All-Electron Gaussian-Based G₀W₀ for Valence and Core Excitation Energies of Periodic Systems

Abstract

We describe an all-electron G 0 W 0 implementation for periodic systems with-point sampling implemented in a crystalline Gaussian basis. Our full-frequency G 0 W 0 method relies on efficient Gaussian density fitting integrals and includes both analytic continuation and contour deformation schemes. Due to the compactness of Gaussian bases, no virtual state truncation is required as is seen in many plane-wave formulations. Finite size corrections are included by taking the → limit of the Coulomb divergence. Using our implementation, we study quasiparticle energies and band structures across a range of systems including molecules, semiconductors, rare gas solids, and metals. We find that the G 0 W 0 band gaps of traditional semiconductors converge rapidly with respect to the basis size, even for the conventionally challenging case of ZnO. Using correlation-consistent bases of polarized triple-zeta quality, we find the mean absolute relative error of the extrapolated G 0 W 0 @PBE band gaps to be only 5.2% when compared to experimental values. For core excitation binding energies (CEBEs), we find that G 0 W 0 predictions improve significantly over those from DFT if the G 0 W 0 calculations are started from hybrid functionals with a high percentage of exact exchange.

A simplified GW/BSE approach for charged and neutral excitation energies of large molecules and nanomaterials

“…All calculations (DFT, GW/BSE, and sGW/sBSE) were performed using a locally modified version of the PySCF software package 32,56,57 using the TZVP basis set. 58 DFT calculations used the B3LYP exchange-correlation functional unless stated otherwise.…”

“…42 The ERI approximation (2) has the same structure as the density fitting approximation (also known as the resolution of the identity approximation), [46][47][48][49] which have been regularly used in ab intio GW/BSE implementations with atomcentered basis sets. 27,[29][30][31][32]50,51 However, we emphasize that the three-index tensors L µ pq are expressible as a product of two-index objects, the MO coefficients. Therefore, the standard density fitting procedure, requiring the calculation of two-center and three-center integrals and the solution of a system of linear equations, is completely bypassed (although we note that it may be used in the initial DFT calculation).…”

“…The computational cost of ab intio GW/BSE calculations depends on implementation details, which yield computational timings that scale as N 3 to N 6 with system size N [22][23][24][25][26][27][28][29][30][31][32][33] (throughout this work we exclusively consider the non-selfconsistent G 0 W 0 approximation but will typically refer to it as the GW approximation, for brevity). Although promising, the storage requirements and computational timing for ab intio GW/BSE calculations are still prohibitive for applications to very large systems or to problems requiring many calculations, such as averaging over the course of a molecular dynamics trajectory or in workflows for materials screening.…”

Accurate computational prediction of core-electron binding energies in carbon-based materials: A machine-learning model combining DFT and $\boldsymbol{GW}$

“…Second, an all-electron treatment is necessary, which we efficiently realize by an implementation with localized basis sets. The implementation of 𝐺𝑊 in localized basis set codes is a rather recent development of the last decade [27], for which the efficient implementation of periodic boundary conditions is still the subject of ongoing work [67][68][69]. Our core-level 𝐺𝑊 implementation [25] is thus currently restricted to cluster calculations.…”

Staggered mesh method for correlation energy calculations of solids: Random phase approximation in direct ring coupled cluster doubles and adiabatic connection formalisms

“…Such performance is consistent with that in MP2 energy calculations 18 . In the AC formalism, one additional advantage of the staggered mesh method is that it naturally avoids the need of the so-called "head/wing" corrections to the dielectric operator [42][43][44] .…”