From 43df8491db783f46bbc906ff35a2296903556b9c Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Tue, 20 Jul 2021 16:00:15 +0200 Subject: [PATCH] fix few typos --- Manuscript/Ec.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Manuscript/Ec.tex b/Manuscript/Ec.tex index 7d337dc..6cff473 100644 --- a/Manuscript/Ec.tex +++ b/Manuscript/Ec.tex @@ -200,7 +200,7 @@ and a second-order perturbative correction \begin{equation} \EPT^{(k)} = \sum_{\alpha \in \cA_k} e_{\alpha}^{(k)} - = \sum_{\alpha \in \cA_k} \frac{\mel*{\Psivar^{(k)}}{\hH}{\alpha}}{\Evar^{(k)} - \mel*{\alpha}{\hH}{\alpha}} + = \sum_{\alpha \in \cA_k} \frac{\abs*{\mel*{\Psivar^{(k)}}{\hH}{\alpha}}^2}{\Evar^{(k)} - \mel*{\alpha}{\hH}{\alpha}} \end{equation} where $\hH$ is the (non-relativistic) electronic Hamiltonian, \begin{equation} @@ -231,7 +231,7 @@ where $\bc$ gathers the CI coefficients, $\bk$ the orbital rotation parameters, \begin{equation} \hk = \sum_{p < q} \sum_{\sigma} \kappa_{pq} \qty(\cre{p\sigma} \ani{q\sigma} - \cre{q\sigma} \ani{p\sigma}) \end{equation} -is a real-valued one-electron anti-hermitian operator, which creates a unitary 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 $\MO{p}(\br)$. Applying the Newton-Raphson method by Taylor-expanding the variational energy to second order around $\bk = \bO$, \ie, \begin{equation}