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

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 Urt ratios on the ground states of some networks containing fused 5-and 6-membered rings with up to N s 32 electrons. It is Ž . shown that single and double excitation configuration interaction SD-CI based on a closed-shell Huckel-type reference determinant plus a correction added for the sizë consistency error using appropriate known correction terms leads to sensible estimates of < < the ground-state energy for up to Urt F 4. The IPM approach is hence well suited for < < treating the chemically relevant region of Urt f 1.5 y 2 for systems. The systems studied in this work involve several fullerene-type fragments with up to N s 16, for Ž . which a full configuration interaction FCI calculation is possible, and three larger Ž . Ž . . 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 Ž . FCI HubbardrPariser᎐Parr᎐Pople PPP calculations as far as computation time is concerned.

Ground and excited Hubbard states for buckminsterfullerene with uniform and alternating bond strengths

“…All results were obtained using the recently developed software package PPPACK, capable of performing direct integral driven Hubbard MRCI calculations at various levels of sophistication with subsequent determination of several expectation values from the resulting CI wave functions. 5 The ground state SDCI dimensions found for the C 60 moeity were not very large. The relevant singlet CI subspace of A g D 2h symmetry is spanned by 51 190 CSF's, with 539 patterns of excitation from the different MO levels for uniform C 60 , and 687 patterns for bond alternant C 60 , respectively ͑because bond alternation partially removes the nine-fold degeneracy of the Hückel HOMO-1 level͒.…”

“…A natural extension, applicable to multireference SDCI calculations, was proposed: the single weight c 0 2 is replaced by the sum ͚ i c i 2 over all reference CSF weights. The PC and DDC corrections were shown in a previous study 5 to perform remarkably well in reproducing FCI uniform Hubbard ground state energies for a set of fullerene fragments up to Nϭ16 and gave very sensible results up to ͉U/t͉ϭ4.0 when applied to larger -electronic systems with high HOMO-LUMO gap such as corannulene and the smallest fullerene anion C 28 4Ϫ . Thus these approximations are expected to be useful as a guide in roughly estimating Hubbard FCI energies for the C 60 moiety, especially if results from other methods are available such as variational ͑VMC͒ 10 and projector quantum Monte Carlo ͑PQMC͒ calculations.…”

“…Ϸ2 h needed for the entire SDCI procedure. The close correspondence of the MP2 energies to the FCI ones for the Hubbard model was also shown to hold in the case of the exactly treatable Nϭ16 system fluoranthene, for which we obtained for the uniform Hubbard model in units of t: E MP2 ϭϪ18.7456 vs E FCI ϭϪ18.7461 at ͉U/t͉ ϭ1.0 and E MP2 ϭϪ15.4902 vs E FCI ϭϪ15.5015 at ͉U/t͉ ϭ2.0 5. Both bond orders BO hh and BO hp decrease in value for the uniform Hubbard model with increasing correlation as opposed to the nearest-neighbor spin-spin correlations,…”