Entropy-Ruled Method on Density of States Proportion for Charge-Energy Transport in Organic Molecular Crystals: A Computational Study

The charge-energy transport mechanism in molecules is of fundamental importance and practical interest in the design of highly efficient molecular electronic devices. Importantly, the production of entropy due to charge dynamics-associated energy flux variation in the molecular solids causes nonequilibrium transport, and it leads to physics of deviation in Einstein’s diffusion-mobility relation of $\frac{D}{\mu }=\frac{k_{\mathrm{B}}T}{q}$ (Hurowitz, D.; Cohen, D., Phys. Rev. E 2014, 90, No. 032129 and Navamani, K., J. Phys. Chem. Lett. 2025, 16, 8596–8612). This urges the requirement of a suitable alternative method to attain better accuracy in semiconducting and optoelectronic properties in different molecular devices. With this motivation, the “density of states (DOS) proportion” is proposed to incorporate a band and nonadiabatic hopping transport mechanism at different thermodynamic conditions. The DOS proportion is in direct proportion with the population of electronic states or normal DOS. In this context, the developed D/μ relation and other extended charge transport (CT) formalism (conductivity, current density, etc.) are used to study the CT in dialkyl substituted dithienothiophene (DSDTT)-based molecular crystals. The CT key parameters such as charge transfer integral, site energy, and spatial overlap integral are computed from the dimer projection (DIPRO) method using electronic structure calculations. These CT key parameters, including reorganization energy, are used in the degeneracy-weighted diffusion equation and the DOS proportion factor to explore the CT in the DSDTT-based molecular derivatives. Using the entropy-ruled method under degenerate and large carrier energy flux approximation, the calculated hole mobility values are around 0.85 and 0.19 cm²/V s for DSDTT-1 and DSDTT-2 molecular crystals, respectively, reaching a proximity value with an experimentally obtained average mobility. From the obtained ideality factor from the quantum-corrected Shockley diode equation, Langevin transport (trap-free diffusion) is observed in these DSDTT molecules, which suggests that these molecules are good candidates for designing hole transporting (or P-type semiconducting) devices.