Localized orbitals based on the fermi hole

Luken, William L.; Culberson, J. Chris

doi:10.1007/bf00554785

Cited by 142 publications

(56 citation statements)

References 37 publications

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“…For example, the Fermi orbital (FO) (Luken and Beratan, 1982;Luken and Culberson, 1984) is a specific example of such a quantity. Given a trial set of KS orbitals, the FO (F iσ ) is defined at any point in space, a iσ , according to:…”

Section: Introduction To the Fermi Orbitalmentioning

confidence: 99%

Self-Interaction Corrections Within the Fermi-Orbital-Based Formalism

Pederson

Baruah

2015

Advances in Atomic, Molecular, and Optical Physics

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Section: Introduction To the Fermi Orbitalmentioning

confidence: 99%

Self-Interaction Corrections Within the Fermi-Orbital-Based Formalism

Pederson

Baruah

2015

Advances in Atomic, Molecular, and Optical Physics

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“…However, there is no consensus in the literature on how to uniquely quantify this effect. Earlier, Weisskopf 19 attributed it to the "kinetic energy pressure" in atoms and molecules, whereas others [7][8][9]11,20,21 employed the quantum contribution from the Pauli exclusion principle ͑Fermi hole͒ [22][23][24][25][26] for the purpose. Different algorithms and disparate implementations using orthogonal/ nonorthogonal localized/delocalized orbitals, natural bond orbitals ͑NBOs͒, and valence bond orbitals lead to subtle but variant explanations and thus ongoing controversy on the matter.…”

Section: Introductionmentioning

confidence: 99%

Exploring the origin of the internal rotational barrier for molecules with one rotatable dihedral angle

Liu

Govind

Pedersen

2008

The Journal of Chemical Physics

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Continuing our recent endeavor, we systematically investigate in this work the origin of internal rotational barriers for small molecules using the new energy partition scheme proposed recently by one of the authors ͓S. B. Liu, J. Chem. Phys. 126, 244103 ͑2007͔͒, where the total electronic energy is decomposed into three independent components, steric, electrostatic, and fermionic quantum. Specifically, we focus in this work on six carbon, nitrogen, and oxygen containing hydrides, CH 3 CH 3 , CH 3 NH 2 , CH 3 OH, NH 2 NH 2 , NH 2 OH, and H 2 O 2 , with only one rotatable dihedral angle ЄH-X -Y -H ͑X , Y =C,N,O͒. The relative contributions of the different energy components to the total energy difference as a function of the internal dihedral rotation will be considered. Both optimized-geometry ͑adiabatic͒ and fixed-geometry ͑vertical͒ differences are examined, as are the results from the conventional energy partition and natural bond orbital analysis. A wealth of strong linear relationships among the total energy difference and energy component differences for different systems have been observed but no universal relationship applicable to all systems for both cases has been discovered, indicating that even for simple systems such as these, there exists no omnipresent, unique interpretation on the nature and origin of the internal rotation barrier. Different energy components can be employed for different systems in the rationalization of the barrier height. Confirming that the two differences, adiabatic and vertical, are disparate in nature, we find that for the vertical case there is a unique linear relationship applicable to all the six molecules between the total energy difference and the sum of the kinetic and electrostatic energy differences. For the adiabatic case, it is the total potential energy difference that has been found to correlate well with the total energy difference except for ethane whose rotation barrier is dominated by the quantum effect.

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“…In other words, the Fermi Orbital (FO) [50,51] depends parametrically on the variational position descriptor, a iσ , and defined according to:…”

Section: Fermi-löwdin Orbitals For Unitarily Invariant Sicmentioning

confidence: 99%

The Role of Self-Interaction Corrections, Vibrations, and Spin-Orbit in Determining the Ground Spin State in a Simple Heme

et al. 2017

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Without self-interaction corrections or the use of hybrid functionals, approximations to the density-functional theory (DFT) often favor intermediate spin systems over high-spin systems. In this paper, we apply the recently proposed Fermi-Löwdin-orbital self-interaction corrected density functional formalism to a simple tetra-coordinated Fe(II)-porphyrin molecule and show that the energetic orderings of the S = 1 and S = 2 spin states are changed qualitatively relative to the results of Generalized Gradient Approximation (developed by Perdew, Burke, and Ernzerhof, PBE-GGA) and Local Density Approximation (developed by Perdew and Wang, PW92-LDA). Because the energetics, associated with changes in total spin, are small, we have also calculated the second-order spin-orbit energies and the zero-point vibrational energies to determine whether such corrections could be important in metal-substituted porphins. Our results find that the size of the spin-orbit and vibrational corrections to the energy orderings are small compared to the changes due to the self-interaction correction. Spin dependencies in the Infrared (IR)/Raman spectra and the zero-field splittings are provided as a possible means for identifying the spin in porphyrins containing Fe(II).

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Localized orbitals based on the fermi hole

Cited by 142 publications

References 37 publications

Self-Interaction Corrections Within the Fermi-Orbital-Based Formalism

Self-Interaction Corrections Within the Fermi-Orbital-Based Formalism

Exploring the origin of the internal rotational barrier for molecules with one rotatable dihedral angle

The Role of Self-Interaction Corrections, Vibrations, and Spin-Orbit in Determining the Ground Spin State in a Simple Heme

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