Communication: Explicitly correlated formalism for second-order single-particle Green’s function

Pavošević, Fabijan; Peng, Chong; Ortiz, J. V.; Valeev, Edward F.

doi:10.1063/1.5000916

Cited by 20 publications

(13 citation statements)

References 36 publications

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“…Recently, GF2 theory has experienced a renaissance [35][36][37] , partially due to its simplicity and the inclusion of dynamical exchange effects. In GF2, the self-energy is described by the second order Born approximation, 38,39 resulting in a class of dynamical exchange effects [40][41][42] that appear only at second and higher orders, and thus are often ignored in GW/BSE.…”

Section: Introductionmentioning

confidence: 99%

Time dependent second order Green's function theory for neutral excitations

Dou¹,

Reichman²,

Baer³

et al. 2022

Preprint

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We develop a time dependent second order Green's function theory (GF2) for calculating neutral excited states in molecules. The equation of motion for the lesser Green's function (GF) is derived within the adiabatic approximation to the Kadanoff-Baym (KB) equation using the second order Born approximation for the selfenergy. In the linear response regime, we recast the time dependent KB equation into a Bethe-Salpeter-like equation (GF2-BSE), with a kernel approximated by the second order Coulomb self-energy. We then apply our GF2-BSE to a set of molecules and atoms and find that GF2-BSE is superior to configuration interaction with singles (CIS) and/or time dependent Hartree-Fock (TDHF), particularly for charge transfer excitations, and is comparable to CIS with perturbative doubles (CIS(D)) in most cases.

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Section: Introductionmentioning

confidence: 99%

Time dependent second order Green's function theory for neutral excitations

Dou¹,

Reichman²,

Baer³

et al. 2022

Preprint

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“…MBPT has been applied to a variety of molecular and bulk systems in predicting, e.g. correlation energies, ionization potentials and electron affinities, [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and excited states. 7,15,[24][25][26][27] Excluding several recent applications, [28][29][30][31][32][33][34] MBPT has been limited to relatively small systems due to the steep computational scaling with the system size.…”

Section: Introductionmentioning

confidence: 99%

“…a) Electronic mail: douw@berkeley.edu; These two authors contributed equally b) Electronic mail: mingchen.chem@berkeley.edu; These two authors contributed equally c) Electronic mail: tyler.takeshita@daimler.com d) Electronic mail: roi.baer@huji.ac.il e) Electronic mail: dxn@chem.ucla.edu f) Electronic mail: eran.rabani@berkeley.edu A particularly interesting implementation of MBPT, relevant to the applications reported below, is based on a second-order approximation to the electron self-energy, 2,4,35 which has received increasing attention in recent years. [8][9][10]36 In contrast to the GW approximation, 1 dynamical exchange correlations are included explicitly in the GF2 self-energy to second order in Coulomb interactions, providing accurate ground state energies 37,38 and quasi-particle energies. 9,10,39,40 Although the results of recent studies are extremely promising, the GF2 approach suffers from a high computational cost (O(N 5 )), limiting its application to relatively small system sizes.…”

Section: Introductionmentioning

confidence: 99%

Range-Separated Stochastic Resolution of Identity: Formulation and Application to Second Order Green's Function Theory

Dou

Chen

Takeshita

et al. 2020

Preprint

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We develop a range-separated stochastic resolution of identity approach for the 4-index electron repulsion integrals, where the larger terms (above a predefined threshold) are treated using a deterministic resolution of identity and the remaining terms are treated using a stochastic resolution of identity. The approach is implemented within a second-order Greens function formalism with an improved O(N 3 ) scaling with the size of the basis set, N . Moreover, the range-separated approach greatly reduces the statistical error compared to the full stochastic version (J. Chem. Phys. 151, 044144 ( 2019)), resulting in computational speedups of ground and excited state energies of nearly two orders of magnitude, as demonstrated for hydrogen dimer chains.

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“…[50][51][52][53][54][59][60][61] Explicitly correlated F12 correction schemes have been derived for second-order Green function methods (GF2) 35,[62][63][64][65][66][67][68][69][70][71][72] by Ten-no and coworkers 73,74 and Valeev and coworkers. 75,76 However, to the best of our knowledge, a F12-based correction for GW has not been designed yet.…”

Section: Introductionmentioning

confidence: 99%

Density-Based Basis-Set Incompleteness Correction for GW Methods

Loos

Pradines

Scemama

et al. 2019

J. Chem. Theory Comput.

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Similar to other electron correlation methods, manybody perturbation theory methods based on Green functions, such as the so-called GW approximation, suffer from the usual slow convergence of energetic properties with respect to the size of the one-electron basis set. This displeasing feature is due to the lack of explicit electron-electron terms modeling the infamous Kato electron-electron cusp and the correlation Coulomb hole around it. Here, we propose a computationally efficient density-based basis-set correction based on short-range correlation density functionals which significantly speeds up the convergence of energetics towards the complete basis set limit. The performance of this density-based correction is illustrated by computing the ionization potentials of the twenty smallest atoms and molecules of the GW100 test set at the perturbative GW (or G 0 W 0 ) level using increasingly large basis sets. We also compute the ionization potentials of the five canonical nucleobases (adenine, cytosine, thymine, guanine, and uracil) and show that, here again, a significant improvement is obtained.

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Communication: Explicitly correlated formalism for second-order single-particle Green’s function

Cited by 20 publications

References 36 publications

Time dependent second order Green's function theory for neutral excitations

Time dependent second order Green's function theory for neutral excitations

Range-Separated Stochastic Resolution of Identity: Formulation and Application to Second Order Green's Function Theory

Density-Based Basis-Set Incompleteness Correction for GW Methods

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