Hermes Matthew R, Hirata So
Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA.
J Chem Phys. 2014 Dec 28;141(24):244111. doi: 10.1063/1.4904220.
A stochastic algorithm based on Metropolis Monte Carlo (MC) is presented for the size-extensive vibrational self-consistent field methods (XVSCF(n) and XVSCF[n]) for anharmonic molecular vibrations. The new MC-XVSCF methods substitute stochastic evaluations of a small number of high-dimensional integrals of functions of the potential energy surface (PES), which is sampled on demand, for diagrammatic equations involving high-order anharmonic force constants. This algorithm obviates the need to evaluate and store any high-dimensional partial derivatives of the potential and can be applied to the fully anharmonic PES without any Taylor-series approximation in an intrinsically parallelizable algorithm. The MC-XVSCF methods reproduce deterministic XVSCF calculations on the same Taylor-series PES in all energies, frequencies, and geometries. Calculations using the fully anharmonic PES evaluated on the fly with electronic structure methods report anharmonic effects on frequencies and geometries of much greater magnitude than deterministic XVSCF calculations, reflecting an underestimation of anharmonic effects in a Taylor-series approximation to the PES.
本文提出了一种基于 metropolis 蒙特卡罗（MC）的随机算法，用于处理非谐分子振动的尺寸扩展振动自洽场方法（XVSCF(n) 和 XVSCF[n]）。新的 MC-XVSCF 方法用少量势能面（PES）函数的高维积分的随机评估来替代涉及高阶非谐力常数的图解方程，该积分是按需采样的。此算法无需评估和存储势能的任何高维偏导数，并且可以在本质上可并行化的算法中应用于完全非谐的 PES，而无需任何泰勒级数近似。MC-XVSCF 方法在所有能量、频率和几何结构上，在相同的泰勒级数 PES 上重现确定性的 XVSCF 计算。使用电子结构方法即时评估的完全非谐 PES 进行的计算表明，与确定性 XVSCF 计算相比，非谐效应在频率和几何结构上的影响要大得多，这反映出在 PES 的泰勒级数近似中对非谐效应的低估。
