Improving approximate determination of the noninteracting electronic kinetic energy density from electron density

Astakhov, Andrey A.; Сташ, А. И.; Tsirelson, Vladimir G.

doi:10.1002/qua.24957

Cited by 31 publications

(42 citation statements)

References 120 publications

(131 reference statements)

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“…A detailed discussion of application of the experimental ED in the DFT formalism can be found in Refs. [77,78,79]. We used the experimental electron density and its derivatives expressed in terms of Hansen-Coppens space-extended multipole structural model [80]; in computations, the actual values of these quantities at each point r have been employed.…”

Section: Methodsmentioning

confidence: 99%

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Bonding in molecular crystals from the local electronic pressure viewpoint

2015

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The spatial distribution of the internal pressure of an electron fluid, which spontaneously arises at the formation of a molecule or a crystal, is linked to the main features of chemical bonding in molecular crystals. The local pressure is approximately expressed in terms of the experimental electron density and its derivatives using the density functional formalism and is applied to identify the bonding features in benzene, formamide and chromium hexacarbonyl. We established how the spatial regions of compression and stretching of the electron fluid in these solids reflect the typical features of chemical bonds of different types. Thus, the internal electronic pressure can serve as a bonding descriptor, which has a clear physical meaning and reveals the specific features of variety of the chemical bonds expressing them in terms of the electron density.

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Section: Methodsmentioning

confidence: 99%

“…Thus, distribution of the isotropic internal pressure of the inhomogeneous electron fluid caused by quantum kinetic and exchange effects equals to ( ) ( [76] or by using some other similar DFT approximations, see [77]. Usually approximate functions ( ) s t r show a wrong asymptotic behavior close to the nuclei positions.…”

Section: Methodsmentioning

confidence: 99%

Bonding in molecular crystals from the local electronic pressure viewpoint

2015

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“…Some quantities are frequently used on BCP to capture the bond specific features and among them, kinetic energy density (KED) at the BCP can be the form of

G_{c} = 2.8173 \times ρ_{c}^{5 / 3} + \nabla^{2} ρ_{c} / 6

in the gradient expansion approximation . Seriani showed that the KED at the BCP is associated with the band gap for alkali and alkaline‐earth oxides . Seriani reported that the band gap of oxides of alkali and alkaline‐earth metals linearly depends on the KED at the BCP.…”

Section: Introductionmentioning

confidence: 99%

Correlation of electron density and bond length to band gap for binary oxides and halides

Ryang¹,

Kang²,

Choe³

et al. 2019

Int J of Quantum Chemistry

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The best quantity correlated to the electronic energy band gap is found for alkali and alkaline‐earth metal oxides and halides with face centered cubic (fcc) structure based on density functional theory and Bader's atom‐in‐molecule theory. Previous studies show the correlation of the band gap to the ground state electron density at the bond critical point (BCP). Whereas, in quantum mechanics, the gap between the energy levels of one dimensional square well potential is inversely proportional to the square of the width of the well which is the metal–nonmetal chemical bond length in our case. These motivate the proposition of a new quantity Q, the ratio of the density at the BCP to the square of the bond length. Our study reveals that, for the aforementioned materials, the band gap has a strong correlation to Q when they are multiplied by the density at the BCP.

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“…[6][7][8][9][10][11][12][13][14][15][16] There are some new developments in applying and understanding the Ghosh-Berkowitz-Parr entropy. [17][18][19][20][21][22][23] The local temperature of Ghosh et al was defined via the kinetic energy density and varies from point to point. However, the kinetic energy density is not uniquely defined.…”

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Thermodynamical transcription of the density functional theory with constant temperature

Nagy

2017

Int J of Quantum Chemistry

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The thermodynamical interpretation of the density functional theory for an electronic ground state is revisited. Ghosh et al. invented the thermodynamical transcription of the ground-state density functional theory into a local thermodynamics. They introduced the idea of the local temperature that varies from point to point. The local temperature is defined via the kinetic energy density. The kinetic energy density is not uniquely defined, usually the everywhere positive gradient form is applied. Now we prove that it is possible selecting the kinetic energy density so that the local temperature be a constant for the whole system under consideration. The kinetic energy density is proportional to the electron density and the temperature is proportional to the kinetic energy. Furthermore, the kinetic energy density corresponding to the constant temperature, maximizes the information entropy.density functional theory, information entropy, thermodynamical transcription | I N T R O D U C T I O NMore than three decades ago Ghosh et al. wrote a paper [1] entitled "Transcription of ground-state density functional theory into a local thermodynamics." They obtained a phase-space distribution function fðr; pÞ by maximizing a phase-space Shannon information entropy subject to the conditions that f yields the density nðrÞ and the local kinetic energy density of the system. A local Maxwell-Boltzmann distribution function was resulted.They introduced the concept of local temperature. This formalism has been used in several applications. [2,3] For example, approximate expressions for the exchange energy were derived. [4,5] It was possible to define local entropy, free energy, and to establish an analogy with the classical thermodynamics of fluids. [2] There have been several extension of the formalism. [6][7][8][9][10][11][12][13][14][15][16] There are some new developments in applying and understanding the Ghosh-Berkowitz-Parr entropy. [17][18][19][20][21][22][23] The local temperature of Ghosh et al. was defined via the kinetic energy density and varies from point to point. However, the kinetic energy density is not uniquely defined. Adding a term that integrates to zero to the kinetic energy density results another kinetic energy density with the same kinetic energy but different local temperature. Usually, the gradient form of the kinetic energy density is applied, because it is everywhere positive. Now we prove that it is possible selecting the kinetic energy density so that the local temperature be a constant for the whole system under consideration. The kinetic energy density is proportional to the electron density and the temperature is proportional to the kinetic energy. Moreover, the kinetic energy density corresponding to the constant temperature, maximizes the information entropy. This very simple interpretation gives a new insight into the density functional theory. Analytical examples for the linear harmonic oscillator and the H-atom are presented.In the following section, the Ghosh-Berkowitz-Parr theory is ...

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Improving approximate determination of the noninteracting electronic kinetic energy density from electron density

Cited by 31 publications

References 120 publications

Bonding in molecular crystals from the local electronic pressure viewpoint

Bonding in molecular crystals from the local electronic pressure viewpoint

Correlation of electron density and bond length to band gap for binary oxides and halides

Thermodynamical transcription of the density functional theory with constant temperature

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