where T is the absolute temperature of the system, k_B is the Boltzmann constant, and E_{j,n} is the energy of j-th mode when it has vibrational quantum number n = 0, 1, 2, \ldots . For an isolated molecule of n atoms, the number of vibrational modes (i.e. values of j) is 3n − 5 for linear molecules and 3n − 6 for non-linear ones.G. Herzberg, Infrared and Raman Spectra, Van Nostrand Reinhold, 1945 In crystals, the vibrational normal modes are commonly known as phonons.
