Hosseini Seyed Mohammadreza, Alavi Ali, López Ríos Pablo
Max-Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany.
Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
J Chem Phys. 2024 May 21;160(19). doi: 10.1063/5.0206478.
We explore the application of an extrapolative method that yields very accurate total and relative energies from variational and diffusion quantum Monte Carlo (VMC and DMC) results. For a trial wave function consisting of a small configuration interaction (CI) wave function obtained from full CI quantum Monte Carlo and reoptimized in the presence of a Jastrow factor and an optional backflow transformation, we find that the VMC and DMC energies are smooth functions of the sum of the squared coefficients of the initial CI wave function and that quadratic extrapolations of the non-backflow VMC and backflow DMC energies intersect within uncertainty of the exact total energy. With adequate statistical treatment of quasi-random fluctuations, the extrapolate and intersect with polynomials of order two method is shown to yield results in agreement with benchmark-quality total and relative energies for the C2, N2, CO2, and H2O molecules, as well as for the C2 molecule in its first electronic singlet excited state, using only small CI expansion sizes.
我们探索了一种外推方法的应用，该方法能从变分量子蒙特卡罗（VMC）和扩散量子蒙特卡罗（DMC）结果中得出非常精确的总能量和相对能量。对于一个由从全CI量子蒙特卡罗获得并在存在雅斯特罗因子和可选的回流变换的情况下重新优化的小配置相互作用（CI）波函数组成的试探波函数，我们发现VMC和DMC能量是初始CI波函数平方系数之和的平滑函数，并且非回流VMC和回流DMC能量的二次外推在精确总能量的不确定度内相交。通过对准随机涨落进行充分的统计处理，结果表明，仅使用小的CI展开规模，外推并与二阶多项式相交的方法就能得出与C2、N2、CO2和H2O分子以及处于第一电子单重激发态的C2分子的基准质量总能量和相对能量一致的结果。
