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 Aug 28;141(8):084105. doi: 10.1063/1.4892614.
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm(-1) and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
开发了一种用于非谐振动零点能和跃迁频率的新量子蒙特卡罗（QMC）方法，该方法将基于戴森方程的图解振动多体微扰理论与蒙特卡罗积分相结合。能量和自能的图解且因此尺寸一致的一阶和二阶非谐修正的无穷和被表示为波函数和势能面（PES）的几个m维或2m维积分的和（m是振动自由度）。这些积分中的每一个都通过将被积函数（包括PES的值）除以在通过 metropolis 算法根据权重函数随机分布但按需在几何构型上评估的明智选择的权重函数的值来计算。通过这种方式，该方法完全避免了在振动微扰理论的原始公式中对高阶力常数进行繁琐的评估和存储；此外，它允许在可扩展、内存高效的算法中考虑甚至高达无穷阶的更高阶力常数。在离散频率下随机评估的对频率相关自能的图解贡献可以可靠地插值，从而获得戴森方程的自洽解。因此，该方法可以直接且随机地计算基频和泛频的跃迁频率以及它们作为极点强度的相对强度，而不会出现困扰一些QMC的固定节点误差。结果表明，对于相同的PES，新方法在几厘米（-1）内再现了能量和频率的正确确定性值，在千分之几内再现了极点强度。通过在随机几何构型上即时评估PES的值，新方法捕捉到了明显更大比例的非谐效应。
