REGULAR ARTICLE A localized electrons detector for atomic and molecular systems Hugo J. Boho ´rquez • Russell J. Boyd Received: 19 November 2009 / Accepted: 14 January 2010 / Published online: 9 February 2010 Ó Springer-Verlag 2010 Abstract The local value of the single-particle momen- tum provides a direct three-dimensional representation of bonding interactions in molecules. It is given exclusively in terms of the electron density and its gradient, and therefore is an ideal localized electrons detector (LED). The results introduced here extend to molecular systems our study of the single-particle local momentum in atomic systems (Boho ´rquez and Boyd in J Chem Phys 129:024110, 2008; Chem Phys Lett 480:127, 2009). LED is able to clearly identify covalent and hydrogen bonding interactions by depicting distinctive regions around the bond critical points, emerging as a complementary tool in conventional atoms in molecules studies. The local variable we introduce here is an intuitively interpretable 3D electron-pairs locator in atoms and molecules that can be computed either from theoretical or experimentally derived electron densities. Keywords Electron pairs  Electron localization  Chemical bond  Quantum topology  Electron momentum  Electron kinetic energy  Local quantum value  Theoretical methods 1 Introduction ‘‘Sometimes it seems to me that a bond between two atoms has become so real, so tangible, so friendly, that I can almost see it. Then I awake with a little shock, for a chemical bond is not a real thing. It does not exist. No one has ever seen one. No one ever can. It is a figment of our own imagination.’’ Charles A. Coulson Electronic bonding interactions are not directly obser- vable, as Coulson asserts, but our intuitive perception of molecular phenomena in the three-dimensional space demands such a representation. With a similar perspective Lewis conceived the idea of electron pairs [1]. It is reason- able to think that an adequate representation of chemical bonding should be given by a physical observable defined in coordinate space. The electron density is the best choice because it is a local function defined within the exact many- body theory, and it is also an experimentally accessible scalar field. Its paramount role in the description of many-body problems is supported by the Hohenberg–Kohn theorem [2]. Although the Hohenberg–Kohn theorem guarantees that all the molecular information is encoded in the electron density, the physical description of chemical systems requires additional postulates for extracting observable information in terms of atomic contributions. This is achieved by the quantum theory of atoms in molecules (QTAIM) introduced by Bader [3]. The proper open system concept provides a quantum topological partitioning of the molecular space into chemically transferable molecular fragments for which the energy and all other measurable properties can be precisely defined [4]. The localization of electron pairs is elusive within the electron density topology analysis, because a direct link between the local maxima in the electron density and the electron pairs of the Lewis model has not been established, despite the fact that the Laplacian of the electron density provides some information about electron localization [5]. Several attempts to depict electron localization from different perspectives have been proposed in recent years. The variety H. J. Boho ´rquez (&)  R. J. Boyd Department of Chemistry, Dalhousie University, Halifax, NS B3H 4J3, Canada e-mail: hugo.j.bohorquez@dal.ca 123 Theor Chem Acc (2010) 127:393–400 DOI 10.1007/s00214-010-0727-5