Crystal-field theory for the Rydberg states of polyatomic molecules

1986 ◽  
Vol 64 (7) ◽  
pp. 782-795 ◽  
Author(s):  
Ying-Nan Chiu
Keyword(s):  
Crystal Field ◽  
Spherical Harmonics ◽  
Rydberg States ◽  
Second Order ◽  
Crystal Field Theory ◽  
Linear Combinations ◽  
Atomic Orbitals ◽  
Square Planar ◽  
Rydberg Electron ◽  
D Orbitals

The potential on a Rydberg electron due to the cluster of atoms near the center of a polyatomic molecule is expanded in powers of spherical harmonics. Nonvanishing potentials in totally symmetric irreducible representations are obtained using the crystal field of the cluster of atoms in D3h, C3v, D4v, C4v, Td, and D2d symmetries. Odd as well as the usual even powers of spherical harmonics are included up to [Formula: see text]. Spectroscopically observable differences in potentials between a planar versus a nonplanar XY3 molecule and among a square planar, pyramidal, tetrahedral, and dihedral XY4 molecule are exhibited. First-order energies are given for a Rydberg [Formula: see text] state showing λ dependence. Second-order energies due to mixing of Rydberg states by odd and even power potentials and splitting of ±λ degeneracies are shown analytically for an nd as well as an nf Rydberg electron. The formalism is applicable to nonpenetrating Rydberg orbitals. Approximate radial integrals are obtained. Exact angular integrals for the first- and second-order energies are given. Symmetry-adapted combinations of the separated Y3 and Y4 ligand atomic orbitals are derived up to d orbitals. The correlations between these linear combinations of atomic orbitals as molecular configurations change are shown, e.g., as an XY4 molecule distorts from (D4h, C4v) to (D2d, Td) and vice versa.

Electronic Structure of Octacyanides of Molybdenum IV and V According to the SCCC MO Method. The D2d Case

1972 ◽  
Vol 27 (11) ◽  
pp. 1672-1677 ◽  
Author(s):  
A. Gołębiewski ◽  
R. Nalewajski
Keyword(s):  
Field Theory ◽  
Electronic Structure ◽  
Crystal Field ◽  
Central Atom ◽  
Molecular Orbitals ◽  
Crystal Field Theory ◽  
D Orbitals

Abstract The electronic structure of dodecahedral octacyanides of molybdenum IV and V is described in terms of SCCC molecular orbitals. Five MO's resemble d orbitals of the central atom. The splitting of appropriate levels is almost exactly the same as that following from the crystal field theory for G4/G2 ~ 0.7. According to the theory stable Mo(CN)84- is dodecahedral and stable MO(CN)83- is antiprismatic. In the dodecahedron the A-type ligands are bonded more strongly than the B-type ligands.

scholarly journals Circular Rydberg states of helium atoms or helium-like ions in a high-frequency laser field

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 11-17
Author(s):  
Nikolay Kryukov ◽  
Eugene Oks
Keyword(s):  
High Frequency ◽  
Laser Field ◽  
Nuclear Charge ◽  
Rydberg States ◽  
Orbital Plane ◽  
Precession Frequency ◽  
Nonmonotonic Dependence ◽  
Absolute Value ◽  
Rydberg Electron ◽  
Frequency Laser

Abstract In the literature, there were studies of Rydberg states of hydrogenic atoms/ions in a high-frequency laser field. It was shown that the motion of the Rydberg electron is analogous to the motion of a satellite around an oblate planet (for a linearly polarized laser field) or around a (fictitious) prolate planet (for a circularly polarized laser field): it exhibits two kinds of precession – one of them is the precession within the orbital plane and another one is the precession of the orbital plane. In this study, we study a helium atom or a helium-like ion with one of the two electrons in a Rydberg state, the system being under a high-frequency laser field. For obtaining analytical results, we use the generalized method of the effective potentials. We find two primary effects of the high-frequency laser field on circular Rydberg states. The first effect is the precession of the orbital plane of the Rydberg electron. We calculate analytically the precession frequency and show that it differs from the case of a hydrogenic atom/ion. In the radiation spectrum, this precession would manifest as satellites separated from the spectral line at the Kepler frequency by multiples of the precession frequency. The second effect is a shift of the energy of the Rydberg electron, also calculated analytically. We find that the absolute value of the shift increases monotonically as the unperturbed binding energy of the Rydberg electron increases. We also find that the shift has a nonmonotonic dependence on the nuclear charge Z: as Z increases, the absolute value of the shift first increases, then reaches a maximum, and then decreases. The nonmonotonic dependence of the laser field-caused energy shift on the nuclear charge is a counterintuitive result.

scholarly journals Crystal Field Theory of Magnetic Behaviour of Er2(SO4)3·8H2O

1996 ◽  
Vol 89 (5-6) ◽  
pp. 649-655
Author(s):  
R. Gupta ◽  
U.S. Ghosh ◽  
C. Basu
Keyword(s):  
Field Theory ◽  
Crystal Field ◽  
Magnetic Behaviour ◽  
Crystal Field Theory

scholarly journals Advances of crystal field theory and exchange charge model

2019 ◽  
Vol 21 (4) ◽  
Author(s):  
M.G. Brik ◽  
◽  
N.M. Avram ◽  
C.N. Avram ◽  
◽  
...  
Keyword(s):  
Field Theory ◽  
Crystal Field ◽  
Crystal Field Theory ◽  
Charge Model ◽  
Exchange Charge Model
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