Assessment of Tuning Methods for Enforcing Approximate Energy Linearity in Range-Separated Hybrid Functionals

Gledhill, Jonathan D.; Peach, Michael J.; Tozer, David J.

doi:10.1021/ct400592a

Cited by 34 publications

(42 citation statements)

References 57 publications

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“…The basic idea is to parametrize the exact-exchange energy such that the linearity condition is restored [19][20][21][22][23]. This route has been predominantly followed with the long-range separated BaerNeuhauser-Livshiz (BNL) hybrid functional [24,25].…”

Section: ∂E ∂Nmentioning

confidence: 99%

Enforcing the linear behavior of the total energy with hybrid functionals: Implications for charge transfer, interaction energies, and the random-phase approximation

et al. 2016

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We obtain the exchange parameter of hybrid functionals by imposing the fundamental condition of a piecewise linear total energy with respect to electron number. For the Perdew-Burke-Ernzerhof (PBE) hybrid family of exchange-correlation functionals (i.e., for an approximate generalized Kohn-Sham theory) this implies that (i) the highest occupied molecular orbital corresponds to the ionization potential (I ), (ii) the energy of the lowest unoccupied molecular orbital corresponds to the electron affinity (A), and (iii) the energies of the frontier orbitals are constant as a function of their occupation. In agreement with a previous study [N. Sai et al., Phys. Rev. Lett. 106, 226403 (2011)], we find that these conditions are met for high values of the exact exchange admixture α and illustrate their importance for the tetrathiafulvalene-tetracyanoquinodimethane complex for which standard density functional theory functionals predict artificial electron transfer. We further assess the performance for atomization energies and weak interaction energies. We find that atomization energies are significantly underestimated compared to PBE or PBE0, whereas the description of weak interaction energies improves significantly if a 1/R 6 van der Waals correction scheme is employed.

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Section: ∂E ∂Nmentioning

confidence: 99%

Enforcing the linear behavior of the total energy with hybrid functionals: Implications for charge transfer, interaction energies, and the random-phase approximation

et al. 2016

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“…The value of µ can be fixed or it can be 'tuned' on a system-by-system basis by minimising some tuning norm. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Whether the parameter is fixed or tuned, it is well established that such functionals yield improvements in many long-range properties, most notably charge-transfer excitation energies, and they have become the functional of choice in many studies.…”

Section: Introductionmentioning

confidence: 99%

“…15, we investigated a wide range of norms for use in tuned, range-separated functionals. The norms were largely based on Koopmans conditions, which arise from the piecewise linearity 21 of the exact electronic energy, E, as a function of electron number,…”

Section: Introductionmentioning

confidence: 99%

Range-Separation Parameter in Tuned Exchange–Correlation Functionals: Successive Ionizations and the Fukui Function

Gledhill

Proft

Tozer

2016

J. Chem. Theory Comput.

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe range-separation parameter in tuned, range-separated exchange-correlation functionals is investigated in two contexts. First, the system-dependence of the parameter is investigated for a series of systems obtained by successively ionising a single species, paying particular attention to the degree of linearity in the energy versus electron number curve. The parameter exhibits significant system-dependence and so achieving near-linearity in one segment of the curve leads to strong non-linearity in other segments. This provides a challenging test case for the development of new functionals designed to overcome the known problems of this class of functional. Next, the study considers whether a range-separation parameter tuned to a Koopmans energy condition is also applicable for the analogous density condition. This is tested by comparing two formulations of the Fukui function of conceptual density functional theory, * To whom correspondence should be addressed † Durham University ‡ Vrije Universiteit Brussel 1 for three representative systems. Both formulations yield the same general features and are not highly sensitive to the range-separation parameter. However, the agreement between the two is near-optimal when the energy-tuned parameter is used, indicating that this parameter is applicable for the analogous density condition.

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“…For molecular systems, tuning strategies [67,68,69,70,71,72,73,74,75,76] have been developed within range-separated hybrid functionals to reproduce piecewise linearity and improve predictions. [71,77] However, the observed curvature shows marked sizedependence [78,79,80,81], apparently vanishing for large systems.…”

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Density functional theory for modelling large molecular adsorbate–surface interactions: a mini-review and worked example

Janet

Zhao

Ioannidis

et al. 2016

Molecular Simulation

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First-principles simulation has played an ever-increasing role in the discovery and interpretation of the chemical properties of surface-adsorbate interactions.Nevertheless, key challenges remain for the computational chemist wishing to study surface chemistry: modelling the full extent of experimental conditions, managing computational cost, minimizing human effort in simulation setup, and maximizing accuracy. This article introduces new tools for streamlining surface chemistry simulation setup and reviews some of the challenges in first-principles, density functional theory (DFT) simulation of surface phenomena. Furthermore, we provide a worked example of Co tetraphenylporphyrin (CoTPP) on Au (111) in which we both analyze electronic and energetic properties with both semi-local DFT and compare to predictions made from hybrid functional and the so-called DFT+U correction. Through both review and the worked example, we aim to provide a pedagogical introduction to both the challenges and the insight that first-principles simulation can provide in surface chemistry.

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Assessment of Tuning Methods for Enforcing Approximate Energy Linearity in Range-Separated Hybrid Functionals

Cited by 34 publications

References 57 publications

Enforcing the linear behavior of the total energy with hybrid functionals: Implications for charge transfer, interaction energies, and the random-phase approximation

Enforcing the linear behavior of the total energy with hybrid functionals: Implications for charge transfer, interaction energies, and the random-phase approximation

Range-Separation Parameter in Tuned Exchange–Correlation Functionals: Successive Ionizations and the Fukui Function

Density functional theory for modelling large molecular adsorbate–surface interactions: a mini-review and worked example

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