Data Compression and Machine Learning in the Analysis of the Entropy of Photodissociation in Organic Donor-Acceptor Interfaces

Organic photovoltaics have become increasingly relevant in recent years, resulting in a growing demand for theoretical models that can accurately approximate the behavior of electrons in organic donor-acceptor inter- faces. As an attempt to simplify the analysis of electron-hole dynamics, we make a case for the use of the Shannon Entropy as measure of the degree of entanglement of e-h pairs using Schmidt decomposition. The Schmidt form also allows us to determine the number of effective dimen- sions occupied by an arbitrary eigenstate Ψk in Hilbert space. In the case of a 50 × 50 diabatic density matrix for a 1-D system, we were able to reduce the number of bytes required to store this information by ∼65% using the Schmidt form. We then reconstructed the original matrix from the reduced model and calculated values for charge transfer character and inverse participation ratio and found that the average percent error was less than 0.05% in both cases. Lastly, we demonstrate that machine learn- ing algorithms can be used to accurately differentiate between excitonic, charge-transfer, and charge-separated states. By combining data compres- sion and machine learning, we developed a simplified and computationally efficient way to quickly sift through thousands of eigenstates and single out relevant information regarding the Shannon Entropy and charge sep- aration. We present the results of this analysis for a 1-D interface with 50 sites and energetic offsets varying between 0.0 - 0.5 eV.