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 first 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-fly updates of the kernel, this formulation provides an efficient and general framework for quantum based Born-Oppenheimer molecular dynamics simulations.

18 pages, 10 figures

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Cited by in corpus (9)

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• Progress and Challenges in Ab Initio Simulations of Quantum Nuclei in Weakly Bonded Systems
• Adiabatic motion and statistical mechanics via mass zero constrained dynamics
• Shadow Energy Functionals and Potentials in Born-Oppenheimer Molecular Dynamics
• Shadow molecular dynamics and atomic cluster expansions for flexible charge models
• Graph-based Quantum Response Theory and Shadow Born-Oppenheimer Molecular Dynamics
• Mass-Zero constrained dynamics and statistics for the shell model in magnetic field
• Positivity Preserving Density Matrix Minimization at Finite Temperatures via Square Root
• Extended Lagrangian molecular dynamics on vibronic surfaces in the nuclear-electronic orbital framework