As the title states, using the following equation to calculate the coupling constant using DFT and experimental values
a = [(e^2)/hbar]*[(1)/(4*pi*e_0)]*[(1/e_infty)-(1/e_stat)]*sqrt((m*)/(2*hbar*w_LO)],
where e = electronic charge, hbar = plancks reduced constant, e_0 = vacuum permittivity, e_infity = high frequency dielectric constant, e_stat = static dielectric constant, m* = electron/hole effective mass, w_LO = longitudinal optical phonon frequency,
what are the units used for each constant in the coupling constant formula?? In this source (Article Large Polaron Formation and its Effect on Electron Transport...
) the effective mass is unitless (as it is a ratio of the band effective mass and the rest mass of an electron), and the phonon frequency is in THz, but I am not sure what unit to use for each constant to obtain a value similar to theirs.My system is a metal halide perovskite in the cubic phase with very similar values to those in reported for the dielectric constants and the effective masses, and the experimental value for the phonon frequency is also similar, but the value for the coupling constant that I calculate is on the order of 10^12 which is obviously incorrect.
The most helpful solution to my problem would be to know the unit used for each constant in Fröhlich's formula above (e, hbar, e_0, e_infty, e_stat, w_LO) when reporting to a journal (note in the paper above that they report values around 2-4, which is near what I am expecting as well for my system).
Thanks in advance for any help.
To help with values, for MAPI I have: e_stat = 14.9, e_infty = 5.31, m*_elec = 0.19, m*_hole = 0.36, w_LO = 3.98 THz