Energies, radial expectation values, hyperfine structures of the ground state and highly excited states for C and O2+

2020 ◽  
Vol 34 (20) ◽  
pp. 2050197
Author(s):  
Chao Chen
Keyword(s):  
Excited States ◽  
Ground State ◽  
Magnetic Coupling ◽  
Wave Functions ◽  
Coupling Constants ◽  
Future Research ◽  
Expectation Values ◽  
Radiative Transitions ◽  
Experimental Values ◽  
Hyperfine Structures

The Rayleigh–Ritz variational method with multiconfiguration interaction wave functions is used to calculate energies, radiative transitions and radial expectation values of the [Formula: see text] [Formula: see text] ground state and the [Formula: see text], [Formula: see text], [Formula: see text] highly excited states of C and [Formula: see text]. Hyperfine structure parameters and magnetic coupling constants of these states are also calculated in this work. The present calculations agree well with theoretical and experimental values available in the literature. Other data not reported in the literature are expected to offer valuable benchmarks for future research.

scholarly journals Anwendungen von INDO-W ellenfunktionen in der Zeeman-Rotationsspektroskopie / Applications of INDO-Wave-functions in Zeeman-rotationsspectroscopy

1974 ◽  
Vol 29 (6) ◽  
pp. 924-932 ◽  
Author(s):  
E. Hamer ◽  
L. Engelbrecht ◽  
D. H. Sutter
Keyword(s):  
Gas Phase ◽  
Ground State ◽  
Close Agreement ◽  
Zeeman Effect ◽  
Wave Functions ◽  
Quadrupole Moments ◽  
Expectation Values ◽  
State Expectation ◽  
Experimental Values

A method is proposed to obtain ground state expectation values for the sums of the squares of the electron coordinates i.e . from INDO-wavefunctions. This leads to molecular quadrupole moments which are in close agreement with experimental values from investigations of the rotational Zeeman-effect. In combination with rotational Zeemaneffect data etc. can be used to predict gas-phase bulk susceptibilities and to determine the sign of the molecular g-tensor.

TWO-ELECTRON SYSTEM IN THE FIELD OF GENERALIZED SCREENED POTENTIAL

2011 ◽  
Vol 25 (19) ◽  
pp. 1619-1629 ◽  
Author(s):  
ARIJIT GHOSHAL ◽  
Y. K. HO
Keyword(s):  
Wave Function ◽  
Ground State ◽  
Electron System ◽  
Wave Functions ◽  
Expectation Values ◽  
Screening Parameter ◽  
System Ground State ◽  
Highly Correlated ◽  
First Time ◽  
Ground State Energies

Ground states of a two-electron system in generalized screened potential (GSP) with screening parameter λ: [Formula: see text] where ∊ is a constant, have been investigated. Employing highly correlated and extensive wave functions in Ritz's variational principle, we have been able to determine accurate ground state energies and wave functions of a two-electron system for different values of the screening parameter λ and the constant ∊. Convergence of the ground state energies with the increase of the number of terms in the wave function are shown. We also report various geometrical expectation values associated with the system, ground state energies of the corresponding one-electron system and the ionization potentials of the system. Such a calculation for the ground state of a two-electron system in GSP is carried out for first time in the literature.

AN INTERPRETATION OF THE LOW-LYING EXCITED STATES OF Mg25 AND Al25

1958 ◽  
Vol 36 (3) ◽  
pp. 378-404 ◽  
Author(s):  
A. E. Litherland ◽  
H. McManus ◽  
D. A. Bromley ◽  
H. E. Gove ◽  
E. B. Paul
Keyword(s):  
Excited States ◽  
Ground State ◽  
Salient Feature ◽  
Negative Parity ◽  
State Transitions ◽  
Rotational Model ◽  
Rotational States ◽  
Γ Ray ◽  
Deuteron Stripping ◽  
Experimental Values

A description of the experimental results obtained for Mg25 and Al25 is given based upon the assumption that the excited nuclear states are rotational states. In Mg25 and Al25 members of four rotational bands can be identified. The band based on the ground state can be assigned K = 5/2 whilst the three excited-state bands, two positive parity and one negative parity, can be assigned K = 1/2. The dipole γ-ray transitions between the K = 1/2 bands and the ground state K = 5/2 band are forbidden on the rotational model and it is a salient feature of the γ-ray cascading in Mg25 and Al25 that the ground-state transitions are always amongst the weakest transitions from excited states assigned to K = 1/2 bands. Besides giving a quantitative account of the γ-ray decay of the excited states the rotational model also predicts the number and type of the bands observed. The experimental values of the Mg24(d, p)Mg25 deuteron stripping reduced widths can also be approximately predicted by the model.

Theory of spin-orbit coupling in atoms, II. Comparison of theory with experiment

1963 ◽  
Vol 271 (1347) ◽  
pp. 565-578 ◽  
Keyword(s):  
Wave Functions ◽  
Coupling Constants ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Outer Electron ◽  
Coupling Constant ◽  
Radial Wave ◽  
Order Of Magnitude ◽  
Experimental Values

Results of calculations of the spin-orbit coupling constant for 2 p , 3 p , 4 p , and 3 d shell ions and atoms are presented. The calculations are based on a theory developed in a previous paper. Excellent agreement of this theory with experiment is obtained for the 2 p and 3 d shell ions, while calculations using the familiar < ∂ V / r ∂ r > expression for the coupling constant lie 10 to 20 % too high. The exchange terms discussed in the earlier paper make a contribution to the coupling constant of the same sign and order of magnitude as the ordinary shielding terms. For the 3 p and 4 p shell atoms, the calculated coupling constants based on the exact theory and on the < ∂ V / r ∂ r > expression both tend to lie below the experimental values. An explanation for this disagreement is suggested, based on the noded nature of the outer-electron radial wave functions for these atoms. The importance of the residual-spin-other-orbit interaction is discussed, and it is shown that ignoring the form of this interaction may lead to a large variation in the coupling constant within a configuration.

scholarly journals Resolution of Low-Energy States in Spin-Exchange Transition-Metal Clusters: Case Study of Singlet States in [Fe(III)4S4] Cubanes

2020 ◽  
Author(s):  
Giovanni Li Manni ◽  
Werner Dobrautz ◽  
Nikolay A. Bogdanov ◽  
Kai Guther ◽  
Ali Alavi
Keyword(s):  
Transition Metal ◽  
Ab Initio ◽  
Ground State ◽  
Wave Functions ◽  
Low Energy ◽  
Coupling Constants ◽  
Direct Access ◽  
Teller Distortion ◽  
Spin Structures ◽  
Singlet States

<p>Polynuclear transition-metal (PNTM) clusters, ubiquitous in biological systems, owe their catalytic activity to the presence of a large manifold of low-lying spin states, and a number of stable oxidation states. The ab initio description of such systems - starting from the electronic Schrodinger equation - represents one of the greatest challenges of modern quantum chemistry, requiring highly multiconfigurational treatments. We propose a theoretical framework of simple and physically motivated molecular-orbital transformations that enable the resolution and characterization of targeted electronic wave functions with ease. This paradigm allows us to unravel the complicated electronic correlations in PNTM clusters. We apply it to two super-oxidized iron-sulfur cubane [Fe4S4] structures, and accurately characterize their singlet ground and low-lying excited states. Through direct access to their wave functions, we identify the important correlation mechanisms and their interplay with the geometrical distortions observed in these clusters. Our results unambiguously reveal a hidden magnetic order in the manifold of singlet states. Namely, that in all low-energy singlet states of the two compounds, well-defined spin structures are formed within two pairs of magnetic sites. For instance, in the ground state of one compound two iron sites of local S = 5/2 spins are strongly ferromagnetically correlated to form two S = 5 intermediate pair states; two such pairs are then anti-ferromagnetically coupled to yield an overall singlet. In the five excited singlets, the spin of these hidden pair-states is reduced in steps to zero. We find that the ab initio results for these compounds can be mapped with high fidelity onto a four-site Heisenberg–Dirac–van Vleck Hamiltonian with two anti-ferromagnetic coupling constants. Thus, the complexes are intrinsically frustrated anti-ferromagnets, and the obtained spin structures, together with the geometrical distortions represent two possible ways to release spin frustration. The geometrical distortions may be seen as the result of a spin-driven Jahn-Teller distortion, that lifts the electronic ground state degeneracies. Our paradigm provides a simple yet rigorous wave function-based route to uncover the electronic structure of PNTM clusters, and may be applied to a wide variety of such clusters.</p>

An Exciton Approach to the Excited States of Two Electron Atoms. II. Determination of Spectroscopic Parameters, Polarizabilities and Dispersion Coefficients of H-, He, Li+, Be2+ and Ne8+

1985 ◽  
Vol 38 (1) ◽  
pp. 11
Author(s):  
PE Schipper ◽  
B Martire
Keyword(s):  
Excited States ◽  
Ground State ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Exciton Model ◽  
Interaction Coefficients ◽  
Isoelectronic Series ◽  
Helium Isoelectronic Series ◽  
Good Agreement

The exciton model developed in an earlier paper is applied quantitatively to a description of the excited states of representative members of the helium isoelectronic series; viz. H-, He, Li+,Be2+ and Ne8+. The energies of the eight lowest excited states are in good agreement with experiment, for a relatively small (1s-4p) hydrogenic basis; the ground state is obtained with slightly less precision. Response properties including oscillator strengths, polarizabilities and dispersion interaction coefficients are also calculated. The method appears to be quantitatively sound, and, above all, leads to particularly simple interpretations of the wave functions and the energies.

scholarly journals Resolution of Low-Energy States in Spin-Exchange Transition-Metal Clusters: Case Study of Singlet States in [Fe(III)4S4] Cubanes

2020 ◽  
Author(s):  
Giovanni Li Manni ◽  
Werner Dobrautz ◽  
Nikolay A. Bogdanov ◽  
Kai Guther ◽  
Ali Alavi
Keyword(s):  
Transition Metal ◽  
Ab Initio ◽  
Ground State ◽  
Wave Functions ◽  
Low Energy ◽  
Coupling Constants ◽  
Direct Access ◽  
Teller Distortion ◽  
Spin Structures ◽  
Singlet States

<p>Polynuclear transition-metal (PNTM) clusters, ubiquitous in biological systems, owe their catalytic activity to the presence of a large manifold of low-lying spin states, and a number of stable oxidation states. The ab initio description of such systems - starting from the electronic Schrodinger equation - represents one of the greatest challenges of modern quantum chemistry, requiring highly multiconfigurational treatments. We propose a theoretical framework of simple and physically motivated molecular-orbital transformations that enable the resolution and characterization of targeted electronic wave functions with ease. This paradigm allows us to unravel the complicated electronic correlations in PNTM clusters. We apply it to two super-oxidized iron-sulfur cubane [Fe4S4] structures, and accurately characterize their singlet ground and low-lying excited states. Through direct access to their wave functions, we identify the important correlation mechanisms and their interplay with the geometrical distortions observed in these clusters. Our results unambiguously reveal a hidden magnetic order in the manifold of singlet states. Namely, that in all low-energy singlet states of the two compounds, well-defined spin structures are formed within two pairs of magnetic sites. For instance, in the ground state of one compound two iron sites of local S = 5/2 spins are strongly ferromagnetically correlated to form two S = 5 intermediate pair states; two such pairs are then anti-ferromagnetically coupled to yield an overall singlet. In the five excited singlets, the spin of these hidden pair-states is reduced in steps to zero. We find that the ab initio results for these compounds can be mapped with high fidelity onto a four-site Heisenberg–Dirac–van Vleck Hamiltonian with two anti-ferromagnetic coupling constants. Thus, the complexes are intrinsically frustrated anti-ferromagnets, and the obtained spin structures, together with the geometrical distortions represent two possible ways to release spin frustration. The geometrical distortions may be seen as the result of a spin-driven Jahn-Teller distortion, that lifts the electronic ground state degeneracies. Our paradigm provides a simple yet rigorous wave function-based route to uncover the electronic structure of PNTM clusters, and may be applied to a wide variety of such clusters.</p>

Experimentelle und Quantenchemische Untersuchungen der Dipolmomente von Substituierten Stilbenen im Ersten Angercgten Singulettzustand / Experimental and Quantum Chemical Investigations of Dipole Moments of Substituted Stilbens in the First Excited Singlet State

1977 ◽  
Vol 32 (5) ◽  
pp. 420-425 ◽  
Author(s):  
A. Kawski ◽  
I. Gryczyński
Keyword(s):  
Dipole Moment ◽  
Excited States ◽  
Ground State ◽  
Quantum Chemical ◽  
Singlet State ◽  
Dipole Moments ◽  
Excited Singlet State ◽  
Excited Singlet ◽  
Fluorescent State ◽  
Experimental Values

Abstract The values a/a3 (α = polarizability), the Onsager cavity radii a and the dipole moments μe of six substituted stilbens in the fluorescent state have been determined. It is shown that if the dipole moment of the lowest excited singlet state μe is parallel to the dipole moment in the ground state μg, the values of μe and a can be determined from the solvent effects. Moreover, quantum chemical investigations of the dipole moments in the ground and excited states were carried out with the Pariser-Parr-Pople method and compared with the experimental values.

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