Spin-Philicity and Spin-Donicity of Substituted Carbenes, Silylenes, Germylenes, and Stannylenes Julianna Ola ´ h, †,‡ Frank De Proft, † Tama ´ s Veszpre ´ mi, ‡ and Paul Geerlings* ,† Eenheid Algemene Chemie (ALGC), Vrije UniVersiteit Brussel (VUB), Pleinlaan 2, B-1050, Brussels, Belgium, and Inorganic Chemistry Department, Budapest UniVersity of Technology and Economics (BUTE), Szent Gelle ´ rt te ´ r 4, H-1521, Budapest, Hungary ReceiVed: August 7, 2003; In Final Form: October 28, 2003 Spin potential, spin hardness, spin-philicity, and spin-donicity indices have been extensively studied on a large set of carbenes, silylenes, germylenes, and stannylenes at the B3LYP/6-31G(d) level. The effect of the substituents and that of the central atom have been investigated. The sum of the spin potentials calculated in the singlet and triplet states correlates excellently with the vertical singlet-triplet energy gap. A very good quadratic relationship between the spin-philicity and spin-donicity indices and the vertical singlet-triplet energy gaps is obtained. The analogy of the spin-philicity and spin-donicity indices with the electrophilicity index is discussed in detail. 1. Introduction Conceptual DFT 1 provides precise definitions of well-known, but historically often vaguely defined chemical properties such as the hardness 2 or the electronegativity. 3 However, new quantities have been introduced as well to better understand and describe atomic and molecular interactions and properties. An important step along this way was among others the definition of the electrophilicity index (ω) 4,5 of a given ligand. Parr et al. suggested a model in which the ligand is embedded in an ideal zero-temperature free electron sea of zero chemical potential. In this case, the ligand A will be filled with electrons up to the point that its chemical potential becomes equal to that of the sea implying: as the chemical potential is defined as µ ) (∂E/∂N) V 3 with E the energy of the system and N the number of electrons. The energy change of the ligand (ΔE A ) up to second order due to electron flow (ΔN) from the free electron sea is (the index A will be dropped from now on) is where η ) (∂ 2 E/∂N 2 ) V is the chemical hardness of the ligand. 2 Minimizing ΔE with respect to ΔN yields the optimal ΔN for the ligand, for which the energy change then becomes: It was then proposed to call the quantity ω ) µ 2 /2η the electrophilicity of the ligand, where it was shown that it depends on both the ionization potential and the electron affinity of ligand. Moreover, as intuitively expected, the electrophilicity index was shown to increase with increasing electron affinity. Very recently Chattaraj et al. have introduced a generalized concept of philicity. 6 They claim that this generalized philicity is even a more powerful index than the global electrophilicity of Parr et al., 5 as it contains information both on the Fukui function and the global electrophilicity of the atom or molecule. The spin-philicity and spin-donicity indices 7 have been defined by using similar arguments within the context of spin- polarized DFT. Spin-polarized DFT 8 allows one to get some insight into the chemical properties related to the change in spin number. Vargas et al. used the spin potentials in the analysis of the singlet-triplet gap of a small set of halocarbenes and found that the sum of the spin potentials correlates linearly with the vertical singlet-triplet energy gap. 9 Recent work by Pe ´rez et al. 7 demonstrated the applicability of the spin-related DFT indices in the interpretation of spin-catalysis phenomena. 10 For a small set of di- and triatomic molecules these authors showed that the spin-philicity and -donicity indices qualitatively account for their observed spin-catalytic effect and that the spin potentials quantitatively define the direction and magnitude of the spin transfer process involved in spin-catalysis phenomena. This phenomenon is induced by both magnetic and nonmagnetic (exchange) interactions. 10 It operates in triads of spin carriers (the simplest case being three radicals); pairwise exchange between either of the partners of the pair and a third spin carrier induces the spin conversion in the pair of selected spin carriers (e.g. radical pair); the latter acts as a spin catalyst that transforms nonreactive spin states of the pair into the reactive one. Overall this physical phenomenon manifests itself in chemical reactions of radicals, ions, carbenes, and high-spin molecules and strongly affects their reaction rates and competition of reaction channels. However, so far, no detailed investigation has been performed on a large set of molecules confirming the usefulness of spin- philicity and spin-donicity. Substituted divalent forms of the Group 14 elements constitute a suitable set of molecules to be * Corresponding author. E-mail: pgeerlin@vub.ac.be. Phone: +32.2.629. 33.14. Fax: +32.2.629.33.17. † Vrije Universiteit Brussel. ‡ Budapest University of Technology and Economics. µ A ) ( ∂E A ∂N 29 V ) 0 (1) ΔE ) µΔN + 1/2η(ΔN) 2 (2) ΔE )- µ 2 2η (3) 490 J. Phys. Chem. A 2004, 108, 490-499 10.1021/jp0363390 CCC: $27.50 © 2004 American Chemical Society Published on Web 12/16/2003