Density Matrix Implementation of the Fermi–Löwdin Orbital Self-Interaction Correction Method

Abstract

The Fermi−Loẅdin orbital self-interaction correction (FLOSIC) method effectively provides a transformation from canonical orbitals to localized Fermi−Loẅdin orbitals which are used to remove the self-interaction error in the Perdew−Zunger (PZ) framework. This transformation is solely determined by a set of points in space, called Fermi−Loẅdin descriptors (FODs), and the occupied canonical orbitals or the density matrix. In this work, we provide a detailed workflow for the implementation of the FLOSIC method for removal of self-interaction error in DFT calculations in an orbital-by-orbital basis that takes advantage of the unitary invariant nature of the FLOSIC method. In this way, it is possible to cast the self-consistent energy minimization at fixed FODs in the same manner than standard Kohn−Sham with one additional term in the Kohn−Sham Hamiltonian that introduces the PZ self-interaction correction. Each energy minimization iteration is divided in two substeps, one for the density matrix and one for the FODs. Expressions for the effective Kohn−Sham matrix and FOD gradients are provided such that its implementation is suitable for most electronic structure codes. We analyze the convergence characteristics of the algorithm and present applications for the evaluation of NMR shielding constants and real-time time-dependent DFT simulations based on the Liouville−von Neumann equation to calculate excitation energies.

MQM 2022: The 10th Triennial Conference on Molecular Quantum Mechanics

“…14 They make use of new partitioning algorithms to overcome problems with electrostatic, induction, and exchange-induction components. Next, in an effort to understand the nature of π-stacking in porous, conjugated aromatic frameworks, Gray and Herbert at The Ohio State University used extended SAPT to decompose the interaction energies of several representative systems, including the [18]annulene dimer. 15 In their paper, which appears in section C4 ("Physical Properties of Materials and Interfaces") of J. Phys.…”

“…Next, Melo, Pederson, and Peralta describe an implementation of the Fermi-Loẅdin orbital self-interaction correction (FLOSIC) method that is suitable for existing quantum chemistry programs. 18 They examine the convergence behavior of the algorithm for properties such as NMR shielding constants and excitation energies. Then, Moura and co-workers from the Kraka group at Southern Methodist University outline a new protocol called "LModeAGen" for the determination and analysis of local vibrational modes.…”

“…Heat-bath configuration interaction (HCI) methods are the focus of a paper by the Zimmerman group at the University of Michigan, and they report on a series of algorithmic improvements that take advantage of distributed- and shared-memory parallelism to achieve highly scalable performance. Next, Melo, Pederson, and Peralta describe an implementation of the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method that is suitable for existing quantum chemistry programs . They examine the convergence behavior of the algorithm for properties such as NMR shielding constants and excitation energies.…”

DOCSIC: A Mean-Field Method for Orbital-by-Orbital Self-Interaction Correction

“…The first implementation of the FLOSIC methodology is based on Jacobi (or Givens)-type rotations to zero the overlap between the occupied and virtual orbitals at each self-consistent iteration, much like standard implementations of Foster-Boys, , Edmiston-Ruedenberg, Pipek-Mezey, or other localization schemes with various target functions, , at fixed FODs. Recently, some of us have proposed a mean-field scheme for relaxing the density in FLOSIC . Other implementations of FLOSIC based on unified Hamiltonian schemes and effective potentials have been reported. − In all these implementations, FODs are relaxed in-between self-consistent loops at fixed density in a double-loop fashion.…”

“…Recently, some of us have proposed a mean-field scheme for relaxing the density in FLOSIC. 45 Other implementations of FLOSIC based on unified Hamiltonian schemes and effective potentials have been reported. 46 − 50 In all these implementations, FODs are relaxed in-between self-consistent loops at fixed density in a double-loop fashion.…”