Simple and accurate exchange energy for density functional theory

Chachiyo, Teepanis; Chachiyo, Hathaithip

doi:10.48550/arxiv.1706.01343

Cited by 3 publications

(4 citation statements)

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“…In addition to SAP, we have discussed, implemented and assessed a variant of SAD we call SADNO that produces guess orbitals by purification of the nonidempotent SAD guess density matrix, which does not appear to have been previously considered in the literature, as well as pointed out and demonstrated that an extended Huckel guess can be easily implemented on top of a pre-existing SAD solver, based on the procedure of ref 43. The SAP guess was shown to yield excellent guess wave functions in combination with the Chachiyo generalized gradient exchange functional; 106 almost as good results could also be obtained with the CAP 105 and LDA 103,104 exchange functionals.…”

Section: Summary and Discussionmentioning

confidence: 83%

“…Initial experimentation with various functionals in LIBXC revealed that the best results were obtained from exchangeonly calculations, and that the best exchange functionals were the local spin-density approximation (LDA-X), 103,104 the ''correct asymptotic potential'' (CAP-X), 105 as well as the Chachiyo 106 (CHA-X) generalized gradient exchange functionals. Self-consistent atomic potentials were generated for these three functionals at the nonrelativistic and scalarrelativistic levels of theory.…”

Section: Theorymentioning

confidence: 99%

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Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials: Simple yet Efficient

Lehtola

2019

J. Chem. Theory Comput.

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Electronic structure calculations, such as in the Hartree–Fock or Kohn–Sham density functional approach, require an initial guess for the molecular orbitals. The quality of the initial guess has a significant impact on the speed of convergence of the self-consistent field (SCF) procedure. Popular choices for the initial guess include the one-electron guess from the core Hamiltonian, the extended Hückel method, and the superposition of atomic densities (SAD). Here, we discuss alternative guesses obtained from the superposition of atomic potentials (SAP), which is easily implementable even in real-space calculations. We also discuss a variant of SAD which produces guess orbitals by purification of the density matrix that could also be used in real-space calculations, as well as a parameter-free variant of the extended Hückel method, which resembles the SAP method and is easy to implement on top of existing SAD infrastructure. The performance of the core Hamiltonian, the SAD, and the SAP guesses as well as the extended Hückel variant is assessed in nonrelativistic calculations on a data set of 259 molecules ranging from the first to the fourth periods by projecting the guess orbitals onto precomputed, converged SCF solutions in single- to triple-ζ basis sets. It is shown that the proposed SAP guess is the best guess on average. The extended Hückel guess offers a good alternative, with less scatter in accuracy.

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Section: Summary and Discussionmentioning

confidence: 83%

Section: Theorymentioning

confidence: 99%

Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials: Simple yet Efficient

Lehtola

2019

J. Chem. Theory Comput.

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“…To produce the results as shown in the following section one also needs an exchange energy contribution which we used our previously proposed exchange functional [23].…”

Section: Methodsmentioning

confidence: 99%

Understanding electron correlation energy through density functional theory

Chachiyo¹,

Chachiyo²

2020

Computational and Theoretical Chemistry

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A curious behavior of electron correlation energy is explored. Namely, the correlation energy is the energy that tends to drive the system toward that of the uniform electron gas. As such, the energy assumes its maximum value when a gradient of density is zero. As the gradient increases, the energy is diminished by a gradient suppressing factor, designed to attenuate the energy from its maximum value similar to the shape of a bell curve. Based on this behavior, we constructed a very simple mathematical formula that predicted the correlation energy of atoms and molecules. Combined with our proposed exchange energy functional, we calculated the correlation energies, the total energies, and the ionization energies of test atoms and molecules; and despite the unique simplicities, the functionals' accuracies are in the top tier performance, competitive to the B3LYP, BLYP, PBE, TPSS, and M11. Therefore, we propose that, as guided by the simplicities and supported by the accuracies, the correlation energy is the energy that locally tends to drive the system toward the uniform electron gas. Without Correlation Include Correlation ExactlyHarmonic Potential Coulomb Repulsion

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“…20,21,[26][27][28][29][30][31][32][33][34] These functionals which incorporate density gradients such that the potential is asymptotically well behaved, 21,[33][34][35][36] are mathematically easy to handle and often produced good results without much computational cost. 27,34,36 Similarly, accurate exact-exchange functionals with variations that approach the form enforced by LDA+vLB have appeared, 37 but not yet explored for solids.…”

Section: Introductionmentioning

confidence: 99%

Simple correction to bandgap problems in IV and III–V semiconductors: an improved, local first-principles density functional theory

Datta

Singh

Chaudhuri³

et al. 2019

J. Phys.: Condens. Matter

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We report results from a fast, efficient and first-principles full-potential N th -order muffin-tin orbital (FP-NMTO) method combined with van Leeuwen-Baerends correction to local density approximation exchange-correlation potential. We show that more complete and compact basis set is critical in improving the electronic and structural properties. We exemplify the self-consistent (non-relativistic) FP-NMTO calculations on group IV and III-V semiconductors. Notably, predicted bandgap, lattice constant, and bulk modulus are in good agreement with experiments (e.g., for Ge we find 0.86 eV, 5.57Å, 75 GPa vs. measured: 0.74 eV, 5.66Å, 77.2 GPa). We also showcase its application to the electronic properties of 2-dimensional h−BN and h−SiC, again finding good agreement with experiments. arXiv:1807.07606v3 [cond-mat.mtrl-sci]

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Simple and accurate exchange energy for density functional theory

Cited by 3 publications

References 0 publications

Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials: Simple yet Efficient

Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials: Simple yet Efficient

Understanding electron correlation energy through density functional theory

Simple correction to bandgap problems in IV and III–V semiconductors: an improved, local first-principles density functional theory

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