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 A pencil-and-paper method for elucidating halide double perovskite band structures

2019 ◽  
Vol 10 (48) ◽  
pp. 11041-11053 ◽  
Author(s):  
Adam H. Slavney ◽  
Bridget A. Connor ◽  
Linn Leppert ◽  
Hemamala I. Karunadasa
Keyword(s):  
Linear Combination ◽  
Electronic Structures ◽  
Double Perovskite ◽  
Band Structures ◽  
Atomic Orbitals ◽  
Pencil And Paper ◽  
Paper Method

Explaining most known double perovskite electronic structures and predicting new ones using Linear Combination of Atomic Orbitals analysis.

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

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

An essay on periodic tables

2019 ◽  
Vol 91 (12) ◽  
pp. 1959-1967 ◽  
Author(s):  
Pekka Pyykkö
Keyword(s):  
Electronic Structures ◽  
Molecular Electronic ◽  
Atomic Orbitals ◽  
Theoretical Predictions ◽  
History Of ◽  
Local Connection ◽  
Stability Limits ◽  
Electron Shells ◽  
Secondary Periodicity

Abstract After a compact history of the PT, from Döbereiner’s triads to the theoretical predictions up to element 172, a number of particular issues is discussed: Why may Z = 172 be a limit for stable electron shells? What are the expected stability limits of the nuclear isotopes? When are formally empty atomic orbitals used in molecular electronic structures? What is ‘Secondary Periodicity’? When do the elements (Ir, Pt, Au), at the end of a bond, simulate (N, O, I), respectively? Some new suggestions for alternative PTs are commented upon. As a local connection, Johan Gadolin’s 1794 analysis of the Ytterby mineral is mentioned.

A Formation Mechanism of X Level due to an Indium-Carbon Dimer in Silicon

2012 ◽  
Vol 502 ◽  
pp. 154-158 ◽  
Author(s):  
Hiroyuki Kawanishi ◽  
Yoshinori Hayafuji
Keyword(s):  
Energy Level ◽  
Formation Mechanism ◽  
Electronic Structures ◽  
Ab Initio Calculation ◽  
Indium Atom ◽  
Acceptor Level ◽  
Calculation Methods ◽  
Atomic Orbitals ◽  
Bonding Interaction ◽  
Acceptor Energy Level

It is known that acceptor-carbon complexes have ionization energies less than those of the corresponding substitutional, separate acceptors in silicon. We present the formation mechanism for a shallower acceptor energy level called an X level that is due to an indium- carbon pair. Ab initio calculation methods were used to evaluate electronic structures and lattice relaxations of silicon with indium, carbon or a carbon-indium dimer. The results shows that the bonding interaction between the 5p orbitals of the indium atom and the 3sp orbitals of the silicon atoms bound with the indium atom mainly determines the ionization energy of the X level, and the ionic bonding interaction of the carbon atomic orbitals with the indium atomic orbitals in the X level enables the bonding interaction of the orbitals between the indium atom and the silicon atom to lower the corresponding indium acceptor level, and then to form the shallower X level.

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