Orthogonalized linear combinations of atomic orbitals. II. Calculation of optical properties of polymorphs of silicon

1977 ◽  
Vol 16 (6) ◽  
pp. 2989-2993 ◽  
Author(s):  
W. Y. Ching ◽  
Chun C. Lin
Keyword(s):  
Optical Properties ◽  
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

scholarly journals Helical Electronic Transitions of Spiroconjugated Molecules

2021 ◽  
Author(s):  
Marc Hamilton Garner ◽  
Clemence Corminboeuf
Keyword(s):  
Optical Properties ◽  
Electronic Structure ◽  
Electron Density ◽  
Relative Orientation ◽  
Molecular Orbitals ◽  
Electronic Transitions ◽  
Linear Combinations ◽  
Electronic And Optical Properties ◽  
Symmetry Protected ◽  
Opposite Helicity

The two perpendicularly oriented π-systems of allene mix into helical molecular orbitals (MOs) when the symmetry of the molecule is reduced. However, the π-π<sup>∗</sup> transitions of allenes are linear combinations of two excitations that always consist of both helicities; consequently, the electronic transitions are not helical. Here, we examine the electronic structure of spiroconjugated molecules, which have the same parent symmetry as allene but with different relative orientation of the two π-systems. We show how the π-mixing in spiropentadiene is analogous to the helical π-mixing in allene. However, in spiroconjugated systems only half the π-MOs become helical. Due to this difference, the π-π<sup>∗</sup> transitions in substituted spiropentadiene come in near-degenerate pairs where the helicity is symmetry protected, and consequently there is no significant mixing between excitations involving MOs of opposite helicity. This inherent helicity of the π-π<sup>*</sup> transitions is verified by computation of the change of electron density. These transitions have big rotatory strengths where the sign correlates with the helicity of the transition. The electronic helicity of spiroconjugated molecules thus manifests itself in observable electronic and optical properties.

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

scholarly journals Helical Electronic Transitions of Spiroconjugated Molecules

2021 ◽  
Author(s):  
Marc Hamilton Garner ◽  
Clemence Corminboeuf
Keyword(s):  
Optical Properties ◽  
Electronic Structure ◽  
Electron Density ◽  
Relative Orientation ◽  
Molecular Orbitals ◽  
Electronic Transitions ◽  
Linear Combinations ◽  
Electronic And Optical Properties ◽  
Symmetry Protected ◽  
Opposite Helicity

The two perpendicularly oriented π-systems of allene mix into helical molecular orbitals (MOs) when the symmetry of the molecule is reduced. However, the π-π<sup>∗</sup> transitions of allenes are linear combinations of two excitations that always consist of both helicities; consequently, the electronic transitions are not helical. Here, we examine the electronic structure of spiroconjugated molecules, which have the same parent symmetry as allene but with different relative orientation of the two π-systems. We show how the π-mixing in spiropentadiene is analogous to the helical π-mixing in allene. However, in spiroconjugated systems only half the π-MOs become helical. Due to this difference, the π-π<sup>∗</sup> transitions in substituted spiropentadiene come in near-degenerate pairs where the helicity is symmetry protected, and consequently there is no significant mixing between excitations involving MOs of opposite helicity. This inherent helicity of the π-π<sup>*</sup> transitions is verified by computation of the change of electron density. These transitions have big rotatory strengths where the sign correlates with the helicity of the transition. The electronic helicity of spiroconjugated molecules thus manifests itself in observable electronic and optical properties.

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