Nonlocal Wigner-like correlation energy density functional: Parametrization and tests on two-electron systems

Katriel, Jacob; Bauer, Michael; Springborg, Michael; McCarthy, Shane P.; Thakkar, Ajit J.

doi:10.1063/1.2747242

Cited by 12 publications

(12 citation statements)

References 46 publications

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“…Energies Derived from Linear Interpolation. As seen in Figure 1, deducting the first-order perturbation term rendered the dependence on δ = 1/D nearly linear and nearly flat for ε D − ε D (1) λ but slanted for the corresponding HF approximation and hence also for the correlation energy. Interpolation between D → ∞ and D = 1 was previously found to work well.…”

Section: ■ Basic Theorymentioning

confidence: 91%

Exploring Unorthodox Dimensions for Two-Electron Atoms

2017

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Melding quantum and classical mechanics is an abiding quest of physical chemists who strive for heuristic insights and useful tools. We present a surprisingly simple and accurate treatment of ground-state two-electron atoms. It makes use of only the dimensional dependence of a hydrogen atom, together with the exactly known first-order perturbation value of the electron-electron interaction, both quintessentially quantum, and the D → ∞ limit, entirely classical. The result is an analytic formula for D-dimensional two-electron atoms with Z ≥ 2. For D = 3 helium, it gives accuracy better than 2 millihartrees, which is better than current density functional theory. A kindred explicit formula for correlation energy exploits interpolation between D → ∞ and D = 1 or 2; when added to the Hartree-Fock energy, it improves accuracy for D = 3 helium to better than 0.1 millihartrees.

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Section: ■ Basic Theorymentioning

confidence: 91%

Exploring Unorthodox Dimensions for Two-Electron Atoms

2017

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“…. ,36 in all the cases, (2) quantum Monte Carlo (QMC) calculations for both positive and negative singly charged ions from Li through Ar [35] (Mal2010), (3) Fadeev random phase approximation calculations [36] (Bar2012) for light atoms and ions up to Ar, which includes He, Be 2+ , Be, Ne, Mg 2+ , Mg, and Ar 14+ , (4) He isoelectronic series (2 Z 10) computed by Katriel et al [37] (Kat2007), and (5) [26].…”

Section: Testing the Relation For Other Calculationsmentioning

confidence: 99%

Scaling in the correlation energies of atomic ions

2014

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We show through numerical investigations that the ground-state correlation energies of atomic ions follow an unexpectedly simple scaling relation, E c ≈ Z 4/3 f c (Z/N), where N is the number of electrons, Z is the atomic number, and f c is a universal function, for which an analytic expression with a one-parameter fit can be provided. The relation agrees well with several sets of correlation energies obtained from different methods for atomic ions with N = 2, . . . ,18 and Z = 2, . . . ,28. Moreover, our relation gives a good agreement with neutral atoms up to N ≈ 90. Our main result is readily applicable to estimating correlation energies of heavy elements, for which there are no available data in the literature. The simplicity of the relation may also have implications in the development of correlation functionals within density-functional theory.

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“…The loss of carbon monoxide from these intermediates results in the formation of the corresponding electronic ground-state acetylenes. Ab initio and DFT quantum mechanical methods [12][13][14][15][16] have been used to examine the following current topics of interest [17][18][19][20][21][22][23][24][25][26]: the elucidation of electronic structures and related chemical and spectroscopic properties of the molecules, the design of routes for synthesis and theoretical characterization of novel molecules of medicinal and biochemical importance, and the discovery of reaction paths. Newer functional approaches and methodologies are currently being devised for such a purpose [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Theoretical investigation of the photochemical reaction mechanism of cyclopropenone decarbonylation

2011

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The gas-phase decomposition mechanism of the photochemical and thermal reaction of cyclopropenone leading to carbon monoxide and acetylene has been investigated theoretically. We employed the B3LYP, MP2, and CASSCF methods with the 6-311 þ G** basis set to determine the pathways and the potential energy surface (PES) of this reaction. PES minima were characterized by the absence of any imaginary frequencies and compared with the transition states that contained single imaginary frequencies. The intrinsic reaction coordinate (IRC) method was used to find the minimum energy paths in which reactants and products were connected to the transition states. Activation barrier, thermodynamic, and IRC analyses were performed using the above three methods. Our computations indicated that the decomposition of cyclopropenone proceeds through a stepwise mechanism containing two transition states (TS1 and TS2) and an intermediate. The results show that TS1, the critical transition state, determines the rate of the cyclopropenone decomposition reaction. Therefore, we employed natural bond order (NBO) calculations to probe the structure of the intermediate. The calculations showed that the intermediate has resonance structures containing a carbene and a zwitterion. Our results are in good agreement with previous theoretical and experimental studies.

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Nonlocal Wigner-like correlation energy density functional: Parametrization and tests on two-electron systems

Cited by 12 publications

References 46 publications

Exploring Unorthodox Dimensions for Two-Electron Atoms

Exploring Unorthodox Dimensions for Two-Electron Atoms

Scaling in the correlation energies of atomic ions

Theoretical investigation of the photochemical reaction mechanism of cyclopropenone decarbonylation

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