物理化学学报 >> 1999, Vol. 15 >> Issue (07): 599-605.doi: 10.3866/PKU.WHXB19990705

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剩余函数量子Monte Carlo方法

黄宏新, 廉世勋, 曹泽星   

  1. 湖南师范大学化学系，长沙 410081|厦门大学化学系，厦门 361005
  • 收稿日期:1998-09-21 修回日期:1999-01-01 发布日期:1999-07-15
  • 通讯作者: 黄宏新

Surplus Function Quantum Monte Carlo Approach

Huang Hong-Xin, Lian Shi-Xun, Cao Ze-Xing   

  1. Department of Chemistry,Hunan Normal University,Changsha 410081|Department of Chemistry,Xiamen University,Xiamen 361005
  • Received:1998-09-21 Revised:1999-01-01 Published:1999-07-15
  • Contact: Huang Hong-Xin

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摘要：

为量子Monte Carlo方法提出一条新途径──剩余函数法；引入了Schrodinger方程剩余函数的概念，利用剩余函数将一种新的有明显物理意义的试探函数应用到量子Monte Carlo过程中；这种试探函数是通过一种迭进式的方式确定的，它不需要在Monte Carlo过程中优化参数．文中我们将给出这种试探函数的具体形式，证明由这种试探函数求出的能量期望值收敛于体系真实的能量值；文中还给出这种试探函数能量期望值的计算公式以及它在变分Monte Carlo过程中的具体运算步骤；几个分子的算例说明这种试探函数的能量期望值不仅逐步逼近体系真实的能量值，而且逼近速度也非常快，一般只需要4～5次迭进即可获得90％以上的相关能．据作者所知，这种试探函数的计算精度和收敛速度在目前量子Monte Carlo方法中均是最高的．

关键词: 量子Monte Carlo方法, Schrdinger方程的剩余函数, 能量期望值

Abstract:

 A concept of surplus function for Schrodinger equation is put forward. A novel quantum Monte Carlo approach entitled surplus function method is suggested with use of a novel trial function of significant physical meaning which is based on the proposed surplus function. The trial function is of an iteration-type and suffers no time-consuming parameter optimum in a quantum Monte Carlo process. It is theoretically proved that the energy expectation value obtained from the proposed trial function converges to the exact energy value of the system investigated. In addition, computation formulas and procedures for energy expectation value are presented. Calculations for several molecules indicate that the energy expectation value obtained from the trial function does converge to the exact energy value of the investigated system and the converging rate is very fast as generally only 4-5 iterations achieves over 90% correlation energy. To our knowledge, both the calculating precision and converging rate of the trial function proposed are the highest one in the quantum Monte Carlo approach at present time. 

Key words: Quantum Monte Carlo approach, Surplus function for Schrdinger equation, Energy expectation value