fix few typos

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}