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Acta Phys. -Chim. Sin.  2018, Vol. 34 Issue (6): 650-655    DOI: 10.3866/PKU.WHXB201710251
Special Issue: Special issue for Chemical Concepts from Density Functional Theory
ARTICLE     
The Influence of the Exchange-Correlation Functional on the Non-Interacting Kinetic Energy and Its Implications for Orbital-Free Density Functional Approximations
Kati. FINZEL*(),Patrick. BULTINCK
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Abstract  

In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other. This aspect is first derived in an orbital-free context. It is shown that the total Fermi potential depends on the density only, the individual parts, the Pauli kinetic energy and the exchange-correlation energy, however, are orbital dependent and as such mutually influence each other. The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy. The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the order of a few Hartrees. For chemical purposes, however, the energetic performance as a function of the nuclear coordinates is much more important than total energies. Therefore, the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide. The data reveals that, the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances. Therefore, the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.



Key wordsDensity functional approximation      Density functional approximation      Kinetic energy functional      Exchangecorrelation functional      Bond dissociation energy      Bond distance     
Received: 25 August 2017      Published: 25 October 2017
Fund:  The project was supported by the Fund for Scientific Research in Flanders (FWO-Vlaanderen) for Research Grant G021115N
Corresponding Authors: Kati. FINZEL     E-mail: Kati.Finzel@UGent.be
Cite this article:

Kati. FINZEL,Patrick. BULTINCK. The Influence of the Exchange-Correlation Functional on the Non-Interacting Kinetic Energy and Its Implications for Orbital-Free Density Functional Approximations. Acta Phys. -Chim. Sin., 2018, 34(6): 650-655.

URL:

http://www.whxb.pku.edu.cn/10.3866/PKU.WHXB201710251     OR     http://www.whxb.pku.edu.cn/Y2018/V34/I6/650

 
 
$V^{\textrm{XC}}$
$T_{\textrm{s}}^{\textrm{XC}}$ LDA X$\alpha$ PW91 PBE VSXC revTPSS B3LYP
LDA 1.138(0.0) 1.135(0.3) 1.150(1.2) 1.148(1.0) 1.134(-0.1) 1.141(0.4) 1.117(-1.2)
X$\alpha$ 1.129(-0.3) 1.126(0.0) 1.140(0.9) 1.138(0.7) 1.125(-0.3) 1.132(0.1) 1.109(-1.4)
PW91 1.123(-1.3) 1.120(-0.9) 1.134(0.0) 1.132(-0.3) 1.119(-1.2) 1.126(-0.7) 1.104(-2.2)
PBE 1.126(-0.9) 1.123(-1.1) 1.137(0.3) 1.135(0.0) 1.122(-0.9) 1.129(-0.5) 1.107(-2.0)
VSXC 1.135(0.1) 1.132(0.3) 1.147(1.4) 1.145(1.0) 1.131(0.0) 1.138(0.5) 1.115(-1.1)
revTPSS 1.131(-0.4) 1.128(-0.2) 1.143(0.8) 1.141(-0.1) 1.127(-0.5) 1.134(0.0) 1.111(-1.6)
B3LYP 1.146(1.3) 1.143(1.6) 1.150(1.9) 1.150(1.8) 1.141(1.2) 1.149(1.7) 1.124(0.0)
 
$V^{\textrm{XC}}$
$T_{\textrm{s}}^{\textrm{XC}}$ LDA X$\alpha$ PW91 PBE VSXC revTPSS B3LYP
LDA -0.419(0.0) -0.385(-9.3) -0.372(-12.2) -0.380(-10.4) -0.326(-21.5) -0.332(-19.3) -0.287(-30.5)
X$\alpha$ -0.463(9.2) -0.429(0.0) -0.416(-3.1) -0.424(-1.2) -0.371(-11.9) -0.377(-9.7) -0.332(-20.6)
PW91 -0.477(13.5) -0.443(3.2) -0.430(0.0) -0.438(1.8) -0.384(-8.7) -0.390(-6.4) -0.347(-17.2)
PBE -0.469(10.5) -0.435(-2.8) -0.422(-1.8) -0.430(0.0) -0.376(-10.6) -0.382(-8.4) -0.339(-19.2)
VSXC -0.505(21.5) -0.471(11.9) -0.458(10.7) -0.466(10.7) -0.412(0.0) -0.418(2.5) -0.374(-8.9)
revTPSS -0.491(19.3) -0.457(9.6) -0.444(6.5) -0.452(2.3) -0.398(-2.4) -0.404(0.0) -0.360(-11.3)
B3LYP -0.540(30.6) -0.506(20.9) -0.494(17.9) -0.502(19.8) -0.447(9.0) -0.454(11.7) -0.408(0.0)
 
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