Exploring the statically screened<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>G</mml:mi><mml:mn>3</mml:mn><mml:mi>W</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:math>correction to the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>G</mml:mi><mml:mi>W</mml:mi></mml:mrow></mml:math>self-energy: Charged excitations and total energies of finite systems
A. Förster, Lucas Visscher
Abstract
Electron correlation in finite and extended systems is often described in an effective single-particle framework within the $GW$ approximation. Here, we use the statically screened second-order exchange (SOX) contribution to the self-energy ($G3W2$) to calculate a perturbative correction to the $GW$ self-energy. We use this correction to calculate total correlation energies of atoms, relative energies, as well as charged excitations of a wide range of molecular systems. We show that the second-order correction improves correlation energies with respect to the random-phase approximation and also improves relative energies for many, but not all, considered systems. The dynamically screened SOX term has previously been shown to consistently lower the highest occupied molecular orbital (HOMO) quasiparticle (QP) energies and to increase the lowest unoccupied molecular orbitals (LUMO) QP energies. We show here that the statically screened $G3W2$ correction consistently increases the LUMO QP energies, while no consistent trend can be observed for the HOMO levels. Also, confirming previous results, the magnitude of the correction is much smaller with the statically screened interaction than with the dynamically screened one. Quasiparticle self-consistent $\mathit{GW}$ by itself is shown to be an excellent method for the calculation of charged excitation of finite systems, and it cannot consistently be improved upon by the $G3W2$ correction. For range-separated hybrid starting points, the description of fundamental gaps and HOMO QP energies is slightly worsened. However, tremendous improvements upon the $GW$ LUMO energies, leading to almost perfect agreement with high-level coupled cluster reference methods, are observed. The evaluation of the statically screened $G3W2$ correction only comes with small additional computational cost compared to ${G}_{0}{W}_{0}$ for systems with up to 100 atoms and should therefore be suitable for practical applications.