Optimal Power Series Expansions of the Kohn–Sham Potential
Tim Callow, Tom Pitts and Nikitas Gidopoulos
Department of Physics, Durham University, Durham DH1 3LE, England, U.K.
Email: nikitas.gidopoulos@durham.ac.uk
Accurate and reliable approximations for the exchange-correlation functional are critical to the success of density functional theory (DFT). In our group these approximations are obtained systematically from many body perturbation theory [1,2] or by identifying and targeting specific errors in density functional approximations (DFAs), such as the self-interaction error.
The use of many body perturbation techniques in DFT, through the adiabatic
connection path formulation is a cornerstone in the development of the accurate approximations but still, the requirement to maintain the electronic density fixed as the strength of the electron repulsion changes complicates the formalism. By contrast, wave-function theory (WFT) and WF methods lend themselves directly to systematic improvement with many body perturbation theory (MBPT) techniques. In our work, based on WFT, we use an energy difference that is a potential functional, whose minimizing potential is the Kohn-Sham (KS) potential of DFT [1]; this draws DFT and WFT together. We then use second order MBPT to construct approximations for the energy difference and for the KS potential, and argue that those expressions with smallest magnitude of correlation energy will converge fastest [2]. With this approach, we not only derive in a novel manner the exchange-only optimized effective potential and the local Fock exchange potential [3], but we also develop a new effective potential with exchange and correlation (XC) potential to first order [2]. In a complementary line of research we identify the effect of the self-interaction error in the effective potential of popular DFAs. By appropriately constraining the KS minimization of the total energy, in a way that corrects the effective KS potential but does not change the XC energy functional, we manage to improve significantly the single-particle eigenvalue spectrum of the effective potential [4]. The hybrid version of this single particle scheme gives surprisingly accurate single-particle energies (interpreted as negative IPs) for all the occupied orbitals, while keeping the resulting DF total energies as accurate as in the original uncorrected DFA.
[1] N I Gidopoulos, Phys. Rev. A 83, 040502 (2011); https://doi.org/10.1103/PhysRevA.83.040502
[2] T J Callow, N I Gidopoulos, Eur. Phys. J. B 91, 209 (2018); https://doi.org/10.1140/ep jb/e2018-90189-2
[3] T W Hollins, S J Clark, K Refson and N I Gidopoulos, J. Phys.: Condens. Matter 29 04LT01 (2017); https://doi.org/10.1088/1361-648X/29/4/04LT0
[4] T Pitts, N I Gidopoulos and N N Lathiotakis, Eur. Phys. J. B (2018) 91: 130;
https://doi.org/10.1140/ep jb/e2018-90123-8