eq 7 8 9
This commit is contained in:
parent
f3629cc974
commit
20aa963400
@ -146,7 +146,7 @@
|
|||||||
\newcommand{\bB}[1]{\mathbf{B}^{#1}}
|
\newcommand{\bB}[1]{\mathbf{B}^{#1}}
|
||||||
\newcommand{\bX}[1]{\mathbf{X}^{#1}}
|
\newcommand{\bX}[1]{\mathbf{X}^{#1}}
|
||||||
\newcommand{\bY}[1]{\mathbf{Y}^{#1}}
|
\newcommand{\bY}[1]{\mathbf{Y}^{#1}}
|
||||||
\newcommand{\bZ}[1]{\mathbf{Z}^{#1}}
|
\newcommand{\bZ}[2]{\mathbf{Z}_{#1}^{#2}}
|
||||||
\newcommand{\bK}{\mathbf{K}}
|
\newcommand{\bK}{\mathbf{K}}
|
||||||
\newcommand{\bP}[1]{\mathbf{P}^{#1}}
|
\newcommand{\bP}[1]{\mathbf{P}^{#1}}
|
||||||
|
|
||||||
@ -302,14 +302,14 @@ In the following, the index $m$ labels the $\Nocc \Nvir$ single excitations, $i$
|
|||||||
In the absence of instabilities (\ie, when $\bA{\IS} - \bB{\IS}$ is positive-definite), \cite{Dreuw_2005} Eq.~\eqref{eq:LR} is usually transformed into an Hermitian eigenvalue problem of smaller dimension
|
In the absence of instabilities (\ie, when $\bA{\IS} - \bB{\IS}$ is positive-definite), \cite{Dreuw_2005} Eq.~\eqref{eq:LR} is usually transformed into an Hermitian eigenvalue problem of smaller dimension
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
\label{eq:small-LR}
|
\label{eq:small-LR}
|
||||||
(\bA{\IS} - \bB{\IS})^{1/2} (\bA{\IS} + \bB{\IS}) (\bA{\IS} - \bB{\IS})^{1/2} \bZ{\IS}_m = (\Om{m}{\IS})^2 \bZ{\IS}_m,
|
(\bA{\IS} - \bB{\IS})^{1/2} (\bA{\IS} + \bB{\IS}) (\bA{\IS} - \bB{\IS})^{1/2} \bZ{m}{\IS} = (\Om{m}{\IS})^2 \bZ{m}{\IS},
|
||||||
\end{equation}
|
\end{equation}
|
||||||
where the excitation amplitudes are
|
where the excitation amplitudes are
|
||||||
\begin{subequations}
|
\begin{subequations}
|
||||||
\begin{align}
|
\begin{align}
|
||||||
\bX{\IS} + \bY{\IS} = (\bOm{\IS})^{-1/2} (\bA{\IS} - \bB{\IS})^{+1/2} \bZ{\IS},
|
(\bX{\IS} + \bY{\IS})_m = (\Om{m}{\IS})^{-1/2} (\bA{\IS} - \bB{\IS})^{+1/2} \bZ{m}{\IS},
|
||||||
\\
|
\\
|
||||||
\bX{\IS} - \bY{\IS} = (\bOm{\IS})^{+1/2} (\bA{\IS} - \bB{\IS})^{-1/2} \bZ{\IS}.
|
(\bX{\IS} - \bY{\IS})_m = (\Om{m}{\IS})^{+1/2} (\bA{\IS} - \bB{\IS})^{-1/2} \bZ{m}{\IS}.
|
||||||
\end{align}
|
\end{align}
|
||||||
\end{subequations}
|
\end{subequations}
|
||||||
Introducing the so-called Mulliken notation for the bare two-electron integrals
|
Introducing the so-called Mulliken notation for the bare two-electron integrals
|
||||||
|
Binary file not shown.
Loading…
Reference in New Issue
Block a user