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.