Other contributions to the barrier (continued)

· In addition, laboratory measurements are obviously not carried out at absolute zero on single molecules.

· Experiments are done at higher temperatures on large numbers of molecules.

· We ideally need to include the vibrational, translational and rotational energy at a particular temperature to compare with experimental results.

· We can write the total energy as the sum of translational, vibrational, rotational and electronic contributions:

U = U_trans + U_rot + U_vib + U_elec (1)

· The (mean) translational energy is 3/2 kT per molecule (from the equipartition theorem), so 3/2 RT per mole of molecules.

· Similarly, for a non-linear molecule (3 degrees of rotational freedom) at normal temperatures, the rotational energy is 3/2 RT per mole.

· The enthalpy, for example, can be calculated from the internal energy as usual:

H = U + pV (2)

Thermodynamic properties can be calculated from the partition function. For example, the vibrational partition function can be calculated from the normal mode vibrational frequencies.