scholarly journals Cyclopentadienyl System: Solving the Secular Determinant, π Energy, Delocalization Energy, Wave Functions, Electron Density and Charge Density

2020 ◽  
Vol 6 (2) ◽  
Author(s):  
Vikram R. Jadhav ◽  
Jamdhade Madhuri ◽  
Wadhawane Pooja ◽  
Y.R. Baste
Keyword(s):  
Charge Density ◽  
Electron Density ◽  
Wave Functions ◽  
Stable Configuration ◽  
Overlap Integrals ◽  
Delocalization Energy ◽  
Study Characteristics ◽  
Secular Equations ◽  
Coulomb Integrals ◽  
Secular Determinant

In this study, characteristics of Hückel strategy, were abused so as to acquire some significant outcomes, through a theoretical technique with which it is conceivable to get secular equations, π energy, wave functions, electron density and charge density, as an account of cyclopentadienyl system i.e. C5H5+ (cation), C5H5- (anion), and C5H5. (radical) and permitting the expression of delocalization energy of conjugated cyclopentadienyl ring framework. Here, it was presented the secular determinant of the Hückel technique and applied to cyclopentadienyl system framework so as to communicate their orbital energies of cyclopentadienyl system, also to communicate its electron and charge density in terms of stable configuration of a system. It is settled by the Hückel strategy and applied by the assumptions for nearby comparability such as coulomb integrals, exchange integrals and overlap integrals. This simple way hypothetical strategy will allow to graduate and post graduate understudies to understanding the investigation of stable configuration, electron and charge density and also other parameters.

Revisiting the charge density analysis of 2,5-dichloro-1,4-benzoquinone at 20 K

2017 ◽  
Vol 73 (4) ◽  
pp. 654-659 ◽  
Author(s):  
Zhijie Chua ◽  
Bartosz Zarychta ◽  
Christopher G. Gianopoulos ◽  
Vladimir V. Zhurov ◽  
A. Alan Pinkerton
Keyword(s):  
Charge Density ◽  
Electron Density ◽  
Topological Analysis ◽  
Diffraction Measurement ◽  
X Ray Diffraction ◽  
Total Electron Density ◽  
Total Electron ◽  
Structure Factors ◽  
Density Analysis ◽  
Experimental Charge Density

A high-resolution X-ray diffraction measurement of 2,5-dichloro-1,4-benzoquinone (DCBQ) at 20 K was carried out. The experimental charge density was modeled using the Hansen–Coppens multipolar expansion and the topology of the electron density was analyzed in terms of the quantum theory of atoms in molecules (QTAIM). Two different multipole models, predominantly differentiated by the treatment of the chlorine atom, were obtained. The experimental results have been compared to theoretical results in the form of a multipolar refinement against theoretical structure factors and through direct topological analysis of the electron density obtained from the optimized periodic wavefunction. The similarity of the properties of the total electron density in all cases demonstrates the robustness of the Hansen–Coppens formalism. All intra- and intermolecular interactions have been characterized.

Angular terms in the electron density for the phosphine molecule

1956 ◽  
Vol 52 (4) ◽  
pp. 703-711 ◽  
Author(s):  
R. A. Ballinger ◽  
N. H. March
Keyword(s):  
Variational Method ◽  
Charge Density ◽  
Electron Density ◽  
Legendre Polynomials ◽  
Molecular Axis ◽  
Thomas Fermi ◽  
Line Charge ◽  
Density Map ◽  
Circular Line

ABSTRACTAn attempt is made to calculate the first few angular terms in an expansion of the electron density for the phosphine molecule in Legendre polynomials. Such an expansion is appropriate for a model in which the three hydrogen nuclei are smeared to form a circular line charge. The Thomas–Fermi approximation has been used in conjunction with the variational method. The variational density employed includes p and f angular terms. An approximate charge density map is constructed for a plane containing the molecular axis in order to demonstrate the effect of the angular terms.

Nonnuclear Maxima in the Charge Density

1993 ◽  
Vol 48 (1-2) ◽  
pp. 127-133 ◽  
Author(s):  
Kenneth E. Edgecombe ◽  
Vedene H. Smith, Jr. ◽  
Florian Müller-Plathe
Keyword(s):  
Charge Density ◽  
Electron Density ◽  
Electron Correlation ◽  
Basis Set ◽  
Valence Shell ◽  
Correlation Effects ◽  
Electron Correlation Effects

Abstract Basis-set and electron-correlation effects on the appearance and disappearance of nonnuclear maxima in the electron density are examined in Li2 , Na2 , Na4 and Na5 . It is shown that nonnuclear attractors can be removed in all cases except Li2 . The appearance of a pseudoatom in a lithium molecule correlates remarkably well with the size of the region, in an atomic calculation, of V2r(r) for the valence shell of the atom. This and the fact that the pseudoatom is also present in the promolecule indicate that the pseudoatoms are remnants of, or in fact are portions of, atoms that are not perturbed enough in the molecule to remove an essentially atomic characteristic.

The dependence of the hyperfine interaction on the cellular potential in Na and K. II

1969 ◽  
Vol 47 (13) ◽  
pp. 1331-1336 ◽  
Author(s):  
R. A. Moore ◽  
S. H. Vosko
Keyword(s):  
Fermi Surface ◽  
Electron Density ◽  
Wave Functions ◽  
Electron Wave ◽  
Surface Electron ◽  
Conduction Electrons ◽  
Hartree Fock ◽  
A Value ◽  
Dependent Potential ◽  
Conduction Electron Density

The dependence of the Fermi surface electron wave functions in Na and K on (i) an L-dependent effective local cellular potential constructed to simulate Hartree-Fock theory and (ii) the inclusion of the Hartree field due to the conduction electrons in the cellular potential is investigated. All calculations are performed using the Wigner–Seitz spherical cellular approximation and the Schrödinger equation is solved by the Kohn variational method. It is found that to ensure a value of the Fermi surface electron density at the nucleus accurate to ~5%, it is necessary to use the L-dependent potential along with the Hartree field due to a realistic conduction electron density.

scholarly journals Exploring charge density analysis in crystals at high pressure: data collection, data analysis and advanced modelling

2017 ◽  
Vol 73 (4) ◽  
pp. 584-597 ◽  
Author(s):  
Nicola Casati ◽  
Alessandro Genoni ◽  
Benjamin Meyer ◽  
Anna Krawczuk ◽  
Piero Macchi
Keyword(s):  
High Pressure ◽  
Density Distribution ◽  
Charge Density ◽  
Electron Density ◽  
Electron Density Distribution ◽  
Theoretical Work ◽  
Specific Information ◽  
Collection Data ◽  
Modelling Techniques ◽  
Density Analysis

The possibility to determine electron-density distribution in crystals has been an enormous breakthrough, stimulated by a favourable combination of equipment for X-ray and neutron diffraction at low temperature, by the development of simplified, though accurate, electron-density models refined from the experimental data and by the progress in charge density analysis often in combination with theoretical work. Many years after the first successful charge density determination and analysis, scientists face new challenges, for example: (i) determination of the finer details of the electron-density distribution in the atomic cores, (ii) simultaneous refinement of electron charge and spin density or (iii) measuring crystals under perturbation. In this context, the possibility of obtaining experimental charge density at high pressure has recently been demonstrated [Casatiet al.(2016).Nat. Commun.7, 10901]. This paper reports on the necessities and pitfalls of this new challenge, focusing on the speciessyn-1,6:8,13-biscarbonyl[14]annulene. The experimental requirements, the expected data quality and data corrections are discussed in detail, including warnings about possible shortcomings. At the same time, new modelling techniques are proposed, which could enable specific information to be extracted, from the limited and less accurate observations, like the degree of localization of double bonds, which is fundamental to the scientific case under examination.

scholarly journals Systematic Experimental Charge Density: Linking Structural Modifications to Electron Density Distributions

2015 ◽  
Vol 44 (1) ◽  
pp. 2-9 ◽  
Author(s):  
Isabelle L. Kirby ◽  
Mateusz B. Pitak ◽  
Simon J. Coles ◽  
Philip A. Gale
Keyword(s):  
Charge Density ◽  
Electron Density ◽  
Structural Modifications ◽  
Density Distributions ◽  
Experimental Charge Density
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