From the Hubbard to the PPP Model

Abstract

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 1 B u 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 MatagaNishimoto 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.

Low-depth circuit ansatz for preparing correlated fermionic states on a quantum computer

“…The t ij , U , and V c parameters were obtained from [78,79] as a function of the dimensionless reaction coordinate, λ, and the geometries of the ground as well as transition states were optimized at this level of theory. Figure 5 compares the accuracies of different ansatzes for the cyclobutadiene automerization reaction.…”