多体微扰理论

基本假设

${\displaystyle H_{0}=\sum _{i}^{N}f_{i}}$

${\displaystyle H_{0}|\Psi _{0}>=\sum _{i}^{N}\epsilon _{i}|\Psi _{0}>}$

${\displaystyle H_{ele}=H_{0}+V}$

 ${\displaystyle V}$ ${\displaystyle =H_{ele}-H_{0}}$ ${\displaystyle =\sum _{i,j>i}^{N}{\frac {1}{r_{ij}}}-\sum _{i}^{N}\sum _{b}^{N}\left(K_{b}-J_{b}\right)}$

能量和波函数的各级近似

一级校正

${\displaystyle E_{0}^{(1)}=<\Psi _{0}^{(0)}|V|\Psi _{0}^{(0)}>}$

 ${\displaystyle E_{0}^{(1)}}$ ${\displaystyle =<\Psi _{0}^{(0)}|H_{ele}|\Psi _{0}^{(0)}>-<\Psi _{0}^{(0)}|H_{0}|\Psi _{0}^{(0)}>}$ ${\displaystyle =E_{0}^{HF}-\sum _{a}^{N}\epsilon _{a}}$

 ${\displaystyle E}$ ${\displaystyle =E_{0}^{(0)}+E_{0}^{(1)}}$ ${\displaystyle =\sum _{a}^{N}\epsilon _{a}+E_{0}^{HF}-\sum _{a}^{N}\epsilon _{a}}$ ${\displaystyle =E_{0}^{HF}}$

二级校正

${\displaystyle E_{0}^{(2)}=\sum _{n\neq \;0}{\frac {{\begin{vmatrix}<\Psi _{0}^{(0)}|V|\Psi _{n}^{(0)}>\end{vmatrix}}^{2}}{E_{0}^{(0)}-E_{n}^{(0)}}}}$

${\displaystyle E_{0}^{(2)}=\sum _{a\end{vmatrix}}^{2}}{\epsilon _{a}+\epsilon _{b}-\epsilon _{r}-\epsilon _{s}}}}$

${\displaystyle E_{0}^{(2)}=\sum _{a\end{vmatrix}}^{2}}{\epsilon _{a}+\epsilon _{b}-\epsilon _{r}-\epsilon _{s}}}}$

${\displaystyle E=E_{0}^{HF}+\sum _{a\end{vmatrix}}^{2}}{\epsilon _{a}+\epsilon _{b}-\epsilon _{r}-\epsilon _{s}}}}$

方法评价

MPn方法是一个大小一致的方法，即对电子数不同的体系，使用MPn计算的精度是相同的，这一特性使得MPn方法特别适合进行化学反应的模拟计算。但是由于MPn方法以HF方程为基础，因而受到HF方程的局限，对于那些应用HF方程不能很好处理的体系，如非限制性开壳层体系，MPn方法也不能很好处理。