Nodes in Hartree-Fock 1s atomic orbitals caused by exchange interactions

In this paper we report on electron momentum densities in ZnSe using Compton scattering technique. For the directional measurements we have employed a newly developed 100 mCi 241Am Compton spectrometer which is based on a small disc source with shortest geometry. For the theoretical calculations we have employed a self-consistent Hartree-Fock linear combination of atomic orbitals (HF-LCAO) approach. It is seen that the anisotropy in the measured Compton profiles is well reproduced by our HF-LCAOcalculation and the other available pseudopotential data. The anisotropy in the Compton profiles is explained in terms of energy bands and bond length. - PACS numbers: 13.60.Fz, 78.70. Ck, 78.70.-g

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From Atomic Orbitals to Molecular Orbitals and Chemical Bonds

Quantum Theory for Chemical Applications ◽

10.1093/oso/9780190920807.003.0009 ◽

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.

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Treatment of the exchange interactions in Hartree-Fock LCAO calculations of periodic systems

The Journal of Physical Chemistry ◽

10.1021/j100315a010 ◽

1988 ◽

Vol 92 (4) ◽

pp. 909-913 ◽

Cited By ~ 38

Author(s):

M. Causa ◽

R. Dovesi ◽

R. Orlando ◽

Cesare Pisani ◽

V. R. Saunders

Keyword(s):

Exchange Interactions ◽

Periodic Systems ◽

Hartree Fock

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Improvement of the long-range behavior of Gaussian basis sets using asymptotic constraints

Canadian Journal of Chemistry ◽

10.1139/v92-051 ◽

1992 ◽

Vol 70 (2) ◽

pp. 362-365 ◽

Cited By ~ 7

Author(s):

Toshikatsu Koga ◽

Ajit J. Thakkar

Keyword(s):

Long Range ◽

Basis Sets ◽

Gaussian Basis Sets ◽

Atomic Orbitals ◽

Hartree Fock

It is suggested that atomic orbitals with improved long-range behavior can be obtained by using energy-optimized Gaussian basis sets to which Gaussians have been added to satisfy a subset of some recently derived constraints that must be satisfied by the exact Hartree–Fock orbitals. This procedure is demonstrated by illustrative calculations for helium. This method is found to be superior to the adhoc method of adding diffuse Gaussians in an even-tempered fashion. Keywords: Gaussian basis sets, long-range behavior, asymptotic constraints.

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

Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences ◽

10.1098/rsta.1992.0094 ◽

1992 ◽

Vol 341 (1661) ◽

pp. 203-210 ◽

Cited By ~ 93

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.

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