Searching for an effective Hamiltonian

In less than two weeks I head off to Bangalore, India for a week. I will be speaking at a School and Conference on “Emergent Properties and Novel Behavior at the Nanoscale” organised byI2CAM and the Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR) in Bangalore.

Here is the abstract I have submitted for my conference talk.

Effective Hamiltonians for Excited States of Fluorescent Protein Chromophores

An emergent perspective on photoactive molecules leads to a search for organizing principles and effective Hamiltonians which can describe broad classes of molecules. This is in contrast to a reductionist view that claims that for each new system one must perform ab initio quantum chemistry calculations.

The expression of the Green Flourescent Protein in a wide range of systems has led to a revolution in the imaging of biomolecular processes in cells. There are now hundreds of such photoactive proteins with a wide range of tuneable photochemical properties. Developing structure-property-function relations for these molecules presents a major scientific challenge.

We have shown that insight is gained by considering a fluorescent protein chromophores as Brooker dyes which consist of two aromatic groups on either side of a methine bridge. A key feature for understanding the low-lying excited states are the resonating valence bond structures associated with this bridge [1].

We have provided a rigorous quantum chemical justification for the application of Platt’s resonance colour theory to these methine dyes. This is done by a CAS-SCF(4,3) treatment where there are four electrons in an active space of three orbitals. These orbitals turn out to be invariant for a range of protonation states, molecular geometries and substitutions. Furthermore, diabatic states in this active space can be mapped onto valence bond structures [1].

A natural consequence of this valence bond picture is the existence of a dark singlet state lying above the bright state responsible for the absorption and emission [2].

This mapping allows us to define a three state effective Hamiltonian which depends on the molecular geometry and describes the conical intersections between excited state potential energy surfaces and charge separation associated with twisting and photo-isomerisation [3].

[1] S.C. Olsen and R.H. McKenzie, J. Chem. Phys. 130, 184302 (2009). [2] S.C. Olsen and R.H. McKenzie, arXiv:1001.2593, submitted to Chem. Phys. Lett. [3] S.C. Olsen and R.H. McKenzie, J. Chem. Phys. 131, 234306 (2009).