Theoretical Chemistry
My interest is in the interaction of light with atoms
and molecules;
this includes the behavior of atoms and molecules in
intense light beams, and phenomena, such as optical rotation which
occurs at lower light intensities. The approach is mainly
semiclassical, i.e., the atom or molecule is treated quantum
mechanically but the light beam it interacts with is treated as a
classical electromagnetic field. However, we also use fully
quantized models when appropriate. Problems of present active
interest include:
I. Microwave Optical Rotation
We have been able to show that optical
activity exists in the microwave region for molecules of appropriate
symmetry. Questions remaining are: How large are the effects?
Can they be measured? Do the effects provide any
new and interesting molecular information?
II. Non-Perturbation Theory Methods
We have been treating the interaction of
light with matter in intense fields by numerically integrating
Schrödinger's
equation in model systems. This technique gives results that are
not easily derived by common theoretical methods.
Open
theoretical questions are: Can we find closed-form theoretical
methods which will give us these same results,
and can this technique provide useful information regarding the
dynamics of internal energy transfer in molecules?
III. Optical Rotation Near Resonance Absorption
We have developed a formulation of the theory
of optical activity in which the fundamental parameters do not go
to infinity as the driving frequency passes through a resonance
absorption. It remains to be seen whether this
formulation will provide any new insight or lead to new molecular
information. The consequences of this
formulation need to be explored further.
IV. The Magnus Expansion in Time-Dependent Perturbation Theory
We have recently developed an alternative to the Magnus
expansion in time-dependent perturbation theory. This
new form of
the expansion is easy to derive and the form of the
higher order terms is so simple that they can be
written to arbitrary order by inspection. The new expansion removes
the principal barrier to the wide-spread use
of the Magnus expansion in quantum dynamics, namely the extreme
complexity of the conventional forms of the
terms above third order. This development permits us to study the
detailed properties of the expansion as well as
apply it to problems of spectroscopic and dynamic interest.
In addition, it is now possible to study carefully the
convergence properties of the Magnus expansion. Preliminary work
indicates that there may be unsuspected
problems with convergence for some simple
models of physical interest.
