The orthogonality assumption in the Hartree–Fock approximation for 2pn3p configurations

1968 ◽  
Vol 46 (21) ◽  
pp. 2435-2440 ◽  
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Total Energy ◽  
Hartree Fock ◽  
Orthogonality Constraints ◽  
Orthogonality Constraint

Hartree–Fock (HF) results for Na+ 2p53p1S and Ne+ 1s2p53p2S are reported. In order for the SCF process to converge, additional orthogonality constraints to the corresponding 2p6 states had to be introduced. The resulting 2p functions were nodeless. Similar calculations were performed for O 2p33p2P and Ne+ 2p43p2P for which standard HF results were available. A comparison of the two methods indicates that, unlike the He 1s2s1S case, the additional orthogonality constraint did not improve the total energy although it removed the extra node from the 2p function.

HARTREE–FOCK WAVE FUNCTIONS FOR EXCITED STATES: II. SIMPLIFICATION OF THE ORBITAL EQUATIONS

1966 ◽  
Vol 44 (12) ◽  
pp. 3227-3240 ◽  
Author(s):  
Maurice Cohen ◽  
Paul S. Kelly
Keyword(s):  
Total Energy ◽  
Excited States ◽  
Wave Functions ◽  
Lower State ◽  
Hartree Fock ◽  
Orthogonality Constraint ◽  
State Functions

Hartree–Fock wave functions have been calculated for a number of excited states of the helium sequence, the wave functions being constrained to be orthogonal to all lower state functions. The effect of choosing the inner 1s orbital so that the orthogonality constraint is satisfied automatically has been examined, and it is shown that such a choice has a very small effect on the total energy. An extension to heavier systems is proposed.

The quantum theory of lattice dynamics. Il

1969 ◽  
Vol 310 (1500) ◽  
pp. 89-99 ◽  
Keyword(s):  
Quantum Theory ◽  
Total Energy ◽  
Ground State ◽  
Lattice Dynamics ◽  
Equilibrium Configuration ◽  
Third Order ◽  
Hartree Fock

Expressions are derived for the expansion of the total energy of the electrons in their ground state in a crystal in powers of displacements of the nuclei from their equilibrium configuration. The expansion is taken up to third order on the basis of the coupled Hartree-Fock equations and thus one obtains expressions for the electronic contributions to the dynamical and anharmonic tensors.

Stationary properties of approximate wave functions

1969 ◽  
Vol 47 (21) ◽  
pp. 2355-2361 ◽  
Author(s):  
A. R. Ruffa
Keyword(s):  
Wave Function ◽  
Total Energy ◽  
Helium Atom ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Mechanical Wave ◽  
Expectation Value ◽  
Charge Densities ◽  
Hartree Fock ◽  
Approximate Wave

The accuracy of quantum mechanical wave functions is examined in terms of certain stationary properties. The most elementary of these, namely that displayed by the class of wave functions which yields a stationary value for the total energy of the system, is demonstrated to necessarily require few other stationary properties, and none of these appear to be particularly useful. However, the class of wave functions which yields both stationary energies and charge densities has very important stationary properties. A theorem is proven which states that any wave function in this class yields a stationary expectation value for any operator which can be expressed as a sum of one-particle operators. Since the Hartree–Fock wave function is known to possess these same stationary properties, this theorem demonstrates that the Hartree–Fock wave function is one of the infinitely many wave functions of the class. Methods for generating other wave functions in this class by modifying the Hartree–Fock wave function without changing its stationary properties are applied to the calculation of wave functions for the helium atom.

scholarly journals Quantum Mechanical Study of YTiO3 to the Investigation of Piezoelectricity

2011 ◽  
Vol 2011 ◽  
pp. 1-5
Author(s):  
Raimundo Dirceu de Paula Ferreira ◽  
Marcos Antonio Barros dos Santos ◽  
Maycon da Silva Lobato ◽  
Jardel Pinto Barbosa ◽  
Marcio de Souza Farias ◽  
...  
Keyword(s):  
Total Energy ◽  
Piezoelectric Properties ◽  
Piezoelectric Effect ◽  
Basis Set ◽  
Basis Sets ◽  
Gaussian Basis Sets ◽  
Hartree Fock ◽  
Generator Coordinate ◽  
Mechanical Study ◽  
Quantum Mechanical Study

In previous articles we reported through theoretical studies the piezoelectric effect in BaTiO3, SmTiO3, and YFeO3. In this paper, we used the Douglas-Kroll-Hess (DKH) second-order scalar relativistic method to investigate the piezoelectricity in YTiO3. In the calculations we used the [6s4p] and [10s5p4d] Gaussian basis sets for the O (3P) and Ti (5S) atoms, respectively, from the literature in combination with the (30s21p16d)/[15s9p6d] basis set for the Y (3D) atom, obtained by generator coordinate Hartree-Fock (GCHF) method, and they had their quality evaluated using calculations of total energy and orbital energies (HOMO and HOMO-1) of the 2TiO+1 and 1YO+1 fragments. The dipole moment, the total energy, and the total atomic charges in YTiO3 in Cs space group were calculated. When we analyze those properties we verify that it is reasonable to believe that YTiO3 does not present piezoelectric properties.

scholarly journals QMC Calculations of Total Energy and Bond Length of Some Polyatomic Organic Molecules

2016 ◽  
Vol 64 ◽  
pp. 63-68
Author(s):  
Sylvester A. Ekong ◽  
David A. Oyegoke
Keyword(s):  
Wave Function ◽  
Total Energy ◽  
Quantum Monte Carlo ◽  
Organic Molecules ◽  
Linus Pauling ◽  
Hartree Fock ◽  
Total Energies ◽  
Experimental Values ◽  
Significant Figures ◽  
Good Agreement

This paper aims at determining the total energy and bond lengths of some polyatomic organic molecules, using quantum Monte Carlo (QMC) CASINO-code. The QMC code employed the VMC and DMC methods in the computations with emphasis on DMC, and using Slater-Jastrow trial wave-function formed from Hartree-Fock orbitals. The calculated results show that our reported values are in good agreement with the experimental values of both Hehre et al., and Linus Pauling. The total energies obtained in this study are 6 significant figures more accurate than those of previous studies.

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