal Properties of the Inhomogeneous Electron Gas journal, March 1965

Born-Oppenheimer molecular-dynamics simulations of finite systems: Structure and dynamics of ( H 2 O ) 2 journal, July 1993

Spin eigenstate-dependent Hartree—Fock molecular dynamics journal, February 1992

Molecular dynamics without effective potentials via the Car-Parrinello approach journal, August 1990

Tight-binding models and density-functional theory journal, June 1989

Extended Lagrangian Born–Oppenheimer molecular dynamics with dissipation journal, June 2009

Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem journal, December 1979

Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix journal, March 1950

Lagrangian formulation with dissipation of Born-Oppenheimer molecular dynamics using the density-functional tight-binding method journal, July 2011

PARSEC – the pseudopotential algorithm for real-space electronic structure calculations: recent advances and novel applications to nano-structures journal, April 2006

Ab initio molecular simulations with numeric atom-centered orbitals journal, November 2009

High performance computing in biology: Multimillion atom simulations of nanoscale systems journal, March 2007

Computer Simulation of Molecular Dynamics: Methodology, Applications, and Perspectives in Chemistry journal, September 1990

Linear Scaling Self-Consistent Field Calculations with Millions of Atoms in the Condensed Phase journal, March 2012

Periodic Pulay method for robust and efficient convergence acceleration of self-consistent field iterations journal, March 2016

Wave function extended Lagrangian Born-Oppenheimer molecular dynamics journal, August 2010

An extended-Lagrangian scheme for charge equilibration in reactive molecular dynamics simulations journal, July 2015

Electronic structure optimization in plane-wave-based density functional calculations by direct inversion in the iterative subspace journal, March 1994

Structural and dynamical properties of hot dense matter by a Thomas-Fermi-Dirac molecular dynamics journal, September 2006

Fractional occupations and density-functional energies and forces journal, June 1992

Daubechies wavelets as a basis set for density functional pseudopotential calculations journal, July 2008

Density functionals for coulomb systems journal, September 1983

The accuracy of symplectic integrators journal, March 1992

The Role and Perspective of Ab Initio Molecular Dynamics in the Study of Biological Systems journal, June 2002

Analytic hyperpolarizability and polarizability derivative with fractional occupation numbers for large extended systems journal, February 2017

Molecular dynamics simulations in biology journal, October 1990

A theoretical view of protein dynamics journal, January 2014

The Dalton quantum chemistry program system: The Dalton program journal, September 2013

\mathcal{O}(N) methods in electronic structure calculations journal, February 2012

Car-Parrinello molecular dynamics: Car-Parrinello molecular dynamics journal, September 2011

Accurate and Scalable O ( N ) Algorithm for First-Principles Molecular-Dynamics Computations on Large Parallel Computers journal, January 2014

QM/MM Methods for Biomolecular Systems journal, January 2009

Synchronization in chaotic systems journal, February 1990

Symplectic integration of Hamiltonian systems journal, May 1990

Higher-order response in O(N) by perturbed projection journal, July 2005

A note on the Pulay force at finite electronic temperatures journal, December 2008

Energy versus free-energy conservation in first-principles molecular dynamics journal, May 1992

On the theory underlying the Car-Parrinello method and the role of the fictitious mass parameter journal, January 2006

First-principles molecular dynamics of metallic systems journal, November 1999

An efficient and stable hybrid extended Lagrangian/self-consistent field scheme for solving classical mutual induction journal, November 2015

Theory of ab initio molecular-dynamics calculations journal, November 1991

A unified formulation of the constant temperature molecular dynamics methods journal, July 1984

Efficient projector expansion for the ab initio LCAO method journal, July 2005

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory journal, March 2017

Accelerated, energy-conserving Born–Oppenheimer molecular dynamics via Fock matrix extrapolation journal, January 2005

Molecular dynamics simulations at constant pressure and/or temperature journal, February 1980

Monitoring energy drift with shadow Hamiltonians journal, July 2005

Ab initio molecular dynamics: basic concepts, current trends and novel applications journal, December 2002

Convergence acceleration of iterative sequences. the case of scf iteration journal, July 1980

Kohn−Sham Density Functional Theory Electronic Structure Calculations with Linearly Scaling Computational Time and Memory Usage journal, December 2010

Direct energy functional minimization under orthogonality constraints journal, February 2008

General atomic and molecular electronic structure system journal, November 1993

Energy conserving, linear scaling Born-Oppenheimer molecular dynamics
journal, October 2012

Curvy-steps approach to constraint-free extended-Lagrangian ab initio molecular dynamics, using atom-centered basis functions: Convergence toward Born–Oppenheimer trajectories
journal, December 2004

Graph-based linear scaling electronic structure theory
journal, June 2016

Linear-scaling density-functional theory with tens of thousands of atoms: Expanding the scope and scale of calculations with ONETEP
journal, July 2009

Ab initio molecular dynamics: Propagating the density matrix with Gaussian orbitals
journal, June 2001

Hybrid Extended Lagrangian, Post-Hartree–Fock Born–Oppenheimer ab Initio Molecular Dynamics Using Fragment-Based Electronic Structure
journal, May 2016

Parallel sparse matrix multiplication for linear scaling electronic structure calculations
journal, June 2001

Understanding Modern Molecular Dynamics: Techniques and Applications
journal, January 2000

Fock matrix dynamics
journal, March 2004

Modified Broyden’s method for accelerating convergence in self-consistent calculations
journal, December 1988

Efficient iteration scheme for self-consistent pseudopotential calculations
journal, March 1981

Dyanmics of organic reactions
journal, November 1973

Generalized extended Lagrangian Born-Oppenheimer molecular dynamics
journal, October 2014

Extended Lagrangian Born-Oppenheimer molecular dynamics in the limit of vanishing self-consistent field optimization
journal, December 2013

Geometric integration in Born-Oppenheimer molecular dynamics
journal, December 2011

Synchronization of chaotic systems
journal, September 2015

Electronic structure calculations on workstation computers: The program system turbomole
journal, October 1989

Stable and Efficient Linear Scaling First-Principles Molecular Dynamics for 10000+ Atoms
journal, November 2014

Large-Scale Electronic-Structure Calculations Based on the Adaptive Finite-Element Method
journal, November 1998

Classical trajectories using the full a b i n i t i o potential energy surface H ⁻ +CH ₄ →CH ₄ +H ⁻
journal, May 1978

Accurate Classical Polarization Solution with No Self-Consistent Field Iterations
journal, April 2017

HONPAS: A linear scaling open-source solution for large system simulations
journal, December 2014

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

Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics
journal, April 2015

Analysis of Time Reversible Born-Oppenheimer Molecular Dynamics
journal, December 2013

Thermal Properties of the Inhomogeneous Electron Gas
journal, March 1965

Born-Oppenheimer molecular-dynamics simulations of finite systems: Structure and dynamics of ( $H_{2}$ O $)_{2}$
journal, July 1993

Spin eigenstate-dependent Hartree—Fock molecular dynamics
journal, February 1992

Molecular dynamics without effective potentials via the Car-Parrinello approach
journal, August 1990

Tight-binding models and density-functional theory
journal, June 1989

Extended Lagrangian Born–Oppenheimer molecular dynamics with dissipation
journal, June 2009

Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem
journal, December 1979

Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix
journal, March 1950

Lagrangian formulation with dissipation of Born-Oppenheimer molecular dynamics using the density-functional tight-binding method
journal, July 2011

PARSEC – the pseudopotential algorithm for real-space electronic structure calculations: recent advances and novel applications to nano-structures
journal, April 2006

Ab initio molecular simulations with numeric atom-centered orbitals
journal, November 2009

High performance computing in biology: Multimillion atom simulations of nanoscale systems
journal, March 2007

Computer Simulation of Molecular Dynamics: Methodology, Applications, and Perspectives in Chemistry
journal, September 1990

Linear Scaling Self-Consistent Field Calculations with Millions of Atoms in the Condensed Phase
journal, March 2012

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journal, March 2016

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journal, August 2010

An extended-Lagrangian scheme for charge equilibration in reactive molecular dynamics simulations
journal, July 2015

Electronic structure optimization in plane-wave-based density functional calculations by direct inversion in the iterative subspace
journal, March 1994

Structural and dynamical properties of hot dense matter by a Thomas-Fermi-Dirac molecular dynamics
journal, September 2006

Fractional occupations and density-functional energies and forces
journal, June 1992

Daubechies wavelets as a basis set for density functional pseudopotential calculations
journal, July 2008

Density functionals for coulomb systems
journal, September 1983

The accuracy of symplectic integrators
journal, March 1992

The Role and Perspective of Ab Initio Molecular Dynamics in the Study of Biological Systems
journal, June 2002

Analytic hyperpolarizability and polarizability derivative with fractional occupation numbers for large extended systems
journal, February 2017

Molecular dynamics simulations in biology
journal, October 1990

A theoretical view of protein dynamics
journal, January 2014

The Dalton quantum chemistry program system: The Dalton program
journal, September 2013

\mathcal{O}(N) methods in electronic structure calculations
journal, February 2012

Car-Parrinello molecular dynamics: Car-Parrinello molecular dynamics
journal, September 2011

Accurate and Scalable $O (N)$ Algorithm for First-Principles Molecular-Dynamics Computations on Large Parallel Computers
journal, January 2014

QM/MM Methods for Biomolecular Systems
journal, January 2009

Synchronization in chaotic systems
journal, February 1990

Symplectic integration of Hamiltonian systems
journal, May 1990

Higher-order response in O(N) by perturbed projection
journal, July 2005

A note on the Pulay force at finite electronic temperatures
journal, December 2008

Energy versus free-energy conservation in first-principles molecular dynamics
journal, May 1992

On the theory underlying the Car-Parrinello method and the role of the fictitious mass parameter
journal, January 2006

First-principles molecular dynamics of metallic systems
journal, November 1999

An efficient and stable hybrid extended Lagrangian/self-consistent field scheme for solving classical mutual induction
journal, November 2015

Theory of ab initio molecular-dynamics calculations
journal, November 1991

A unified formulation of the constant temperature molecular dynamics methods
journal, July 1984

Efficient projector expansion for the ab initio LCAO method
journal, July 2005

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory
journal, March 2017

Accelerated, energy-conserving Born–Oppenheimer molecular dynamics via Fock matrix extrapolation
journal, January 2005

Molecular dynamics simulations at constant pressure and/or temperature
journal, February 1980

Monitoring energy drift with shadow Hamiltonians
journal, July 2005

Ab initio molecular dynamics: basic concepts, current trends and novel applications
journal, December 2002

Convergence acceleration of iterative sequences. the case of scf iteration
journal, July 1980

Kohn−Sham Density Functional Theory Electronic Structure Calculations with Linearly Scaling Computational Time and Memory Usage
journal, December 2010

Direct energy functional minimization under orthogonality constraints
journal, February 2008

General atomic and molecular electronic structure system
journal, November 1993

ImprovedSCF convergence acceleration
journal, January 1982

Linear scaling electronic structure methods
journal, July 1999

Canonical density matrix perturbation theory
journal, December 2015