Cuzzocrea Alice, Scemama Anthony, Briels Wim J, Moroni Saverio, Filippi Claudia
MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.
Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, 118 route de Narbonne, 31062 Toulouse Cedex 09, France.
J Chem Theory Comput. 2020 Jul 14;16(7):4203-4212. doi: 10.1021/acs.jctc.0c00147. Epub 2020 Jun 15.
We investigate the use of different variational principles in quantum Monte Carlo, namely, energy and variance minimization, prompted by the interest in the robust and accurate estimation of electronic excited states. For two prototypical, challenging molecules, we readily reach the accuracy of the best available reference excitation energies using energy minimization in a state-specific or state-average fashion for states of different or equal symmetry, respectively. On the other hand, in variance minimization, where the use of suitable functionals is expected to target specific states regardless of the symmetry, we encounter severe problems for a variety of wave functions: as the variance converges, the energy drifts away from that of the selected state. This unexpected behavior is sometimes observed even when the target is the ground state and generally prevents the robust estimation of total and excitation energies. We analyze this problem using a very simple wave function and infer that the optimization finds little or no barrier to escape from a local minimum or local plateau, eventually converging to a lower-variance state instead of the target state. For the increasingly complex systems becoming in reach of quantum Monte Carlo simulations, variance minimization with current functionals appears to be an impractical route.
受对电子激发态进行稳健且准确估计的兴趣驱使，我们研究了量子蒙特卡罗中不同变分原理的应用，即能量最小化和方差最小化。对于两个典型的具有挑战性的分子，我们分别以状态特定或状态平均的方式使用能量最小化，对于不同或相同对称性的状态，很容易达到现有最佳参考激发能的精度。另一方面，在方差最小化中，预计使用合适的泛函可以针对特定状态而不考虑对称性，但对于各种波函数我们都遇到了严重问题：随着方差收敛，能量偏离所选状态的能量。即使目标是基态，有时也会观察到这种意外行为，并且通常会妨碍对总能量和激发能的稳健估计。我们使用一个非常简单的波函数分析了这个问题，并推断优化过程几乎找不到或根本找不到从局部最小值或局部平台逃逸的障碍，最终收敛到方差更低的状态而不是目标状态。对于量子蒙特卡罗模拟能够处理的日益复杂的系统，使用当前泛函进行方差最小化似乎是一条不切实际的途径。
