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Volumn 79, Issue 4, 2009, Pages

Multicenter-type corrections to standard DFT exchange and correlation functionals

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EID: 59249096225     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.045106     Document Type: Article
Times cited : (29)

References (29)
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    • Strictly speaking, the local maxima at the nuclear positions are not "true" (3,-3) critical points because the gradient vector of the charge density is discontinuous at the nuclear cusp that is present in both the wave function and the density. The critical point is labeled by its rank ω and signature σ in the form of (ω,σ). The former is equal to the number of nonzero eigenvalues (of the Hessian matrix) of ρ at the critical point and the latter is the algebraic sum of the signs of the eigenvalues, i.e., (3,-3) denotes the critical point where all curvatures are negative and ρ is a local maximum (Ref.). Nevertheless, there always exists a function homeomorphic to ρ (r; RI) which coincides with ρ almost everywhere and for which the nuclear positions are (3,-3) critical points (Ref.). In this sense, the nuclear positions behave topologically as do (3,-3) critical points in the charge distribution.
    • Strictly speaking, the local maxima at the nuclear positions are not "true" (3,-3) critical points because the gradient vector of the charge density is discontinuous at the nuclear cusp that is present in both the wave function and the density. The critical point is labeled by its rank ω and signature σ in the form of (ω,σ). The former is equal to the number of nonzero eigenvalues (of the Hessian matrix) of ρ at the critical point and the latter is the algebraic sum of the signs of the eigenvalues, i.e., (3,-3) denotes the critical point where all curvatures are negative and ρ is a local maximum (Ref.). Nevertheless, there always exists a function homeomorphic to ρ (r; RI) which coincides with ρ almost everywhere and for which the nuclear positions are (3,-3) critical points (Ref.). In this sense, the nuclear positions behave topologically as do (3,-3) critical points in the charge distribution.
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    • edited by J. Grotendorst, NIC Series (John von Neumann Institute for Computing, Jülich
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* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.