Niklasson Anders M N
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA and Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden.
J Chem Phys. 2020 Mar 14;152(10):104103. doi: 10.1063/1.5143270.
It is shown how the electronic equations of motion in extended Lagrangian Born-Oppenheimer molecular dynamics simulations [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008); J. Chem. Phys. 147, 054103 (2017)] can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born-Oppenheimer molecular dynamics. The low-rank approximation of the Jacobian is directly related to Broyden's class of quasi-Newton algorithms and Jacobian-free Newton-Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.
展示了在扩展拉格朗日玻恩-奥本海默分子动力学模拟中[A. M. N. 尼克拉斯森，《物理评论快报》100, 123004 (2008); 《化学物理杂志》147, 054103 (2017)]，如何使用逆雅可比核的低秩近似来积分电子运动方程。该核决定了拉格朗日量的谐振子扩展中的度规张量，它驱动着电子自由度的演化。所提出的核近似是从雅可比矩阵的低秩估计的伪逆导出的，该伪逆用一组广义方向导数表示，其方向由克里洛夫子空间近似给出。该方法允许一种可调谐且自适应的近似，能够利用高效的预处理技术。所提出的用于积分电子运动方程的核近似使得将扩展拉格朗日第一性原理分子动力学模拟应用于更广泛的问题成为可能，包括具有数值敏感和不稳定电荷解的反应性化学系统。这可以在不需要在每个时间步精确完全计算逆雅可比核，也不需要像常规直接玻恩-奥本海默分子动力学那样在力评估之前依赖电子基态的迭代非线性自洽场优化的情况下实现。雅可比矩阵的低秩近似与布罗伊登类拟牛顿算法和无雅可比牛顿-克里洛夫子方法直接相关，并为非线性方程组的求解提供了一种补充形式。
