A Localized Electrons Detector For Atomic And Molecular Systems

Theor Chem Acc (2010) 127:393–400 DOI 10.1007/s00214-010-0727-5

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A localized electrons detector for atomic and molecular systems
´ Hugo J. Bohorquez • 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 momentum provides a directthree-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 ´ (Bohorquez 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 experimentallyderived electron densities. Keywords Electron pairs Á Electron localization Á Chemical bond Á Quantum topology Á Electron momentum Á Electron kinetic energy Á Local quantum value Á Theoretical methods

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 observable, 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 reasonable 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 localfunction defined within the exact manybody 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 additionalpostulates 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 electronlocalization from different perspectives have been proposed in recent years. The variety

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

´ H. J. Bohorquez (&) Á R. J. Boyd Department of Chemistry, Dalhousie University,Halifax, NS B3H 4J3, Canada e-mail: hugo.j.bohorquez@dal.ca

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Theor Chem Acc (2010) 127:393–400

of proposals for assessing that single task leads to the logical question of why the conventional analysis seems to be insufficient to fully explain electron localization in molecules. We identify two main causes: one is interpretation, and the other is of a practical nature. The...