Bond Paths

Communications
Bond or No Bond?
DOI: 10.1002/anie.200805751

When Do Interacting Atoms Form a Chemical Bond? Spectroscopic Measurements and Theoretical Analyses of Dideuteriophenanthrene
Stefan Grimme,* Christian Mück-Lichtenfeld, Gerhard Erker,* Gerald Kehr, Huadong Wang, Helmut Beckers, and Helge Willner
The concept of chemical bonding is fundamental to natural science.[1] Despite itsimportance, a precise and unambiguous definition of when a chemical bond exists between (usually two) atoms is difficult. For diatomic and small molecules energetic (thermochemical) criteria are sufficient, but for polyatomic systems, the problem prevails although experimental data, for example from vibrational spectroscopy (bond force constants), can be related to bonding. The other approach isbased entirely on theory in the context of ab initio schemes derived from wave function and electron density calculations. Although these methods have advanced extraordinarily in recent years,[2] the theoretical definition of bonding is still problematic. The simple reason is that no quantum mechanical “bond operator” exists that would provide the desired answer, for example, as a conventionalexpectation value. In any case one basic assumption of the present work (that is likely shared by many chemists and physicists) is that the existence of a chemical bond must be related to some observable; in other words, chemical bonding must have an effect on measurable properties of the system. Any definition of bonding that has no real consequences is meaningless in our opinion and must be abandoned.Of the many theoretical bond concepts that have been proposed in the past, R. Baders “Theory of Atoms in Molecules” (AIM)[3] is certainly the most fundamental and has also had a strong influence on the thinking of many chemists.[4] In AIM the electron density (which according to the Hohenberg–Kohn theorems of density functional theory (DFT)[5] contains all necessary information) is analyzedtopologically. Bonds are defined by a bond path (BP) and a bond critical point (BCP). The BP is a line in space linking the nuclei of bonded atoms where the electron density is a maximum with respect to any neighboring line. It is assumed that a BP is necessary for chemical bonding regardless of its nature (e.g. ionic, covalent, or van der Waals).[6] The BCP represents a stationary point in theelectron density and is a minimum along the BP but a maximum in directions perpendicular to the bond path. The values of the density, its Laplacian, or energy-based properties at the BCP can be used to characterize the nature of the interaction.[3, 4] Note that we question neither the foundations of AIM nor its usefulness for the interpretation of electronic structure. However, like every theory AIM hasa limited scope which may lead to misinterpretations if it is applied in a too general sense. Herein we describe the rational design of a suitable system and a combination of spectroscopic (infrared and Raman) measurements with a thorough theoretical analysis. To the best of our knowledge, we show for the first time that the results of a rigorous interpretation of AIM regarding the existence ofputative bonds are in complete disagreement with our experimental data. The existence of a BCP and a BP is established as a necessary and sufficient condition for a bond in the basic interpretation of AIM.[3, 4] In more recent literature this concept has been extended even further, and BCP and BP are often related to attractive interactions (see, for example, Ref. [7]). The most controversial aspectof this interpretation is the concept of HÀH bonding, which was introduced by Matta and co-workers.[6] In many organic molecules (or in molecular crystals) fragments containing CÀH bonds are in close proximity in the equilibrium structure, and H···H contacts below the van der Waals distance (2.2–2.4 Š) are found. In such cases a BCP and BP between these formally nonbonded hydrogen atoms is...