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A Simple and Accurate Method for Computing Optimized Effective Potentials for Exact Exchange Energy (2403.01772v1)
Published 4 Mar 2024 in physics.chem-ph and quant-ph
Abstract: The inverse Kohn-Sham density-functional theory (inv-KS) for the electron density of the Hartree-Fock (HF) wave function was revisited within the context of the optimized effective potential (HF- OEP). First, it is proved that the exchange potential created by the inv-KS is equivalent to the potential obtained by the HF-OEP when the HF-OEP realizes the HF energy of the system under consideration. Next the real-space grid (RSG) implementations of the inv-KS and the HF-OEP are addressed. The total HF energies EHF for the wave functions on the effective potentials optimized by the inv-KS are computed for a set of small molecules. It is found that the mean absolute deviation (MAD) of EHF from the HF energy is clearly smaller than the MAD of EHF, demonstrating that the inv-KS is advantageous in constructing the detailed structure of the exchange potential vx as compared with the HF-OEP. The inv-KS method is also applied to an ortho-benzyne radical known as a strongly correlated polyatomic molecule. It is revealed that the spin populations on the atomic sites computed by the UHF calculation can be faithfully reproduced by the wave functions on the inv-KS potential.
- P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964).
- W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
- R. G. Parr and W. Yang, Density-functional theory of atoms and molecules (Oxford university press, New York, 1989).
- R. M. Martin, Electronic Structure, Basic Theory and Practical Methods (Cambridge University Press, Cambridge, 2004).
- J. C. Slater, A simplification of the hartree-fock method, Phys. Rev. 81, 385 (1951).
- A. D. Becke, Density-functional exchange-energy approximation with correct asymptotic behavior, Phys. Rev. A 38, 3098 (1988a).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- A. D. Becke and M. R. Roussel, Exchange holes in inhomogeneous system: a coordinate-space model, Phys. Rev. A 39, 3761 (1989).
- A. D. Becke, A new mixing of hartree-fock and local density-functional theories, J. Chem. Phys. 98, 1372 (1993a).
- A. D. Becke, Density-functional thermochemistry. iii. the role of exact exchange, J. Chem. Phys. 98, 5648 (1993b).
- J. D. Talman and W. F. Shadwick, Optimized effective atomic central potential, Phys. Rev. A 14, 36 (1976).
- A. Görling, New ks method for molecules based on an exchange charge density generating the exact local ks exchange potential, Phys. Rev. Lett. 83, 5459 (1999).
- S. Ivanov, S. Hirata, and R. J. Bartlett, Exact exchange treatment for molecules in finite-basis-set kohn-sham theory, Phys. Rev. Lett. 83, 5455 (1999).
- R. Colle and R. K. Nesbet, Optimized effective potential in finite-basis-set treatment, J. Phys. B: At. Mol. Opt. Phys. 34, 2475 (2001).
- F. D. Sala and A. Görling, Efficient localized hartree–fock methods as effective exact-exchange kohn–sham methods for molecules, J. Chem. Phys. 115, 5718 (2001).
- W. Yang and Q. Wu, Direct method for optimized effective potentials in density-functional theory, Phys. Rev. Lett. 89, 143002 (2002).
- S. Kummel and J. P. Perdew, Simple iterative construction of the optimized effective potential for orbital functionals, including exact exchange, Phys. Rev. Lett. 90, 043004 (2003).
- R. van Leeuwen and E. J. Baerends, Exchange-correlation potential with correct asymptotic behavior, Phys. Rev. A 49, 2421 (1994).
- Q. Wu and W. Yang, A direct optimization method for calculating density functionals and exchange–correlation potentials from electron densities, J. Chem. Phys. 118, 2498 (2003).
- E. S. Kadantsev and M. J. Stott, Variational method for inverting the kohn-sham procedure, Phys. Rev. A 69, 012502(7) (2004).
- B. Kanungo, P. M. Zimmerman, and V. Gavini, Exact exchange-correlation potentials from ground-state electron densities, Nat. Commun. 10, 4497 (2019).
- Y. Shi and A. Wasserman, Inverse Kohn-Sham density functional theory: Progress and challenges, J. Phys. Chem. Lett. 12, 5308 (2021).
- W. M. C. Foulkes and R. Haydock, Tight-binding models and density-functional theory, Phys. Rev. B 39, 12520 (1989).
- R. T. Sharp and G. K. Horton, A variational approach to the unipotential many-electron problem, Phys. Rev. 90, 317 (1953).
- J. B. Krieger, Y. Li, and G. J. Iafrate, Construction and application of an accurate local spin-polarized kohn-sham potential with integer discontinuity: Exchange-only theory, Phys. Rev. A 45, 101 (1992).
- A. Görling and M. Levy, Exact kohn-sham scheme based on perturbation theory, Phys. Rev. A 50, 196 (1994).
- T. Heaton-Burgess, F. A. Bulat, and W. Yang, Optimized effective potentials in finite basis sets, Phys. Rev. Lett. 98, 256401(4) (2007).
- J. R. Chelikowsky, N. Troullier, and Y. Saad, Finite-difference pseudopotential method: electronic structure calculations without a basis, Phys. Rev. Lett. 72, 1240 (1994b).
- H. Takahashi, S. Sakuraba, and A. Morita, Large-scale parallel implementation of Hartree-Fock exchange energy on real-space grids using 3d-parallel fast Fourier transform, J. Chem. Inf. Model 60, 1376 (2020).
- L. Kleinman and D. M. Bylander, Efficacious form for model pseudopotentials, Phys. Rev. Lett. 48, 1425 (1982).
- H. Takahashi, Density-functional theory based on the electron distribution on the energy coordinate, J. Phys. B: Atomic, Molecular and Optical Physics 51, 055102(11pp) (2018).
- H. Takahashi, Development of static correlation functional using electron distribution on the energy coordinate, J. Phys. B: At. Mol. Opt. Phys. 53, 245101(9pp) (2020).
- T. Ono and K. Hirose, Timesaving double-grid method for real-space electronic-structure calculations, Phys. Rev. Lett. 82, 5016 (1999).
- C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 37, 785 (1988).
- A. D. Becke, A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys. 88, 2547 (1988b).
- J. C. Slater, Atomic radii in crystals, J. Chem. Phys. 41, 3199 (1964).
- M. Weimer, F. Sala, and A. Gorling, Multiconfigurational optimized effective potential method for a density-functional treatment of static correlation, J. Chem. Phys. 128, 144109 (2008).
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