In memoriam Andy C. Albrecht [1]

We have previously noticed [2] that a strikingly simple rule interrelates the values of A (A stands for the equilibrium bond length), for four isomolecular species at their equilibrium geometries: a singlet ground state of a neutral closed shell molecule, M^S, its first excited triplet state, M^T··, a doublet ground state of its radical-cation, M^·+, and a doublet ground state of its radical-anion, M^·-. The rule predicts that A^T·· = A^·+ + A^·- - A^S, i.e. that property of a triplet state is a 'hybrid' of properties of the remaining species. This relationship has been explained using formalism of Fukui function [3]. Using QM computations accounting to some extent for electronic correlation (DFT and MP2), we now provide evidence [4] that 'hybrid' rule works well also for other properties A, such as Mulliken charges, spin densities on atoms, or force constants. The relationship holds well for alternant hydrocarbons (antiaromatic as cyclobutadiene or 4.2.2.-bicyklooktatetraene, and aromatic such as benzene or naphthalene), while it fails for non-alternant hydrocarbons (antiaromatic as 3.3.2.-bicyklooktatetraene and aromatic as azulene). The Jahn-Teller distortion ratio (R_long/R_short) in polyatomic species is predicted with excellent accuracy, based on bond lengths derived from the 'hybrid' relationship, for all quasi-equivalent JT minima (benzene: quinoid & antiquinoid). The hybrid relationship also applies to inorganic molecules with π electron system (N₂, P₂, As₂, B₄), while it falls short for systems where sigma orbitals are responsible for geometry distortion upon electronic excitation or an electron addition/removal from M^S (CO, BF, Pd(FH)₆²⁺, H₂). The rule holds only if no major breakdowns of molecular symmetry are allowed. It might possibly be used to provide reasonable initial guess of molecular geometry and electron density during demanding geometry optimizations for organic radical anions.

[1] W. Grochala, Andreas Albrecht's Tribute Symposium, Cornell University, Ithaca, NY, USA, June 2004.

[2] W. Grochala et al., J. Phys. Chem. A 2000, 104, 2195-2203.

[3] P. W. Ayers, R. G. Parr, J. Phys. Chem. A 2000, 104, 2211-2220.

[4] A. Sokołowski, W. Grochala, Pol. J. Chem., invited paper in preparation 2006.

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