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.

The Rotational Zeeman Effect of 1,2,4-Trifluorobenzene

1989 ◽  
Vol 44 (7) ◽  
pp. 687-691 ◽  
Author(s):  
W. H. Stolze ◽  
D. H. Sutter
Keyword(s):  
Ground State ◽  
Zeeman Effect ◽  
Electric Quadrupole ◽  
Quadrupole Moments ◽  
Expectation Values ◽  
Magnetic Susceptibility Tensor ◽  
Second Moments ◽  
Plane Component ◽  
Out Of Plane ◽  
State Expectation

Abstract The rotational Zeeman effect of 1,2,4-trifluorobenzene has been studied for 8 low-J rotational transitions in magnetic fields between 1.9 and 2.4 Tesla. The observed susceptibility anisotropics and molecular g-values are: (2χaa−χbb−χcc) = 37.85(69) • 10−6 erg G−2 mole−1, (2χbb−χcc−χaa) = 56.85(54) • 10−6 erg G−2 mole−1, gaa= −0.0393(3), gbb= −0.0277(3), and gcc = 0.0042(2). The Zeeman parameters have been used to derive the molecular electric quadrupole moments and vibronic ground state expectation values for the electronic second moments. The observed out-of-plane quadrupole moment is discussed with reference to an additivity scheme proposed earlier. The observed out-of-plane component of the molecular magnetic susceptibility tensor is in excellent agreement with the value predicted earlier from the CNDO/2-π-electron density alternation at the ring atoms.

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 The Molecular Zeeman Effect of Imines. I. Methanimine, its Molecular g-Tensor, its Magnetic Susceptibility Anisotropies, its Molecular Electric Quadrupole Moment, its Electric Field Gradient at the Nitrogen Nucleus, and its Nitrogen Spin-Rotation Coupling

1989 ◽  
Vol 44 (11) ◽  
pp. 1063-1078 ◽  
Author(s):  
H. Krause ◽  
D. H. Sutter
Keyword(s):  
Magnetic Susceptibility ◽  
Zeeman Effect ◽  
Electric Quadrupole ◽  
Spin Rotation ◽  
Coupling Constants ◽  
Zero Field ◽  
Quadrupole Moments ◽  
Magnetic Susceptibility Tensor ◽  
State Expectation ◽  
The Individual

Abstract The rotational Zeeman effect has been observed in methanimine which was produced from ethylenediamine by flash pyrolysis. The observed vibronic ground state expectation values of the molecular g-values, the magnetic susceptibility anisotropies and the molecular electric quadrupole moments are: gaa = -1.27099(22), gbb= -0.18975(7), gcc= -0.03440(8), 2ξaa-ξbb-ξcc = 12.49(19) · 10-6 ergG-2mol-1, 2ξbb-ξcc-ξaa = 5.22(11) · 10-6 ergG-2 mol-1 Qaa = 0.43(17) · 10-26esu cm2, Qbb= 1.08(10) · 10-26 esu cm2, and Qcc= -1.51 (26) . 10-26 esu cm2. With the TZVP ab initio value for the out-off plane electronic second moment as additional input, reliable values can be given also for the individual components of the magnetic susceptibility tensor and for the bulk susceptibility:ξ = (ξaa + ξbb + ξcc)/3=-13.13(88) · 10-6 erg G -2 mol-1. From low-J a-and b-type zero field transitions the spin-rotation coupling constants and the 14N nuclear quadrupole coupling constants could be redetermined with improved accuracy. These data are compared with our new theoretical results.

LONG RANGE FORCES BETWEEN HYDROGEN MOLECULES

1955 ◽  
Vol 33 (11) ◽  
pp. 668-678 ◽  
Author(s):  
F. R. Britton ◽  
D. T. W. Bean
Keyword(s):  
Wave Function ◽  
Long Range ◽  
Ground State ◽  
Close Agreement ◽  
Van Der Waals ◽  
Wave Functions ◽  
Numerical Factor ◽  
Hydrogen Molecules ◽  
Static Quadrupole

Long range forces between two hydrogen molecules are calculated by using methods developed by Massey and Buckingham. Several terms omitted by them and a corrected numerical factor greatly change results for the van der Waals energy but do not affect their results for the static quadrupole–quadrupole energy. By using seven approximate ground state H2 wave functions information is obtained regarding the dependence of the van der Waals energy on the choice of wave function. The value of this energy averaged over all orientations of the molecular axes is found to be approximately −11.0 R−6 atomic units, a result in close agreement with semiempirical values.

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.

CALCULATION OF THE GROUND STATE HYPERFINE STRUCTURE FOR MUONIC HELIUM ATOMS WITH THE USE OF SOME LOCAL PROPERTIES OF THE WAVE FUNCTIONS

2005 ◽  
Vol 19 (18) ◽  
pp. 889-897 ◽  
Author(s):  
M. R. ESKANDARI ◽  
B. REZAIE ◽  
S. MOHAMMADI
Keyword(s):  
Correlation Function ◽  
Hyperfine Structure ◽  
Ground State ◽  
Simple Wave ◽  
Hyperspherical Harmonic ◽  
Wave Functions ◽  
Variational Parameter ◽  
Expectation Values ◽  
Helium Atoms ◽  
Local Properties

The ground-state hyperfine structure and other properties are calculated for muonic helium atoms (3 He +2μ-e- and 4 He +2μ-e-), with the use of some local properties of the wave functions in the domains where two particles are close to each other or far away. Simple wave functions incorporating these properties with one variational parameter is developed. Also, the electron-muon correlation function is considered in proposed wave functions. It has a correct behavior for r12 tending to zero and infinity. The calculated values for hyperfine structure, energy and expectation values of r2n in ground-state, are compared with the multibox variational approach and the correlation function hyperspherical harmonic method. Our obtained results are very close to the values calculated by mentioned methods and giving strong indications that the proposed wave functions in addition to being very simple, provide relatively accurate values for hyperfine structure, energy and expectation values of r2n, emphasizing on the importance of the local properties of the wave functions.

scholarly journals The Molecular Zeeman Effect of Norbornadiene, its g-Values, Magnetizability Anisotropics, and Molecular Electric Quadrupole Moment; A High-Resolution Microwave Fourier-Transform Study Combined with Quantum Chemical Calculations

1998 ◽  
Vol 53 (1-2) ◽  
pp. 67-76 ◽  
Author(s):  
K. Voges ◽  
D. H. Sutter ◽  
K. Ruud ◽  
T. Helgaker
Keyword(s):  
Gas Phase ◽  
Quadrupole Moment ◽  
Equilibrium Configuration ◽  
Moment Tensor ◽  
Zeeman Effect ◽  
Electric Quadrupole ◽  
Quadrupole Moments ◽  
Electric Quadrupole Moment ◽  
Atomic Orbitals ◽  
Experimental Findings

Abstract The molecular Zeeman effect is reported for norbornadiene at fields near 18 kG. The experimental results are for the molecular g-values: gaa = 0.02860(16), gbb = 0.05271(11), gcc = 0.00142(26), for the magnetizability anisotropics: 2ξaa - ξbb - ξcc = -0.41(26) · 10-6 ergG-2 mol-1 , 2ξbb - ξcc - ξaa = +40.72(27) · 10-6 erg G-2 mol-1 and for the molecular electric quadrupole moments: Qaa = -1.78(20) · 10 -26 esu cm2 , Qbb = 3.73(20) · 10-26 esu cm2 , Qcc = -1.94(30) · 10-26 esu cm2 , with the c-axis of the molecular inertia tensor aligned to the C2v-axis of the equilibrium configuration. The results of ab-initio calculations, using London type atomic orbitals as basis functions, are reported for the g-tensor, the magnetizability tensor and the molecular electric quadrupole moment tensor and are compared to the experimental findings. The possibilities of strain induced magnetizability exaltations and of systematic differences between gas phase and bulk phase magnetizabilities are discussed.

scholarly journals Some ground-state expectation values for the free parafermion Z(N) spin chain

2019 ◽  
Vol 2019 (12) ◽  
pp. 124002 ◽  
Author(s):  
Zi-Zhong Liu ◽  
Robert A Henry ◽  
Murray T Batchelor ◽  
Huan-Qiang Zhou
Keyword(s):  
Ground State ◽  
Spin Chain ◽  
Expectation Values ◽  
State Expectation
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