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- W2032056270 abstract "The asymptotic behavior of direct lattice sums for exact, nonlocal exchange in polymer Hartree-Fock calculations is analyzed. That behavior is entirely determined by that of the density matrix. An exactly solvable two-band model, describing both filled- and half-filled-band situations, allows the study of the density-matrix asymptotics for various realistic parameter choices. For filled bands it is found that the density matrix falls off exponentially in the latticevector index $n$. This is due to the presence of first-order branch points in the complex Bloch vector plane, symmetrically placed about the real axis. With the use of contour integration, formulas for large-$n$ behavior are obtained, including one valid for all $n$ values when parameters are chosen that correspond to Huckel theory. A simple relationship is found between band gap, bandwidth, and the (exponential) large-$n$ behavior of filled-band density-matrix elements. The results are related to work by Kohn and Des Cloiseaux on Wannier functions but are more specific about the relation between exponential behavior and band properties. With inspiration from numerical experiments, a conjecture for multiband exchange asymptotics is formulated. Half-filled-band results verify earlier work by Ukrainskii, and it is shown how exchange-sum truncation errors increase dramatically when the nearly-half-filled-band situation is reached. This is borne out by recent work by Piela, Andr'e, Fripiat, and Delhalle." @default.
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- W2032056270 date "1981-09-15" @default.
- W2032056270 modified "2023-09-28" @default.
- W2032056270 title "Exact-exchange asymptotics in polymer Hartree-Fock calculations" @default.
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- W2032056270 doi "https://doi.org/10.1103/physrevb.24.3015" @default.
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