Dr. Loeser's research involves the development of dimensional scaling methods for treating electronic structure. Dimensional scaling is still a relatively new field. It is based on the recognition that for certain types of problems it may be useful to consider the spatial dimensionality as a parameter, which for most people seems to have the value D=3.
The reason for taking this unusual approach is that many problems, especially those in electronic structure, simplify dramatically at certain values of D. Essentially every problem simplifies in the infinite-D limit, where all particles have unlimited degrees of freedom. For many problems one can also find useful simplifications when the dimensionality is lowered.
Several different methods have been developed for utilizing results obtained at non-physical values of D to construct approximate D=3 solutions. One is the method of 1/D expansions, in which the infinite-D limit is used as a starting point, and then systematically corrected by means of perturbation theory. Another approach is to use results obtained at two or more nonphysical values of D to interpolate approximate D=3 solutions. A third approach is to use only the very simple infinite-D limit solutions explicitly, but to correct these for finite-D effects by means of scale factors derived from the analytic structure of dimensional singularities.
As might be expected, dimensional scaling results are in general not highly accurate, at least by the standards of modern ab initio calculations. On the other hand, the methods are computationally extremely simple. This renders them useful for treating otherwise insoluble problems. Perhaps even more important, the simplicity of the methods means that one can often use them to gain insight into complex processes. The insights are typically geometric in nature, since the infinite-D limit is in fact a classical limit characterized by localization of the electrons relative to each other.
On the quantitative side, dimensional scaling has proven to be most useful for studying electron correlation (that is, the error associated with the use of the orbital approximation). Electron correlation remains a very challenging problem, even with high-end computational facilities. The fundamental reason that dimensional scaling has proven to be so useful in treating correlation is that the simplifications that occur in the dimensional limits are not due to dynamical approximations which destroy correlation; thus the dimensional limit solutions upon which the method relies are fully correlated. By isolating the correlation component of the energy and treating this by dimensional scaling, results competitive in accuracy with ab initio calculations are obtained.