Skip to content

fix typo in chap3 and appendix A #41

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
jeanwsr merged 1 commit into from
Mar 11, 2024
Merged

fix typo in chap3 and appendix A #41

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
2 changes: 1 addition & 1 deletion Chaps/AppendixA.tex
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -92,7 +92,7 @@ \chapter{$1s$原初高斯函数的积分计算方法}
最后一个积分的值恰好是$(\pi/p)^{\frac{3}{2}}/{4\pi}$，所以
\begin{align}
\label{A.9}
(A|B)=[pi/(\alpha+\beta)]^{\frac{3}{2}}\exp[-\alpha\beta/(\alpha+\beta)\lvert \bo{R}_A-\bo{R}_B \rvert ^2]
(A|B)=[\pi/(\alpha+\beta)]^{\frac{3}{2}}\exp[-\alpha\beta/(\alpha+\beta)\lvert \bo{R}_A-\bo{R}_B \rvert ^2]
\end{align}

动能积分为
Expand Down
12 changes: 6 additions & 6 deletions Chaps/Chap3.tex
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -71,7 +71,7 @@ \chapter{Hartree-Fock近似}
我们将不加推导地直接给出这节的一些结果, 这些结果可做为Hartree-Fock理论中主要方程的一个总结.

3.2节会补足前一节的推导. 本节和前一节的材料经过人为组织, 以使如果读者愿意, 可以跳过本节.
若想充分了解Hartree-Fock理论, 那么可以阅读这一节. 本节现介绍泛函变分, 然后用这个级数来最小化单行列式的能量.
若想充分了解Hartree-Fock理论, 那么可以阅读这一节. 本节先介绍泛函变分, 然后用这个级数来最小化单行列式的能量.
接下来对自旋轨道进行酉变换以导出正则Hartree-Fock方程.

3.3节继续介绍Hartree-Fock理论的形式部分.
Expand Down Expand Up @@ -285,7 +285,7 @@ \subsection{Fock算符}
f\ket{\chi_a} = \epsilon_a\ket{\chi_a}
\end{align}
这就是Hartree-Fock方程的常见形式.
Fock算符$f(1)$就是芯哈密顿算符$h(1)$加上如下的有效单电子势算符(称作Hartree-Fcok势)：
Fock算符$f(1)$就是芯哈密顿算符$h(1)$加上如下的有效单电子势算符(称作Hartree-Fock势)：
\begin{align}
\label{3.18}
v^\mathrm{HF}(1) = \sum_b\mathscr{J}_b(1) - \mathscr{K}_b(1)
Expand Down Expand Up @@ -1140,7 +1140,7 @@ \subsection{闭壳层H-F：限制性自旋轨道}\label{sec3.4.1}
左乘$\alpha^*(\omega_1)$并对自旋积分可得
\begin{align}
\label{3.114}
\left[ \int\dd\omega_1\alpha^*(\omega_1)f(\mathbf{x}_1)\alpha(\omega_1) \right]\psi_j(\mathbf{r}_1) = \epsilon_i\psi_j(\mathbb{r}_1)
\left[ \int\dd\omega_1\alpha^*(\omega_1)f(\mathbf{x}_1)\alpha(\omega_1) \right]\psi_j(\mathbf{r}_1) = \epsilon_i\psi_j(\mathbf{r}_1)
\end{align}
下一步需算出\autoref{3.114}左侧的式子.
将自旋轨道的Fock算符写为
Expand Down Expand Up @@ -1348,7 +1348,7 @@ \subsection{引入基函数：Roothaan方程}
就将这个积分微分方程转化为矩阵方程
\begin{align}
\label{3.135}
\sum_\nu C_{\nu i}\int\dd{r}_1\,\phi_\nu^*(1)f(1)\phi_\nu(1) = \epsilon_i\sum_\nu C_{\nu i}\int\dd{r}_1\,\phi_\nu^*(1)\phi_\nu(1)
\sum_\nu C_{\nu i}\int\dd{r}_1\,\phi_\mu^*(1)f(1)\phi_\nu(1) = \epsilon_i\sum_\nu C_{\nu i}\int\dd{r}_1\,\phi_\mu^*(1)\phi_\nu(1)
\end{align}

现在定义两个矩阵：
Expand Down Expand Up @@ -1581,7 +1581,7 @@ \subsection{Fock矩阵的表达式}
还包括双电子部分$\mathbf{G}$,
它依赖密度矩阵$\mathbf{P}$及一组双电子积分:
\begin{align}
(\mu\nu|\lambda\sigma) = \int\dd{r}_2\,\phi_\mu^*(1)\phi_\nu(1)\twoe\phi_\lambda^*(2)\phi_\sigma(2)
(\mu\nu|\lambda\sigma) = \int\dd{r}_1\,\int\dd{r}_2\,\phi_\mu^*(1)\phi_\nu(1)\twoe\phi_\lambda^*(2)\phi_\sigma(2)
\end{align}
由于双电子积分数目较多,
所以\hft 计算中的主要困难就是操作、计算这些双电子积分.
Expand Down Expand Up @@ -1621,7 +1621,7 @@ \subsection{Fock矩阵的表达式}
\subsection{基的正交归一化}
分子的计算中所使用的基组是非正交归一基.
基函数确实是归一的,
单它们之间不正交.
但它们之间不正交.
这就产生了Roothaan方程中的重叠矩阵.
为将Roothaan写为通常的矩阵本征值问题,
需要正交化基函数.
Expand Down