scholarly journals Electron Coincidence Spectroscopy: An Introduction to Momentum Space Chemistry

1982 ◽  
Vol 35 (5) ◽  
pp. 571 ◽  
Author(s):  
Erich Weigold
Keyword(s):  
Molecular Orbital ◽  
Momentum Space ◽  
Dynamic Structure ◽  
Energy Spectra ◽  
Many Body ◽  
Atomic Orbitals ◽  
Hartree Fock ◽  
Valence Region ◽  
Momentum Distributions ◽  
Lcao Mo

The application of electron coincidence or (e,2e) spectroscopy to obtaining detailed information on the dynamic structure of atoms and molecules is discussed. The technique obtains separation energy spectra and spherically averaged electron momentum distributions for each molecular orbital in the valence region. A brief discussion of molecular orbital density functions in momentum space is given. The results using Hartree-Fock wavefunctions for atomic orbitals and LCAO-MO wavefunctions for molecular orbitals are compared with (e, 2e) data. The sensitivity of the data to electron correlations in either the initial or final ion many body states is discussed and examples are given.

A simple quality test for self-consistent-field atomic orbitals

1993 ◽  
Vol 71 (2) ◽  
pp. 175-179 ◽  
Author(s):  
N. Desmarais ◽  
G. Dancausse ◽  
S. Fliszár
Keyword(s):  
Basis Functions ◽  
Quality Test ◽  
Linear Combinations ◽  
Atomic Orbitals ◽  
Hartree Fock ◽  
Consistent Field ◽  
Valence Region ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Finite Linear

A quality test is proposed for SCF atomic orbitals, [Formula: see text] approximated as finite linear combinations of suitable basis functions [Formula: see text] The key is in a function, readily derived from the Hartree–Fock equation [Formula: see text] which is identically zero for true Hartree–Fock spin orbitals and not so for approximate orbitals. In this way, our test measures how closely approximate orbital descriptions approach the true Hartree–Fock limit and thus provides a quality ordering of orbital bases with respect to one another and with respect to that limit, in a scale uniquely defined by the latter. Moreover, this analysis also holds for atomic subspaces of our choice, e.g., the valence region. Examples are offered for representative collections of Slater- and Gaussian-type orbital expansions.

On the Nature of Halide-Water Interactions: Insights from Many-Body Representations and Density Functional Theory

2019 ◽  
Author(s):  
Brandon B. Bizzarro ◽  
Colin K. Egan ◽  
Francesco Paesani
Keyword(s):  
Density Functional Theory ◽  
Charge Transfer ◽  
Molecular Orbital ◽  
Density Functional ◽  
Decomposition Analysis ◽  
Orbital Energy ◽  
Energy Decomposition Analysis ◽  
Interaction Energies ◽  
Many Body ◽  
Functional Theory

<div> <div> <div> <p>Interaction energies of halide-water dimers, X<sup>-</sup>(H<sub>2</sub>O), and trimers, X<sup>-</sup>(H<sub>2</sub>O)<sub>2</sub>, with X = F, Cl, Br, and I, are investigated using various many-body models and exchange-correlation functionals selected across the hierarchy of density functional theory (DFT) approximations. Analysis of the results obtained with the many-body models demonstrates the need to capture important short-range interactions in the regime of large inter-molecular orbital overlap, such as charge transfer and charge penetration. Failure to reproduce these effects can lead to large deviations relative to reference data calculated at the coupled cluster level of theory. Decompositions of interaction energies carried out with the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) method demonstrate that permanent and inductive electrostatic energies are accurately reproduced by all classes of XC functionals (from generalized gradient corrected (GGA) to hybrid and range-separated functionals), while significant variance is found for charge transfer energies predicted by different XC functionals. Since GGA and hybrid XC functionals predict the most and least attractive charge transfer energies, respectively, the large variance is likely due to the delocalization error. In this scenario, the hybrid XC functionals are then expected to provide the most accurate charge transfer energies. The sum of Pauli repulsion and dispersion energies are the most varied among the XC functionals, but it is found that a correspondence between the interaction energy and the ALMO EDA total frozen energy may be used to determine accurate estimates for these contributions. </p> </div> </div> </div>

scholarly journals THE METHOD OF INCREMENTS — A WAVEFUNCTION-BASED AB-INITIO CORRELATION METHOD FOR SOLIDS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2204-2214 ◽  
Author(s):  
BEATE PAULUS
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Ground State ◽  
Infinite System ◽  
Correlation Energy ◽  
Correlation Method ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Good Agreement

The method of increments is a wavefunction-based ab initio correlation method for solids, which explicitly calculates the many-body wavefunction of the system. After a Hartree-Fock treatment of the infinite system the correlation energy of the solid is expanded in terms of localised orbitals or of a group of localised orbitals. The method of increments has been applied to a great variety of materials with a band gap, but in this paper the extension to metals is described. The application to solid mercury is presented, where we achieve very good agreement of the calculated ground-state properties with the experimental data.

EVOLUTION OF DEFORMATIONS IN SD AND PF SHELL NUCLEI

2006 ◽  
Vol 15 (08) ◽  
pp. 1779-1788
Author(s):  
XIAN-RONG ZHOU ◽  
H. SAGAWA ◽  
XI-ZHEN ZHANG
Keyword(s):  
Mass Number ◽  
Nuclear Deformation ◽  
Quadrupole Moments ◽  
Many Body ◽  
Hartree Fock ◽  
Pairing Correlations ◽  
Many Body Systems ◽  
Pf Shell ◽  
Vibration Coupling ◽  
Hf Calculations

In the frame of deformed Skyrme Hartree-Fock (HF) model with pairing correlations, the strong mass number dependence of quadrupole deformations in sd and pf shell nuclei with mass A =(16 ~ 56) is studied as a clear manifestation of the evolution of nuclear deformation in nuclear many-body systems. The competition between the deformation driving particle-vibration coupling and the shell structure is shown by a systematic study on the ratios of the protons to neutrons quadrupole moments in nuclei with T =| T z|=1. The mass number dependence of deformations obtained by deformed HF calculations is compared with the results of shell model and experimental data.

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