On the role of symmetry in the ab initio hartree-fock linear-combination-of-atomic-orbitals treatment of periodic systems

1986 ◽  
Vol 29 (6) ◽  
pp. 1755-1774 ◽  
Author(s):  
Roberto Dovesi
Keyword(s):  
Ab Initio ◽  
Linear Combination ◽  
Periodic Systems ◽  
Atomic Orbitals ◽  
Hartree Fock

On Rüdenberg’s Integral Approximations and Their Unrestricted and Combined Use in Crystal Orbital Theories of Hartree-Fock Type

2003 ◽  
Vol 58 (12) ◽  
pp. 785-800 ◽  
Author(s):  
Wolfhard Koch ◽  
Bastian Frey ◽  
Juan Francisco Sánchez Ruiza ◽  
Thomas Scior
Keyword(s):  
Linear Combination ◽  
Three Dimensions ◽  
Approximation Schemes ◽  
Periodic Systems ◽  
Atomic Orbitals ◽  
Hartree Fock ◽  
Zero Differential ◽  
Extended Hückel ◽  
Crystal Orbital ◽  
Combined Use

The analysis based on Rüdenberg’s well-known letter of 1951, which has been outlined for molecules in a preceding contribution, now will be transfered to translational periodic systems in one, two, or three dimensions. Again, when applied unrestrictedly to “Linear Combination of Atomic Orbitals” representations (LCAO) of both “Unrestricted” and “Restricted Hartree-Fock” pictures (UHF and RHF), Rüdenberg’s integral approximations of Mulliken type lead to a thorough interpretation of “Extended Hückel” crystal orbital theories (EHT). Moreover, Rüdenberg’s ideas provide us with “Unrestricted and Combined” extensions (U&C) of the widely-used approximation schemes “Zero Differential Overlap” (ZDO) and “Neglect of Diatomic Differential Overlap” (NDDO). An improved variant of EHT is also presented. Corresponding “Restricted and Combined” concepts (R&C), which overcome some shortcomings inherent in Rüdenberg’s original recipes, will be sketched.

From Atomic Orbitals to Molecular Orbitals and Chemical Bonds

2020 ◽  
pp. 150-187
Author(s):  
Jochen Autschbach
Keyword(s):  
Hydrogen Molecule ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Basis Set ◽  
Orbital Method ◽  
Chemical Bonds ◽  
Atomic Orbitals ◽  
Hartree Fock ◽  
Generalized Matrix

It is shown how an aufbau principle for atoms arises from the Hartree-Fock (HF) treatment with increasing numbers of electrons. The Slater screening rules are introduced. The HF equations for general molecules are not separable in the spatial variables. This requires another approximation, such as the linear combination of atomic orbitals (LCAO) molecular orbital method. The orbitals of molecules are represented in a basis set of known functions, for example atomic orbital (AO)-like functions or plane waves. The HF equation then becomes a generalized matrix pseudo-eigenvalue problem. Solutions are obtained for the hydrogen molecule ion and H2 with a minimal AO basis. The Slater rule for 1s shells is rationalized via the optimal exponent in a minimal 1s basis. The nature of the chemical bond, and specifically the role of the kinetic energy in covalent bonding, are discussed in details with the example of the hydrogen molecule ion.

Ab initio Hartree-Fock treatment of ionic and semi-ionic compounds: state of the art

1992 ◽  
Vol 341 (1661) ◽  
pp. 203-210 ◽  
Keyword(s):  
Ab Initio ◽  
State Of The Art ◽  
Basis Set ◽  
Equilibrium Geometry ◽  
Mulliken Population ◽  
Atomic Orbitals ◽  
Oxygen Ions ◽  
Hartree Fock ◽  
Ionic Compounds ◽  
Mn Oxides

The periodic ab initio Hartree-Fock approach is applied to the Li, Na, K, Be, Mg, Ca and Mn oxides, and to Al 2 O 3 (corundum) and SiO 2 (a-quartz). A local basis set (‘atomic orbitals’) is used. The equilibrium geometry, the formation energy and the bulk modulus are calculated, with reasonable agreement with experiment. The influence of the environment on the oxygen ions is discussed through the Mulliken population and band structure data.

Single-layer structures of a100- and b010-Gallenene: a tight-binding approach

2019 ◽  
Vol 21 (28) ◽  
pp. 15798-15804 ◽  
Author(s):  
M. Nakhaee ◽  
M. Yagmurcukardes ◽  
S. A. Ketabi ◽  
F. M. Peeters
Keyword(s):  
Ab Initio ◽  
Linear Combination ◽  
Crystal Structures ◽  
Tight Binding ◽  
Single Layer ◽  
Atomic Orbitals ◽  
Layer Structures

Using the simplified linear combination of atomic orbitals (LCAO) method in combination with ab initio calculations, we construct a tight-binding (TB) model for two different crystal structures of monolayer gallium: a100- and b010-Gallenene.

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