Density-Based Basis-Set Incompleteness Correction for <i>GW</i> Methods

Loos, Pierre‐François; Pradines, Barthélémy; Scemama, Anthony; Giner, Emmanuel; Toulouse, Julien

doi:10.1021/acs.jctc.9b01067

Cited by 37 publications

(38 citation statements)

References 117 publications

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“…In the latter case the polarizability is obtained by the Adler-Wiser construction, which involves terms of a sum over all empty eigenstates. It is in principle exact for the RPA polarizability, but it is known to converge slowly and alternative schemes have been proposed [31][32][33]. The situation is quite different for the basis we use: quasiparticle levels converge very quickly with the rank of the basis set, as was shown in some detail for a number of semiconductors [34].…”

Section: Methodsmentioning

confidence: 99%

Optical response and band structure of LiCoO2 including electron-hole interaction effects

et al. 2021

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The optical response functions and band structures of LiCoO 2 are studied at different levels of approximation, from density functional theory (DFT) in the generalized gradient approximation (GGA) to quasiparticle selfconsistent QSGW (with G for Green's function and W for screened Coulomb interaction) without and with ladder diagrams (QSG Ŵ ) and the Bethe Salpeter Equation (BSE) approach. The QSGW method is found to strongly overestimate the band gap and electron-hole or excitonic effects are found to be important. They lower the quasiparticle gap by only about 11% but the lowest energy peaks in absorption are found to be excitonic in nature. The contributions from different band to band transitions and the relation of excitons to band-to-band transitions are analyzed. The excitons are found to be strongly localized. A comparison to experimental data is presented.

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Section: Methodsmentioning

confidence: 99%

Optical response and band structure of LiCoO2 including electron-hole interaction effects

et al. 2021

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“…All our TD-DFT calculations have been performed with GAUSSIAN 16, 108 using the ultrafine quadrature grid. As the convergence with respect to the basis set size of vertical excitation energies stemming from density-based methods (such as TD-DFT) and wavefunction-based methods tend to significantly differ, [101][102][103] we have decided to perform the TD-DFT benchmarks with the aug-cc-pVQZ basis set (i.e., using the TBE/aug-cc-pVQZ values as references), which is likely large enough to be close to the CBS limit for both families of methods. We have selected the following XCFs to perform our calculations: two global hybrids with rather low exact exchange percentage, B3LYP (20%) 10,137-139 and PBE0 (25%), 11,12 one global hybrid with a much larger share of exact exchange, M06-2X (54%), 78 and five RSHs (CAM-B3LYP, 15 LC-HPBE, 140 B97X, 17 B97X-D, 141 and M11 142 ).…”

Section: Td-dft Benchmarksmentioning

confidence: 99%

Reference Energies for Double Excitations

Loos

Boggio‐Pasqua

Scemama

et al. 2019

J. Chem. Theory Comput.

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182

378

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Excited states exhibiting double excitation character are notoriously di cult to model using conventional singlereference methods, such as adiabatic time-dependent density-functional theory (TD-DFT) or equation-of-motion coupled cluster (EOM-CC). In addition, these states are typical experimentally "dark" making their detection in photo-absorption spectra very challenging. Nonetheless, they play a key role in the faithful description of many physical, chemical, and biological processes. In the present work, we provide accurate reference excitation energies for transitions involving a substantial amount of double excitation using a series of increasingly large di use-containing atomic basis sets. Our set gathers 20 vertical transitions from 14 small-and medium-size molecules (acrolein, benzene, beryllium atom, butadiene, carbon dimer and trimer, ethylene, formaldehyde, glyoxal, hexatriene, nitrosomethane, nitroxyl, pyrazine, and tetrazine). Depending on the size of the molecule, selected con guration interaction (sCI) and/or multicon gurational (CASSCF, CASPT2, (X)MS-CASPT2 and NEVPT2) calculations are performed in order to obtain reliable estimates of the vertical transition energies. In addition, coupled cluster approaches including at least contributions from iterative triples (such as CC3, CCSDT, CCSDTQ, and CCSDTQP) are assessed. Our results clearly evidence that the error in CC methods is intimately related to the amount of double excitation character of the transition. For "pure" double excitations (i.e. for transitions which do not mix with single excitations), the error in CC3 can easily reach 1 eV, while it goes down to few tenths of an eV for more common transitions (like in trans-butadiene) involving a signi cant amount of singles. As expected, CC approaches including quadruples yield highly accurate results for any type of transitions. e quality of the excitation energies obtained with multicon gurational methods is harder to predict. We have found that the overall accuracy of these methods is highly dependent of both the system and the selected active space. e inclusion of the σ and σ orbitals in the active space, even for transitions involving mostly π and π orbitals, is mandatory in order to reach high accuracy. A theoretical best estimate (TBE) is reported for each transition. We believe that these reference data will be valuable for future methodological developments aiming at accurately describing double excitations. TOC graphical abstract arXiv:1811.12861v1 [physics.chem-ph] 30 Nov 2018

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“… 46 , 96 , 97 Consequently, the last years have witnessed some effort to reduce time-to-solution further, which resulted in massively parallel implementations optimized for state-of-the-art supercomputers 98 , 99 but also in notable algorithmic developments, including stochastic approaches, 100 − 102 implementations avoiding the explicit summation over empty electronic states in the polarizability, P ( 103 − 106 ) low-rank approximations to the dielectric function ϵ 64 , 97 , 107 or the screened interaction W , 108 , 109 and basis set error (BSE) correction schemes. 110 − 112 …”

Section: Introductionmentioning

confidence: 99%

Low-Order Scaling G₀W₀ by Pair Atomic Density Fitting

Förster

Visscher

2020

J. Chem. Theory Comput.

172

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We derive a low-scaling G 0 W 0 algorithm for molecules using pair atomic density fitting (PADF) and an imaginary time representation of the Green’s function and describe its implementation in the Slater type orbital (STO)-based Amsterdam density functional (ADF) electronic structure code. We demonstrate the scalability of our algorithm on a series of water clusters with up to 432 atoms and 7776 basis functions and observe asymptotic quadratic scaling with realistic threshold qualities controlling distance effects and basis sets of triple-ζ (TZ) plus double polarization quality. Also owing to a very small prefactor, a G 0 W 0 calculation for the largest of these clusters takes only 240 CPU hours with these settings. We assess the accuracy of our algorithm for HOMO and LUMO energies in the GW100 database. With errors of 0.24 eV for HOMO energies on the quadruple-ζ level, our implementation is less accurate than canonical all-electron implementations using the larger def2-QZVP GTO-type basis set. Apart from basis set errors, this is related to the well-known shortcomings of the GW space-time method using analytical continuation techniques as well as to numerical issues of the PADF approach of accurately representing diffuse atomic orbital (AO) products. We speculate that these difficulties might be overcome by using optimized auxiliary fit sets with more diffuse functions of higher angular momenta. Despite these shortcomings, for subsets of medium and large molecules from the GW5000 database, the error of our approach using basis sets of TZ and augmented double-ζ (DZ) quality is decreasing with system size. On the augmented DZ level, we reproduce canonical, complete basis set limit extrapolated reference values with an accuracy of 80 meV on average for a set of 20 large organic molecules. We anticipate our algorithm, in its current form, to be very useful in the study of single-particle properties of large organic systems such as chromophores and acceptor molecules.

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Density-Based Basis-Set Incompleteness Correction for GW Methods

Cited by 37 publications

References 117 publications

Optical response and band structure of LiCoO2 including electron-hole interaction effects

Optical response and band structure of LiCoO2 including electron-hole interaction effects

Reference Energies for Double Excitations

Low-Order Scaling G₀W₀ by Pair Atomic Density Fitting

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Density-Based Basis-Set Incompleteness Correction for GW Methods

Cited by 37 publications

References 117 publications

Optical response and band structure of LiCoO2 including electron-hole interaction effects

Optical response and band structure of LiCoO2 including electron-hole interaction effects

Reference Energies for Double Excitations

Low-Order Scaling G0W0 by Pair Atomic Density Fitting

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Product

Resources

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Low-Order Scaling G₀W₀ by Pair Atomic Density Fitting