The Distinguished Seminar Series Sponsored by the Texas Quantum Institute hosts 

Speaker: Dr. Mark R. Pederson, The University of Texas at El Paso 

Since the earliest days of quantum mechanics researchers have philosophized about the physical meaning of single-electron orbitals and have often sought to find rigorous means for interpreting both localized and delocalized representations of these electronic degrees of freedom (EDOF). Beyond conceptualization, the subject was of interest to building more effective theories based upon localized orbitals that might be both more transferable between similar chemical systems and allow for greater computational efficiency by capitalizing upon sparsity. Early papers by Pauling and Koopmans highlight the dichotomy of viewpoints. Pauling pointed out that localized sp³ orbitals helped to explain energy differences between separated and condensed phases while Koopmans showed that it was in fact canonical (delocalized) orbitals that best explained energy differences involving removal or addition of electrons.  These issues, based on single configuration theories, get more interesting, and perhaps murkier, in multi-determinantal theories. In this talk I will review the Fermi-Löwdin-Orbital (FLO) formulation [1] for localized theories as an umbrella for most versions localized representations – past and present.  FLOs are defined partially in terms of the one-electron density matrix.  Examples of the use of this formulation, within the inspirational framework of a unitarily-invariant self-interaction corrected method (FLOSIC), will be provided along with a discussion about how quasi-classical “electronic positions” or Fermi-Löwdin-descriptors (FODs) become part of the optimization of a variational density-functional or wavefunction-based representation of the EDOF.  I will review the computational implementation [1], applications to solvated trianions [2], and a rigorous existence theorem [3] that was needed for convincing proof that the FLOSIC was indeed applicable to all atoms and materials.  Interestingly, this proof demonstrated an unexpected path between this density-matrix based picture and the wavefunction itself. More recent extensions of the FLO formulation to other types of physical problems will be reviewed along with some suggestions or speculations on how the formulation might be used within GASSCF and multi-configurational methods to define a localized basis from the FLOSIC formulation.

[1]        Communication: Self-interaction corrections with unitary invariance in density functional theory, MR Pederson, A Ruzsinszky and JP Perdew, JCP 140 121103 (2014).

[2]        Use of FLOSIC for understanding anion-solvent interactions, MR Pederson, KPK Withanage, Z Hooshmand, AI Johnson, T Baruah, Y Yamamoto, RR Zope, DY Kao, PB Shukla, JK Johnson, JE Peralta, KA Jackson, JCP 159, 154112 (2023).

[3         Downward quantum learning from element 118: Automated generation of Fermi-Löwdin-Orbitals for all atoms, MR Pederson, AI Johnson, KPK Withanage, S Dolma, G Bravo Flores, Z Hooshmand, K Khandal, PO Lasode, T Baruah, KA