A Fullerene Project: C20
The fullerene project began with the three primary isomers ( different orientations of the twenty carbon atoms) and nothing that they all can be found within the fabric of the 20-carbon potential energy surface. Our goal was to determine and describe the potential surface that exists in around these three isomers.
The three primary isomers of the C20 system, pictured above, were created using the Winmopac software package. Comparing the atomic coordinates within the ring and bowl structures, a saddle-point calculation enables one to obtain a two-dimensional energy profile of the potential surface that separates the two isomers. Basically, this profile is analogous to, but not indicative to, a topographical map of a mountain range, indicating energy valleys and energy ridges/peaks. These are not stationary points, but estimations of the absolute energy associated with the particular atomic orientation within the system. We are interested in obtaining stationary points (thermodynamically stable isomeric structures) from the optimization of the Cartesian coordinates that correspond to what appear to energy minima in the profile. Below is the energy profile obtained between the ring and the bowl isomers. The atomic coordinates that correspond to the energy minima in the above profile were then geometrically optimized, resulting in the identification of additional isomers of C20 that are predicted to be energetically stable (existing in their own specific potential well). Based on these additional isomers,
a step-wise transformation, or mechanism, that links the ring to the bowl isomer was proposed, and is illustrated below.
Therefore, these five theoretically stable isomers provide a proposed step-wise process by which the ring could evolve into the bowl structure as the temperature of the system is lowered. Much like a child’s game of hop-scotch, these seven isomers all lie adjacent to one another on the potential surface as is evidenced by the energy profile that separates the ring from the “1st hop” in the step-wise transformation, shown below. Note that a single energy barrier, void of any intermediate energy minima, separates these two isomers.
The investigation into the region of the potential surface in which the bowl and cage isomers of C20 occupy, we followed the same general approach. In general, this region of the surface appears to be much more cluttered with pseudo-stable isomeric structures, with 8 new thermodynamically stable identified that lie between the cage and bowl structures in a step-wise transformation (shown below).
Each one of the eight intervening isomers occupy their own distinctive potential energy wells, as is evidenced by being geometrically optimized and from force constant analysis. Of particular interest, two of these isomers (2 and 7) possess energy wells of comparable depth to that of the cage isomer; therefore, making these two isomers possible candidates for spectroscopic identification and investigation. In addition to have a well-establish potential well (as illustrated in the below figure), isomer 7 also possesses C2v symmetry, further supporting its stability.
In the above schematic, we have taken the potential wells of each isomer, located in 3D space, and pulled them into a two-dimensional profile in order to illustrate and compare the relative depths of their potential wells. It should be pointed out that the barriers (transition states) between are not stationary points and have no physical meaning. The barriers are estimations generated in the theoretical calculation. This project is ongoing, as we begin to locate and identify theoretically stable isomeric structures that lie between the ring and the bowl structures.
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