Application of the generalized-gradient approximation to rare-gas dimers

171

Density functional theory ͑DFT͒ has become the method of choice for many applications of quantum mechanics to the study of the electronic properties of molecules and solids. Despite the enormous progress in improving the functionals, the current generation is inadequate for many important applications. As part of the quest of finding better functionals, we consider in this paper the Perdew-Burke-Ernzerhof ͑PBE͒ functional, which we believe to have the best theoretical foundation, but which leads to unacceptable errors in predicting thermochemical data ͑heats of formation͒ of molecular systems ͓mean absolute deviation ͑MAD͒ϭ16.9 kcal/mol against the extended G2 data set of 148 molecules͔. Much improved thermochemistry is obtained with hybrid DFT methods that include part of the Hartree-Fock exchange ͓thus B3LYP ͑Becke's three parameter scheme combining Hartree-Fock exchange, Becke gradient corrected exchange functional and Lee-Yang-Parr correlational functional͒ with MADϭ3.1 kcal/mol and PBE0 ͑Perdew's hybrid scheme using PBE exchange and correlation functionals͒ with MADϭ4.8 kcal/mol͔. However we wish to continue the quest for a pure density-based DFT. Thus we optimized the four free parameters ͑ , , ␣, and ␤͒ in PBE theory against experimental atomic data and the van der Waals interaction properties of Ne 2 , leading to the xPBE extended functional, which significantly outperforms PBE for thermochemical properties MAD reduced to 8.0 kcal/mol while being competitive or better than PBE for predictions of geometric parameters, ionization potentials, electron affinities, and proton affinities and for the description of van der Waals and hydrogen bond interactions. Thus xPBE significantly enlarges the field of applications available for pure DFT. The functional forms thus obtained for the exchange and correlational functionals may be useful for discovering new improved functionals or formalisms.

Section: Ionization Potentials Electron Affinities and Proton Afsupporting

confidence: 72%

The extended Perdew-Burke-Ernzerhof functional with improved accuracy for thermodynamic and electronic properties of molecular systems

Goddard

2004

171

“…Undeterred, a few studies of conventional DFAs and noble-gas vdW curves appeared in the DFT literature. [139][140][141][142] Some functionals, including the LDA, bound noble-gas dimers. Some did not.…”

Section: Dispersion Interactions: the Floodgates Openmentioning

confidence: 99%

Perspective: Fifty years of density-functional theory in chemical physics

Becke

2014

1,326

964

Since its formal inception in 1964-1965, Kohn-Sham density-functional theory (KS-DFT) has become the most popular electronic structure method in computational physics and chemistry. Its popularity stems from its beautifully simple conceptual framework and computational elegance. The rise of KS-DFT in chemical physics began in earnest in the mid 1980s, when crucial developments in its exchange-correlation term gave the theory predictive power competitive with welldeveloped wave-function methods. Today KS-DFT finds itself under increasing pressure to deliver higher and higher accuracy and to adapt to ever more challenging problems. If we are not mindful, however, these pressures may submerge the theory in the wave-function sea. KS-DFT might be lost. I am hopeful the Kohn-Sham philosophical, theoretical, and computational framework can be preserved. This Perspective outlines the history, basic concepts, and present status of KS-DFT in chemical physics, and offers suggestions for its future development. © 2014 AIP Publishing LLC.

“…17 Common conclusions are reached. The local density approximation ͑LDA͒ tends to overbind 1,2,4,5,16 while the performance of generalized gradient approximation ͑GGA͒ and hybrid functionals is sensitive to the choice of exchange approximation. Functionals based on Becke 1988 exchange 18 often predict a repulsive interaction;…”

Section: Introductionmentioning

confidence: 99%

Helium dimer dispersion forces and correlation potentials in density functional theory

Allen

Tozer

2002

148

101

The dispersion interaction in the helium dimer is considered from the viewpoint of the force on a nucleus. At large internuclear separations, Brueckner coupled cluster BD(T) forces agree well with near-exact dispersion forces. The atomic density distortion associated with the dispersion force is quantified by comparing the BD(T) dimer density with a superposition of atomic densities. For density functional theory calculations in the Hartree–Fock–Kohn–Sham (HFKS) formalism, the accuracy of the dispersion force is governed by the correlation potential. Calculations using the conventional Lee–Yang–Parr [Phys. Rev. B 37, 785 (1988)] potential only generate a small density distortion, giving forces significantly smaller than BD(T). The BD(T) electron densities are therefore used to determine improved correlation potentials using a modified Zhao–Morrison–Parr (ZMP) approach [Phys. Rev. A 50, 2138 (1994)]. HFKS calculations using these ZMP potentials quantitatively reproduce the distortion, giving dispersion forces in good agreement with BD(T). The dimer ZMP correlation potential is partitioned into two parts, one equal to the sum of two unperturbed spherical atomic correlation potentials and the other representing an interaction potential. HFKS calculations using the former do not generate the distortion; forces are close to Hartree–Fock. Calculations using the latter do generate the distortion, giving forces essentially identical to those from the full dimer potential. The origin of the distortion is traced to the asymmetric structure of the interaction correlation potential in the vicinity of each nucleus.