59th Annual Report on Research 2014

The research project has two main foci, the development of computational methods for the characterization of intermediates in electron-induced reactions, and the characterization of these intermediates themselves. During the second year (1) work on some specific systems has been finalized, and work on new molecules has been started, (2) the project on extrapolation methods has been considerably extended, and (3) a new project regarding the development of better absorbing potentials has been started.

(1) One project aimed at studying intermediates was a collaboration with Dr. Robert Compton's group at the University of Tennessee and Dr. Kit Bowen's group at John Hopkins University. Negative ion states of large molecules (nitro benzene moieties coupled to amino acid) were characterized by photoelectron spectroscopy, collision induced dissociation (by the experimentalists), and computationally (by us). The combined results were then used to shed light on the possibility of electron-induced reactions after electron trapping through a doorway mechanism, and this project is now complete. The second group of molecules studied were molecules without a dipole but with a large quadrupole moment. Our results clearly indicate not only that a “critical quadrupole moment” –a notion analogous to the critical dipole moment– does not exist, but also that electrons bound to this type of molecule are better understood as correlation-bound than quadrupole-bound species. Hence, our findings have influenced the anion community's thinking at a fundamental level.

Figure 1: Electron binding energy vs quadrupole magnitude for several molecules with large quadrupoles but vanishing dipoles. Clearly, there is no trend or cutoff. 

(2) The idea of the extrapolation method is that energy of temporary anions, which are perhaps from a theoretical viewpoint the most challenging intermediate of electron-induced reactions, can be obtained from a series of bound state calculations for a single state. This is done by adding an artificial stabilizing potential to the Hamiltonian, increasing it until the temporary state becomes bound, and increasing it further until enough data have been collected so that one can extrapolate back to zero stabilization. Unfortunately, any extrapolation as such is to some extent arbitrary, and in addition, it was widely assumed that extrapolation schemes could only yield energies, but no lifetimes. As it turns out, in the nuclear physics community similar methods were independently developed even earlier. These methods do yield the lifetime, however, they require somewhat different stabilizing potentials than those typically used in quantum chemistry–a short-range potential as opposed to long-range Coulomb stabilizations. While a Coulomb stabilization can be “implemented” by changing the nuclear charges or adding additional point charges, adding a short-range potential to the one-electron Hamiltonian in a quantum chemistry code requires implementing numerical integrals. This has been done, and first applications to a few well-known resonance states of small molecules look highly promising.

Figure 2: Extrapolation of the energies of the temporary state, once it becomes the ground state (red), back through threshold, yields the energy (green) and the decay constant  (purple) of the temporary state in the region where it is unstable.

(3) The complex absorbing potential method is another way to characterize temporary anions. Here an imaginary, that is, absorbing, potential is added to the Hamiltonian, and one follows the eigenvalues of the Hamiltonian into the complex plane as the strength of the imaginary potential is increased. Continuum states simply accelerate into the complex plane, whereas temporary anion states show a pronounced stabilization at their complex energy – the real part is the energy itself, the imaginary part is the half width, where the lifetime is equal to the inverse of the width. So far most complex absorbing potential calculations have used the so called box-CAP, an absorbing potential that has the shape of a box around the molecule, and then grows quadratically in each Cartesian direction, because the integrals of this potential can be evaluated analytically. This functional form itself is adequate for most small molecules and larger molecules with box-like shapes, but is obviously inadequate in other cases. More adequate potentials would encase a molecule more closely following its shape. The disadvantage, however, is again that numerical integrals are needed. This type of absorbing potential has been implemented, and applied to several small molecules with p* temporary anions, and these pilot applications look highly promising.

Figure 3: The novel potential used as an absorbing potential. 

The work I can do because of this grant clearly has a huge impact on my career. Without support for summer research any meaningful professional development at a primary undergraduate institution would be next to impossible. But especially in these times of frugality even activities once taken for granted, such as making presentations at or taking students to regional meetings, become increasingly difficult. Thus, this grant is key to maintaining an active and professional research program as such.

For my students essentially the same is true. It makes a huge difference to know that they do not just participate in some educational project, but in a real research project that may at some point land them a poster presentation, a trip to a regional or national meeting, or even a co-authorship on a paper. They take their work more seriously, begin to see the value of a deeper level of understanding, and are more likely to continue “their” research after the mandatory research classes have been taken.