add command

This commit is contained in:
Antoine Marie 2022-11-08 15:58:08 +01:00
parent db67674616
commit 1ed9b62cee
2 changed files with 139 additions and 2 deletions

137
Notes/Commands.tex Executable file
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@ -0,0 +1,137 @@
%============================================================%
%%% NEWCOMMANDS %%%
% ============================================================%
%%% This latex gather all the latex commands that I use to facilitate the writing of electronic structure manuscript, report...
%%% You can import these commands by adding the following line in you .text
%%% \input{commands}
%%% Latin %%%
\newcommand{\ie}{\textit{i.e.}~}
\newcommand{\eg}{\textit{e.g.}~}
\newcommand{\etal}{\textit{et al.}~}
%%% Operators %%%
\newcommand{\hH}{\Hat{H}} % Hamiltonian operator
\newcommand{\HN}{\Hat{\mathnormal{H}}_{\text{N}}} % Normal ordered Hamiltonian
\newcommand{\Hsim}{\hat{\bar{H}}} % Similarity transformed Hamiltonian
\newcommand{\hC}{\Hat{C}} % CI operator
\newcommand{\hT}{\Hat{T}} % Cluster operator
\newcommand{\T}[1]{\Hat{\mathnormal{T}}_{#1}} % Cluster operator of a given excitation number
\newcommand{\hsig}{\Hat{\sigma}} % Unitary cluster operator
\newcommand{\hK}{\Hat{K}} % Anti-hermitian orbital rotation operator
\newcommand{\hS}{\Hat{S}} % Anti-hermitian CI coefficients rotation operator
\newcommand{\hP}[1]{\Hat{\mathnormal{P}}_{#1}} % Permutation operators
\newcommand{\hE}{\Hat{E}} % Spin averaged single excitation operator
\newcommand{\cre}[1]{a_{#1}^\dagger} % Creation operator
\newcommand{\ani}[1]{a_{#1}} % Annihilation operator
\newcommand{\bcre}[1]{b_{#1}^\dagger} % Boson creation operator
\newcommand{\bani}[1]{b_{#1}} % Boson annihilation operator
\newcommand{\no}[2]{\mleft\{ \hat{a}_{#1}^{#2}\mright\} }
%%% Matrices %%%
\newcommand{\bA}{\boldsymbol{A}}
\newcommand{\bB}{\boldsymbol{B}}
\newcommand{\bC}[2]{\boldsymbol{C}_{#1}^{#2}}
\newcommand{\bD}{\boldsymbol{D}}
\newcommand{\bE}{\boldsymbol{E}}
\newcommand{\bF}[2]{\boldsymbol{F}_{#1}^{#2}}
\newcommand{\bG}{\boldsymbol{G}}
\newcommand{\bH}{\boldsymbol{H}}
\newcommand{\bJ}{\boldsymbol{J}}
\newcommand{\bK}{\boldsymbol{K}}
\newcommand{\bL}{\boldsymbol{L}}
\newcommand{\bM}{\boldsymbol{M}}
\newcommand{\bN}{\boldsymbol{N}}
\newcommand{\bP}{\boldsymbol{P}}
\newcommand{\bQ}{\boldsymbol{Q}}
\newcommand{\bR}{\boldsymbol{R}}
\newcommand{\bS}{\boldsymbol{S}}
\newcommand{\bT}{\boldsymbol{T}}
\newcommand{\bU}{\boldsymbol{U}}
\newcommand{\bV}[2]{\boldsymbol{V}_{#1}^{#2}}
\newcommand{\bW}{\boldsymbol{W}}
\newcommand{\bX}{\boldsymbol{X}}
\newcommand{\bY}{\boldsymbol{Y}}
\newcommand{\bZ}[2]{\boldsymbol{Z}_{#1}^{#2}}
\newcommand{\bO}{\boldsymbol{0}}
\newcommand{\bI}{\boldsymbol{1}}
\newcommand{\bc}{\boldsymbol{c}}
\newcommand{\br}{\boldsymbol{r}}
\newcommand{\bx}{\boldsymbol{x}}
\newcommand{\bSig}{\boldsymbol{\Sigma}}
\newcommand{\bSigC}{\boldsymbol{\Sigma}^{\text{c}}}
\newcommand{\be}{\boldsymbol{\epsilon}}
\newcommand{\bOm}{\boldsymbol{\Omega}}
\newcommand{\bEta}[1]{\boldsymbol{\eta}^{(#1)}(s)}
\newcommand{\bHd}[1]{\bH_\text{d}^{(#1)}}
\newcommand{\bHod}[1]{\bH_\text{od}^{(#1)}}
\newcommand{\FC}[1]{F_{#1}^{\text{C}}} % Core Fock matrix
\newcommand{\FA}[1]{F_{#1}^{\text{A}}} % Active Fock matrix
%%% Wave functions %%%
\newcommand{\MO}[1]{\phi_{#1}}
\newcommand{\SO}[1]{\psi_{#1}}
%%% Matrix and tensor elements %%%
\newcommand{\oa}{O_{\alpha}}
\newcommand{\ob}{O_{\beta}}
\newcommand{\eri}[2]{\braket{#1}{#2}} % Electron repulsion integral physician notation
\newcommand{\ceri}[2]{\mleft(#1|#2\mright)} % Electron repulsion integral chemist notation
\newcommand{\aeri}[2]{\mel{#1}{}{#2}} % Double bar integral
\newcommand{\kron}[1]{\delta_{#1}} % Kronecker delta
\newcommand{\cbra}[1]{(#1|} % Chemist bra
\newcommand{\cket}[1]{|#1)} % Chemist ket
%%% Mathematics %%%
\newcommand{\ii}{\mathrm{i}}
%%% Text acronyms and abbreviations %%%
\newcommand{\FCI}{\text{FCI}}
\newcommand{\HF}{\text{HF}}
\newcommand{\MCSCF}{\text{MCSCF}}
\newcommand{\occ}{\text{occ}}
\newcommand{\vir}{\text{vir}}
\newcommand{\HOMO}{\text{HOMO}}
\newcommand{\LUMO}{\text{LUMO}}
\newcommand{\nuc}{\text{nuc}}
\newcommand{\KS}{\text{KS}}
\newcommand{\RPA}{\text{RPA}}
\newcommand{\phRPA}{\text{ph-RPA}}
\newcommand{\ppRPA}{\text{pp-RPA}}
\newcommand{\h}{\text{1h}}
\newcommand{\p}{\text{1p}}
\newcommand{\hp}{\text{1h+1p}}
\newcommand{\hhp}{\text{2h1p}}
\newcommand{\pph}{\text{2p1h}}
\newcommand{\dRPA}{\text{dRPA}}
\newcommand{\RPAx}{\text{RPAx}}
\newcommand{\QP}{\textsc{quantum package}}
\newcommand{\Hxc}{\text{Hxc}}
\newcommand{\xc}{\text{xc}}
\newcommand{\x}{\text{x}}
\newcommand{\GW}{\text{GW}}
\newcommand{\GF}{\text{GF(2)}}
\newcommand{\GT}{\text{$GT$}}
\newcommand{\evGW}{ev$GW$}
\newcommand{\qsGW}{qs$GW$}
\newcommand{\GOWO}{$G_0W_0$}
%%% Notations %%%
\newcommand{\Ne}{N}
\newcommand{\Norb}{K}
\newcommand{\Nocc}{O}
\newcommand{\Nvir}{V}

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@ -688,8 +688,8 @@ Which finally gives
The expression for the GF(2) case is
\begin{align}
\epsilon_r^{(2)}(s) &= \sum _{ija} \frac{\aeri{ra}{ij}^2}{\epsilon_r ^{(0)}- \Delta_{ij}^a} \left(1 - e^{-2(\epsilon_r^{(0)} - \Delta_{ij}^a)^2s}\right) \notag \\
&+ \sum _{iab} \frac{\aeri{ri}{ab}^2}{\epsilon_r^{(0)} - \Delta_{i}^{ab}} \left(1 - e^{-2(\epsilon_r^{(0)} - \Delta_{i}^{ab})^2s}\right) \notag
\epsilon_r^{(2)}(s) &= \frac{1}{2} \sum _{ija} \frac{\aeri{ra}{ij}^2}{\epsilon_r ^{(0)}- \Delta_{ij}^a} \left(1 - e^{-2(\epsilon_r^{(0)} - \Delta_{ij}^a)^2s}\right) \notag \\
&+ \frac{1}{2} \sum _{iab} \frac{\aeri{ri}{ab}^2}{\epsilon_r^{(0)} - \Delta_{i}^{ab}} \left(1 - e^{-2(\epsilon_r^{(0)} - \Delta_{i}^{ab})^2s}\right) \notag
\end{align}
\end{itemize}