Hartree cyclic cluster

The above consideration can be interpreted as deduction of the cyclic cluster model of the infinite crystal when the Hartree-Fock LCAO method (or its semiempirical version with nonlocal exchange) is applied. 

The study of the approximate density matrix properties allowed the implementation of the cyclic cluster model in the Hartree- Fock LCAO calculations of crystalUne systems [100] based on the idempotency relations of the density matrix. The results... 

Implementation of the Cyclic-cluster Model in MSINDO and Hartree-Fock LCAO Methods... 

The band structures have been calculated by a computer code Solid 2000. The code is based on the Hartree-Fock SCF method for infinite 3D-periodic cyclic cluster [55] with the quasi-relativistic INDO Flamiltonian [56]. Based on the results... 

As has been pointed out in the past (e.g. concerning the linear-cyclic equilibrium in Ceand Cio carbon clusters (40)), Hartree-Fock underestimates the resonance stabilization of aromatic relative to non-aromatic systems (in the case at hand, between the N- and / -protonated isomers) and MP2 overcorrects. The structures are found to be nearly isoenergetic at the CCSD level inclusion of connected triple excitations favors the N-protonated ion. The direction of the effect of connected quadruples is somewhat unclear, and a CCSD(TQ) or CCSDT(Q) calculation impossible on systems this size, but the contribution will anyhow be much smaller in absolute magnitude than that of connected triple excitations, particularly for systems like these which are dominated by a single reference determinant. We may therefore infer that at the full Cl limit, the N-protonated species will be slightly more stable than its / -protonated counterpart. 

In many cases electronic properties calculated at the Hartree-Fock level do not have the accuracy sufficient to make them useful in chemical predictions. For example, as revealed in a recent study,the stability of the cage isomer of the C20 carbon cluster relative to that of the cyclic isomer is underestimated at the Flartree-Fock level by as much as 200 kcal/mol. In such systems, the electron correlation effects have to be taken into account in quantum chemical calculations through application of approximate methods. One such approximate electron correlation methods that has gained a widespread popularity is the second-order Moller-Plesset perturbation theory (MP2). Until recently calculations involving the MP2 approach have used a traditional formulation in which the MP2 energy is evaluated as the sum... 

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