On the localization of π-electrons in linear and cyclic hydrocarbons

Abstract

The localization properties of π-electrons in alternant and nonalternant hydrocarbons are investigated by calculating the mean-square deviation <(Δn ² _i )>_corr of the electronic charge <n_i > at the ith π-centre in the correlated ground state |Ψ_corr> The interatomic π-correlations are determined by the method of the local approach (LA) in the framework of a zero differential overlap (ZDO) model-Hamiltonian supplemented by the tight-binding approximation. The necessary integrals are calculated parameter-free, i.e. ab initio, in a Slater-type basis. Comparison of the <(Δn ² _i )>_corr numbers with the charge fluctuations predicted in the independent-particle picture |Ψ_SCF> allows for the definition of correlation-strength parameters Δ _i , Σ _i which measure the many-particle character of π-bonding. It is demonstrated that electronic correlations are sizeable in the π-network of hydrocarbons. This is also valid for conjugated polyenes and cyclic (4n + 2) systems. The π-electron localization exceeds throughout the degree of localization encountered in σ-bonds of main-group elements. Dimerization in alternant hydrocarbons leads to an enhancement of the charge fluctuations and thus to stronger atomic electronic density delocalization. The charge fluctuations and correlation-strength parameters in alternant hydrocarbons depend sensitively on the topology of the considered π-center. The different types of π-atoms can be subdivided into characteristic classes according to their <(Δn ² _i )>_corr and Δ _i , Σ _i elements. For nonalternant hydrocarbons it is shown that noneven charge distributions conserve sizeable charge fluctuations in the presence of stronger π-electron correlations. The influence of the π-electron density <n_i > on the allowed mean-square deviations of the corresponding charges <(Δn ² _i )>_corr for different ratios between the potential and kinetic energy is studied by a simple analytic model.