Original scientific paper

https://doi.org/10.5562/cca2297

From the Hubbard to the PPP Model

Thomas G. Schmalz ; Texas A&M University at Galveston, P. O. Box 1675, Galveston, Texas 77553 USA

Abstract

This paper presents an extension of the Hubbard Model to Pariser-Parr-Pople form. Although
the Hubbard model contains most of the essentials of chemical bonding, it is unable to describe excited
states with separated charges, such as the lowest 1Bu states of linear polyenes. The PPP model adds longrange
electron-electron repulsions to the Hubbard model to remedy this defect. If the long range repulsion
integrals are assumed to follow a standard form, all parameters in the model can be evaluated exactly from
high accuracy ab initio computations on stretched ethlyene. This yields a model based on the Mataga-
Nishimoto form for the long-range integrals which gives excellent agreement with both excitation energies
and ground-state bond lengths, but with a significantly smaller value of the one center electron repulsion
U than is usually assumed. A major conclusion of this work is that the exact form of the long-range
integrals is not so important, but that the value of the one center integral U must be chosen smaller than
traditional values. The PPP-MN model is recommended for applications because it contains no adjustable
parameters, with all parameter values determined directly from ab initio results. (doi: 10.5562/cca2297)

Keywords

pi-electron systems; Pariser-Parr-Pople model; Hubbard model; excitation energies; equilibrium bond lengths

Hrčak ID:

112765

URI

https://hrcak.srce.hr/112765

Publication date:

16.12.2013.

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