Le spectre électronique de BS. Partie I : Analyse des perturbations du système A2Π–X2Σ+

1981 ◽  
Vol 59 (12) ◽  
pp. 1851-1861 ◽  
Author(s):  
A. Jenouvrier ◽  
B. Pascat
Keyword(s):  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Coupling Constant ◽  
Perturbation Matrix ◽  
Electronic Perturbation ◽  
Vibration Rotation ◽  
Π State

The deperturbed vibration–rotation constants of the A2Π and X2Σ+ states of BS are obtained. The perturbations in the levels of the A2Π state observed in the A2Π–X2Σ+ system are treated and are the result of interactions with high levels of the X2Σ+ state. The electronic factors of the spin–orbit and rotation–electronic perturbation matrix elements for the A ~ X interaction are evaluated. The deperturbed spin–orbit coupling constant of the A state is determined.

Theory of spin-orbit coupling in atoms I. Derivation of the spin-orbit coupling constant

1962 ◽  
Vol 270 (1340) ◽  
pp. 127-143 ◽  
Keyword(s):  
Exact Expression ◽  
Orbit Coupling ◽  
Tensor Operator ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Coupling Constant ◽  
Hartree Fock ◽  
Operator Form ◽  
Hartree Potential

An exact expression for the spin-orbit coupling constant is derived within the Hartree-Fock description of the atom by considering the two body mutual spin-orbit interaction between electrons. The interaction is rewritten in tensor operator form and the contribution of outer electron-core interactions to the coupling constant is calculated. We find that the usual expression < 3F/r8r > where V is the Hartree potential is only approximate, and that certain exchange type terms, which arise because we are dealing with a two-body interaction and determinantal wave function, must also be included. These exchange terms are not simply related to the ordinary electrostatic exchange. The resulting expression for the spin-orbit coupling constant is given in terms of radial integrals which can be calculated using Hartree or Hartree—Fock wave functions. We also discuss the effective magnetic Hamiltonian to be used for the calculation of matrix elements within an atomic configuration.

Rotational analysis of hydroxyl vibration–rotation emission bands: Molecular constants for OH X2Π, 6 ≤ ν ≤ 10

1982 ◽  
Vol 60 (1) ◽  
pp. 41-48 ◽  
Author(s):  
J. A. Coxon ◽  
S. C. Foster
Keyword(s):  
Hydroxyl Radical ◽  
Least Squares ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Rotational Analysis ◽  
Coupling Constant ◽  
Molecular Constants ◽  
Vibration Rotation ◽  
Measured Line

Seven vibration–rotation emission bands of the hydroxyl radical with 6 ≤ ν′ ≤10 have been recorded photoelectrically in the range λ6250–8500 Å. The first reliable constants for levels 6 ≤ ν ≤10 of OH X2Π are obtained by direct least-squares fitting of the measured line frequencies. The vibrational dependences of the Λ-doubling parameters (p and q) and the spin–orbit coupling constant (A) are well defined. A minimum value of Aν is found at ν = 7.

Quantum Number Dependence of the Spin–Orbit Coupling in the X2Π State of PO

1975 ◽  
Vol 53 (4) ◽  
pp. 420-423 ◽  
Author(s):  
H. R. Zaidi ◽  
R. D. Verma
Keyword(s):  
Coupling Parameter ◽  
Orbit Coupling ◽  
Second Derivative ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Coupling Constant ◽  
Common Assumption ◽  
Derivatives Of ◽  
Π State

Expressions are derived for the spin–orbit coupling constant, AvJ, for an isolated 2Π state of a diatomic molecule. These results are applied to the X2Π states of PO. Comparison with the available experimental results allows a determination of the first three derivatives of the coupling parameter at the equilibrium position. It is found that the second derivative gives the largest contribution, thus invalidating a common assumption of the existing theories.

Spectre du radical P2+ : Etude des transitions C2Π – X2Π et D2Π–X2Π

1976 ◽  
Vol 54 (8) ◽  
pp. 907-914 ◽  
Author(s):  
J. Malicet ◽  
J. Brion ◽  
H. Guenebaut
Keyword(s):  
Emission Spectrum ◽  
High Frequency ◽  
Orbit Coupling ◽  
High Dispersion ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Coupling Constant ◽  
Centrifugal Distortion ◽  
High Frequency Discharge ◽  
Π State

The emission spectrum of the P2+ molecular ion has been obtained with a high frequency discharge through a mixture of helium and phosphorus vapour. Both the C2Π–X2Π and D2Π–X2Π systems have been photographed under high dispersion and their rotational structure analysed.The previously known C2Π–X2Π system has been completed by analysing 21 new bands. The D2Π(inv)–X2Π system has not been observed previously. For the three states, involved in these two transitions, the vibrational and rotational constants have been calculated or refined. The p constants for the Λ-doubling for each state have been evaluated. Finally the interpretation of the data of the C2Π state requires a centrifugal distortion term AD in the spin–orbit coupling constant A.

Ground configuration splitting in UCl5

1977 ◽  
Vol 55 (10) ◽  
pp. 937-942 ◽  
Author(s):  
A. F. Leung ◽  
Ying-Ming Poon
Keyword(s):  
Crystal Field ◽  
Energy Levels ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Coupling Constant ◽  
Point Charge Model ◽  
X Ray Crystallography ◽  
Charge Model ◽  
Crystal Field Parameters

The absorption spectra of UCl5 single crystal were observed in the region between 0.6 and 2.4 μm at room, 77, and 4.2 K temperatures. Five pure electronic transitions were assigned at 11 665, 9772, 8950, 6643, and 4300 cm−1. The energy levels associated with these transitions were identified as the splittings of the 5f1 ground configuration under the influence of the spin–orbit coupling and a crystal field of C2v symmetry. The number of crystal field parameters was reduced by assuming the point-charge model where the positions of the ions were determined by X-ray crystallography. Then, the crystal field parameters and the spin–orbit coupling constant were calculated to be [Formula: see text],[Formula: see text], [Formula: see text], and ξ = 1760 cm−1. The vibronic analysis showed that the 90, 200, and 320 cm−1 modes were similar to the T2u(v6), T1u(v4), and T1u(v3) of an UCl6− octahedron, respectively.

Magnetic Susceptibilities of 2T2 Ions. Part 1

1972 ◽  
Vol 50 (10) ◽  
pp. 1468-1471 ◽  
Author(s):  
Alan D. Westland
Keyword(s):  
Magnetic Susceptibility ◽  
Excited State ◽  
Reduction Factor ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Coupling Constant ◽  
Magnetic Susceptibilities

An expression for the magnetic susceptibility of octahedral d1 complexes is derived exactly in terms of an orbital reduction factor k taking into account the presence of the formal 2E excited state. Sample calculations show that the improved expression gives results for susceptibility which are lower at times by several percent from those given by previous expressions. The results given by Figgis using Kotani's method are adequately precise when the spin–orbit coupling constant is no larger than ~0.1 Dq.

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.

Sign in / Sign up

Export Citation Format

Share Document