An Experimentalist’s Reply to “What Is an Atom in a Molecule?” Che ´ rif F. Matta † and Richard F. W. Bader* ,‡ Department of Chemistry, Dalhousie UniVersity, Halifax, NS B3H 4J3, Canada, and Department of Chemistry, McMaster UniVersity, Hamilton, ON L8S 4M1, Canada ReceiVed: February 6, 2006; In Final Form: March 23, 2006 Parr, Ayers and Nalewajski have opined in this Journal that the concept of an atom in a molecule “is an object knowable by the mind or intellect, not by the senses.” This view is countered by the two hundred years of experimental chemistry underlying the realization that the properties of some total system are the sum of its atomic contributions. This paper concludes that an experimentalist has no doubt but that he or she is measuring the properties of atoms when performing an experiment. Introduction An article recently appeared in this Journal by Parr, Ayers and Nalewajski (PAN) entitled “What is an atom in a mol- ecule?” 1 The paper argues that though the atom in a molecule (AIM) concept is highly usefuls“a central vital concept, compulsively needed in chemistrysAIM remains ambiguous, subject to arbitrary (but disciplined) personal choice when specificity is required”. It concludes with the espousing of Kantian philosophy that AIM is a noumenon, “an object knowable by the mind or intellect, not by the senses”. PAN are theoreticians and the conclusion stated in their paper is at odds with an experimentalist’s view of chemistry. The concept of a functional group, consisting of a single atom or a linked set of atoms, with characteristic additive properties forms the cornerstone of chemical thinking of both molecules and crystals and Dalton’s atomic hypothesis has emerged from the cauldron of experiment, as the operational theory of chemistry. We have no desire to enter into a philosophical discussion. Instead, our intent is to review the experimental justification of the AIM concept in chemistry beginning with Dalton and ending with the development of the quantum theory of atoms in molecules, QTAIM, wherein an atom is defined as a region of space bounded by a surface satisfying the quantum boundary condition of zero-flux in the gradient vector field of the electron density F(r) 2 As demonstrated for many properties and applicable to all, QTAIM recovers the values that are measured in the laboratory and ascribed to atoms and functional groupings of atoms. Every statement in this paper, as required in the practice of science, is based upon observation and/or quantum mechanics and subject to the single test one has of a scientific theory: prediction. It is this approach that underlies Hans Bethe’s view of science: 3 “its great advantage is you can prove something is true or something is false”, a statement he further paraphrased as “In science, you know you know.” A recent paper details how QTAIM evolved from studies on the topology of the measurable density F(r) leading to the observation of the paralleling behavior of F(r) and the kinetic energy density, an observation indicating the applicability of the virial theorem and hence of quantum mechanics to such regions obtained through the action principle. 4 The reader is reminded that QTAIM recovers all of the concepts of experimental chemistry: of atoms with character- istic, definable properties, 5 of molecular structure and structural change determined by the dynamics of the gradient vector field of F(r), 6 and of electron localization/delocalization determined by the atomic expectation value of the exchange density 7 and brought to the fore in the topology of the Laplacian of the electron density. 8 Dalton and the First Additive Atomic Property We begin at the beginning with Dalton. In 1803 Dalton rationalized the then known combining weight relationships between the elements by postulating the atomic concept of matter with the important proviso that each atom of a given element had the same weight and this weight was an intrinsic property of the atom, free or in chemical combination. The atomic hypothesis enabled Dalton to predict the soon to be confirmed law of multiple proportions. Thus Dalton postulated the first additive, characteristic atomic property, boldly asserting the immutability of its mass 100 years in advance of Ruther- ford’s demonstration of the nuclear atom in 1911. The atomic nature of matter is a consequence of the form imposed by the presence of a chemically inert nucleus and the dominance of the electron-nuclear force, a consequence of the attraction of the pointlike nuclei for the diffuse distribution of electron density. It is well to bear in mind that the nuclear-electron force is the only attractive force operative in chemistry and is the sole force responsible for chemical bonding. It is this force that determines the principal topological feature of the density - that it exhibits a maximum at a nuclear position thereby leading to the partitioning of space into atomic regions satisfying eq 1. 2 The nuclear charge thus stamps each atom with its chemical identity, thereby justifying Dalton’s further postulate that the atoms of a given element maintained their individuality in any physical or chemical change. The atomic hypothesis led to the assignment of relative atomic combining or equivalent weights and these, together with the ideas Avogadro put forth in 1811 and promulgated by Canniz- * Corresponding author. E-mail: bader@mcmaster.ca, Fax: +1-(905) 522-2509, Tel.: +1 (905) 525-9140 ext. 23499. † Dalhousie University. ‡ McMaster University. ∇F(r)‚n(r) ) 0 for all r on the atomic surface (1) 6365 J. Phys. Chem. A 2006, 110, 6365-6371 10.1021/jp060761+ CCC: $33.50 © 2006 American Chemical Society Published on Web 04/27/2006