Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
J Chem Phys. 2017 Aug 7;147(5):054103. 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.
扩展拉格朗日 Born-Oppenheimer 分子动力学 [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] 是为一般 Hohenberg-Kohn 密度泛函理论制定的，并与第一性原理分子动力学的 Car 和 Parrinello 的扩展拉格朗日框架进行了比较 [Phys. Rev. Lett. 55, 2471 (1985)]。展示了扩展拉格朗日 Born-Oppenheimer 分子动力学如何克服了常规直接 Born-Oppenheimer 分子动力学的几个缺点，同时改进或保持了 Car-Parrinello 模拟的重要特征。扩展拉格朗日 Born-Oppenheimer 分子动力学中电子自由度的准确性，相对于精确的 Born-Oppenheimer 解，在积分时间步长的大小上是二阶的，在势能面上是四阶的。通过将理论推广到有限温度系综，使用分数占据数来计算扩展谐振子的内积核，该核作为电子运动方程中的预条件器，从而实现了对最近提出的扩展拉格朗日 Born-Oppenheimer 分子动力学的稳定性的改进。在直接 Born-Oppenheimer 分子动力学中，通常表现出缓慢的自洽场收敛的材料系统可以使用相同阶的积分时间步长进行模拟，但不需要在力评估之前进行迭代、非线性电子基态优化，也不需要总能量的系统漂移。与提出的低秩和实时内核更新相结合，该公式为基于量子的 Born-Oppenheimer 分子动力学模拟提供了一个高效、通用的框架。
