Matches in SemOpenAlex for { <https://semopenalex.org/work/W2078362502> ?p ?o ?g. }
Showing items 1 to 80 of
80
with 100 items per page.
- W2078362502 endingPage "3862" @default.
- W2078362502 startingPage "3859" @default.
- W2078362502 abstract "Lower bounds for the first-order gradient corrections to the kinetic- and exchange-energy functionals in atoms are derived using Benson's inequality. They are formulated in terms of the expectation values and the momentum expectation value in a simple manner, namely, ${mathit{T}}_{2}$[ensuremath{rho}]=1/72 ensuremath{int} |ensuremath{nabla}ensuremath{rho}(r)${mathrm{|}}^{2}$/ensuremath{rho}(r) drensuremath{geqslant}${mathit{n}}^{2}$/72 〈${mathbf{r}}^{phantom{rule{0ex}{0ex}}mathit{n}mathrm{ensuremath{-}}3}$${mathrm{〉}}^{2}$〈${mathbf{r}}^{2mathit{n}mathrm{ensuremath{-}}4}$${mathrm{〉}}^{mathrm{ensuremath{-}}1}$ and |${mathit{K}}_{2}$[ensuremath{rho}]|=ensuremath{beta}ensuremath{int} |ensuremath{nabla}ensuremath{rho}(r)${mathrm{|}}^{2}$/${mathrm{ensuremath{rho}}}^{4/3}$(r) drensuremath{geqslant}0.051 05〈${mathbf{r}}^{mathrm{ensuremath{-}}1}$${mathrm{〉}}^{2}$〈p${mathrm{〉}}^{mathrm{ensuremath{-}}1}$, where n is the natural number, 〈${mathit{r}}^{mathit{n}mathrm{ensuremath{-}}3}$〉 and 〈${mathit{r}}^{2mathit{n}mathrm{ensuremath{-}}4}$〉 are the expectation values, 〈p〉 is the momentum value, and ensuremath{rho}(r) is the electron density with the normalization condition of ensuremath{int}ensuremath{rho}(r)dr=N, the number of electrons. The bounds derived in this work are tested for atoms Z=1--36. A comparison is also made with the previously derived lower bound estimates for ${mathit{T}}_{2}$[ensuremath{rho}] and ${mathit{K}}_{2}$[ensuremath{rho}]. The bounds presented are sharper than the previous ones given by Pathak and Gadre [Phys. Rev. A 25, 3426 (1982); 24, 2906 (1981)] (atomic units are used throughout the paper). textcopyright{} 1996 The American Physical Society." @default.
- W2078362502 created "2016-06-24" @default.
- W2078362502 creator A5034054749 @default.
- W2078362502 creator A5074027830 @default.
- W2078362502 date "1996-11-01" @default.
- W2078362502 modified "2023-10-09" @default.
- W2078362502 title "Lower bounds to the first-order gradient corrections in the gradient expansion of the kinetic- and exchange-energy functionals" @default.
- W2078362502 cites W1738089450 @default.
- W2078362502 cites W1980224611 @default.
- W2078362502 cites W1982133197 @default.
- W2078362502 cites W1990318823 @default.
- W2078362502 cites W1996415711 @default.
- W2078362502 cites W2002255959 @default.
- W2078362502 cites W2006012227 @default.
- W2078362502 cites W2030976617 @default.
- W2078362502 cites W2033157165 @default.
- W2078362502 cites W2047595826 @default.
- W2078362502 cites W2049515435 @default.
- W2078362502 cites W2050593941 @default.
- W2078362502 cites W2081951485 @default.
- W2078362502 cites W2166511501 @default.
- W2078362502 cites W2230728100 @default.
- W2078362502 cites W2619609791 @default.
- W2078362502 cites W2998313242 @default.
- W2078362502 cites W4317523908 @default.
- W2078362502 doi "https://doi.org/10.1103/physreva.54.3859" @default.
- W2078362502 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/9913932" @default.
- W2078362502 hasPublicationYear "1996" @default.
- W2078362502 type Work @default.
- W2078362502 sameAs 2078362502 @default.
- W2078362502 citedByCount "7" @default.
- W2078362502 crossrefType "journal-article" @default.
- W2078362502 hasAuthorship W2078362502A5034054749 @default.
- W2078362502 hasAuthorship W2078362502A5074027830 @default.
- W2078362502 hasConcept C10138342 @default.
- W2078362502 hasConcept C114614502 @default.
- W2078362502 hasConcept C121332964 @default.
- W2078362502 hasConcept C135889238 @default.
- W2078362502 hasConcept C162324750 @default.
- W2078362502 hasConcept C182306322 @default.
- W2078362502 hasConcept C186370098 @default.
- W2078362502 hasConcept C2779557605 @default.
- W2078362502 hasConcept C33923547 @default.
- W2078362502 hasConcept C37914503 @default.
- W2078362502 hasConcept C54207081 @default.
- W2078362502 hasConcept C62520636 @default.
- W2078362502 hasConceptScore W2078362502C10138342 @default.
- W2078362502 hasConceptScore W2078362502C114614502 @default.
- W2078362502 hasConceptScore W2078362502C121332964 @default.
- W2078362502 hasConceptScore W2078362502C135889238 @default.
- W2078362502 hasConceptScore W2078362502C162324750 @default.
- W2078362502 hasConceptScore W2078362502C182306322 @default.
- W2078362502 hasConceptScore W2078362502C186370098 @default.
- W2078362502 hasConceptScore W2078362502C2779557605 @default.
- W2078362502 hasConceptScore W2078362502C33923547 @default.
- W2078362502 hasConceptScore W2078362502C37914503 @default.
- W2078362502 hasConceptScore W2078362502C54207081 @default.
- W2078362502 hasConceptScore W2078362502C62520636 @default.
- W2078362502 hasIssue "5" @default.
- W2078362502 hasLocation W20783625021 @default.
- W2078362502 hasLocation W20783625022 @default.
- W2078362502 hasOpenAccess W2078362502 @default.
- W2078362502 hasPrimaryLocation W20783625021 @default.
- W2078362502 hasRelatedWork W1539596337 @default.
- W2078362502 hasRelatedWork W1855007440 @default.
- W2078362502 hasRelatedWork W2024985363 @default.
- W2078362502 hasRelatedWork W2156911440 @default.
- W2078362502 hasRelatedWork W2229925025 @default.
- W2078362502 hasRelatedWork W2389313303 @default.
- W2078362502 hasRelatedWork W2557979085 @default.
- W2078362502 hasRelatedWork W2788247819 @default.
- W2078362502 hasRelatedWork W33469805 @default.
- W2078362502 hasRelatedWork W4301243416 @default.
- W2078362502 hasVolume "54" @default.
- W2078362502 isParatext "false" @default.
- W2078362502 isRetracted "false" @default.
- W2078362502 magId "2078362502" @default.
- W2078362502 workType "article" @default.