Electron–Phonon Coupling in CdSe Nanocrystals from an Atomistic Phonon Model

Phonon frequencies and eigenvectors, electron-phonon couplings, and the associated resonance Raman spectra have been calculated for approximately spherical, wurtzite form CdSe nanocrystals having radii of 1.4 to 2.3 nm and containing 318 to 1498 atoms. Calculations of the equilibrium geometries and phonon modes are carried out using an empirical force field, and the electron and hole wave functions are calculated as particle-in-a-sphere envelope functions multiplying the Bloch functions, with valence-band mixing included for the hole functions. The coupling of each phonon mode to the 1S(e)-1S(3/2) and 1S(e)-2S(3/2) excitations is evaluated directly from the change in Coulombic energy along the phonon coordinate. Ten to 50 different modes in each crystal have significant Huang-Rhys factors, clustered around two frequency regions: acoustic phonons at 20-40 cm(-1) depending on crystal size, and optical phonons at 185-200 cm(-1). The Huang-Rhys factors are larger for the acoustic modes than for the optical modes and decrease with increasing crystal size, and the Huang-Rhys factors for each group of modes are smaller for the 1S(e)-2S(3/2) than for the 1S(e)-1S(3/2) excitation. These results are compared with measurements of electron-phonon coupling in CdSe nanocrystals using different experimental techniques.