Figure 9. Computing the transition dipole moment ACF: a) a code snippet detailing how to read the propagated RDM and calculate the transition dipole moment ACF; b) the computed ACFs.
Finally, the computed ACFs can be Fourier-transformed (FT) to yield the spectra according to Eq. 14. The FT of this type is implemented in the “libra_py.ft” module. The underlying “ft2” function takes the initial time-series of data to be computed, the range of the frequencies one is interested in, as well as the corresponding resolution, which is related to the number of time-steps (the number of data points in the time-series). The function yields a number of properties, including the sine and cosine FTs of the data (“ampl_im” and “ampl_re”, in line 8, Figure 10a, “ampl_re” is assigned to variable “intensity[]”), the absolute value of the complex FT amplitude (variable “I”) and the square of its magnitude (variable “I2”). The constructed frequency-domain grid (variable “W”) is also reported, primarily for plotting purposes. The computed absorption line shapes (in the shifted and scaled axes) for two considered temperatures are illustrated in Figure 10b.