Aspects of three-electron two-centre, four-electron three-centre and six-electron five-centre bonding in cycloimmonium ylides Padeleimon Karafiloglou a, * , Richard D. Harcourt b a Department of General and Inorganic Chemistry, Faculty of Chemistry, Aristotle University of Thessaloniki, P.O. Box 135, 54124 Thessaloniki, Greece b School of Chemistry, The University of Melbourne, Parkville, Vic. 3010, Australia Received 28 January 2005; revised 8 March 2005; accepted 8 March 2005 Available online 20 July 2005 Abstract The weights for several types of local valence bond structures which are involved in two-electron two-centre, three-electron two-centre and four-electron three-centre bonding units for the p-electrons of pyridinium dicyanomethylide are calculated via a Poly-Electron Population Analysis of a Hartree–Fock MO wavefunction. It is shown that three-electron two-centre and four-electron three-centre behavior for the ylide bond is better developed towards the substituents of the ylide carbon atom, rather than the pyridinium group; this gives rise to a polarized increased-valence bonding, which is the principal specificity of cycloimmonium ylides. Qualitative consideration is given to six-electron five-centre bonding units for the p-electrons. q 2005 Elsevier B.V. All rights reserved. 1. Introduction Increased-valence theory [1,2], with three-electron two- centre (3e–2c) bonds as diatomic components of the associated valence bond (VB) structures, provides new insights into the origin of bond properties, and can be used to provide qualitative VB representations of the electronic structures of various types of electron-rich molecules in particular. In a recent publication [3], using pyridinium dicyanomethylide (PDCM, Fig. 1) as the example for cycloimmonium ylides [4,5], it is shown that 3e–2c bonding is developed better between the N 2 and C 1 atoms than it is between the N 2 and C 3 atoms. The 3e–2c bond is also designated as either a ‘three-electron hemi bond’, or ‘(Pauling) three-electron bond’. The preferred VB symbolism for the 3e–2c bond is that which has been provided by Green and Linnett [6]. The 3e–2c bond is a diatomic component of four- electron three-centre (4e,3c) increased-valence structures for three-centre and polycentre-centre electron-rich bonding units [1,2], for which the number of electrons exceeds the number of overlapping atomic orbitals (AOs), with one hybrid or non- hybrid AO per atomic center [1,2]. The main purpose of the present work is to provide quantitative estimates of the extent to which 3e–2c and 2e–2c bonding occurs for a variety of bonds that arise in several of the PDCM 4e–3c bonding units. Without calculation, we shall also focus attention on the presence of six-electron five-center (6e–5c) bonding units in PDCM. The weights of 2e–2c Lewis-type VB structures, 3e–2c Linnett-type VB structures and 4e–3c increased-valence structures are obtained by means of the weights of spin- dependent local structures, calculated in the framework of the Poly-Electron Population Analysis (PEPA) [7–9]. This method is based on both the second quantized formulation [10] of density matrices [11] and Moffitt’s theorem, being a direct consequence of Cauchy’s expansions [12,13]. Orbitals appropriate for population analysis, such as the (either orthogonal or non-orthogonal) Natural Atomic Orbitals (NAOs) and Natural Bond Orbitals (NBOs) [14,15], which have been introduced within the Natural Population Analysis [16,17], can be used as analysers to construct second quantized density operators. Quantitative variational methods, such as the breathing orbital VB [18], can provide quite accurate results concerning mainly the energy of various small systems involving 3e–2c bonds [19]. Unlike these methods, which provide information for Journal of Molecular Structure: THEOCHEM 729 (2005) 155–161 www.elsevier.com/locate/theochem 0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.03.019 * Corresponding author. Tel.: C30 2310997703; fax: C30 2310997783. E-mail addresses: karafilo@chem.auth.gr (P. Karafiloglou), rdharc@ unimelb.edu.au (R.D. Harcourt).