The Ultraviolet Emission Spectra of OH+ and OD+. Rotational Structure and Perturbations in the A3Πi–X3Σ− Transition

1975 ◽  
Vol 53 (3) ◽  
pp. 251-283 ◽  
Author(s):  
A. J. Merer ◽  
D. N. Malm ◽  
R. W. Martin ◽  
M. Horani ◽  
J. Rostas
Keyword(s):  
Interaction Parameter ◽  
Emission Spectra ◽  
Orbit Coupling ◽  
Rotational Structure ◽  
Spin Interaction ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Coupling Constant ◽  
Ultraviolet Emission ◽  
Rotational Constants

The A3Πi–X3Σ− emission systems of OH+ and OD+ have been reinvestigated in detail. Fourteen bands have been analyzed (of which seven are new), and accurate rotational constants have been obtained for the levels ν = 0–2 in the two states of OH+ and ν = 0–3 in the two states of OD+. Corrected assignments are given for the low J lines in the bands of OH+ (which are important in astrophysical spectra, such as those of H2O containing comets).The perturbations in the A3Π states of both isotopes have been studied quantitatively, and the erratic Λ doubling explained in detail. The position of the perturbing b1Σ+ state has been determined to within a few cm−1, and minor perturbations by the A1Δ state have been characterized. Values of the spin–orbit coupling constant, A, and the spin–spin interaction parameter, α, have been extracted from the data for OD+A3Π ν = 0.

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.

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.

Spin–orbit splitting in 2Δ states of diatomic molecules

1969 ◽  
Vol 47 (23) ◽  
pp. 2727-2730 ◽  
Author(s):  
H. Lefebvre-Brion ◽  
N. Bessis
Keyword(s):  
Diatomic Molecules ◽  
Orbit Interaction ◽  
Second Order ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Coupling Constant ◽  
Orbit Splitting ◽  
Spin Orbit Splitting ◽  
Good Agreement

The origin of the splitting of the 2Δ states arising from the σπ2 configuration is studied. For light diatomic molecules, the splitting is shown to arise from the spin–other–orbit interaction which gives a small negative value for the spin–orbit coupling constant A. Non-empirical calculations of A for the 2Δ states of the CH, NH+, and NO molecules are in good agreement with experiment. In heavier molecules, the spin–other–orbit interaction becomes negligible and the second-order spin–orbit effect is dominant.

Electron resonance of SO ( 3 Ʃ ) in the gas phase

1967 ◽  
Vol 298 (1454) ◽  
pp. 340-358 ◽  
Keyword(s):  
Coupling Constants ◽  
Orbit Coupling ◽  
Spin Coupling ◽  
Zero Field ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Coupling Constant ◽  
Molecular Constants ◽  
Excited Vibrational State ◽  
Electron Resonance

The electron resonance spectrum of SO has been previously shown to arise from SO in two electronic states, the ground 3 Ʃ - and the excited 1 ∆ state. In this paper the portion of the spectrum assigned to the 3 Ʃ - state is analysed and shown to arise from three isotopic species, 32 S 16 O, 33 S 16 O, and 34 S 16 O. The analysis shows that besides the dominant interaction of the unpaired electronic spins with the magnetic field; other interactions must be taken into account to interpret the spectrum accurately. Interactions with electronic orbital angular momentum of π states mixed in by spin-orbit coupling and with rotationally induced magnetic moments have been observed. Values for parameters measuring such interactions have been determined from the spectrum, and these values lead to a resolution of the first- and second-order contributions to the zero-field molecular constants as well as an approximate value for the spin-orbit coupling constant. The hyperftne structure resulting from 33 S in 33 S 16 O has also been observed and is related to the usual hyperfine coupling constants. The expected line strengths and widths for SO have been calculated and these are compared with the observed quantities. Besides the expected lines from the isotopic SO species in the 3 Ʃ - state, several other lines have been detected. These lines are interpreted as arising from 32 S 16 O in the ground electronic state, but in the first excited vibrational level. The spectrum of vibrationally excited SO allows a value of the spin-spin coupling constant in the first excited vibrational state to be determined.

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