Remarks on the use of the average occupation numbers in theSCF process for open shell systems

1982 ◽  
Vol 22 (2) ◽  
pp. 289-292 ◽  
Author(s):  
Renato Colle ◽  
Oriano Salvetti
Keyword(s):  
Open Shell ◽  
Occupation Numbers ◽  
Average Occupation

scholarly journals NATURAL ORBITALS REPRESENTATION AND FERMI SEA DEPLETION IN FINITE NUCLEI AND NUCLEAR MATTER

2013 ◽  
Vol 22 (07) ◽  
pp. 1350047
Author(s):  
V. P. PSONIS ◽  
Ch. C. MOUSTAKIDIS ◽  
S. E. MASSEN
Keyword(s):  
Density Matrix ◽  
Nuclear Matter ◽  
Experimental Studies ◽  
Approximate Expression ◽  
Closed Shell ◽  
Open Shell ◽  
Natural Orbitals ◽  
Occupation Numbers ◽  
Closed Shell Nuclei ◽  
Finite Nuclei

The natural orbitals (NOs) and natural occupation numbers (NON) of various N = Z, sp and sd shell nuclei are calculated by applying a correlated one-body density matrix (OBDM). The correlated density matrix has been evaluated by considering central correlations of Jastrow type and an approximation named factor cluster expansion. The correlation effects on NOs, NON and the Fermi sea depletion (FSD) are discussed and analyzed. In addition, an approximate expression for the correlated OBDM of the nuclear matter has been used for the evaluation of the relative momentum distribution and FSD. We found that the value of FSD is higher in closed shell nuclei compared to open shell ones and it is lower compared to the case of nuclear matter. This statement could be confirmed by relevant experimental studies.

scholarly journals Erratum to: (Hyper)polarizability density analysis for open-shell molecular systems based on natural orbitals and occupation numbers

2011 ◽  
Vol 130 (4-6) ◽  
pp. 725-726 ◽  
Author(s):  
Masayoshi Nakano ◽  
Hitoshi Fukui ◽  
Takuya Minami ◽  
Kyohei Yoneda ◽  
Yasuteru Shigeta ◽  
...  
Keyword(s):  
Open Shell ◽  
Natural Orbitals ◽  
Molecular Systems ◽  
Occupation Numbers ◽  
Density Analysis

scholarly journals Quantum Chaos in Multicharged Ions and Statistical Approach to the Calculation of Electron - Ion Resonant Radiative Recombination

1999 ◽  
Vol 52 (3) ◽  
pp. 443 ◽  
Author(s):  
G. F. Gribakin ◽  
A. A. Gribakina ◽  
V. V. Flambaum
Keyword(s):  
Quantum Chaos ◽  
Radiative Recombination ◽  
Statistical Approach ◽  
Chemical Potential ◽  
Open Shell ◽  
Canonical Distribution ◽  
Atomic Ions ◽  
Occupation Numbers ◽  
Low Energy Electrons ◽  
High Level

We show that the spectrum and eigenstates of open-shell multicharged atomic ions near the ionisation threshold are chaotic, as a result of extremely high level densities of multiply excited electron states (103 eV–1 in Au24+) and strong configuration mixing. This complexity enables one to use statistical methods to analyse the system. We examine the dependence of the orbital occupation numbers and single-particle energies on the excitation energy of the system, and show that the occupation numbers are described by the Fermi–Dirac distribution, and the temperature and chemical potential can be introduced. The Fermi–Dirac temperature is close to the temperature defined through the canonical distribution. Using a statistical approach we estimate the contribution of multielectron resonant states to the radiative capture of low-energy electrons by Au25+ and demonstrate that this mechanism fully accounts for the 102 times enhancement of the recombination over the direct radiative recombination, in agreement with recent experimental observations.

(Hyper)polarizability density analysis for open-shell molecular systems based on natural orbitals and occupation numbers

2011 ◽  
Vol 130 (4-6) ◽  
pp. 711-724 ◽  
Author(s):  
Masayoshi Nakano ◽  
Hitoshi Fukui ◽  
Takuya Minami ◽  
Kyohei Yoneda ◽  
Yasuteru Shigeta ◽  
...  
Keyword(s):  
Open Shell ◽  
Natural Orbitals ◽  
Molecular Systems ◽  
Occupation Numbers ◽  
Density Analysis

The Interplay of Open-Shell Spin-Coupling and Jahn-Teller Distortion in Benzene Radical Cation Probed by X-ray Spectroscopy

2020 ◽  
Author(s):  
Marta L. Vidal ◽  
Michael Epshtein ◽  
Valeriu Scutelnic ◽  
Zheyue Yang ◽  
Tian Xue ◽  
...  
Keyword(s):  
High Harmonic ◽  
Open Shell ◽  
Spin Coupling ◽  
High Symmetry ◽  
Teller Distortion ◽  
Spectral Window ◽  
X Ray ◽  
Jahn Teller ◽  
X Ray Absorption ◽  
Jahn Teller Distortion

We report a theoretical investigation and elucidation of the x-ray absorption spectra of neutral benzene and of the benzene cation. The generation of the cation by multiphoton ultraviolet (UV) ionization as well as the measurement of<br>the carbon K-edge spectra of both species using a table-top high-harmonic generation (HHG) source are described in the companion experimental paper [M. Epshtein et al., J. Phys.<br>Chem. A., submitted. Available on ChemRxiv]. We show that the 1sC -> pi transition serves as a sensitive signature of the transient cation formation, as it occurs outside of the spectral window of the parent neutral species. Moreover, the presence<br>of the unpaired (spectator) electron in the pi-subshell of the cation and the high symmetry of the system result in significant differences relative to neutral benzene in the spectral features associated with the 1sC ->pi* transitions. High-level calculations using equation-of-motion coupled-cluster theory provide the interpretation of the experimental spectra and insight into the electronic structure of benzene and its cation.<br>The prominent split structure of the 1sC -> pi* band of the cation is attributed to the interplay between the coupling of the core -> pi* excitation with the unpaired electron<br>in the pi-subshell and the Jahn-Teller distortion. The calculations attribute most of<br>the splitting (~1-1.2 eV) to the spin coupling, which is visible already at the Franck-Condon structure, and estimate the additional splitting due to structural relaxation to<br>be around ~0.1-0.2 eV. These results suggest that x-ray absorption with increased resolution might be able to disentangle electronic and structural aspects of the Jahn-Teller<br>effect in benzene cation.<br>

Room Temperature Alkali Metal Reduction of Carbon Dioxide

2020 ◽  
Author(s):  
Lucas A. Freeman ◽  
Akachukwu D. Obi ◽  
Haleigh R. Machost ◽  
Andrew Molino ◽  
Asa W. Nichols ◽  
...  
Keyword(s):  
Alkali Metal ◽  
Alkali Metals ◽  
Room Temperature ◽  
Chemical Reduction ◽  
Bond Cleavage ◽  
Open Shell ◽  
Metal Reduction ◽  
One Pot ◽  
Earth Abundant ◽  
Electron Reduction

The reduction of the relatively inert carbon–oxygen bonds of CO<sub>2</sub> to access useful CO<sub>2</sub>-derived organic products is one of the most important fundamental challenges in synthetic chemistry. Facilitating this bond-cleavage using earth-abundant, non-toxic main group elements (MGEs) is especially arduous because of the difficulty in achieving strong inner-sphere interactions between CO<sub>2</sub> and the MGE. Herein we report the first successful chemical reduction of CO<sub>2</sub> at room temperature by alkali metals, promoted by a cyclic(alkyl)(amino) carbene (CAAC). One-electron reduction of CAAC-CO<sub>2</sub> adduct (<b>1</b>) with lithium, sodium or potassium metal yields stable monoanionic radicals clusters [M(CAAC–CO<sub>2</sub>)]<sub>n</sub>(M = Li, Na, K, <b> 2</b>-<b>4</b>) and two-electron alkali metal reduction affords open-shell, dianionic clusters of the general formula [M<sub>2</sub>(CAAC–CO<sub>2</sub>)]<sub>n </sub>(<b>5</b>-<b>8</b>). It is notable that these crystalline clusters of reduced CO<sub>2</sub> may also be isolated via the “one-pot” reaction of free CO<sub>2</sub> with free CAAC followed by the addition of alkali metals – a reductive process which does not occur in the absence of carbene. Each of the products <b>2</b>-<b>8</b> were investigated using a combination of experimental and theoretical methods.<br>

Form Factor of an Open-Shell Atom

2000 ◽  
Vol 89 (1) ◽  
pp. 4
Author(s):  
A. N. Khoperskiı̆
Keyword(s):  
Form Factor ◽  
Open Shell
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