From 1ed9b62cee9cd3204b1cada2f33f14a0edcce1a1 Mon Sep 17 00:00:00 2001 From: Antoine MARIE Date: Tue, 8 Nov 2022 15:58:08 +0100 Subject: [PATCH] add command --- Notes/Commands.tex | 137 +++++++++++++++++++++++++++++++++++++++++++++ Notes/Notes.tex | 4 +- 2 files changed, 139 insertions(+), 2 deletions(-) create mode 100755 Notes/Commands.tex diff --git a/Notes/Commands.tex b/Notes/Commands.tex new file mode 100755 index 0000000..7af1bea --- /dev/null +++ b/Notes/Commands.tex @@ -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} \ No newline at end of file diff --git a/Notes/Notes.tex b/Notes/Notes.tex index c9e3abe..e55d9d1 100644 --- a/Notes/Notes.tex +++ b/Notes/Notes.tex @@ -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}