Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space
Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space
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DOI：
10.1063/1.3193710
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发表时间：
2009-08-07
影响因子：
4.4
通讯作者：
Alavi, Ali
中科院分区：
文献类型：
--
作者：
Booth, George H.;Thom, Alex J. W.;Alavi, Ali
我们发展了一种新的量子蒙特卡罗方法，用于在全组态相互作用（斯莱特行列式）空间中模拟关联多电子系统。新方法是一组步行者的种群动力学，并被设计来模拟相互作用哈密顿量的基本时间Schroumldinger方程。步行者（带有正或负符号）居住在斯莱特决定空间，并根据一套简单的规则进化，包括产卵，死亡和湮灭过程。我们表明，这种方法是能够收敛到全组态相互作用（FCI）的能量和波函数的问题，没有任何先验信息的波函数的节点结构。步行者湮灭被证明起着关键作用。步行者的生长模式一旦达到临界（系统依赖）步行者数量，就会表现出一个特征性的平台期。在这一点上，相关能量可以测量使用两个独立的方法-投影公式和能量转移;这些之间的协议提供了一个强有力的措施，在计算的相关能量的准确性的信心。我们已经验证了该方法进行计算的FCI计算已经存在的系统。此外，我们报告了一些新的系统，包括CO，O-2，CH 4，和NaH-与FCI空间范围从10（9）到10（14），其FCI能量，我们计算使用适度的计算资源。
We have developed a new quantum Monte Carlo method for the simulation of correlated many-electron systems in full configuration-interaction (Slater determinant) spaces. The new method is a population dynamics of a set of walkers, and is designed to simulate the underlying imaginary-time Schroumldinger equation of the interacting Hamiltonian. The walkers (which carry a positive or negative sign) inhabit Slater determinant space, and evolve according to a simple set of rules which include spawning, death and annihilation processes. We show that this method is capable of converging onto the full configuration-interaction (FCI) energy and wave function of the problem, without any a priori information regarding the nodal structure of the wave function being provided. Walker annihilation is shown to play a key role. The pattern of walker growth exhibits a characteristic plateau once a critical (system-dependent) number of walkers has been reached. At this point, the correlation energy can be measured using two independent methods-a projection formula and a energy shift; agreement between these provides a strong measure of confidence in the accuracy of the computed correlation energies. We have verified the method by performing calculations on systems for which FCI calculations already exist. In addition, we report on a number of new systems, including CO, O-2, CH4, and NaH-with FCI spaces ranging from 10(9) to 10(14), whose FCI energies we compute using modest computational resources.