arXiv 2302.067032023-02-13physics.chem-ph

玻恩-奥本海默分子动力学中的阴影能量泛函与势

Shadow Energy Functionals and Potentials in Born-Oppenheimer Molecular Dynamics

Anders M. N. Niklasson, Christian F. A. Negre

备注：: 16 pages, 3 figures
DOI：: 10.1063/5.0146431

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AI总结：

针对BOMD模拟中自洽场不完全收敛导致的能量漂移与不稳定问题，提出基于向后误差分析的阴影BOMD方法，构建可系统改进的阴影能量泛函与势，实现长期能量稳定的准确模拟，且理论通用性强。

摘要：

在基于密度泛函理论（DFT）的玻恩-奥本海默分子动力学（BOMD）模拟中，势能和原子间作用力由电子基态密度计算得到，而该密度通过迭代自洽场优化程序确定，实际操作中该程序永远无法完全收敛。因此计算得到的能量和作用力只是近似值，可能导致非物理的能量漂移和不稳定性。本文讨论了一种基于向后误差分析的替代阴影BOMD方法。我们并非为底层的精确常规BO势计算近似解，而是反其道而行之：计算精确的电子密度、能量和作用力，但对应于一个底层的近似阴影BO势。通过这种方式，计算得到的作用力相对于阴影势是保守的，能够生成具有长期能量稳定性的准确分子轨迹。我们展示了如何根据积分时间步长dt，通过最小化一系列可系统改进的近似阴影能量密度泛函，构建不同精度水平的此类阴影BO势。每个泛函都对应一个基态BO势。这些阴影能量泛函与势的配对，是扩展拉格朗日BOMD中使用的原始“0级”阴影能量泛函与势的更高阶推广[《欧洲物理杂志B》第94卷，第164页（2021年）]。所提出的阴影能量泛函和势仅在该动力学框架内有用，该框架中电子自由度也会与原子位置和速度一同传播。该理论具有通用性，可应用于使用近似DFT、Hartree-Fock或半经验方法的分子动力学模拟，以及粗粒化柔性电荷模型。

英文摘要：

In Born-Oppenheimer molecular dynamics (BOMD) simulations based on density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which in practice never is fully converged. The calculated energies and the forces are therefore only approximate, which may lead to an unphysical energy drift and instabilities. Here we discuss an alternative shadow BOMD approach that is based on a backward error analysis. Instead of calculating approximate solutions for an underlying exact regular BO potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow BO potential. In this way the calculated forces are conservative with respect to the shadow potential and generate accurate molecular trajectories with long-term energy stability. We show how such shadow BO potentials can be constructed at different levels of accuracy as a function of the integration time step, dt, from the minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each functional there is a corresponding ground state BO potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original "0th-level" shadow energy functionals and potentials used in extended Lagrangian BOMD [Eur. Phys. J. B vol. 94, 164 (2021)]. The proposed shadow energy functionals and potentials are useful only within this dynamical framework, where also the electronic degrees of freedom are propagated together with the atomic positions and velocities. The theory is general and can be applied to MD simulations using approximate DFT, Hartree-Fock or semi-empirical methods, as well as to coarse-grained flexible charge models.

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