Extension of the cumulant definition for low particle number systems

Kong, Liguo

doi:10.1002/qua.22832

Cited by 7 publications

(1 citation statement)

References 50 publications

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“…Kong claimed that EPV cumulants were unphysical due to their disconnected nature, and proposed an ad-hoc modification of Eq. (2.1.27) that ensured their cancellation [28]; doing so, however, would lead to unwanted side effects (see Sec. 3.2).…”

Section: Vanishing and Non-vanishing Of Cumulantsmentioning

confidence: 99%

Dressing of Interaction Verticles in Multi-Reference Coupled Cluster Theory

Margócsy¹

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Section: Vanishing and Non-vanishing Of Cumulantsmentioning

confidence: 99%

Dressing of Interaction Verticles in Multi-Reference Coupled Cluster Theory

Margócsy¹

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Unpaired electrons at the second‐order reduced density matrix level: Covalent bonding, and coulomb and fermi correlations in closed shell systems

Karafiloglou

Kyriakidou

2013

Int J of Quantum Chemistry

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The usual one‐electron populations in atomic orbitals of closed shell systems are split into unpaired and paired at the (spin‐dependent) second‐order reduced density matrix level. The unpaired electron in an orbital is defined as the “simultaneous occurrence of an electron and an electron hole of opposite spins in the same spatial orbital,” which for simplicity is called “electropon.” The electropon population in a given orbital reveals whether and to what degree the Coulomb correlations, and hence, the chemical bonding between this orbital and the remaining orbitals of the system are globally favorable or unfavorable. The interaction of two electropons in two target orbitals reveals the quality (favorable or unfavorable) and the strength of the covalent bonding between these orbitals; this establish a bridge between the notion of “unpaired electrons” and the traditional covalent structure of valence‐bond (VB) theory. Favorable/unfavorable bonding between two orbitals is characterized by the positive/negative (Coulomb) correlation of two electropons of opposite spins, or alternatively, by the negative/positive (Fermi) correlation of two parallel spin electropons. A spin‐free index is defined, and the relationship between the electropon viewpoint for chemical bonding and the well‐known two‐electron Coulomb and Fermi correlations is established. Benchmark calculations are achieved for ethylene, hexatriene, benzene, pyrrole, methylamine, and ammonia molecules on the basis of physically meaningful natural orbitals. The results, obtained in the framework of both orthogonal and nonorthogonal population analysis methods, provide the same conceptual pictures, which are in very good agreement with elementary chemical knowledge and VB theory. © 2013 Wiley Periodicals, Inc.

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Unpaired electrons, spin polarization, and bond orders in radicals from the 2‐RDM in orbital spaces: Basic notions and testing calculations

Karafiloglou

Kyriakidou

2014

Int J of Quantum Chemistry

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Adopting the second‐order reduced density matrix level, the conventional α‐ and β‐spin populations in radicals are split into paired and unpaired or electropon (referring to the simultaneous occurrence of an electron and a hole of opposite spins in an orbital) populations. This analysis gives the possibility to distinguish the (un)favorable for chemical bonding electronic interactions by means of positive or negative Coulomb and/or Fermi correlations of two electropons. To overcome the conceptual difficulties originated from the subtle superposition of unpaired electrons due to spin density and those responsible for chemical bonding, we use the notion of properly unpaired electrons. The quantity describing this notion provides a global picture for the ability of electrons of a given orbital to form covalent bonds with the electrons of all remaining orbitals. More detailed information, concerning the behavior of electrons in two distinct target orbitals, is obtained by means of the two‐electropon correlations. As shown, the boundary values of the used quantities are physically meaningful, and the whole theory is tested from various points of view concerning: localized and delocalized radical centers, orthogonal and nonorthogonal orbitals, uncorrelated and correlated levels, Coulomb and Fermi correlations. We also check the electropon based analysis by investigating the spin polarization effects and bond orders in radicals. The tests are achieved for well‐known radicals, and to preserve the stability of the numerical results and the invariance of the obtained conceptual pictures, we used natural basis sets introduced within the natural bond orbital methodology. © 2014 Wiley Periodicals, Inc.

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Extension of the cumulant definition for low particle number systems

Cited by 7 publications

References 50 publications

Dressing of Interaction Verticles in Multi-Reference Coupled Cluster Theory

Dressing of Interaction Verticles in Multi-Reference Coupled Cluster Theory

Unpaired electrons at the second‐order reduced density matrix level: Covalent bonding, and coulomb and fermi correlations in closed shell systems

Unpaired electrons, spin polarization, and bond orders in radicals from the 2‐RDM in orbital spaces: Basic notions and testing calculations

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