A nonempirical scaling correction approach for density functional methods involving substantial amount of Hartree–Fock exchange

Abstract

A nonempirical scaling correction (SC) approach has been developed for improving bandgap prediction in density functional theory [X. Zheng, A. J. Cohen, P. Mori-Sánchez, X. Hu, and W. Yang, Phys. Rev. Lett. 107, 026403 (2011)]. For finite systems such as atoms and molecules, the SC approach restores the Perdew-Parr-Levy-Balduz condition [Phys. Rev. Lett. 49, 1691 (1982)] that the total electronic energy should scale linearly with number of electrons between integers. Although the original SC approach is applicable to a variety of mainstream density functional approximations, it gives zero correction to the Hartree-Fock method. This is because the relaxation of orbitals with the change in electron number is completely neglected. In this work, with an iterative scheme for the evaluation of Fukui function, the orbital relaxation effects are accounted for explicitly via a perturbative treatment. In doing so, the SC approach is extended to density functionals involving substantial amount of Hartree-Fock exchange. Our new SC approach is demonstrated to improve systematically the predicted Kohn-Sham frontier orbital energies, and alleviate significantly the mismatch between fundamental and derivative gaps.

Assessment of Tuning Methods for Enforcing Approximate Energy Linearity in Range-Separated Hybrid Functionals

“…The MCY3 and rCAM-B3LYP functionals 14 were specifically designed to achieve near-linear behaviour and they have shown some success. 24 Zheng et al 25 proposed a non-empirical scaling correction to largely restore linearity, which was 3 later extended 26 and A M , of the integer systems, determined as the differences between the energies of the integer systems, calculated using the same approximate functional. The solid black curve indicates a linear interpolation between the integer energies, which will more closely resemble the shape of the exact curve because approximate functionals tend to perform more accurately at integer electron-number.…”

Fundamental gaps with approximate density functionals: The derivative discontinuity revealed from ensemble considerations

“…Practical GKS schemes often rely on the Fock operator, or variants thereof. Such GKS calculations were performed, e.g., by employing the screened exchange approach [69,[71][72][73][74][75], by using global hybrid functionals [76][77][78][79][80][81][82][83][84][84][85][86], range-separated hybrid functionals [80,81,[87][88][89][90][91][92][93][94][95][96], and by applying a scaling correction to the Hartree and exchange functionals [97,98]. Alternatively, one can step outside the KS scheme by introducing orbital-specific corrections, where different electrons of the KS system are subject to different potentials.…”

Strong Correlation and Charge Localization in Kohn-Sham Theories with Fractional Orbital Occupations: The Role of the Potential

“…13 Much attention has been paid to overcoming static correlation and delocalization errors in density functional approaches. [14][15][16][17][18][19][20][21][22][23] An alternative pathway is to use reduced density matrix functional theory (RDMFT), by directly approximating the first-and second-order reduced density matrices. 1,24,25 The resulting energy expression then becomes a simultaneous functional of (natural) orbital occupation factors, and a corresponding set of orthonormal (natural) orbitals.…”