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.
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