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Register a new userLocalized resolution of identity approach to the analytical gradients of random-phase approximation ground-state energy: algorithm and benchmarks
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We develop and implement a formalism which enables calculating the analytical gradients of particle-hole random-phase approximation (RPA) ground-state energy with respect to the atomic positions within the atomic orbital basis set framework. Our approach is based on a localized resolution of identity (LRI) approximation for evaluating the two-electron Coulomb integrals and their derivatives, and the density functional perturbation theory for computing the first-order derivatives of the Kohn-Sham (KS) orbitals and orbital energies. Our implementation allows one to relax molecular structures at the RPA level using both Gaussian-type orbitals (GTOs) and numerical atomic orbitals (NAOs). Benchmark calculations show that our approach delivers high numerical precision compared to previous implementations. A careful assessment of the quality of RPA geometries for small molecules reveals that post-KS RPA systematically overestimates the bond lengths. We furthermore optimized the geometries of the four low-lying water hexamers -- cage, prism, cyclic and book isomers, and determined the energy hierarchy of these four isomers using RPA. The obtained RPA energy ordering is in good agreement with that yielded by the coupled cluster method with single, double and perturbative triple excitations, despite that the dissociation energies themselves are appreciably underestimated. The underestimation of the dissociation energies by RPA is well corrected by the renormalized single excitation correction.
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We describe a finite-field approach to compute density response functions, which allows for efficient $G_0W_0$ and $G_0W_0Gamma_0$ calculations beyond the random phase approximation. The method is easily applicable to density functional calculations performed with hybrid functionals. We present results for the electronic properties of molecules and solids and we discuss a general scheme to overcome slow convergence of quasiparticle energies obtained from $G_0W_0Gamma_0$ calculations, as a function of the basis set used to represent the dielectric matrix.
Following the recent work of Eriksen et al. [arXiv:2008.02678], we report the performance of the textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI) method on the non-relativistic frozen-core correlation energy of the benzene molecule in the cc-pVDZ basis. Following our usual protocol, we obtain a correlation energy of $-863.4$ m$E_h$ which agrees with the theoretical estimate of $-863$ m$E_h$ proposed by Eriksen et al. using an extensive array of highly-accurate new electronic structure methods.
The many-body theory of interacting electrons poses an intrinsically difficult problem that requires simplifying assumptions. For the determination of electronic screening properties of the Coulomb interaction, the Random Phase Approximation (RPA) provides such a simplification. Here, we explicitly show that this approximation is justified for band structures with sizeable band gaps. This is when the electronic states responsible for the screening are energetically far away from the Fermi level, which is equivalent to a short electronic propagation length of these states. The RPA contains exactly those diagrams in which the classical Coulomb interaction covers all distances, whereas neglected vertex corrections involve quantum tunneling through the barrier formed by the band gap. Our analysis of electron-electron interactions provides a real-space analogy to Migdals theorem on the smallness of vertex corrections in electron-phonon problems. An important application is the increasing use of constrained Random Phase Approximation (cRPA) calculations of effective interactions. We find that their usage of Kohn-Sham energies already accounts for the leading local (excitonic) vertex correction in insulators.
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