ISSN:
0020-7608
Keywords:
cyclic polyenes
;
exchange energy
;
asymptotic behavior
;
finite size correction
;
Pariser-Parr-Pople
;
Chemistry
;
Theoretical, Physical and Computational Chemistry
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
The large N expansion of the restricted Hartree-Fock (RHF) exchange energy per atom E(N) of the Pariser-Parr-Pople (PPP) model of cyclic polyenes (annulenes) CNHN is derived in detail. We explicitly derive the coefficients E0 and E1 of the asymptotic expansion: E(N)=E0+E1 ln N/N2+O(N-2), N→∞, in the very simple case of half-filling and no bond alternation. The exchange energy per atom in the infinite chain can be written as Eex=(2/π2)∑∞j=1{[γ∞(2j-1)]/[(2j-1)2]}, where γ∞ is the two-electron repulsion integral in the infinite chain. On the other hand, the second coefficient E1 giving a finite-size correction is found to be 1/2b, where b is the bond length. This value of E1 differs slightly from that of a linear chain with periodic boundary conditions because the distance between sites depends upon the radius of the ring, i.e., upon N. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66: 397-407, 1998
Additional Material:
1 Ill.
Type of Medium:
Electronic Resource
Permalink
