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Wednesday, July 11, 2018

What does Electron Density Analysis tell us about Bonding in Transition Metal-doped Boron and Carbon Clusters?

Sagamore XIX Conference on Quantum Crystallography
Halifax, Canada, July 11, 2018

Video link: https://youtu.be/qxu5uALd6Xs


N. Sukumar1, Pinaki Saha2, Amol B. Rahane3, Rudra Agarwal4, Vijay Kumar5

1  Department of Chemistry and Center for Informatics, Shiv Nadar University, Dadri, India – n.sukumar@snu.edu.in
2  Department of Chemistry, Shiv Nadar University, Dadri, India – ps630@snu.edu.in
3  Dr. Vijay Kumar Foundation, Gurgaon, India – amol_rahane2000@yahoo.com
4  Department of Chemistry, Shiv Nadar University, Dadri, India – ra298@snu.edu.in
5  Dr. Vijay Kumar Foundation, Gurgaon & Center for Informatics, Shiv Nadar University, Dadri, India – vijay.kumar@snu.edu.in

Keywords: electron density analysis, boron clusters, carbon clusters, electron delocalization, structural stability

ABSTRACT


Although the nature of the chemical bond is at the heart of chemistry, chemists often work with several distinct conceptions of the chemical bond, which are not necessarily compatible with each other. The Lewis concept of the electron pair bond [1] is now over a century old, predating the quantum mechanical theory of bonding in molecules. We now recognize electron pairing to be a consequence of the Pauli exclusion principle and the associated Fermi hole. The traditional Lewis electron pair bond concept has been extended to admit the possibility of 3-center, 2-electron bonds in “electron deficient” boranes, and subsequently further extended, using AdNDP analysis [2] (an extension of natural bond orbitals NBO analysis), to include n-center (but always 2-electron) objects (with n arbitrarily large). An alternate to such orbital treatments is provided by examination of topological features of the electron density, such as bond paths (gradient paths of the electron density) connecting pairs of nuclei. Such bond paths are not associated with a fixed electron count. However, as has been pointed out by several authors [3,4], the mere existence of a bond path between a pair of nuclei does not signify the existence of a chemical bond between them or indicate the strength of the interaction. Double integration of the Fermi hole density over spatial regions provides a valid measure of electron localization and delocalization [5]. One can also conceive of the chemical bond as a force that holds a pair of atoms together, quantified by the dissociation energy required to break the bond. While this works well for simple diatomics, the correlation between dissociation energy and electron count or the electron density between a pair of nuclei is not straightforward for open shell systems or polyatomic molecules.
The divergence between these different conceptions of the chemical bond is particularly dramatic for “electron deficient” boron compounds and for metallic nanoclusters, where extensive electron delocalization and multi-center bonding are prevalent. Nevertheless, combining information from topological features of the electron density with orbital-based models allows meaningful chemical conclusions about bonding to be drawn, even for unusual molecular systems.
Here we have analyzed trends in bonding and stability for several clusters including ring-shaped clusters for boron and carbon as well as drum-shaped and fullerene-like clusters of boron, from computed ab initio electron density distributions, and investigated the effects of transition metal (TM) doping on their structural and physical properties. Analysis of the electron density at bond and ring critical points, the Laplacian of the electron density, the electron localization function [6], the source function [7], and localization-delocalization indices, all indicate the coexistence of covalent bonds and delocalized charge distribution in boron clusters [8]. Rings of carbon atoms too seem to be stabilized by metal coordination for selected sizes and electron counts. For drum-shaped M@B14 (M = a 3d TM atom) and M@B16 (M = 3d, 4d, and 5d TM atom) clusters, our results suggest two- and three-center σ bonding within and between two B7/B8 rings, respectively, and hybridization between the TM d orbitals and the π bonded molecular orbitals of the drum. Assembly of Co@B14 clusters has been shown to stabilize a metallic Co atomic nanowire within a boron nanotube [9].
We have also studied metal atom encapsulated fullerene-like boron cage structures and shown that Cr@B20 is the smallest cage for Cr encapsulation, while B22 is the smallest symmetric cage for Mo and W encapsulation. Electron density and molecular orbital analysis suggests that Cr@B18, Cr@B20, M@B22 (M = Cr, Mo, and W) and M@B24 (M = Mo and W) cages are stabilized by 18 p-bonded valence electrons, whereas the drum-shaped M@B18 (M = Mo and W) clusters are stabilized by 20 p-bonded valence electrons [10]. We have also studied larger boron clusters in the size range 68-74 and shown that the global minimum structure for B70 is a tubular structure, which is nearly degenerate with a quasi-planar structure having three hexagonal vacancies [10]. Analysis of a large number of atomic clusters, of various shapes and sizes, indicates a broad parallelism between different measures of bonding and localization in these clusters.

Fig. 1 Electrostatic potential of (a) Cr@B22 and (b) tubular B70 cluster mapped onto a r(r) = 0.1 e/Bohr3 electron density isosurface. Blue regions indicate negative electrostatic potentials associated with the boron atoms. (c) Contour plot of the Laplacian of Cr@B22 cluster in a plane passing through atoms B7, B8, B15, B16, B21, B22, and Cr. Solid (dashed blue) contours indicate positive (negative) values of L = -Ñ2r(r)

Acknowledgements


The authors gratefully acknowledge use of the high-performance computing facility Magus of Shiv Nadar University. ABR and VK thankfully acknowledge financial support from International Technology Center - Pacific. We thank Prof. Cherif Matta for providing access to AIMLDM software.

References


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[10] P. Saha, Ph.D. thesis, Shiv Nadar University, India (2018); A.B. Rahane, P. Saha, N. Sukumar, and V. Kumar, to be published.



 

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