Here, g f is the degeneracy, n, l, and j are the transitional, vibrational and rotational quantum numbers, T f,v is the characteristic temperature for vibration (= ħω f,v / k B, : vibration frequency), and T f,r is the rotational temperature [= ħ /(2 I f k B)]. The average specific internal energy is related to the partition function through Z f, e f = ( k B T 2 / m ) ( ∂ ∂ l n Z f / ∂ ∂ T ) | N , V .