From 5132286092318e23a0f8ab8fcd238b45b78af121 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Fri, 29 May 2020 21:25:57 +0200 Subject: [PATCH] fix problem --- Manuscript/BSE_JPCL.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/Manuscript/BSE_JPCL.tex b/Manuscript/BSE_JPCL.tex index e235a04..3279ac5 100644 --- a/Manuscript/BSE_JPCL.tex +++ b/Manuscript/BSE_JPCL.tex @@ -404,7 +404,7 @@ Taking the static limit, \ie, $W(\omega=0)$, for the screened Coulomb potential, \begin{pmatrix} R & C \\ - -C^* & R^{*} + -C^* & -R^{*} \end{pmatrix} \begin{pmatrix} X^m @@ -427,7 +427,7 @@ with electron-hole ($eh$) eigenstates written as \end{equation} where $m$ indexes the electronic excitations. The $\lbrace \phi_{i/a} \rbrace$ are, in the case of $G_0W_0$ and ev$GW$, the input (KS) eigenstates used to build the $GW$ self-energy. -The resonant and anti-resonant parts of the BSE Hamiltonian read +The resonant and coupling parts of the BSE Hamiltonian read \begin{gather} R_{ai,bj} = \qty( \varepsilon_a^{\GW} - \varepsilon_i^{\GW} ) \delta_{ij} \delta_{ab} + \kappa (ia|jb) - W_{ij,ab}, \\ @@ -446,7 +446,7 @@ $(ia|jb)$ bare Coulomb term defined as \phi_i(\br) \phi_a(\br) v(\br-\br') \phi_j(\br') \phi_b(\br'), \end{equation} -Neglecting the anti-resonant term $C$ in Eq.~\eqref{eq:BSE-eigen}, which is usually much smaller than its resonant counterpart $R$, leads to the well-known Tamm-Dancoff approximation. +Neglecting the coupling term $C$ between the resonant term $R$ and anti-resonant term $-R^*$ in Eq.~\eqref{eq:BSE-eigen}, leads to the well-known Tamm-Dancoff approximation. As compared to TD-DFT, \begin{itemize} \item the $GW$ quasiparticle energies $\lbrace \varepsilon_{i/a}^{\GW} \rbrace$ replace the KS eigenvalues