scholarly journals Substituent Effect in the Cation Radicals of Monosubstituted Benzenes

2021 ◽  
Vol 22 (13) ◽  
pp. 6936
Author(s):  
Jan Cz. Dobrowolski ◽  
Wojciech M. Dudek ◽  
Grażyna Karpińska ◽  
Anna Baraniak
Keyword(s):  
Long Range ◽  
Ground State ◽  
Substituent Effect ◽  
Electron System ◽  
Partial Charge ◽  
Electron Charge ◽  
Electron Systems ◽  
Cation Radicals ◽  
Phenyl Rings ◽  
Monosubstituted Benzenes

In 30 monosubstituted benzene cation radicals, studied at the ωB97XD/aug-cc-pVTZ level, the phenyl rings usually adopt a compressed form, but a differently compressed form—equivalent to an elongated one—may coexist. The computational and literature ionization potentials are well correlated. The geometrical and magnetic aromaticity, estimated using HOMA and NICS indices, show the systems to be structurally aromatic but magnetically antiaromatic or only weakly aromatic. The partial charge is split between the substituent and ring and varies the most at C(ipso). In the ring, the spin is 70%, concentrated equally at the C(ipso) and C(p) atoms. The sEDA(D) and pEDA(D) descriptors of the substituent effect in cation radicals, respectively, were determined. In cation radicals, the substituent effect on the σ-electron system is like that in the ground state. The effect on the π-electron systems is long-range, and its propagation in the radical quinone-like ring is unlike that in the neutral molecules. The pEDA(D) descriptor correlates well with the partial spin at C(ipso) and C(p) and weakly with the HOMA(D) index. The correlation of the spin at the ring π-electron system and the pEDA(D) descriptor shows that the electron charge supplied to the ring π-electron system and the spin flow oppositely.

A Cluster Expansion Formalism for Direct Calculation of Ionisation Potential and Excitation Energy of Many Electron Systems Using H-F Ground State as Vacuum

1978 ◽  
Vol 33 (12) ◽  
pp. 1549-1551
Author(s):  
D. Mukherjee ◽  
A. Mukhopadhyay ◽  
R. K. Moitra
Keyword(s):  
Excitation Energy ◽  
Cluster Expansion ◽  
Ground State ◽  
Shell Theory ◽  
State Energy ◽  
Direct Calculation ◽  
Electron System ◽  
Open Shell ◽  
Electron Systems ◽  
Ionisation Potential

Abstract In this note, the authors’ recently developed non-perturbative open-shell theory is adapted for direct calculation o f ionisation potential and excitation energy of m any-electron systems. The H -F ground state is used as the “vacuum ” or “ core” in order to achieve a transparent separation o f the ground state energy. An application to a simple 4 π-electron system is discussed as an illustration o f the workability of the theory.

scholarly journals Direct Calculation of Natural Orbitals of Two-Electron Systems

1985 ◽  
Vol 40 (10) ◽  
pp. 995-997
Author(s):  
Heinz Kleindienst ◽  
Kai Rossen
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Direct Calculation ◽  
Electron System ◽  
Integrodifferential Equations ◽  
Electron Systems ◽  
Natural Orbitals ◽  
System Of Integrodifferential Equations

A new method is proposed, which allows for the determination of the ground state energy and the natural orbitals (NO's) of a two-electron system directly and simultaneously. The basis for this calculation is a system of integrodifferential-equations, which defines those NO's.

CNDO/2-Elektronenladungsdichten und 13C-chemische Verschiebungen von Phenylacetylenen / CNDO/2-Electron Charge Densities and 13C-Chemical Shifts of Phenylacetylenes

1972 ◽  
Vol 27 (12) ◽  
pp. 1772-1776 ◽  
Author(s):  
L Klasinc ◽  
J.V. Knop ◽  
H.-J Meiners ◽  
W Zeil
Keyword(s):  
Charge Transfer ◽  
Nmr Spectra ◽  
Chemical Shifts ◽  
Electron System ◽  
Total Charge ◽  
Electron Charge ◽  
Substituted Benzenes ◽  
Charge Densities ◽  
Inductive Effects ◽  
Monosubstituted Benzenes

AbstractThe 13C FT NMR spectra of phenylacetylene (1), p-methoxyphenylacetylene (2), p-fluorophenyl-acetylene (3), p-chlorophenylacetylene (4), p-bromophenylacetylene (5), p-ethylphenylacetylene (6) and p-isopropylphenylacetylene (7) as well as of a number of monosubstituted benzenes have been measured. The 13 C-chemical shifts in these compounds are correlated with the total charge densities at the corresponding carbon atoms, calculated by the CNDO/2 method. The present results show that a simple additivity exists between 13C-chemical shifts in substituted benzenes, phenylacetylene and substituted phenylacetylenes and that practically no charge transfer between the linked sub-stituted phenyl and the ethinyl groups takes place. The interaction of the ethinyl substituent and the π-electron system can mainly be attributed to inductive effects.

scholarly journals GROUND-STATE ENERGY AND COMPRESSIBILITY OF A DISORDERED TWO-DIMENSIONAL ELECTRON GAS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2134-2144 ◽  
Author(s):  
B. TANATAR ◽  
A. L. SUBAŞI ◽  
K. ESFARJANI ◽  
S. M. FAZELI
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Density Functional ◽  
State Energy ◽  
Critical Density ◽  
Electron System ◽  
Local Spin Density Approximation ◽  
Two Dimensional ◽  
Electron Systems ◽  
Dimensional Electron Gas

Two-dimensional (2D) electron systems in the presence of disorder are of interest in connection with the observed metal-insulator transition in such systems. We use density functional theory in its local-spin density approximation (LSDA) to calculate the ground-state energy of a 2D electron system in the presence of remote charged impurities which up on averaging provides disorder. The inverse compressibility calculated from the ground-state energy exhibits a minimum at a critical density controlled by the disorder strength. Our findings are in agreement with experimental results.

scholarly journals LOCALIZATION OF THE NUMBER OF PHOTONS OF GROUND STATES IN NONRELATIVISTIC QED

2003 ◽  
Vol 15 (03) ◽  
pp. 271-312 ◽  
Author(s):  
FUMIO HIROSHIMA
Keyword(s):  
Radiation Field ◽  
Ground State ◽  
Fock Space ◽  
Adjoint Operator ◽  
Ground States ◽  
Electron System ◽  
Number Operator ◽  
Position Variable ◽  
Boson Fock Space ◽  
Quantized Radiation Field

One electron system minimally coupled to a quantized radiation field is considered. It is assumed that the quantized radiation field is massless, and no infrared cutoff is imposed. The Hamiltonian, H, of this system is defined as a self-adjoint operator acting on L2 (ℝ3) ⊗ ℱ ≅ L2 (ℝ3; ℱ), where ℱ is the Boson Fock space over L2 (ℝ3 × {1, 2}). It is shown that the ground state, ψg, of H belongs to [Formula: see text], where N denotes the number operator of ℱ. Moreover, it is shown that for almost every electron position variable x ∈ ℝ3 and for arbitrary k ≥ 0, ‖(1 ⊗ Nk/2) ψg (x)‖ℱ ≤ Dk e-δ|x|m+1 with some constants m ≥ 0, Dk > 0, and δ > 0 independent of k. In particular [Formula: see text] for 0 < β < δ/2 is obtained.

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