Aborption spectrum with local field effects (test included) + test for Equation of Motion PCM propagation
Local field effects has been included in the calculation of the absorption spectrum of solvated molecules within the PCM framework. It is worth to stress that when calculating the polarizability of a solvated molecule the spectroscopic observable is not derived from the induced dipole of the solute molecule alone with local field effects, there is an additional contribution to it coming from the induced dipole of the polarization charges at the cavity interface due to the solute molecule itself (see e.g., Cammi et al., J. Phys. Chem. A 104, 44 (2000)). For a detailed reference on non-equilibrium local field effects and its influence in the absorption spectrum, see https://pubs.acs.org/doi/10.1021/acs.jctc.9b00010.
The main changes were in the src/hamiltonian/pcm.F90 and src/td/spectra.F90, and they do not affect the octopus executable but the utility oct-propagation_spectrum utility. No new keywords are used for this kind of calculation, since it inherits the ones from the TD-PCM calculation with local field effects. In src/td/spectra.F90, the key subroutine that has been modified is spectrum_cross_section. Subroutines spectrum_add_pcm_dipole and spectrum_times_pcm_epsilon were duly added to src/td/spectra.F90 to keep the code as close to the original one as possible and to increase in readability. Subroutines pcm_dipole, pcm_eps, pcm_eps_deb and pcm_eps_drl were added to the src/hamiltonian/pcm.F90 module instead where they fit best.
The calculation of the spectrum with local field effects is not robust with respect to setting up high values of the dynamic dielectric constant (>~10), due to numerical problems. Notwithstanding, it works well for a nonequilibrium or equation-of-motion PCM propagation even using a very polar solvent as water (\epsilon_0 = 78.39, \epsilon_d = 1.789), and we don't anticipate any other issues with other kinds of realistic solvent.
Furthermore, tests were included for the absorption spectrum with local field effects and equation-of-motion PCM propagation.