Next generation extended Lagrangian first principles molecular dynamics

• Published in: The Journal of chemical physics 2017-08, Vol.147 (5), p.054103-054103
• Main Author: Niklasson, Anders M. N.
• Format: Article
• Language: English
• Subjects: ATOMIC AND MOLECULAR PHYSICS; Dynamic stability; Equations of motion; First principles; Formulations; Harmonic oscillators; Lagrangian function; Mathematical analysis; Mathematics; Molecular dynamics; Molecular dynamics, electronic structure theory; Potential energy; Simulation; Surface stability
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.4985893

Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density-functional theory and compared with 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. Material 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.