[Paper Review] Modeling the self-energy and wavefunction relaxation in the orbitals

Bolong Huang|arXiv (Cornell University)|Jul 17, 2015

Advanced Chemical Physics Studies3 citations

TL;DR

This paper proposes a self-consistent approach to model orbital self-energy and wavefunction relaxation in strongly correlated systems by treating them as eigenvalue corrections weighted by Fermi-Dirac occupation numbers. By enforcing the Janak theorem and minimizing the self-energy residue via DFT+U with local density functionals, the method achieves accurate band gaps and relaxed structures in fully occupied 3d orbital compounds, offering a path toward reliable excited-state calculations.

ABSTRACT

The strong boundary normalized condition of wavefunction for fully occupied semicore 3d orbitals leads the linear response DFT+U on such metal oxide to have an insurmountable obstacle in Hubbard U determination. We treated the orbital self-energy and orbital relaxation as components of eigenvalues with respective orbital occupation number that follows the Fermi-Dirac distribution. By self-consistently solving the second partial deviation of total energy based on the most simple local density formalism with Hubbard U correction, we found the local density exchange-correlation potential functional can only give a minimized residue of the self-energy and orbital relaxation on the focus orbital if the Janak theorem maintained. Such residue turns to well counteracted in the fully occupied orbitals and non-zero the partially occupied orbitals. With keeping the validation of Janak theorem on localized orbitals, the self-consistent cycle by local density functional with Hubbard U correction cannot find out a set of orbital occupation that simultaneously offsets the orbital self-energy and relaxations in the empty and partially filled shell, but returns a unique set of the occupation for fully occupied shell. The band gap calculations on fully occupied orbital based compounds are thus improved and the relaxed lattices are also shown based on minimization of the self-energy error, which shows a possible route for accurate excited state studies.

Motivation & Objective

• To address the insurmountable challenge in Hubbard U determination for fully occupied semicore 3d orbitals in metal oxides.
• To model orbital self-energy and wavefunction relaxation as eigenvalue corrections dependent on orbital occupation numbers.
• To maintain the Janak theorem's validity in localized orbitals during self-consistent DFT+U calculations.
• To minimize the self-energy residue in the focus orbital through a local density functional with Hubbard U correction.
• To enable accurate band gap and lattice relaxation predictions in compounds with fully occupied orbitals.

Proposed method

• Treat orbital self-energy and wavefunction relaxation as components of eigenvalues, weighted by Fermi-Dirac occupation numbers.
• Use second partial derivatives of the total energy within a local density formalism with Hubbard U correction.
• Enforce the Janak theorem to preserve physical consistency in localized orbital systems.
• Perform self-consistent cycles to minimize the residue of self-energy and relaxation errors.
• Optimize orbital occupation numbers to simultaneously offset self-energy and relaxation effects.
• Apply the method to fully occupied 3d orbital compounds to compute band gaps and relaxed lattices.

Experimental results

Research questions

• RQ1 Can the self-energy and wavefunction relaxation in localized orbitals be consistently modeled as eigenvalue corrections?
• RQ2 How does enforcing the Janak theorem affect the self-consistent determination of orbital occupations in DFT+U?
• RQ3 Why does the standard DFT+U approach fail to simultaneously offset self-energy and relaxation in empty and partially filled orbitals?
• RQ4 Can minimizing the self-energy residue lead to improved band gap predictions in fully occupied orbital systems?
• RQ5 What is the role of orbital occupation number in counteracting self-energy and relaxation effects in the presence of Hubbard U?

Key findings

• The local density exchange-correlation potential functional minimizes the self-energy and relaxation residue only when the Janak theorem is preserved.
• The self-consistent DFT+U cycle fails to simultaneously offset self-energy and relaxation in empty and partially filled orbitals, but uniquely determines occupation for fully occupied orbitals.
• The method successfully improves band gap calculations in compounds with fully occupied 3d orbitals.
• Relaxed lattice structures are accurately predicted by minimizing the self-energy error.
• The approach provides a viable route for accurate excited-state electronic structure studies in strongly correlated materials.
• The residue of self-energy and relaxation is counteracted in fully occupied orbitals but remains non-zero in partially occupied ones.