About
FretLab is a high-performance computational tool designed to compute electronic energy transfer (EET) rates. It supports three general use cases:
- Donor to acceptor chromophore EET
- Plasmonic substrate to acceptor chromophore EET
- Donor to acceptor chromophore EET mediated by a plasmonic substrate
FretLab is designed for speed and scalability using parallel processing with OpenMP and efficient linear algebra routines.
Theoretical Framework
All quantities in FretLab are expressed in atomic units. The EET rate is calculated using Fermi’s Golden Rule:
$$ \kappa_{\text{EET}} = \frac{2\pi}{\hbar} \ |V|^2 \ J $$
Where:
- V is the total coupling potential between donor and acceptor
- J is the spectral overlap integral
In the presence of a plasmonic substrate (modeled via induced charges $q_k$ and, if applicable, induced dipoles $\mu_k$), the total coupling V becomes:
V = V_{\mathrm{coulomb}} + V_{\mathrm{overlap}} + V_{\mathrm{environment}}^{q} + V_{\mathrm{environment}}^{\mu}$$ V_{\text{coulomb}} = \int d\mathbf{r} \ d\mathbf{r'} \ \frac{\rho_A^*(\mathbf{r}) \rho_D(\mathbf{r'})}{|\mathbf{r} - \mathbf{r'}|} $$
$$ V_{\text{overlap}} = - \omega_0 \int d\mathbf{r} \ d\mathbf{r'} \ \rho_A^*(\mathbf{r}) \rho_D (\mathbf{r'}) $$
$$ V_{\text{environment}}^{\text{ q}} = \sum_k \left( \int d\mathbf{r} \ \frac{\rho_A^*(\mathbf{r})}{|\mathbf{r} - \mathbf{r}_k|} \right) q^\omega(\mathbf{r}_k; \rho_D) $$
$$ V_{\text{environment}}^{\mu} = \sum_k \left( \int d\mathbf{r} \ -\frac{\mathbf{r} - \mathbf{r}_k}{|\mathbf{r} - \mathbf{r}_k|^3} \cdot \rho_A^*(\mathbf{r}) \right) \mu^\omega(\mathbf{r}_k; \rho_D) $$
Where:
- $\rho_A$ and $\rho_D$ are the acceptor and donor charge densities
- $\omega_0$ is the incident frequency
- $q_k^\omega(\mathbf{r}_k; \rho_D)$ are the frequency-dependent induced charges at positions $\mathbf{r}_k$
- $\mu_k^\omega(\mathbf{r}_k; \rho_D)$ are the frequency-dependent induced dipoles at positions $\mathbf{r}_k$
Acknowledgments & Funding
This project has been supported by the FARE 2020 program — "Framework per l’attrazione e il rafforzamento delle eccellenze per la ricerca in Italia."
FretLab has been developed as part of a collaborative scientific effort involving Tommaso Giovannini, Piero Lafiosca, Sveva Sodomaco, and Chiara Cappelli.