Here are a few of the research projects I have been involved with over the years, in no particular order.
The Maximum Overlap Method
The Maximum Overlap Method (MOM) provides a non-aufbau selection criterion for occupying orbitals in successive iterations in an SCF calculation. The new occupied orbitals are those that overlap maximally with the span of the old occupied orbitals. Using this approach, excited state solutions to the SCF equations can be obtained.
The above image shows a B1 orbital of fluorenone. The MOM can be used to selectivly occupy orbitals in such molecules allowing excited state energies and properties, such as vibrational frequencies, to be obtained.
Multipole Derived Charges
The concept of an "atomic charge" within a molecule is an intrinsically ill-defined concept. There is no way of measuring such charges experimentally, and therefore any definition of atomic charges is to some degree arbitrary. Working in colaboraton with Andrew Simmonett and Peter Gill, we proposed choosing atomic charges that optimally reproduce the (observable) electrostatic potential (ESP). The image below shows the error in fitting the ESP for nitrobenzene using Mulliken (left), CHELP (centre) and MDC (right) charges.
Decay Rate of Least-Squares Fitting Coefficients
Theoreticians often use resolution of the identity (RI) to project a density onto a (simpler) auxiliary basis. However, little attention has been given to how the importance of the auxiliary basis functions decays as you move away from the target density. We studied this problem in-depth and were amazed to find that the decay rate is highly dependent on the dimension of the auxilary basis, ranging from r-1 for 1-D and r-3 for 2-D to exp(-r) for 3-D bases.
The following picture shows a representation of the idealised auxiliary bases used in 1, 2 and 3 dimensions.
... and the associated decay rates on a log-log plot...
The Effect of Charge-Transfer in Circular Dichroism Spectra
The theoretical prediction of circular dichroism spectra from first principles is a difficult task. Excited state calculations on even small molecules are challenging enough and several approximations must be made before we can consider proteins. One approximation that is usually made is the neglect of charge-transfer transtions between adjacent peptide units in a protein. We used high-level CASPT2 calculations to model these transitions and incorporated them in a modified version of the Matrix Method. The computed spectra show better agreement with experimental spectra in the 170 nm range.
The image above shows the transition density for a π->π* charge transfer on a covalent peptide dimer (electron density is shifting from the red to the blue region).