PTEROSOR/BSE_JPCLperspective
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fix problem

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Pierre-Francois Loos 2020-05-29 21:25:57 +02:00
parent 71e03cc6fb
commit 5132286092
1 changed files with 3 additions and 3 deletions
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Manuscript/BSE_JPCL.tex
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@ -404,7 +404,7 @@ Taking the static limit, \ie, $W(\omega=0)$, for the screened Coulomb potential,
\begin{pmatrix} \begin{pmatrix}
R & C R & C
\\ \\
-C^* & R^{*} -C^* & -R^{*}
\end{pmatrix} \end{pmatrix}
\begin{pmatrix} \begin{pmatrix}
X^m X^m
@ -427,7 +427,7 @@ with electron-hole ($eh$) eigenstates written as
\end{equation} \end{equation}
where $m$ indexes the electronic excitations. 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 $\lbrace \phi_{i/a} \rbrace$ 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} \begin{gather}
R_{ai,bj} = \qty( \varepsilon_a^{\GW} - \varepsilon_i^{\GW} ) \delta_{ij} \delta_{ab} + \kappa (ia|jb) - W_{ij,ab}, 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_i(\br) \phi_a(\br) v(\br-\br')
\phi_j(\br') \phi_b(\br'), \phi_j(\br') \phi_b(\br'),
\end{equation} \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, As compared to TD-DFT,
\begin{itemize} \begin{itemize}
\item the $GW$ quasiparticle energies $\lbrace \varepsilon_{i/a}^{\GW} \rbrace$ replace the KS eigenvalues \item the $GW$ quasiparticle energies $\lbrace \varepsilon_{i/a}^{\GW} \rbrace$ replace the KS eigenvalues