<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mi>W</mml:mi></mml:mrow></mml:math>calculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods

Pham, Tuan Anh; Nguyen, Hong Duong; Rocca, Dario; Galli, Giulia

doi:10.1103/physrevb.87.155148

Cited by 139 publications

(149 citation statements)

References 64 publications

(60 reference statements)

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“…This is in close agreement with the 7.45 eV and 4.40 eV plane wave G 0 W 0 @LDA values of Ref. 40 (LDA geometry). The G 0 W 0 @LDA gap remains smaller than the ∼4.9 eV experimental value, an issue that will be addressed by the partially self-consistent scheme used in the present study, as discussed below.…”

Section: Technical Detailssupporting

confidence: 91%

Exploring approximations to theGWself-energy ionic gradients

et al. 2015

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The accuracy of the many-body perturbation theory GW formalism to calculate electron-phonon coupling matrix elements has been recently demonstrated in the case of a few important systems. However, the related computational costs are high and thus represent strong limitations to its widespread application. In the present study, we explore two less demanding alternatives for the calculation of electron-phonon coupling matrix elements on the many-body perturbation theory level. Namely, we test the accuracy of the static Coulomb-hole plus screened-exchange (COHSEX) approximation and further of the constant screening approach, where variations of the screened Coulomb potential W upon small changes of the atomic positions along the vibrational eigenmodes are neglected. We find this latter approximation to be the most reliable, whereas the static COHSEX ansatz leads to substantial errors. Our conclusions are validated in a few paradigmatic cases: diamond, graphene and the C60 fullerene. These findings open the way for combining the present many-body perturbation approach with efficient linear-response theories.

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Section: Technical Detailssupporting

confidence: 91%

Exploring approximations to theGWself-energy ionic gradients

et al. 2015

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“…The most computationally intensive element in the GW method, the calculation of the polarization potential (screen Coulomb interaction), involves an algorithmic complexity that scales as the fourth power of the system size [33,34]. Various approaches have been developed to reduce the computational bottlenecks of the GW approach [8,18,23,[33][34][35][36][37]. Despite these advances, GW calculations are still quite expensive for many of the intended applications in the fields of materials science, surface science and nanoscience.…”

mentioning

confidence: 99%

Breaking the Theoretical Scaling Limit for Predicting Quasiparticle Energies: The StochasticGWApproach

et al. 2014

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We develop a formalism to calculate the quasi-particle energy within the GW many-body perturbation correction to the density functional theory (DFT). The occupied and virtual orbitals of the Kohn-Sham (KS) Hamiltonian are replaced by stochastic orbitals used to evaluate the Green function, the polarization potential, and thereby the GW self-energy. The stochastic GW (sGW) relies on novel theoretical concepts such as stochastic time-dependent Hartree propagation, stochastic matrix compression and spatial/temporal stochastic decoupling techniques. Beyond the theoretical interest, the formalism enables linear scaling GW calculations breaking the theoretical scaling limit for GW as well as circumventing the need for energy cutoff approximations. We illustrate the method for silicon nanocrystals of varying sizes with Ne > 3000 electrons.The GW approximation [1, 2] to many-body perturbation theory (MBPT) [3] offers a reliable and accessible theory for quasi-particles (QPs) and their energies [2,[4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], enabling estimation of electronic excitations [19][20][21][22][23][24][25] quantum conductance [26][27][28][29][30] and level alignment in hybrid systems [31,32]. Practical use of GW for large systems is severely limited because of the steep CPU and memory requirements as system size increases. The most computationally intensive element in the GW method, the calculation of the polarization potential (screen Coulomb interaction), involves an algorithmic complexity that scales as the fourth power of the system size [33,34]. Various approaches have been developed to reduce the computational bottlenecks of the GW approach [8,18,23,[33][34][35][36][37]. Despite these advances, GW calculations are still quite expensive for many of the intended applications in the fields of materials science, surface science and nanoscience.In this letter we develop a stochastic, orbital-less, formalism for the GW theory, unique in that it does not reference occupied or virtual orbitals and orbital energies of the KS Hamiltonian. While the approach is inspired by recent developments in electronic structure theory using stochastic orbitals [38][39][40][41][42] it introduces three powerful and basic notions: Stochastic decoupling, stochastic matrix compression and stochastic time-dependent Hartree (sTDH) propagation. The result is a stochastic formulation of GW, where the QP energies become random variables sampled from a distribution with a mean equal to the exact GW energies and a statistical error proportional to the inverse number of stochastic orbitals (iterations, I sGW ).We illustrate the sGW formalism for silicon nanocrystals (NCs) with varying sizes and band gaps [43,44] and demonstrate that the CPU time and memory required by sGW scales nearly linearly with system size, thereby providing means to study QPs excitations in large systems of experimental and technological interest.In the reformulation of the GW approach, we treat the QP energy (ε QP = ω QP ) as a perturbative correction to th...

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“…However, Kohn-Sham DFT (KS-DFT) approximations predict poorly quasiparticle excitation energies both in confined and in extended systems, [2][3][4] even for the frontier occupied orbital energy, for which KS-DFT is expected to be exact. [5][6][7] This has led to the development of two main first-principles alternative frameworks for quasiparticle excitations: many-body perturbation theory, mainly within the so-called GW approximation 8 on top of DFT, [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and generalized-KS DFT. [26][27][28][29][30] Recently, range-separated hybrid (RSH) functionals 31-37 combined with an optimally-tuned range parameter 38,39 were shown to very successfully predict quasiparticle band gaps, band edge energies and excitation energies for a range of interesting small molecular systems, well matching both experimental results and GW predictions.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Optimally Tuned Range-Separated Hybrid Density Functional Theory

et al. 2015

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We develop a stochastic formulation of the optimally-tuned range-separated hybrid density functional theory which enables significant reduction of the computational effort and scaling of the non-local exchange operator at the price of introducing a controllable statistical error. Our method is based on stochastic representations of the Coulomb convolution integral and of the generalized Kohn-Sham density matrix. The computational cost of the approach is similar to that of usual Kohn-Sham density functional theory, yet it provides much more accurate description of the quasiparticle energies for the frontier orbitals. This is illustrated for a series of silicon nanocrystals up to sizes exceeding 3000 electrons. Comparison with the stochastic GW many-body perturbation technique indicates excellent agreement for the fundamental band gap energies, good agreement for the band-edge quasiparticle excitations, and very low statistical errors in the total energy for large systems. The present approach has a major advantage over one-shot GW by providing a selfconsistent Hamiltonian which is central for additional post-processing, for example in the stochastic Bethe-Salpeter approach.

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GWcalculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods

Cited by 139 publications

References 64 publications

Exploring approximations to theGWself-energy ionic gradients

Exploring approximations to theGWself-energy ionic gradients

Breaking the Theoretical Scaling Limit for Predicting Quasiparticle Energies: The StochasticGWApproach

Stochastic Optimally Tuned Range-Separated Hybrid Density Functional Theory

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