A distance-dependent parameterization of the extended Hubbard model for conjugated and aromatic hydrocarbons derived from stretched ethene

Abstract

The Hubbard model, which is widely used in physics but is mostly unfamiliar to chemists, provides an attractive yet simple model for chemistry beyond the self consistent field molecular orbital approximation. The Hubbard model adds an effective electron-electron repulsion when two electrons occupy the same atomic orbital to the familiar Hückel Hamiltonian. Thus it breaks the degeneracy between excited singlet and triplet states and allows an explicit treatment of electron correlation. We show how to evaluate the parameters of the model from high-level ab initio calculations on twoatom fragments and then to transfer the parameters to large molecules and polymers where accurate ab initio calculations are difficult or impossible. The recently developed MS-RASPT2 method is used to generate accurate potential energy curves for ethene as a function of carbon-carbon bond length, which are used to parameterize the model for conjugated hydrocarbons. Test applications to several conjugated/aromatic molecules show that even though the model is very simple, it is capable of reasonably accurate predictions for bond lengths, and predicts molecular excitation energies in reasonable agreement with those from the MS-RASPT2 method.

Modeling the high-energy electronic state manifold of adenine: Calibration for nonlinear electronic spectroscopy

“…More specifically, the ANO-L basis set contracted to C,N [3s,2p,1d]/H[2s] has been employed, and up to four holes in the RAS1 subspace and up to 4 electrons in the RAS3 were allowed. Another possibility, already employed in other works, 73 would be to use a reduced RAS2 subspace and put the remaining orbitals in RAS1 and RAS3, thereby restricting the number of holes and excitations to two. Unfortunately, already this restricted scheme is beyond the computational capabilities.…”

From the Hubbard to the PPP Model

“…6 All parameters in the model may be evaluated from high-quality ab initio calculations on two-site fragments of whatever type of system is being considered. We illustrated 1 the parameterization and use of the model for the pi electrons in conjugated hydrocarbons, and showed that both the ground state geometry and the lowlying electronic excitation spectrum of a few small test molecules may generally be predicted quite accurately.…”

“…A particularly obvious example of this deficiency occurs with the 1 B u excited state in polyenes such as butadiene and hexatriene. Although in long polyenes the lowest singlet excited state is the optically forbidden socalled homopolar 1 A g state, in butadiene and likely also hexatriene the strongly optically allowed 1 B u state lies lower, with the cross-over probably occurring near octatetraene. 7 The 1 B u state is known as the charge transfer state, and it has important contributions from determinants with the positive charge on one end of the molecule and the negative charge on the other.…”

“…In a recent paper 1 we argued that the Hubbard Model 2,3 provides the simplest and easiest to understand quantitative model of basic chemical bonding effects. The model includes on-site and nearest-neighbor terms of the Hückel model to account for the formation of chemical bonds and on-site and nearest-neighbor electron repulsion terms to account for electron correlation.…”

“…1 The Hubbard model correctly positions ionic excited states (those composed dominantly of determinants in the atomic orbital basis having separated charges) with respect to covalent states (those, such as the ground state, composed dominantly of determinants in the atomic orbital basis with one electron per site). But because it lacks long-range electron-electron repulsion terms, it is incapable of properly positioning states with large distances between the positively and negatively charged sites with respect to those in which the dominant determinants have the charges on adjacent sites.…”