Lee Victor G M, Madison Lindsey R, McCoy Anne B
Department of Chemistry , University of Washington , Seattle , Washington 98195 , United States.
Department of Chemistry , Colby College , Waterville , Maine 04901 , United States.
J Phys Chem A. 2019 May 23;123(20):4370-4378. doi: 10.1021/acs.jpca.8b11213. Epub 2019 May 15.
Approaches for using diffusion Monte Carlo (DMC) to evaluate matrix elements involving two vibrational wave functions are explored. In the first part of this study, overlaps between a wave function obtained using DMC and one that can be calculated analytically are evaluated. In this case, the analytical wave function is used as the guiding function for an importance sampled DMC simulation. The accuracy of the calculated overlaps is found to depend strongly on the accuracy of the calculated descendant weights, which are obtained in the DMC simulation. While a single evaluation of the descendant weights is sufficient for obtaining projected probability amplitudes or expectation values of multiplicative operators, averages of multiple independent evaluations of the descendant weights are required to obtain accurate matrix elements. This approach is investigated for one-dimensional model systems as well as HCO, HD, and DH. The approach is extended to the evaluation of matrix elements of the dipole moment operator between the ground state and states with one quantum of excitation in one of the OH stretching vibrations in HO. For these calculations, the wave functions for both the ground and excited states are evaluated using DMC. The described methodology opens the possibility of evaluating matrix elements involving two different states, both of which are obtained using DMC.
探索了使用扩散蒙特卡罗（DMC）来评估涉及两个振动波函数的矩阵元的方法。在本研究的第一部分，评估了使用DMC获得的波函数与可以解析计算的波函数之间的重叠。在这种情况下，解析波函数用作重要性抽样DMC模拟的引导函数。发现计算重叠的准确性强烈依赖于在DMC模拟中获得的计算后代权重的准确性。虽然对后代权重进行单次评估足以获得投影概率振幅或乘法算符的期望值，但需要对后代权重进行多次独立评估的平均值才能获得准确的矩阵元。针对一维模型系统以及HCO、HD和DH对该方法进行了研究。该方法扩展到评估基态与HO中一个OH伸缩振动有一个量子激发的态之间的偶极矩算符的矩阵元。对于这些计算，基态和激发态的波函数均使用DMC进行评估。所描述的方法为评估涉及两个不同状态的矩阵元开辟了可能性，这两个状态均使用DMC获得。
