IPM approach to Hubbard model. Applications and limitations of restricted CI calculations to ground states of some ? networks containing fused 5- and 6-membered rings

Abstract

The validity of the independent particle model (IPM) approach in treating the Hubbard model with uniform hopping parameter t and uniform on-site repulsion term U is investigated for several |U/t| ratios on the ground states of some π networks containing fused 5- and 6-membered rings with up to N=32 π electrons. It is shown that single and double excitation configuration interaction (SD-CI) based on a closed-shell Hückel-type reference determinant plus a correction added for the size consistency error using appropriate known correction terms leads to sensible estimates of the ground-state energy for up to |U/t|≤4. The IPM approach is hence well suited for treating the chemically relevant region of |U/t|≈1.5−2 for π systems. The systems studied in this work involve several fullerene-type fragments with up to N=16, for which a full configuration interaction (FCI) calculation is possible, and three larger systems, namely Corannulene (N=20), the C26 fullerene (N=26) and the C fullerene anion of Td symmetry (N=32), for which only a limited CI involving single, double, triple, and quadruple excitations (SDTQ-CI) could be performed as a guide. SD-CI calculations on these latter systems further reproduced qualitatively correct charge densities and nearest-neighbor bond orders. Wherever possible, the obtained results were compared with those obtained by different methods present in the literature, based on Monte Carlo approaches. Further we indicated a strategy as to how to perform optimum FCI Hubbard/Pariser–Parr–Pople (PPP) calculations as far as computation time is concerned. © 1999 John Wiley & Sons, Inc. Int J Quant Chem 76: 83–98, 2000