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Global mapping of small carbon clusters using
the scaled hypersphere search method(Tohoku University, Graduate School of Science)

Balázs Hajgató, Satoshi Maeda, Koichi Ohno

Introduction:
The study of pure carbon molecules has engaged great interest for many decades.
Molecules of this kind were first detected in astrophysical sources over a century ago
and continue to be intensely studied in connection with the chemistry of carbon stars,
comets, and interstellar molecular clouds. In particular, long carbon chains haverecently been proposed as possible carriers of the diffuse interstellar bands. Carbon
clusters are known to be present in hydrocarbon flames and other soot-forming
systems, and the study of these species is necessary for acquiring a thoroughunderstanding of these complex chemical environments. Carbon clusters are also
thought to be intermediates in the gas-phase chemistry taking place in chemical vapor
deposition systems for production of thin diamond and silicon carbide films. Clearly, adetailed knowledge of the physical and chemical properties of carbon clusters isimportant for understanding a large variety of chemical systems.
In addition to such practical considerations, carbon clusters are fascinating
examples of the richness and variety of carbon chemistry itself. Due to the enormousbonding flexibility of carbon, its unique ability to form stable single, double, or triple
bonds, carbon clusters appear in a wide range of structural forms that are synthesized
spontaneously in hot carbon plasmas. For example, researchers have been puzzlingfor more than a decade over the ability of a molecule as symmetric as the icosahedral
C60 cluster to form in such spontaneous way. Elucidating the evolution of carbon
cluster structure, from linear chains to rings to closed sphenoidal cages to nanotubes,
that takes place as the cluster size increases constitutes a major scientific challenge
and requires an intimate interplay of state of the art experimental and theoreticaltechniques. While great progress has been made in recent years, many unansweredquestions still remain1,2.
As the first and basic step towards understanding the great variety of chemistry
and astrochemistry involving small carbon clusters it is necessary to make atheoretical study. To achieve a better understanding of these systems, I haveinvestigated small carbon clusters, of up to six atoms. The main focus of this work has
been the extrema on the potential energy surface (PES) of the clusters along withtheir corresponding reaction and dissociation channels. This treatment can becoupledwithremotesensingexperimental

data,

such

as

spectroscopic

measurements, in order to help us to understand the reactions taking place in outerspace, even though it is physically impossible to collect suitable sample materials.
Computational methods:
Both singlet and triplet PES were investigated at the B3LYP/6-311+G* level oftheory. Energy refinements were also performed using CCSD(T) calculations. The
global PES search technique employed was the Scaled Hypersphere Search (SHS)
method3,4. This algorithm searches the pathways leading to transition states anddissociation channels from an arbitrary equilibrium structure. Combining the SHS
technique with a downhill-walk algorithm allows a full topographic analysis of the PES
to be obtained for any given chemical composition.
Results:
The triplet results for C4 and singlet results for C5 are given in figures 1 and 2,respectively. In the case of small carbon clusters the linear ones are the most stable
isomers and in the case of the even numbered clusters the linear triplet one is theglobal minimum while in the case of odd numbered clusters the linear singlet species.
Some compounds seem to be enough stable against monomolecular reactions so
their experimental detection might be possible.
B3LYP/6-311+G*
E in kJ/mol

B3LYP/6-311+G*
E in kJ/mol

200

500

10040000

Figure 1: Triplet PES of C4

Figure 1: Singlet PES of C5(1) A. VAN ORDEN, R. J. SAYKALLY, Chem. Rev. 1998 (98) 2313
(2) G. MERINO, M. A. MÉNDEZ-ROJAS, H. I. BERTRÁN, C. CORMINBOEUF, T. HEINE, A. VELA, J. Am. Chem.
Soc. 2004 (126) 16160(3) K. OHNO, S. MAEDA, Chem. Phys. Lett. 2004 (384) 277(4) S. MAEDA, K. OHNO, J. Phys. Chem A 2005 (109) 5742