Application of cubic-harmonic expansions in energy-band calculations using linear combinations of atomic orbitals

1976 ◽  
Vol 13 (10) ◽  
pp. 4314-4319 ◽  
Author(s):  
K. S. Song ◽  
K. L. Malwal
Keyword(s):  
Energy Band ◽  
Linear Combinations ◽  
Atomic Orbitals

Orthogonalized linear combinations of atomic orbitals. III. Extension tof-electron systems

1985 ◽  
Vol 32 (12) ◽  
pp. 8377-8380 ◽  
Author(s):  
Y. P. Li ◽  
Zong-Quan Gu ◽  
W. Y. Ching
Keyword(s):  
Electron Systems ◽  
Linear Combinations ◽  
Atomic Orbitals

Cluster‐type calculations of electronic structures of crystals by the method of linear combinations of atomic orbitals

1975 ◽  
Vol 63 (11) ◽  
pp. 4708-4715 ◽  
Author(s):  
W. Paul Menzel ◽  
Kenneth Mednick ◽  
Chun C. Lin ◽  
C. Franklin Dorman
Keyword(s):  
Electronic Structures ◽  
Linear Combinations ◽  
Atomic Orbitals ◽  
Cluster Type

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.

Orthogonalized linear combinations of atomic orbitals. IV. Inclusion of relativistic corrections

1990 ◽  
Vol 41 (15) ◽  
pp. 10545-10552 ◽  
Author(s):  
Xue-Fu Zhong ◽  
Yong-Nian Xu ◽  
W. Y. Ching
Keyword(s):  
Linear Combinations ◽  
Atomic Orbitals ◽  
Relativistic Corrections
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