The Implications of Symmetry of the External Potential on Bond Paths

Abstract

The concept of the chemical bond is of paramount importance to the modern chemical language. Similar to other unicorns in the chemical world, like aromaticity, reactivity, or covalency, the chemical bond is a fuzzy entity eluding a precise numerical definition. Guided by the leading role played by the electron density in the Hohenberg and Kohn theorems, Bader proposed a way to use this observable to generate lines connecting atoms that generally are very well aligned with common chemical sense. Avoiding the highly controversial issue about the interpretation of the zero flux basins that are obtained from the least action principle as the “atoms” of chemistry, one cannot raise any doubt regarding the existence of the saddle points (critical points) in the region between some nuclei and the corresponding gradient path connecting the nuclei. This is an experimental fact that in the last 25 years has been widely used to gain a deeper and alternative knowledge about the essence of chemical bonding or, paraphrasing Pauling, the nature of the chemical bond. Despite the uncontroversial physical existence of the gradient paths and critical points, their interpretation as direct manifestations of true chemical interactions has been the source of controversy in the chemical community. The set of critical points and gradient paths, the molecular graph, is a beautiful representation of the structure of the electron density but, its identification with genuine chemical concepts (like a chemical bond) is an interpretation, which like all interpretations, has a degree of subjectivity and, consequently, any inference drawn from it should be taken with judicious care. An illustrative example is the interaction between two helium atoms. He2 is a prototype of a van der Waals dimer, that is, the potential-energy surface of He2 is repulsive, except for the van der Waals minimum. In this entity, there are two maxima of the electron density at the position of the nuclei, a (3, 1) critical point in halfway between both centers, and a bond path connecting the maxima. Since a minimum always exists between two maxima, this bond path will survive even if the nuclei are separated by 2 or by 20 . Certainly, the electron-density value at the (3, 1) critical point is negligible in the latter situation. The central question is the following: Is the existence of a bond path a sufficient condition that proves that two atoms are connected by a bond in the chemical sense of the word? To answer this question, we selected a set of molecules where the number of gradient paths terminating at an atom is chemically meaningless. Consider the He@C8H8 complex. [21] This endohedral system with Oh symmetry is a local minimum on the corresponding potential-energy surface. Using B3LYP/6-311++ GACHTUNGTRENNUNG(d,p) calculations, we found eight bond paths that connect each carbon atom to helium (Figure 1, top left). As expected, the He C distances are short (1.480 ) and, consequently, the value of the electron density at the He C (3, 1) critical points is relatively high (0.140 a.u., see Table 1). However, the dissociation energy associated to the reaction He@C8H8!He+C8H8 is negative ( 322.4 kcalmol ), which indicates that the helium–cubane interaction is destabilizing overall. Note that stability is not the decisive point to define a chemical bond, since also in metastable molecules one can find chemical bonds. The situation is stranger when a noble gas (Ng) is confined in the C20H20 cage. Evidently, in this case the cavity is larger than in cubane, allowing the inclusion in silico of heavier noble gas atoms than helium. Experimentally, only the helium complex has been characterized, adopting an Ih symmetry, despite the fact that the energy to put the He atom inside dodecahedrane is 35.5 kcalmol . No calculation is necessary to predict that the number of bond paths [a] E. Cerpa, Prof. G. Merino Facultad de Qu mica Universidad de Guanajuato Noria Alta s/n C.P. 36050, Guanajuato, Gto. (M xico) Fax: (+52) 473-732-0006/-8120 E-mail : gmerino@quijote.ugto.mx [b] Dr. A. Krapp Senter for teoretisk og beregningsorientert kjemi Kjemisk institutt Universitetet i Oslo Postboks 1033 Blindern, 0315 Oslo (Norway) [c] Prof. A. Vela Departamento de Qu mica Centro de Investigaci n y de Estudios Avanzados A. P. 14-740, M xico, D.F., 07000 (M xico)