Empirical LCAO parameters for $\pi$ molecular orbitals in planar organic molecules

TL;DR

This paper introduces a simplified empirical LCAO model for $\pi$ molecular orbitals in planar organic molecules, accurately predicting key electronic properties with minimal parameters.

Contribution

It provides four empirical parameters for a simplified LCAO model to predict $\pi$ orbital energies and transitions in diverse organic molecules, validated against experimental data.

Findings

Accurately predicts $\pi$ orbital energies and $\pi$-$\pi^*$ transition energies.

Validated against over sixty organic molecules with successful results.

Uses minimal parameters and simple $p_z$ orbital basis.

Abstract

We present a parametrization within a simplified LCAO model (a type of Hueckel model) for the description of $\pi$ molecular orbitals in organic molecules containing $\pi$-bonds between carbon, nitrogen, or oxygen atoms with $sp^2$ hybridization, which we show to be quite accurate in predicting the energy of the highest occupied $\pi$ orbital and the first $\pi$-$\pi*$ transition energy for a large set of organic compounds. We provide four empirical parameter values for the diagonal matrix elements of the LCAO description, corresponding to atoms of carbon, nitrogen with one $p_z$ electron, nitrogen with two $p_z$ electrons, and oxygen. The bond-length dependent formula (proportional to $1/d^2$) of Harrison is used for the non-diagonal matrix elements between neighboring atoms. The predictions of our calculations have been tested against available experimental results in more than sixty organic molecules, including benzene and its derivatives, polyacenes, aromatic hydrocarbons of various geometries, polyenes, ketones, aldehydes, azabenzenes, nucleic acid bases and others. The comparison is rather successful, taking into account the small number of parameters and the simplicity of the LCAO method, involving only $p_z$ atomic orbitals, which leads even to analytical calculations in some cases.