Real-space representation of electron correlation in π-conjugated systems

2015 ◽  
Vol 142 (20) ◽  
pp. 204311 ◽  
Author(s):  
Jian Wang ◽  
Evert Jan Baerends
Keyword(s):  
Electron Correlation ◽  
Real Space ◽  
Space Representation ◽  
Conjugated Systems

Where Does Electron Correlation Lie? Some Answers from a Real Space Partition

ChemPhysChem ◽  
2017 ◽  
Vol 18 (24) ◽  
pp. 3553-3561 ◽  
Author(s):  
José Luis Casalz-Sainz ◽  
José Manuel Guevara-Vela ◽  
Evelio Francisco ◽  
Tomás Rocha-Rinza ◽  
Ángel Martín Pendás
Keyword(s):  
Electron Correlation ◽  
Real Space ◽  
Space Partition

scholarly journals A Comparison between Electron Crystal Scattering Potentials derived from X-ray Electron Densities and from Atom Muffin Tin Potentials

1985 ◽  
Vol 38 (3) ◽  
pp. 487 ◽  
Author(s):  
Andrew E Smith ◽  
DF Lynch
Keyword(s):  
Fourier Coefficients ◽  
Real Space ◽  
Space Representation ◽  
Natural Representation ◽  
X Ray ◽  
Low Energy Electron Diffraction ◽  
Structure Factors ◽  
Structure Determinations ◽  
Low Energy Electron ◽  
Electron Crystal

Two different forms of electron crystal potential are compared for the particular cases of aluminium and niobium diselenide. One of these is the solid-state muffin tin potential frequently used for band structure and low energy electron diffraction problems, and with its natural representation in real space. The other potential, derived from X-ray structure factors, is that most commonly used in electron microscopy structure determinations. It is expressed in terms of its Fourier coefficients and is accordingly a reciprocal space representation. Comparisons are carried out in both spaces. It is concluded that differences between the potentials are only minor and are mainly due to details in truncation and superposition.

On the volume-dependent contribution to the elastic constants of cubic metals

1977 ◽  
Vol 356 (1686) ◽  
pp. 345-350 ◽  
Keyword(s):  
Bulk Modulus ◽  
Density Dependence ◽  
Elastic Constants ◽  
Free Electron ◽  
Equilibrium Condition ◽  
Electron Gas ◽  
Real Space ◽  
Space Representation ◽  
Pseudopotential Theory ◽  
Cubic Metals

The present work deduces the expressions for the elastic constants of b. c. c. and f. c. c. metals in the real space representation, based on the pseudopotential theory of sp-bonded metals. We find that (1) the free electron gas does not contribute to the elastic constants explicitly, and (2) there is an identical term K ( V )in the expressions for C 11 , C 12 and the bulk modulus (but not for C 44 ) because of the dependence of the pairwise forces on the electron density, i.e. on the volume. These volume-dependent forces make a direct contribution to the Cauchy deficiency. The latter contains also another term which may be expressed in terms of the energy of a free electron gas through the use of the equilibrium condition. We discuss in detail how far the Cauchy discrepancy can be ascribed to the density dependence of the pairwise forces and how far it is due to the volume-dependent energy of the electron gas.

scholarly journals Illustrated formalisms for total scattering data: a guide for new practitioners

2021 ◽  
Vol 54 (1) ◽  
pp. 317-332
Author(s):  
Peter F. Peterson ◽  
Daniel Olds ◽  
Marshall T. McDonnell ◽  
Katharine Page
Keyword(s):  
Diffraction Data ◽  
Data Representation ◽  
Real Space ◽  
Reciprocal Space ◽  
Scattering Data ◽  
Space Representation ◽  
Scattering Method ◽  
Total Scattering ◽  
The Real ◽  
Pdf Analysis

The total scattering method is the simultaneous study of both the real- and reciprocal-space representations of diffraction data. While conventional Bragg-scattering analysis (employing methods such as Rietveld refinement) provides insight into the average structure of the material, pair distribution function (PDF) analysis allows for a more focused study of the local atomic arrangement of a material. Generically speaking, a PDF is generated by Fourier transforming the total measured reciprocal-space diffraction data (Bragg and diffuse) into a real-space representation. However, the details of the transformation employed and, by consequence, the resultant appearance and weighting of the real-space representation of the system can vary between different research communities. As the worldwide total scattering community continues to grow, these subtle differences in nomenclature and data representation have led to conflicting and confusing descriptions of how the PDF is defined and calculated. This paper provides a consistent derivation of many of these different forms of the PDF and the transformations required to bridge between them. Some general considerations and advice for total scattering practitioners in selecting and defining the appropriate choice of PDF in their own research are presented. This contribution aims to benefit people starting in the field or trying to compare their results with those of other researchers.

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