Biomedical subjects

David S Watkins

Publications and source records attributed to David S Watkins.

3 recordsLinked to original sources

PubMed2006

Pushing the hyperpolarizability to the limit.

We use numerical optimization to find a one-dimensional potential energy function that yields the largest hyperpolarizability, which we find is within 30% of the fundamental limit. Our results reveal insights into the character of the potential energy functions and wave functions that lead to the largest hyperpolarizability. We suggest that donor-acceptor molecules with a conjugated bridge with many sites of reduced conjugation to impart conjugation modulation may be the best paradigm for making materials with huge hyperpolarizabilities that approach the fundamental limit.

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PubMed2006

The effects of geometry on the hyperpolarizability.

Extensive studies in the past have focused on precise calculations of the nonlinear-optical susceptibility of thousands of molecules. In this work, we use the broader approach of considering how geometry and symmetry alone play a role, irrespective of molecular constraints. We investigate the nonlinear optical response of potential energy functions that are given by a superposition of force centers (representing the nuclear charges) that lie in various planar geometrical arrangements. We find that for certain specific geometries, such as an octupolarlike molecule with donors and acceptors of varying strengths at the branches, the hyperpolarizability is near the fundamental limit. In these cases, the molecule is observed to be well approximated by a three-level model, consistent with the three-level ansatz previously used to calculate the fundamental limits. However, when the hyperpolarizability is below the apparent limit (about a factor of 30 below the fundamental limit), the system is no longer representable by a three-level model, where both two-level and many-state models are found to be appropriate, depending on the symmetry.

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PubMed2004

A framework model based on the Smoluchowski equation in two reaction coordinates.

The general form of the Smoluchowski equation in two reaction coordinates is obtained as the diffusion limit of a random walk on an infinite square grid using transition probabilities that satisfy detailed balance at thermodynamic equilibrium. The diffusion limit is then used to construct a generalization of the single-particle model to two reaction coordinates. The state space includes a square on which diffusion takes place and an isolated empty state. Boundary conditions on opposite sides of the square correspond to transitions between the empty state and the square. The two-dimensional (2D) model can be reduced to a 1D single-particle model by adiabatic elimination. A finite element solution of the 2D boundary value problem is described. The method used to construct the 2D model can be adapted to state spaces that have been constructed by other authors to model K+ conduction through gramicidin, proton conduction through dioxolane-linked gramicidin, and chloride conduction through the bacterial H(+)-Cl- antiporter.

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