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.

Perturbation treatment of the Hartree–Fock equations for the ground states of the boron-like ions

1969 ◽  
Vol 47 (7) ◽  
pp. 699-705 ◽  
Author(s):  
C. S. Sharma ◽  
R. G. Wilson
Keyword(s):  
Ground State ◽  
Atomic System ◽  
Ground States ◽  
Great Accuracy ◽  
Second Order ◽  
Expectation Values ◽  
Third Order ◽  
First Order ◽  
Hartree Fock ◽  
The Third

The first-order Hartree–Fock and unrestricted Hartree–Fock equations for the ground state of a five electron atomic system are solved exactly. The solutions are used to evaluate the corresponding second-order energies exactly and the third-order energies with great accuracy. The first-order terms in the expectation values of 1/r, r, r2, and δ(r) are also calculated.

The quantum theory of lattice dynamics. I

1969 ◽  
Vol 310 (1500) ◽  
pp. 79-87 ◽  
Keyword(s):  
Quantum Theory ◽  
Potential Energy ◽  
Lattice Dynamics ◽  
Adiabatic Approximation ◽  
Nuclear Potential ◽  
Body Interaction ◽  
Hartree Fock ◽  
Nuclear Interactions ◽  
Rigid Ion Model

The dynamics of a crystal is examined on the basis of the adiabatic approximation. In part I we examine the form of the dynamical and anharmonic tensors on the assumption that the effective nuclear potential energy can be represented as a simple two-body interaction. In part II we derive expressions for the electronic contributions on the basis of the Hartree-Fock approximation and show that these electron-nuclear interactions are more complex than a simple two-body interaction. In part III we examine these interactions in more detail and find that the two-body approximation is equivalent to a rigid-ion model and that this approximation becomes exact in the limit q = 0.

The quantum theory of lattice dynamics. IV

1969 ◽  
Vol 310 (1500) ◽  
pp. 111-119 ◽  
Keyword(s):  
Lattice Dynamics ◽  
Equilibrium Configuration ◽  
Real Space ◽  
Electronic Energy ◽  
Nuclear Potential ◽  
Bravais Lattice ◽  
Hartree Fock ◽  
Total Electronic Energy ◽  
The Many ◽  
Condensed Systems

The total electronic energy for condensed systems is examined as a function of nuclear displacements from the equilibrium configuration. The expansion is derived to all orders both for the exact solutions to the many-electron Schrödinger equation and for the approximate Hartree-Fock solutions. The results are shown to be translationally invariant to all orders. Expressions are derived for the electronic contributions to the force-constant tensors in real space and it is shown that the effective nuclear potential has a simple two-body form for a Bravais lattice.

Correlation in the Ground State of He Atom

1981 ◽  
Vol 36 (3) ◽  
pp. 272-275 ◽  
Author(s):  
Subal Chandra Saha ◽  
Sankar Sengupta
Keyword(s):  
Ground State ◽  
Zero Order ◽  
Consistent Variation ◽  
Hartree Fock ◽  
Perturbation Procedure ◽  
Self Consistent ◽  
He Atom ◽  
Atomic Parameters

It is possible to reproduce the entire results of Pekeris et al. of different atomic parameters for the He atom by introducing (ll) type correlation in a self consistent variation perturbation procedure using the Hartree-Fock (HF) wavefunction as the zero-order wavefunction

scholarly journals THE METHOD OF INCREMENTS — A WAVEFUNCTION-BASED AB-INITIO CORRELATION METHOD FOR SOLIDS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2204-2214 ◽  
Author(s):  
BEATE PAULUS
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Ground State ◽  
Infinite System ◽  
Correlation Energy ◽  
Correlation Method ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Good Agreement

The method of increments is a wavefunction-based ab initio correlation method for solids, which explicitly calculates the many-body wavefunction of the system. After a Hartree-Fock treatment of the infinite system the correlation energy of the solid is expanded in terms of localised orbitals or of a group of localised orbitals. The method of increments has been applied to a great variety of materials with a band gap, but in this paper the extension to metals is described. The application to solid mercury is presented, where we achieve very good agreement of the calculated ground-state properties with the experimental data.

scholarly journals Ground state properties of graphene in Hartree-Fock theory

2012 ◽  
Vol 53 (9) ◽  
pp. 095220 ◽  
Author(s):  
Christian Hainzl ◽  
Mathieu Lewin ◽  
Christof Sparber
Keyword(s):  
Ground State ◽  
Hartree Fock ◽  
Ground State Properties

STRUCTURE, STABILITY, AND ELECTRONIC PROPERTIES OF LARGE FULLERENES

1993 ◽  
Vol 07 (26) ◽  
pp. 4305-4329 ◽  
Author(s):  
C.Z. WANG ◽  
B.L. ZHANG ◽  
K.M. HO ◽  
X.Q. WANG
Keyword(s):  
Total Energy ◽  
Electronic Properties ◽  
Ground State ◽  
Relative Stability ◽  
Chemical Reactivity ◽  
Structure Stability ◽  
Quantum Mechanical ◽  
Efficient Scheme ◽  
Ground State Structures ◽  
Fullerene Clusters

The recent development in understanding the structures, relative stability, and electronic properties of large fullerenes is reviewed. We describe an efficient scheme to generate the ground-state networks for fullerene clusters. Combining this scheme with quantum-mechanical total-energy calculations, the ground-state structures of fullerenes ranging from C 20 to C 100 have been studied. Fullerenes of sizes 60, 70, and 84 are found to be energetically more stable than their neighbors. In addition to the energies, the fragmentation stability and the chemical reactivity of the clusters are shown to be important in determining the abundance of fullerene isomers.

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