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• W2080242199 startingPage "7887" @default.
• W2080242199 abstract "For an electronic system, assume that a single-determinant wave function ensuremath{Psi} is to be formed from N space orbitals which, in turn, are constructed from M real one-electron basis orbitals ${ensuremath{chi}}_{1}$,...,${ensuremath{chi}}_{M}$. It is shown that N(M-N) is the minimum number of x-ray diffraction data points that are necessary to fix both ensuremath{Psi} and the density n uniquely. Moreover, it is shown that N(M-N) is the minimum number of linearly independent products, ${ensuremath{chi}}_{i}$${ensuremath{chi}}_{j}$, that are necessary to fix ensuremath{Psi} uniquely from an n. Density-functional theory is invoked to put forth a prescription and formulas for approximating the exact ground-state energy, including correlation effects, and for extracting a meaningful ensuremath{Psi} from a ground-state n, even when ensuremath{Psi} is not unique. In this context, emphasis is placed upon the Kohn-Sham ensuremath{Psi} and its kinetic energy ${T}_{s}$ and upon the universal correlation ${E}_{c}$ and exchange ${E}_{x}$ energy-density functionals. A finite-basis procedure for the approximation of ${T}_{s}$[n] is presented. It is then shown that only ${T}_{s}$[n] and ${E}_{c}$[n] are needed to obtain the exact total ground-state energy from a ground-state n. ${E}_{x}$[n] need not be employed at all. For instance, in Coulomb systems at equilibrium E=-${T}_{s}$[n]+${E}_{c}$[n]-Fdr ${v}_{c}$(r)ensuremath{nabla}ensuremath{cdot}rn(r), where ${v}_{c}$ is the correlation potential.Alternatively, energy formulas involving ${E}_{x}$[n], but not ${T}_{s}$[n], are also put forth. For instance, E=1/2U[n]+1/${2E}_{x}$[n]+${E}_{c}$[n]+1/2Fdr[vr]-${v}_{c}$(r0]ensuremath{nabla}ensuremath{cdot}rn(r) where U[n] is the classical repulsion energy. When the ${E}_{c}$ functional is exact, and ${E}_{x}$ is not exact, then the error in the latter equation is half the error of the familiar ${T}_{s}$[n]+Fdr v(r)n(r)+U[n]+${E}_{mathrm{xc}[mathrm{n}]}$. A few numerical examples are presented for atoms using nonlocal density functionals." @default.
• W2080242199 created "2016-06-24" @default.
• W2080242199 creator A5032939678 @default.
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• W2080242199 date "1987-05-15" @default.
• W2080242199 modified "2023-10-14" @default.
• W2080242199 title "Electron density-functional theory and x-ray structure factors" @default.
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• W2080242199 doi "https://doi.org/10.1103/physrevb.35.7887" @default.
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