The Six Degrees of Freedom of a Diatomic Molecule

For the translations, the kinetic energy is equal to in each direction , , and ; for the rotations, for angles θ and ϕ, where is the moment of inertia of the molecule and is the angular velocity. Finally, the energy associated with the vibrational degree of freedom, in the harmonic oscillator approximation, can be written as , where is the velocity along the direction of the chemical bond, is a spring constant associated with the chemical bond, is the elongation or compression, and is the equilibrium position. Adding the energies of all six degrees gives a theoretical value for the molar heat capacity at constant volume , where is the universal gas constant.