Empirical LCAO parameters forπmolecular orbitals in planar organic molecules

Abstract

We present a parametrization within a simplified LCAO model (a type of Hückel model) for the description of π molecular orbitals in organic molecules containing π-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 π orbital and the first π-π* 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 z p electron, nitrogen with two z p 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 z p atomic orbitals, which leads even to analytical calculations in some cases.Keywords: linear combination of atomic orbitals, Hückel model, empirical parameters, πmolecular structure, highest occupied π orbitals, π-π* transition the assignment of electronic transitions (e.g. singlet-singlet or singlet-triplet transitions, Rydberg transitions, π-π* transitions etc.), and the calculation of the oscillator strength of the transitions. Apart from basic knowledge and the numerous applications of planar organic molecules containing atoms with sp 2 hybridization, the π molecular electronic structure of such compounds is involved in several biological functions. For example, we mention chlorophyll in photosynthesis, the retinal molecule involved in vision or in photondriven ion pumps like bacteriorhodopsin [1], and many molecules with photobiological functions such as vitamin A, vitamin D precursors, carotene etc., containing polyene chromophores [2]. Also new organic semiconductors based in pentacene and other hydrocarbon molecules have attached an enormous interest regarding their use in molecular electronics [3]. Experimental investigations of the electronic structure of organic molecules started very early, by performing absorption measurements. The ultraviolet absorption spectra of eighteen pyridines and purines [4], fourteen ethylenic hydrocarbon molecules [5], and 1,3 cyclohexadiene [6] have been measured already in 30s. Later Platt and Klevens presented the spectra of several alkylbenzenes [7], some ethylenes and acetylenes [8], and seventeen polycyclic aromatic hydrocarbons composed of fused benzene rings [9] (e.g. phenanthrene and chrysene). At the same period spectra were taken from naphthalene and biphenyl derivatives [10], m-and o-disubstituted benzene derivatives [11], and mono-substituded and p-disubstituted benzene derivativ...

Electronic parameters for charge transfer along DNA

“…Following a standard procedure and assuming that the atomic or atomiclike p z orbitals located at different atoms are orthogonal, one obtains that the solution of the linear system of equations determining c i and the corresponding E b , is equivalent to the diagonalization of the Hamiltonian with matrix elements H b ij = d 3 r p i ⋆ z (r) H b p j z (r) (see for example Ref. [38]).…”

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