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Pierre-Francois Loos 2020-01-20 23:37:18 +01:00
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BSE-PES.tex
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@ -386,14 +386,17 @@ As a final remark, we point out that Eq.~\eqref{eq:EtotBSE} can be easily genera
\section{Computational details}
\label{sec:comp_details}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
All the preliminary {\GW} calculations performed to obtain the screened Coulomb operator and the quasiparticle energies have been done using a Hartree-Fock (HF) starting point, which is a very adequate choice in the case of the (small) systems that we consider here.
All the preliminary {\GW} calculations performed to obtain the screened Coulomb operator and the quasiparticle energies have been done using a (restricted) Hartree-Fock (HF) starting point, which is a very adequate choice in the case of the (small) systems that we consider here.
Dunning's basis sets are defined in cartesian gaussians.
Both perturbative {\GW} (or {\GOWO}) \cite{Hybertsen_1985a, Hybertsen_1986} and partially self-consistent {\evGW} \cite{Hybertsen_1986, Shishkin_2007, Blase_2011, Faber_2011} calculations are employed as starting point to compute the BSE neutral excitations.
These will be labeled as BSE@{\GOWO} and BSE@{\evGW}, respectively.
In the case of {\GOWO}, the quasiparticle energies have been obtained by linearizing the non-linear, frequency-dependent quasiparticle equation.
For {\evGW}, the quasiparticle energies are obtained self-consistently and we have used the DIIS convergence accelerator technique proposed by Pulay \cite{Pulay_1980,Pulay_1982} to avoid convergence issues.
Further details about our implementation of {\GOWO} and {\evGW} can be found in Refs.~\onlinecite{Loos_2018,Veril_2018}.
Finally, the infinitesimal $\eta$ has been set to $10^{-3}$ for all calculations.
Finally, the infinitesimal $\eta$ has been set to zero for all calculations.
\titou{For sake of comparison, no frozen core approximation.
The numerical integration required to compute the correlation energy along the adiabatic path has been computed with a 21-point Gauss-Legendre quadrature.
This number of points is probably too big...}
Because Eq.~\eqref{eq:EcBSE} requires the entire BSE excitation spectrum (both singlet and triplet), we perform a complete diagonalization of the $\Nocc \Nvir \times \Nocc \Nvir$ BSE linear response matrix [see Eq.~\eqref{eq:small-LR}], which corresponds to a $\order{\Nocc^3 \Nvir^3}$ computational cost.
This step is, by far, the computational bottleneck in our current implementation.
@ -406,24 +409,39 @@ This step is, by far, the computational bottleneck in our current implementation
%%% TABLE I %%%
\begin{table*}
\caption{
Equilibrium distances of ground and excited states of diatomic molecules obtained at various levels of theory.}
Equilibrium distances (in bohr) of the ground state of diatomic molecules obtained at various levels of theory and basis sets.}
\label{tab:Req}
\begin{ruledtabular}
\begin{tabular}{llcccccccc}
& & \mc{2}{c}{FCI} & \mc{2}{c}{CC3} & \mc{2}{c}{BSE@{\GOWO}} & \mc{2}{c}{BSE@{\evGW}} \\
\cline{3-4} \cline{5-6} \cline{7-8} \cline{9-10}
Molecule & State & cc-pVDZ & cc-pVTZ & cc-pVDZ & cc-pVTZ & cc-pVDZ & cc-pVTZ & cc-pVDZ & cc-pVTZ \\
& & \mc{8}{c}{Molecules} \\
\cline{3-10}
Method & Basis & \ce{H2} & \ce{LiH} & \ce{LiF}& \ce{N2} & \ce{CO} & \ce{BF} & \ce{F2} & \ce{HCl} \\
\hline
\ce{H2} & $S_0$ & 1.438 & 1.403 & & & 1.440 & & 1.432 & \\
& $S_2$ & & & & & 1.451 & & 1.442 & \\
& $S_5$ & & & & & 1.781 & & 1.778 & \\
\ce{LiH} & & & & \\
\ce{LiF} & & & & \\
\ce{HCl} & & & & \\
\ce{N2} & & & & \\
\ce{CO} & & & & \\
\ce{BF} & & & & \\
CC3 & cc-pVDZ & 1.438 & 3.043 & 3.012 & 2.114 & 2.166 & 2.444 & 2.740 & 2.435 \\
& cc-pVTZ & 1.403 & 3.011 & 2.961 & 2.079 & 2.143 & 2.392 & 2.669 & 2.413 \\
& cc-pVQZ & 1.402 & 3.019 & & & & & & \\
CCSD & cc-pVDZ & & & & & & & & \\
& cc-pVTZ & & & & & & & & \\
& cc-pVQZ & & & & & & & & \\
CC2 & cc-pVDZ & & & & & & & & \\
& cc-pVTZ & & & & & & & & \\
& cc-pVQZ & & & & & & & & \\
MP2 & cc-pVDZ & & & & & & & & \\
& cc-pVTZ & & & & & & & & \\
& cc-pVQZ & & & & & & & & \\
BSE@{\GOWO}@HF & cc-pVDZ & & & & & & & & \\
& cc-pVTZ & & & & & & & & \\
& cc-pVQZ & & & & & & & & \\
RPA@{\GOWO}@HF & cc-pVDZ & & & & & & & & \\
& cc-pVTZ & & & & & & & & \\
& cc-pVQZ & & & & & & & & \\
RPAx@HF & cc-pVDZ & & & & & & & & \\
& cc-pVTZ & & & & & & & & \\
& cc-pVQZ & & & & & & & & \\
RPA@HF & cc-pVDZ & & & & & & & & \\
& cc-pVTZ & & & & & & & & \\
& cc-pVQZ & & & & & & & & \\
\end{tabular}
\end{ruledtabular}
\end{table*}