Application of the Lennard-Jones (n,m) potential functions to rare gas solids in the self-consistent phonon approximation

1993 ◽  
Author(s):  
Cecylia Malinowska-Adamska ◽  
I. Maciejewska ◽  
Janusz Tomaszewski
Keyword(s):  
Potential Functions ◽  
The Self ◽  
Rare Gas ◽  
Lennard Jones ◽  
Self Consistent

Thermodynamically self-consistent theories of simple liquids. II. A perturbation scheme for systems with purely repulsive forces

1980 ◽  
Vol 58 (5) ◽  
pp. 713-717 ◽  
Author(s):  
Donald S. Hall ◽  
W. R. Conkie
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Distribution Function ◽  
The Self ◽  
Perturbation Scheme ◽  
Simple Liquids ◽  
Lennard Jones ◽  
Self Consistent ◽  
Repulsive Forces ◽  
Simple Systems

A parametrized perturbation scheme is derived for simple systems with purely repulsive forces. The parameter is chosen so that the pressure in the system found by differentiating the free energy is consistent with that found by integrating over the radial distribution function. Results of calculations for the equation of state of an inverse-12 fluid are presented and found to be in excellent agreement with Monte Carlo simulations. The use of the results of the self-consistent scheme as a reference system for the Lennard-Jones fluid is discussed.

Dynamics of rare-gas floating monolayers in the self-consistent phonon theory

1986 ◽  
Vol 34 (4) ◽  
pp. 2815-2822 ◽  
Author(s):  
L. K. Moleko ◽  
B. Joos ◽  
T. M. Hakim ◽  
H. R. Glyde ◽  
S. T. Chui
Keyword(s):  
The Self ◽  
Rare Gas ◽  
Self Consistent ◽  
Phonon Theory

A Note on the Self Consistent Approximation Method for the Evaluation of Radial Distribution Functions of Simple Fluids

1976 ◽  
Vol 31 (1) ◽  
pp. 31-33 ◽  
Author(s):  
R. V. Gopala Rao ◽  
T. Nammalvar
Keyword(s):  
Radial Distribution ◽  
Approximation Method ◽  
Distribution Functions ◽  
The Self ◽  
Radial Distribution Functions ◽  
Simple Fluids ◽  
Consistent Approximation ◽  
Lennard Jones ◽  
Self Consistent

The self consistent approximation of Rowlinson, Carley and Lado has been applied to calculate the radial distribution functions of simple fluids (Neon, Krypton and Xenon) interacting with a Lennard-Jones 6:12 potential. It has been found that in general the self consistent values are nearer to the exact values than other values.

A study of crystal properties of rare gas solids in the self-consistent phonon theory

1992 ◽  
Vol 71 (3-4) ◽  
pp. 179-191
Author(s):  
C. Malinowska-Adamska ◽  
I. Maciejewska ◽  
J. Tomaszewski
Keyword(s):  
The Self ◽  
Rare Gas ◽  
Crystal Properties ◽  
Self Consistent ◽  
Phonon Theory

scholarly journals The relativistic self-consistent field

1935 ◽  
Vol 152 (877) ◽  
pp. 625-649 ◽  
Keyword(s):  
Wave Equation ◽  
Field Equation ◽  
Wave Functions ◽  
The Self ◽  
Magnetic Interactions ◽  
Consistent Field ◽  
Exchange Effects ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Schrödinger's Equation

1—The method of the self-consistent field for determining the wave functions and energy levels of an atom with many electrons was developed by Hartree, and later derived from a variation principle and modified to take account of exchange and of Pauli’s exclusion principle by Slater* and Fock. No attempt was made to consider relativity effects, and the use of “ spin ” wave functions was purely formal. Since, in the solution of Dirac’s equation for a hydrogen-like atom of nuclear charge Z, the difference of the radial wave functions from the solutions of Schrodinger’s equation depends on the ratio Z/137, it appears that for heavy atoms the relativity correction will be of importance; in fact, it may in some cases be of more importance as a modification of Hartree’s original self-nsistent field equation than “ exchange ” effects. The relativistic self-consistent field equation neglecting “ exchange ” terms can be formed from Dirac’s equation by a method completely analogous to Hartree’s original derivation of the non-relativistic self-consistent field equation from Schrodinger’s equation. Here we are concerned with including both relativity and “ exchange ” effects and we show how Slater’s varia-tional method may be extended for this purpose. A difficulty arises in considering the relativistic theory of any problem concerning more than one electron since the correct wave equation for such a system is not known. Formulae have been given for the inter-action energy of two electrons, taking account of magnetic interactions and retardation, by Gaunt, Breit, and others. Since, however, none of these is to be regarded as exact, in the present paper the crude electrostatic expression for the potential energy will be used. The neglect of the magnetic interactions is not likely to lead to any great error for an atom consisting mainly of closed groups, since the magnetic field of a closed group vanishes. Also, since the self-consistent field type of approximation is concerned with the interaction of average distributions of electrons in one-electron wave functions, it seems probable that retardation does not play an important part. These effects are in any case likely to be of less importance than the improvement in the grouping of the wave functions which arises from using a wave equation which involves the spins implicitly.

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