Construction of the Pauli potential, Pauli energy, and effective potential from the electron density

Holas, A.; March, N. H.

doi:10.1103/physreva.44.5521

Cited by 125 publications

(70 citation statements)

References 27 publications

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“…(1) and (3) is the identification of the Pauli component in the kinetic energy,23-27 E Pauli ≡ T S - T W , which must be included as part of the contribution to the quantum effect.…”

Section: Methods and Computationsmentioning

confidence: 99%

Steric, Quantum, and Electrostatic Effects on S_N2 Reaction Barriers in Gas Phase

Liu¹,

Hu²,

Pedersen³

2010

J. Phys. Chem. A

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Biomolecular nucleophilic substitution reactions, SN2, are fundamental and commonplace in chemistry. It is the well documented experimental finding in the literature that vicinal substitution with bulkier groups near the reaction center significantly slows the reaction due to steric hindrance, but theoretical understanding in the quantitative manner about factors dictating the SN2 reaction barrier height is still controversial. In this work, employing the new quantification approach that we recently proposed for the steric effect from the density functional theory framework, we investigate the relative contribution of three independent effects, steric, electrostatic, and quantum, to the SN2 barrier heights in gas phase for substituted methyl halide systems, R1R2R3CX, reacting with fluorine anion where R1, R2, and R3 denote substituting groups and X=F or Cl. We found that in accordance with the experimental finding, for these systems the steric effect dominates the transition state barrier, contributing positively to barrier heights, but this contribution is largely compensated by the negative, stabilizing contribution from the quantum effect due to the exchange-correlation interactions. Moreover, we find that it is the component from the electrostatic effect that is linearly correlated with the SN2 barrier height for the systems investigated in the present study. In addition, we compared our approach with the conventional method of energy decomposition in density functional theory, as well as examined the steric effect from the wavefunction theory for these systems via the natural bond orbital analysis.

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“…(1) and (3) is the identification of the Pauli component in the kinetic energy,23-27 E Pauli ≡ T S - T W , which must be included as part of the contribution to the quantum effect.…”

Section: Methods and Computationsmentioning

confidence: 99%

Steric, Quantum, and Electrostatic Effects on S_N2 Reaction Barriers in Gas Phase

Liu¹,

Hu²,

Pedersen³

2010

J. Phys. Chem. A

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“…The Pauli energy is defined as T p = T s − T w [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The Euler equation (1) can be rewritten as…”

Section: Introductionmentioning

confidence: 99%

Cusp relation for the Pauli potential

et al. 2014

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“…[13][14][15][16]). The corresponding energy density, τ W (r) = |∇n(r)| 2 8n(r) , plays a crucial role for metaGGA functionals, where it is used to detect one-electron and iso-orbital regions (see, e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic nodal planes in the electron density and the potential in the effective equation for the square root of the density

Gori‐Giorgi

Baerends

2018

Eur. Phys. J. B

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Abstract. It is known that the asymptotic decay (|r| → ∞) of the electron density n(r) outside a molecule is informative about its first ionization potential I0. It has recently become clear that the special circumstance that the Kohn-Sham (KS) highest-occupied molecular orbital (HOMO) has a nodal plane that extends to infinity may give rise to different cases for the asymptotic behavior of the exact density and of the exact KS potential [P. Gori-Giorgi et al., Mol. Phys. 114, 1086(2016]. Here we investigate the consequences of such a HOMO nodal plane for the effective potential in the Schrödinger-like equation for the square root of the density, showing that for atoms and molecules it will usually diverge asymptotically on the plane, either exponentially or polynomially, depending on the coupling between Dyson orbitals. We also analyze the issue in the external harmonic potential, reporting an example of an exact analytic density for a fully interacting system that exhibits a different asymptotic behavior on the nodal plane.

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Construction of the Pauli potential, Pauli energy, and effective potential from the electron density

Cited by 125 publications

References 27 publications

Steric, Quantum, and Electrostatic Effects on S_N2 Reaction Barriers in Gas Phase

Steric, Quantum, and Electrostatic Effects on S_N2 Reaction Barriers in Gas Phase

Cusp relation for the Pauli potential

Asymptotic nodal planes in the electron density and the potential in the effective equation for the square root of the density

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Construction of the Pauli potential, Pauli energy, and effective potential from the electron density

Cited by 125 publications

References 27 publications

Steric, Quantum, and Electrostatic Effects on SN2 Reaction Barriers in Gas Phase

Steric, Quantum, and Electrostatic Effects on SN2 Reaction Barriers in Gas Phase

Cusp relation for the Pauli potential

Asymptotic nodal planes in the electron density and the potential in the effective equation for the square root of the density

Contact Info

Product

Resources

About

Steric, Quantum, and Electrostatic Effects on S_N2 Reaction Barriers in Gas Phase

Steric, Quantum, and Electrostatic Effects on S_N2 Reaction Barriers in Gas Phase