Low-frequency nuclear motion in molecular crystals

We aimed to study how free electronic charge in molecular crystals interact with low-frequency intermolecular fluctuations. While such vibrations have been implicated in the electronic properties of organic molecular crystals, there have been no quantitative characterizations. Our proposed work was a joint experimental and theoretical research agenda. Experimentally, we utilized state-of-the-art low-frequency Raman spectroscopy, recorded as a function of temperature, molecule size, and external bias or illumination.

Theoretically, we planned perform molecular dynamics simulations and Raman spectroscopy calculations, to be compared to experiment and to provide atomistic detail into the vibrations.

In practice, during the short time of the grant (2 years) we were successful in generating the experimental (DOI: 10.1002/adma.201908028) and theoretical (DOI: https://journals.aps.org/prx/accepted/ff076Ka3X061760d846a494202498098dd261ba97) framework to complete the original aims but we are still working on adapting the novel theoretical modeling to the cutting edge experimental results.

The experimental achievements include the performance of polarization‐orientation (PO) Raman measurements that were used to monitor the temperature‐evolution of the symmetry of lattice vibrations in small molecule single crystals. Combined with first‐principles calculations, we showed that at 10 K, the lattice dynamics of the crystals are indeed harmonic. However, as the temperature is increased, specific lattice modes gradually lose their PO dependence and become more liquid‐like. This finding was indicative of a dynamic symmetry breaking of the crystal structure and shows clear evidence of the strongly anharmonic nature of these vibrations. These findings lay the groundwork for accurate predictions of the electronic properties of high‐mobility organic semiconductors at room temperature.

The theoretical achievements include the development of a unified and nonperturbative method for calculating spectral and transport properties of Hamiltonians with simultaneous Holstein (diagonal) and Peierls (off-diagonal) electron-phonon coupling. Our approach was motivated by the separation of energy scales in organic molecular crystals, in which electrons couple to high-frequency intramolecular Holstein modes and to low-frequency intermolecular Peierls modes. We treated the Peierls modes as quasi-classical dynamic disorder, while Holstein modes are included with a Lang-Firsov polaron transformation and no narrow-band approximation. Our method reduces to the popular polaron picture due to Holstein coupling and the dynamic disorder picture due to Peierls coupling. We derive an expression for efficient numerical evaluation of the frequency-resolved optical conductivity based on the Kubo formula and obtain the DC mobility from its zero-frequency component. We also use our method to calculate the electron-addition Green’s function corresponding to the inverse photoemission spectrum. For realistic parameters, temperature-dependent DC mobility is largely determined by the Peierls-induced dynamic disorder with minor quantitative corrections due to polaronic band-narrowing, and an activated regime is not observed at relevant temperatures. In contrast, for frequency-resolved observables, a quantum mechanical treatment of the Holstein coupling is qualitatively important for capturing the phonon replica satellite structure.

Our collaboration is still ongoing regardless of the grant ending. During the grant period we organized a conference in Israel (WIS campus) together on soft semiconductors. OY student, Maor Asher, visited TCB in Columbia and we conducted multiple skype meetings.