Atomic and molecular theory involving symmetry principles and group algebra is one of the specialties for Dr. Harter. This also involves a lot of computer graphics and animation, a good deal of which is used in classes.

Dr. Harter and his students were the first to calculate and predict the form of the rotational and vibrational spectra of the soccer ball shaped Buckminsterfullerene (C60) or "Buckyball" molecule. This was used by experimentalists to help find ways to make enough 'Buckyballs' to prove that this incredible form exists. Since then the study of C60 and related fullerenes has become a worldwide industry. A Nobel prize in chemistry was given in 1996 to the experimental chemists who first made minuscule amounts of C60.

Current work is being done on the symmetry breaking of C60 by one or more 13 C isotopes. A pure 12 C60 buckyball is a giant Bose-symmetric structure or boson with the highest point symmetry that can occur in a molecule. Even a single 13 C breaks this symmetry almost completely and a 13 C60 molecule would be an incredible Fermi-symmetric structure or Fermion with over an octillion of nuclear spin states. The effects of 13 C and its nuclear spin on fullerenes are being pursued now.

Another area of research involves using optimal control theory for quantum systems such as rotating molecules. Classical control theory is a well-known engineering discipline, but quantum control theory is just beginning to be developed. It involves sophisticated and interactive use of computer models and simulations.

Many of the computer simulations are useful for students. Classroom use of computer simulation is one of the areas Dr. Harter has been developing since before 1984. Over twenty Macintosh programs have been developed for student use. Also, his students are being given state-of-the-art tools for learning to make their own high-performance interactive simulation programs (See the Computer Simulations research area for details.)