Atomic Correlation Energy from the Electron Density at the Nucleus†

2007 ◽  
Vol 111 (41) ◽  
pp. 10422-10425 ◽  
Author(s):  
Shubin Liu ◽  
Robert G. Parr
Keyword(s):  
Electron Density ◽  
Correlation Energy ◽  
Atomic Correlation

Correlation energy for a slater determinant fitted to the electron density

2009 ◽  
Vol 28 (S19) ◽  
pp. 525-533
Author(s):  
L. Cohen ◽  
C. Frishberg ◽  
Chongmoon Lee ◽  
L. J. Massa
Keyword(s):  
Electron Density ◽  
Correlation Energy ◽  
Slater Determinant

scholarly journals The experimental and theoretical QTAIMC study of the atomic and molecular interactions in dinitrogen tetroxide

2009 ◽  
Vol 65 (5) ◽  
pp. 647-658 ◽  
Author(s):  
Vladimir G. Tsirelson ◽  
Anastasia V. Shishkina ◽  
Adam I. Stash ◽  
Simon Parsons
Keyword(s):  
Energy Density ◽  
Potential Energy ◽  
Electron Density ◽  
Molecular Interactions ◽  
Electrostatic Potential ◽  
Correlation Energy ◽  
Three Dimensional ◽  
Geometry Optimization ◽  
Intermolecular Bond ◽  
Experimental Electron Density

The atomic and molecular interactions in a crystal of dinitrogen tetraoxide, α-N2O4, have been studied in terms of the quantum topological theory of molecular structure using high-resolution, low-temperature X-ray diffraction data. The experimental electron density and electrostatic potential have been reconstructed with the Hansen–Coppens multipole model. In addition, the three-dimensional periodic electron density of crystalline α-N2O4 has been calculated at the B3LYP/cc-pVDZ level of theory with and without the geometry optimization. The application of the quantum theory of atoms in molecules and crystals (QTAIMC) recovered the two types of intermolecular bond paths between O atoms in crystalline α-N2O4, one measuring 3.094, the other 3.116 Å. The three-dimensional distribution of the Laplacian of the electron density around the O atoms showed that the lumps in the negative Laplacian fit the holes on the O atoms in the adjacent molecules, both atoms being linked by the intermolecular bond paths. This shows that the Lewis-type molecular complementarity contributes significantly to intermolecular bonding in crystalline N2O4. Partial overlap of atomic-like basins created by zero-flux surfaces in both the electron density and the electrostatic potential show that attractive electrostatic interaction exists between O atoms even though they carry the same net formal charge. The exchange and correlation contributions to the potential energy density were also computed by means of the model functionals, which use the experimental electron density and its derivatives. It was found that the intermolecular interactions in α-N2O4 are accompanied by the correlation energy-density `bridges' lowering the local potential energy along the intermolecular O...O bond paths in the electron density, while the exchange energy density governs the shape of bounded molecules.

Comparative electronic analysis between hydrogen transfers in the CH4/CH3+, CH4/CH3•, and CH4/CH3− systems: on the electronic nature of the hydrogen (H−, H•, and H+) being transferred

1996 ◽  
Vol 74 (6) ◽  
pp. 1253-1262 ◽  
Author(s):  
Jordi Mestres ◽  
Miquel Duran ◽  
Juan Bertrán
Keyword(s):  
Charge Density ◽  
Electron Density ◽  
Hydrogen Transfer ◽  
Correlation Energy ◽  
Topological Analysis ◽  
Electronic Nature ◽  
Density Distributions ◽  
Density Maps ◽  
Density Analysis ◽  
A Charge

A comparative electronic analysis of the generally termed hydrogen transfers between CH4 and the CH3+, CH3•, and CH3− fragments is presented. These systems are taken as simple models of hydride (H−), hydrogen (H•), and proton (H+) transfers between two carbon fragments (in these simple cases being modelized by two CH3+, CH3•, and CH3− fragments, respectively). The study is mainly focused on analysis of the electronic nature of the type of hydrogen being transferred in each system, and for this reason a topological analysis of charge density distributions was performed. Computation of Bader atomic charges and construction of the charge density, gradient vector field, and Appalachian of the charge density maps reveal the specific features of the electronic nature of the transferring H−, H•, and H+. Moreover, characterization of the bond critical points on the charge density surface permits clarification of the differences in atomic interactions between H−, H•, and H+ and the carbon belonging to each CH3+, CH3•, and CH3− fragment, respectively. A charge density redistribution analysis is also performed to quantify the reorganization of the electron density when going from the reactant complex to the transition state. Finally, effects of inclusion of the correlation energy at the MP2 and CISD levels are also discussed. Key words: electron density, hydrogen transfer, topological density analysis, molecular similarity, Bader density analysis.

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