I spent this summer modeling small clusters of Boron atoms. The modeling was all done using a series of FORTRAN codes that used Unrestricted Hartree-Fock and 2nd Order Many Body Perturbation Theory to approximate a solution to Schroedinger's equation. The process involved optimizing the distance of whatever model you were working on to get a minimum in energy. The original plan was to model alpha-rhombohedral boron which is made up of eight B12 spheres arranged in a cube with three boron atoms forming a bridge across the middle of the cube. This was too big to start with without redimensioning the codes so we started with two atoms and began to build our way up.

The B2 molecule proved to be quite difficult to deal with. It did not want to behave as a real B2 molecule would. Instead of having a smooth energy curve, the null input runs had a huge jump in energy which would not happen in the real world. I had to walk it very slowly, feeding the file from the previous run into the current run to get it to form a nice energy curve. We ended up finding a separation distance of 3.4 a.u. compared to the CRC's value of 3.004 a.u.

We then moved on to B3. It also proved to be quite difficult, it would take B3's 15 electrons and redistribute them so that there would be nine for one atom and three for the other two atoms. By building the initial input file from the boron dimer and a single boron atom I was able to get B3 to behave properly. B3 was modeled in linear, triangular, and L-shaped configurations. For the linear we found the separation distance to be 3.3 a.u., compared to the published value of 2.67 a.u. (1.41 angstroms). Our separation distance for the triangle was 3.4 a.u., compared to the published value of 3.72 a.u. (1.97 angstroms). For the L-shaped runs we found a separation distance of 3.2 a.u. with no published data to compare it to.

B4 was modeled first as a square. Its input file was build from the L-shaped B3 and a single boron. We were able to get it to behave properly and give a nice energy curve. We found the square's separation distance to be 2.4 a.u. compared to the published value of 3.33 a.u. (1.76 angstroms). B4 was also modeled as a pyramid (tetrahedron). Its initial file was constructed using the triangle and a single boron atom. We found the optimum separation distance to be 3.6 a.u., compared to the published distance of 3.57 a.u. (1.89 angstroms).

For B5 we modeled a pentagon and a bipyramid. For the pentagon we built the initial file from the square and a single boron atom. We found a separation distance of 3.1 a.u. The bipyramid's input file was built using the pyramid and a single boron atom. Its separation distance was 3.6 a.u. There was no published data on these geometries to compare with.

For B6 we modeled a hexagon and an icosahedron cap. Both configuration's initial files were built from the pentagon and a single boron atom. The hexagon had a separation distance of 3.2 a.u. with no published data to compare it to. The icosahedron cap had a separation distance of 3.4 a.u. compared to the published value of 3.35 a.u. (1.77 angstroms).

We also ran some larger runs from null input. B12 was set up in an icosahedron (one atom on each of its 12 vertices) and it ran properly a few times and then began to redistribute its electrons in unphysical ways. B13 was set up as an icosahedron with an atom in the center. Its input file was build using the B12 run and a single boron atom. The runs that we had time to do worked properly, but there was not enough time to do a complete set of runs so no optimized distance was found. We also looked at B20. We used the dodecahedron, putting one atom on each of its 20 vertices. Its first run took three days and did not converge. Given more time we would have tried to construct an input file to hopefully get it to converge.

I also learned FORTRAN programming this summer. I started out writing smaller programs and ended up writing a breathing modes program that would take the coordinates of one of the geometries and either move the distance in or out by a given percent. I also build some small models of some of the bigger runs we did, mainly the B12 icosahedron. Besides learning programming in a new language, I learned a lot about how research is actually performed. This has been a good experience in preparation for going to graduate school in that it has given me a more of an idea of what to expect.