The Six Degrees of Freedom of a Diatomic Molecule

x

y

z

θ

ϕ

r

For a diatomic molecule at sufficiently high temperatures, the equipartition of energy theorem distributes an equal portion of the energy, equal to

1

2

k

B

T

, among each quadratic term in the Hamiltonian. Here

k

B

is the Boltzmann constant and

T

is the absolute temperature. Three of the degrees of freedom are translations, two are rotations, and one is vibration. The vibrational degree of freedom contributes a total energy

k

B

T

since the associated kinetic energy and potential energy are both quadratic forms. The temperature should not be too high (say,

T≲1000

K), otherwise electronic degrees of freedom might be excited.