The Feynman variational path-integral solution to the Frohlich polaron Hamiltonian is surprisingly accurate relative to its simplicity. Parameters for the Frohlich Hamiltonian can be derived from an ab-initio calculation of the infrared activity of the phonon modes: the dielectric electron-phonon coupling.
Further development of the Feynman model included response functions of the polaron quasi-particle, which are of considerable interest in the design and development of solid-state materials. A direct solution of the polaron impedance by contour integration (without recourse to a Boltzmann transport equation picture of individual scattering events), allows for temperature dependent prediction of polaron mobility, with no empirical parameters.
Recently I implemented codes to solve the temperature dependent Feynman variational, and associated mobility theories. 21st century software engineering - most particularly automatic differentiation - enables a numerically stable and computational efficient solution. The temperature dependent mobilities, were found to agree well with later experiment on formamidinium lead triiodide pervoskite.
I will discuss recent developments to extend the solutions for realistic materials with multiple phonon branches, improve the efficiency and accuracy of the variational approximation and in the calculation of additional response functions for direct comparison to experiment.
 Slow Electrons in a Polar Crystal, R. P. Feynman, Phys. Rev. 97, 660 – Published 1 February 1955
 Mobility of Slow Electrons in a Polar Crystal, R. P. Feynman, R. W. Hellwarth, C. K. Iddings, and P. M. Platzman. Phys. Rev. 127, 1004 – Published 15 August 1962
 Calculating polaron mobility in halide perovskites, Jarvist Moore Frost, Phys. Rev. B 96, 195202 – Published 7 November 2017
 Impact of the Organic Cation on the Optoelectronic Properties of Formamidinium Lead Triiodide,
Christopher L. Davies, Juliane Borchert, Chelsea Q. Xia, Rebecca L. Milot, Hans Kraus, Michael B. Johnston, and Laura M. Herz. J. Phys. Chem. Lett. 2018, 9, 16, 4502-4511