Towards an Optimal Gradient-dependent Energy Functional of the PZ-SIC Form

Abstract

Results of Perdew-Zunger self-interaction corrected (PZ-SIC) density functional theory calculations of the atomization energy of 35 molecules are compared to those of high-level quantum chemistry calculations. While the PBE functional, which is commonly used in calculations of condensed matter, is known to predict on average too high atomization energy (overbinding of the molecules), the application of PZ-SIC gives a large overcorrection and leads to significant underestimation of the atomization energy. The exchange enhancement factor that is optimal for the generalized gradient approximation within the Kohn-Sham (KS) approach may not be optimal for the self-interaction corrected functional. The PBEsol functional, where the exchange enhancement factor was optimized for solids, gives poor results for molecules in KS but turns out to work better than PBE in PZ-SIC calculations. The exchange enhancement is weaker in PBEsol and the functional is closer to the local density approximation. Furthermore, the drop in the exchange enhancement factor for increasing reduced gradient in the PW91 functional gives more accurate results than the plateaued enhancement in the PBE functional. A step towards an optimal exchange enhancement factor for a gradient dependent functional of the PZ-SIC form is taken by constructing an exchange enhancement factor that mimics PBEsol for small values of the reduced gradient, and PW91 for large values. The average atomization energy is then in closer agreement with the high-level quantum chemistry calculations, but the variance is still large, the F 2 molecule being a notable outlier.

Calculations of Al dopant inα-quartz using a variational implementation of the Perdew–Zunger self-interaction correction

“…The exchange and correlation term of the PW91 functional is, however, not optimal for PZ-SIC. A smaller exchange enhancement factor can be used [27], bringing the exchange estimate closer to LDA, as illustrated by the fact that PZ-SIC gives an overcorrection when applied to PBE while it is an undercorrection when applied to LDA [24]. By developing an optimal exchange enhancement factor tailored to PZ-SIC, the scaling factor of 1/2 used here as well as in previous calculations based on the PBE functional [24,26] could be dropped.…”

“…While the correction is too small when applied to LDA, it is too large when applied to the PBE [7] and PW91 [25] functionals, as judged from atomization energy of molecules and band gaps [24,26]. Ideally, a new exchange enhancement factor in the generalized gradient functional form should be developed for use with PS-SIC, that has a weaker enhancement factor than PBE or PW91 [27]. Here, a scaling with a factor of 1/2 will be used as has been justified based on the adiabatic connection formula and has been shown to work well for a wide range of properties and various different types of systems [24,26] ( )…”

Strain Engineering of Adsorbate Self-Assembly on Graphene for Band Gap Tuning

“…Core electrons are represented using Vanderbilt's ultrasoft pseudopoentials 29 . Due to a technical feature of the code it is convenient to compute the phonon modes in the LDA approximation using a Perdew-Zunger (PZ) functional 30 and norm-conserving pseudopotentials 29 33 with a spread value of 0.008 Ryd has been applied. The "Davidson" diagonalisation method with a mixing factor of 0.2 has been chosen for self consistency 34 .…”

A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction

“…These found that while PZSIC improves properties like the dissociation pathway of heteroatomic molecules, it worsens the good description of semi-local functionals for nearequilibrium properties such as atomization energies, due to overcorrection 44,73 . This has come to be known as the paradox of SIC 74 .…”