State Functions for Many Electron Atoms: Eigenfunctions of L2 and S2 for One Open Shell Configurations

1974 ◽  
Vol 52 (17) ◽  
pp. 1672-1675
Author(s):  
Jacek Karwowski ◽  
Serafin Fraga
Keyword(s):  
Open Shell ◽  
New Formalism ◽  
State Functions

The construction of eigenfunctions of L2 and S2 using a new formalism, that represents an alternative to the Racah genealogical scheme, is discussed. The corresponding functions have been tabulated for all the states arising from pN, dN, and fN configurations; this tabulation, not presented here because of space restrictions, is available as indicated in the text.

State Functions for Many Electron Atoms: Eigenfunctions of J2 and S2 for One Open Shell Configurations

1974 ◽  
Vol 52 (18) ◽  
pp. 1845-1846 ◽  
Author(s):  
Jacek Karwowski ◽  
Serafin Fraga
Keyword(s):  
Open Shell ◽  
New Formalism ◽  
State Functions

Eigenfunctions of J2 and S2 are constructed using a new formalism that represents an alternative to the Racah genealogical scheme. These functions have been tabulated for all the states arising from pN, dN, and fN configurations; this tabulation, not presented here because of space restrictions, is available as indicated in the text.

scholarly journals Open shell electronic state calculations on quantum computers: A quantum circuit for the preparation of configuration state functions based on Serber construction

2019 ◽  
Vol 1 ◽  
pp. 100002 ◽  
Author(s):  
Kenji Sugisaki ◽  
Satoru Yamamoto ◽  
Shigeaki Nakazawa ◽  
Kazuo Toyota ◽  
Kazunobu Sato ◽  
...  
Keyword(s):  
Electronic State ◽  
Quantum Circuit ◽  
Open Shell ◽  
Quantum Computers ◽  
State Functions

Method for Molecular Electronic State Multiplet Structure Calculation in the Space of Xα-SW-Orbitals

1991 ◽  
Vol 02 (01) ◽  
pp. 510-514
Author(s):  
I.A. TOPOL ◽  
V.I. POLYAKOV
Keyword(s):  
Energy Levels ◽  
Scattered Wave ◽  
Open Shell ◽  
Hamiltonian Matrix ◽  
Matrix Elements ◽  
Multiplet Structure ◽  
Molecular Electronic ◽  
Present Scheme ◽  
Molecular Integrals ◽  
State Functions

The SCF-Xα-scattered wave method (Xα-SW) as well as other versions of the density function approach cannot give a proper description of the open-shell many-electron energy levels and thus it is not always possible to reproduce electron spectra adequately by this method. We propose the following way to overcome this drawback of the X α-SW method. First one- and two-particle molecular integrals with Xα-SW molecular orbitals (MO) are calculated numerically. Then these integrals are used to evaluate Hamiltonian matrix elements (both diagonal and off-diagonal) in the basis of configuration state functions. The present scheme allows us to describe molecular electronic spectra in various approximations: a) one-configurational frozen orbitals approach; b) ΔSCF; c) configuration interaction (CI). Our method gives an opportunity to go beyond the muffin-tin (MT) approximation for a potential; inherent in the X α-SW method. In the X α-SW-MO basis it is simple enough to construct the full electron Hamiltonian matrix elements for various open-shell systems.

State Functions of Nostalgia Scale

2012 ◽  
Author(s):  
Erica G. Hepper ◽  
Timothy D. Ritchie ◽  
Constantine Sedikides ◽  
Tim Wildschut
Keyword(s):  
State Functions

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>

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