Photoluminescence line shapes of nanocrystals: Contributions from first- and second-order vibronic couplings

We present a microscopic, parameter-free approach for computing the photoluminescence spectra of a single semiconductor nanocrystal. The method derives exciton-phonon coupling directly from the semi-empirical pseudopotential framework and systematically incorporates both diagonal and off-diagonal exciton-phonon interactions, expanded to second-order in the phonon coordinates. The dipole-dipole correlation function was calculated using a Dyson expansion within the Kubo-Toyozawa formalism, enabling a consistent description of the role of pure dephasing and population transfer on the photoluminescence spectral features. Applied to CdSe/CdS core-shell nanocrystals, the approach quantitatively reproduces experimental photoluminescence spectra over a wide temperature range, revealing that quadratic phonon couplings account for nearly half of the homogeneous linewidth above ≈100-150 K, while off-diagonal couplings leading to exciton thermalization play only a minor role and only as T → 300 K.