Large Scale GW Calculations

Govoni, Marco; Galli, Giulia

doi:10.1021/ct500958p

Cited by 327 publications

(479 citation statements)

References 113 publications

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“…[313][314][315] However, in view of the on-going development of more efficient QM algorithms 179,[316][317][318][319] in conjunction with the use of graphics processing units 124,318,320,321 (GPUs), this limitation may be overcome in the near future. The calculation for anions is of particular interest considering that the accurate calculation of salt (cation plus anion) hydration free energies, which are not elusive quantities (just as the cation-to-cation difference considered here), would represent an important further validation of the present QM/MM methodology.…”

Section: Discussionmentioning

confidence: 99%

Absolute proton hydration free energy, surface potential of water, and redox potential of the hydrogen electrode from first principles: QM/MM MD free-energy simulations of sodium and potassium hydration

Hofer

Hünenberger

2018

The Journal of Chemical Physics

104

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The absolute intrinsic hydration free energy G • H + ,wat of the proton, the surface electric potential jump χ • wat upon entering bulk water, and the absolute redox potential V • H + ,wat of the reference hydrogen electrode are cornerstone quantities for formulating single-ion thermodynamics on absolute scales. They can be easily calculated from each other but remain fundamentally elusive, i.e., they cannot be determined experimentally without invoking some extra-thermodynamic assumption (ETA). The Born model provides a natural framework to formulate such an assumption (Born ETA), as it automatically factors out the contribution of crossing the water surface from the hydration free energy. However, this model describes the short-range solvation inaccurately and relies on the choice of arbitrary ion-size parameters. In the present study, both shortcomings are alleviated by performing first-principle calculations of the hydration free energies of the sodium (Na + ) and potassium (K + ) ions. The calculations rely on thermodynamic integration based on quantum-mechanical molecular-mechanical (QM/MM) molecular dynamics (MD) simulations involving the ion and 2000 water molecules. The ion and its first hydration shell are described using a correlated ab initio method, namely resolution-of-identity second-order Møller-Plesset perturbation (RIMP2). The next hydration shells are described using the extended simple point charge water model (SPC/E). The hydration free energy is first calculated at the MM level and subsequently increased by a quantization term accounting for the transformation to a QM/MM description. It is also corrected for finite-size, approximate-electrostatics, and potentialsummation errors, as well as standard-state definition. These computationally intensive simulations provide accurate first-principle estimates for G • H + ,wat , χ • wat , and V • H + ,wat , reported with statistical errors based on a confidence interval of 99%. The values obtained from the independent Na + and K + simulations are in excellent agreement. In particular, the difference between the two hydration free energies, which is not an elusive quantity, is 73.9 ± 5.4 kJ mol 1 (K + minus Na + ), to be compared with the experimental value of 71.7 ± 2.8 kJ mol 1 . The calculated values of G • H + ,wat , χ • wat , and V • H + ,wat ( 1096.7 ± 6.1 kJ mol 1 , 0.10 ± 0.10 V, and 4.32 ± 0.06 V, respectively, averaging over the two ions) are also in remarkable agreement with the values recommended by Reif and Hünenberger based on a thorough analysis of the experimental literature ( 1100 ± 5 kJ mol 1 , 0.13 ± 0.10 V, and 4.28 ± 0.13 V, respectively). The QM/MM MD simulations are also shown to provide an accurate description of the hydration structure, dynamics, and energetics. Published by AIP Publishing.

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Section: Discussionmentioning

confidence: 99%

Absolute proton hydration free energy, surface potential of water, and redox potential of the hydrogen electrode from first principles: QM/MM MD free-energy simulations of sodium and potassium hydration

Hofer

Hünenberger

2018

The Journal of Chemical Physics

104

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“…In general a real time or real frequency one-body Green's function is a function used to describe spectral properties such as ionization potentials, electron affinities, or the single-particle spectral function. Methods such as the random phase approximation (RPA) and GW usually express the Green's function using real frequencies to obtain spectra at zero temperature [37,38]. While, in general, the real frequency Green's function is an exponentially decaying function of frequency, it is very difficult to employ it in iterative methods such as DMFT or other embedding methods such as self-energy embedding theory (SEET) [39,40] since iterating usually requires pole shifting algorithms [41][42][43].…”

Section: Theorymentioning

confidence: 99%

Efficient Temperature-Dependent Green’s Function Methods for Realistic Systems: Using Cubic Spline Interpolation to Approximate Matsubara Green’s Functions

Kananenka

Welden

Lan

et al. 2016

J. Chem. Theory Comput.

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The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate modifications the temperature dependence can be preserved while the Green's function grid size can be reduced by about two orders of magnitude by replacing the standard Matsubara frequency grid with a sparser grid and a set of interpolation coefficients. We benchmarked the accuracy of our algorithm as a function of a single parameter sensitive to the shape of the Green's function. Through numerous examples, we confirmed that our algorithm can be utilized in a systematically improvable, controlled, and black-box manner and highly accurate one-and two-body energies and one-particle density matrices can be obtained using only around 5% of the original grid points. Additionally, we established that to improve accuracy by an order of magnitude, the number of grid points needs to be doubled, whereas for the Matsubara frequency grid an order of magnitude more grid points must be used. This suggests that realistic calculations with large basis sets that were previously out of reach because they required enormous grid sizes may now become feasible.

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“…20 This method has been shown to 5 provide quantitative predictions for the quasi-particle (QP) spectrum of organic and inorganic systems. 18,[21][22][23][24] However, not only is GW computationally much more demanding than DFT, the fact that it is typically employed non-self-consistently also leads to a significant starting-point dependence. [25][26][27][28][29][30][31] For the case of the pentacene molecule, for example, it has been found that nonself-consistent G 0 W 0 calculations based on a (semi-)local DFT starting point underestimate the fundamental gap E g in the gas phase by as much as 0.7 eV, while E g calculated at the same level of theory for the pentacene crystal are found in good agreement with the experimentally determined solid-state E g , likely due to a fortuitous cancelation of errors.…”

mentioning

confidence: 99%

Ionization Energies, Electron Affinities, and Polarization Energies of Organic Molecular Crystals: Quantitative Estimations from a Polarizable Continuum Model (PCM)-Tuned Range-Separated Density Functional Approach

Sun

Ryno

Zhong

et al. 2016

J. Chem. Theory Comput.

135

130

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We propose a new methodology for the first-principles description of the electronic properties relevant for charge transport in organic molecular crystals. This methodology, which is based on the combination of a nonempirical, optimally tuned range-separated hybrid functional with the polarizable continuum model, is applied to a series of eight representative molecular semiconductor crystals. We show that it provides ionization energies, electron affinities, and transport gaps in very good agreement with experimental values, as well as with the results of many-body perturbation theory within the GW approximation at a fraction of the computational costs. Hence, this approach represents an easily applicable and computationally efficient tool to estimate the gas-to-crystal phase shifts of the frontier-orbital quasiparticle energies in organic electronic materials.

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Large Scale GW Calculations

Cited by 327 publications

References 113 publications

Absolute proton hydration free energy, surface potential of water, and redox potential of the hydrogen electrode from first principles: QM/MM MD free-energy simulations of sodium and potassium hydration

Absolute proton hydration free energy, surface potential of water, and redox potential of the hydrogen electrode from first principles: QM/MM MD free-energy simulations of sodium and potassium hydration

Efficient Temperature-Dependent Green’s Function Methods for Realistic Systems: Using Cubic Spline Interpolation to Approximate Matsubara Green’s Functions

Ionization Energies, Electron Affinities, and Polarization Energies of Organic Molecular Crystals: Quantitative Estimations from a Polarizable Continuum Model (PCM)-Tuned Range-Separated Density Functional Approach

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