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fix few typos

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Pierre-Francois Loos 2021-07-20 16:28:51 +02:00
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16
Manuscript/Ec.bib
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@ -1,13 +1,27 @@
%% This BibTeX bibliography file was created using BibDesk. %% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/ %% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2021-07-19 13:49:57 +0200 %% Created for Pierre-Francois Loos at 2021-07-20 16:08:44 +0200
%% Saved with string encoding Unicode (UTF-8) %% Saved with string encoding Unicode (UTF-8)
@article{Bozkaya_2011,
author = {Bozkaya,U{\u g}ur and Turney,Justin M. and Yamaguchi,Yukio and Schaefer,Henry F. and Sherrill,C. David},
date-added = {2021-07-20 16:08:28 +0200},
date-modified = {2021-07-20 16:08:40 +0200},
doi = {10.1063/1.3631129},
journal = {J. Chem. Phys.},
number = {10},
pages = {104103},
title = {Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order M{\o}ller-Plesset perturbation theory},
url = {https://doi.org/10.1063/1.3631129},
volume = {135},
year = {2011},
Bdsk-Url-1 = {https://doi.org/10.1063/1.3631129}}
@book{Nocedal_1999, @book{Nocedal_1999,
address = {New York, NY, USA}, address = {New York, NY, USA},
author = {Nocedal, Jorge and Wright, Stephen J.}, author = {Nocedal, Jorge and Wright, Stephen J.},

4
Manuscript/Ec.tex
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@ -231,7 +231,7 @@ where $\bc$ gathers the CI coefficients, $\bk$ the orbital rotation parameters,
\begin{equation} \begin{equation}
\hk = \sum_{p < q} \sum_{\sigma} \kappa_{pq} \qty(\cre{p\sigma} \ani{q\sigma} - \cre{q\sigma} \ani{p\sigma}) \hk = \sum_{p < q} \sum_{\sigma} \kappa_{pq} \qty(\cre{p\sigma} \ani{q\sigma} - \cre{q\sigma} \ani{p\sigma})
\end{equation} \end{equation}
is a real-valued one-electron antisymmetric operator, which creates an orthogonal transformation of the orbital coefficients when exponentiated, $\ani{p\sigma}$ ($\cre{p\sigma}$) being the second quantization annihilation (creation) operator which annihilates (creates) a spin-$\sigma$ electron in the (real-valued) spatial orbital $\MO{p}(\br)$. is a real-valued one-electron antisymmetric operator, which creates an orthogonal transformation of the orbital coefficients when exponentiated, $\ani{p\sigma}$ ($\cre{p\sigma}$) being the second quantization annihilation (creation) operator which annihilates (creates) a spin-$\sigma$ electron in the (real-valued) spatial orbital $\MO{p}(\br)$. \cite{Helgaker_2013}
Applying the Newton-Raphson method by Taylor-expanding the variational energy to second order around $\bk = \bO$, \ie, Applying the Newton-Raphson method by Taylor-expanding the variational energy to second order around $\bk = \bO$, \ie,
\begin{equation} \begin{equation}
@ -243,7 +243,7 @@ one can iteratively minimize the variational energy with respect to the paramete
\bk = - \bH^{-1} \cdot \bg, \bk = - \bH^{-1} \cdot \bg,
\end{equation} \end{equation}
where $\bg$ and $\bH$ are the orbital gradient and Hessian, respectively, both evaluated at $\bk = \bO$. where $\bg$ and $\bH$ are the orbital gradient and Hessian, respectively, both evaluated at $\bk = \bO$.
Their elements are explicitly given by the following expressions: \cite{Henderson_2014a} Their elements are explicitly given by the following expressions: \cite{Bozkaya_2011,Henderson_2014a}
\begin{equation} \begin{equation}
\begin{split} \begin{split}
g_{pq} g_{pq}