scholarly journals Local behavior of the first-order gradient correction to the Thomas–Fermi kinetic energy functional

2009 ◽  
Vol 131 (16) ◽  
pp. 164117 ◽  
Author(s):  
David García-Aldea ◽  
T. Martín-Blas ◽  
J. E. Alvarellos
Keyword(s):  
Kinetic Energy ◽  
Energy Functional ◽  
Local Behavior ◽  
Thomas Fermi ◽  
First Order ◽  
Kinetic Energy Functional ◽  
Gradient Correction

Gradient expansion of the atomic kinetic energy functional

1976 ◽  
Vol 43 (3) ◽  
pp. 409-412 ◽  
Author(s):  
Wen-Ping Wang ◽  
Robert G. Parr ◽  
Danny R. Murphy ◽  
George A. Henderson
Keyword(s):  
Kinetic Energy ◽  
Energy Functional ◽  
Gradient Expansion ◽  
Kinetic Energy Functional

THE THOMAS–FERMI–GOMBÁS ATOM MODELS IN WHICH THE ELECTRONS ARE GROUPED INTO n- AND nl-SHELLS AND A CALCULATION OF THE ATOMIC FORM FACTOR

2004 ◽  
Vol 18 (03) ◽  
pp. 409-419
Author(s):  
V. F. TARASOV
Keyword(s):  
Form Factor ◽  
Kinetic Energy ◽  
Total Energy ◽  
Hypergeometric Functions ◽  
Fermi Theory ◽  
Thomas Fermi ◽  
Atomic Form Factor ◽  
First Time ◽  
Analytical Expressions ◽  
Gradient Correction

This article, considers in detail P. Gombás's idea of grouping electrons into n- and nl-shells in the Thomas–Fermi theory of free atoms briefly, the TFG n- and TFG nl-models respectively). Using these models, exact analytical expressions for the total energy E and the atomic form factor F(κ) are obtained. All integrals of the TFG nl-model are computed by means of the hypergeometric functions 2F1(x), 3F2(x), F2(x,y) and FA(x1,…,x6) for the first time. In particular, Weizsäcker's gradient correction to the kinetic energy of the nl-th shell [Formula: see text] generates a new numerical triangle [Formula: see text] with coefficients bw=n+2l(n-l-1).

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