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

Use of orthogonalised atomic orbitals in ?-electron systems

1968 ◽  
Vol 10 (4) ◽  
pp. 364-366 ◽  
Author(s):  
J. A. Chapman ◽  
D. P. Chong
Keyword(s):  
Electron Systems ◽  
Atomic Orbitals

Quantum electron liquid and its possible phase transition

2021 ◽  
Author(s):  
Sunghun Kim ◽  
Joonho Bang ◽  
Chan-young Lim ◽  
Seung Yong Lee ◽  
Jounghoon Hyun ◽  
...  
Keyword(s):  
Fermi Liquid ◽  
Degrees Of Freedom ◽  
Liquid Crystalline ◽  
Electron Interaction ◽  
High Electron ◽  
Electron Systems ◽  
Atomic Orbitals ◽  
Quantum Electron ◽  
Dependent Measurement ◽  
Band Deformation

Abstract Pure quantum electrons render intriguing correlated electronic phases by virtue of quantum fluctuations in addition to an exclusive electron-electron interaction. To realise such quantum electron systems, a key ingredient is dense electrons decoupled from other degrees of freedom. Here, we report the discovery of a pure quantum electron liquid, which spreads up to ~ 3 Å in the vacuum on the surface of electride crystal. An extremely high electron density and its scant hybridization with underneath atomic orbitals evidence quantum and pure nature of electrons, exhibiting polarized liquid phase demonstrated by spin-dependent measurement. Further, upon reducing the density, the dynamics of quantum electrons drastically changes to that of non-Fermi liquid along with an anomalous band deformation, manifesting a possible transition to a hexatic liquid crystalline phase. Our findings cultivate the frontier of quantum electron systems, which serve as an ideal platform for exploring the correlated electronic phases in a pure manner.

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 How to Calculate Condensed Matter Electronic Structure Based on Multi-Electron Atom Semi-Classical Model

2021 ◽  
Vol 6 (4) ◽  
pp. 46
Author(s):  
Levan Chkhartishvili
Keyword(s):  
Electronic Structure ◽  
Condensed Matter ◽  
Classical Model ◽  
Preliminary Test ◽  
Electron Energy Spectrum ◽  
Electronic Systems ◽  
Electron Systems ◽  
Atomic Orbitals ◽  
Quantum Electron ◽  
The Matrix

Atoms are proved to be semi-classical electronic systems in the sense of closeness of their exact quantum electron energy spectrum with that calculated within semi-classical approximation. Introduced semi-classical model of atom represents the wave functions of bounded in atom electrons in form of hydrogen-like atomic orbitals with explicitly defined effective charge numbers. The hydrogen-like electron orbitals of constituting condensed matter atoms are used to calculate the matrix elements of the secular equation determining the condensed matter electronic structure in the linear-combination-of-atomic-orbitals (LCAO) approach. Preliminary test calculations are conducted for boron B atom and diboron B2 molecule electron systems. 

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