ARTICLE pubs.acs.org/JPCA
Dynamic and Static Behaviors of NZN σ(3c4e) (Z = S, Se, and Te) Interactions: Atoms-in-Molecules Dual Functional Analysis with High-Resolution X-ray Diffraction Determination of Electron Densities for 2-(2-Pyridylimino)-2H-1,2,4-thiadiazolo[2,3-a]pyridine Waro Nakanishi,*,† Satoko Hayashi,† Mateusz B. Pitak,*,‡ Michael B. Hursthouse,‡ and Simon J. Coles‡ †
Department of Material Science and Chemistry, Faculty of Systems Engineering, Wakayama University, 930 Sakaedani, Wakayama, 640-8510 Japan ‡ School of Chemistry, University of Southampton, Highfield Campus, Southampton SO17 1BJ, United Kingdom
bS Supporting Information ABSTRACT: The structure of 2-(2-pyridylimino)-2H-1,2,4-thiadiazolo[2,3-a]pyridine (NSN) indicates that the molecule has a planar geometry with a linear N 3 3 3 S 3 3 3 N linkage, creating a tetracyclic structure of the formal C2v symmetry. To clarify the nature of the NSN σ(3c4e) bonding, together with the related NSeN and NTeN, the dynamic and static behaviors are investigated by applying atoms-in-molecules (AIM) dual functional analysis to both the fully optimized and perturbed structures. The structures were optimized computationally, retaining C2v symmetry. All bond critical points are detected as expected and exhibited on both sides of the N 3 3 3 Z 3 3 3 N moiety which supports the formation of NZN σ(3c4e). It is confirmed that N 3 3 3 S 3 3 3 N is of the covalent nature close to Me2S+-/-Cl or Me2Se+-/-Br, whereas N 3 3 3 Se 3 3 3 N and N 3 3 3 Te 3 3 3 N have the (regular) CS nature close to the CT adducts of Me2S(-/Cl)2 (TBP) and Me2Se-/-Br2 (MC), respectively. An experimental high-resolution charge density determination has been performed on NSN, which thoroughly supports the theoretical results. Very similar results are obtained in the analogous pyrimidyl derivatives for N 3 3 3 S 3 3 3 N, N 3 3 3 Se 3 3 3 N, and N 3 3 3 Te 3 3 3 N. AIM dual functional analysis, as validated by experimental high-resolution charge densities, is thus confirmed to be an excellent method to elucidate the nature of these interactions.
’ INTRODUCTION The concept of three centerfour electron bonds of the σ-type [σ(3c4e)] was proposed by Musher, Pimentel, and Rundle.1 The concept was developed through the preparation and characterization of such compounds24 and theoretical investigations5 by Martin,2 Akiba,3 Schleyer,5e and others.4 The importance of σ(3c4e) interactions in chemical sciences has been widely pointed out.24,68 Figure 1 shows the molecular orbital approximation of linear Z3 σ(3c4e), exemplified by Br3. Atomic s-orbitals contribute to the molecular orbitals more or less depending on the symmetry, especially at the central Br atom in ψ2. The modeling of the σ(3c4e) nature for the NSN linkage in 2-(2-pyridylimino)-2H-1,2,4-thiadiazolo[2,3-a]pyridine (1) and the pyrimidyl derivatives, via complementary experimental and computational methods, is thus a very important step in the development of this concept (Chart 1).9 The AIM (atoms-in-molecules) approach, introduced by Bader,10,11 enables us to analyze the nature of chemical bonds and interactions.1217 Electron densities at bond critical points (BCPs; rc, /) of (ω, σ) = (3,1)10 (Fb(rc)) are closely related to the binding energies1824 and bond orders.25 The sign of the Laplacian of Fb(rc) (r2Fb(rc)) indicates that Fb(rc) is depleted or concentrated with respect to its surroundings, since r2Fb(rc) is the second derivative of Fb(rc). Fb(rc) is locally depleted r 2011 American Chemical Society
Figure 1. Molecular orbital approximation of Z3 σ(3c4e), exemplified by Br3.
relative to the average distribution around rc if r2Fb(rc) > 0, but it is concentrated when r2Fb(rc) < 0. Highly negative values of r2Fb(rc) associated with high values of Fb(rc) at BCPs are typically indicative of the covalent character of the bond (shared shell interactions, SS), whereas the highly positive values accompanied Received: May 13, 2011 Revised: September 2, 2011 Published: September 08, 2011 11775
dx.doi.org/10.1021/jp2044898 | J. Phys. Chem. A 2011, 115, 11775–11787
The Journal of Physical Chemistry A
ARTICLE
by small values of Fb(rc) correspond to closed shell interactions (CS). A positive value of the r2Fb(rc) can indicate a noncovalent dative bond, ionic interactions, or van der Waals interactions.21b,26,27 Total electron energy densities at BCPs (Hb(rc)) would be a more appropriate measure for weak interactions on the energy basis.10,11,2832 Hb(rc) are the sums of kinetic energy densities (Gb(rc)) and potential energy densities (Vb(rc)) at BCPs, as shown in eq 1. Wozniak and co-workers demonstrate that Hb(rc) describes quantitatively which type of energy density (Gb(rc) or Vb(rc)) dominates for a given range of bond path lengths, Rij.33 A negative value of Hb(rc) indicates that Vb(rc) dominates, which is characteristic for the covalent nature. If Hb(rc) is positive, Gb(rc) dominates and this is characteristic for ionic interactions. The region for Hb(rc) = 0 corresponds to the boundary between the covalency and ionicity. The k value defined by Vb(rc)/Gb(rc) (
