Fig. 2: Summary of ab initio calculations.

a Left-hand side panel: Optical matrix elements along the a-axis calculated for the frequency region between 0.4 to 0.9 eV. The size of the circles is proportional to the magnitude of the matrix elements and indicates which electronic valence(yellow) and conduction(blue) bands are involved in photo-absorption. Right-hand side panel: Imaginary part of permittivity along the a-axis as a function of frequency with the experimentally relevant frequency window shaded. b IR activity of the most IR active phonons; the phonon at 4.7 THz which dominates electron-phonon interactions in that region is highlighted with the mode character shown in the inset. A complete list of IR active phonons in this region for TNS is given in Methods. c and d show the effect of electron-phonon coupling on the band structure in the monoclinic and orthorhombic phases respectively. The electron-phonon coupling is captured by calculating the electronic band-structures using DFT in the presence of either negative or positive phonon displacement (frozen phonon approximation). The phonon 4.7 THz in the monoclinic phase is strongly coupled to the electronic bands 2 and 3 which are highlighted in the figure. In the high-temperature orthorhombic phase, the effective electron-phonon coupling is reduced by an order of magnitude. This indicates that the electron-phonon interaction is very sensitive to the order parameter.