Thermodynamics

At the end of a completed Frequencies calculation, a survey is given of thermodynamic properties: Heat Capacity, Internal Energy, Entropy. The computed results assume an ideal gas, and electronic contributions are ignored. The latter is a serious omission if the electronic configuration is (almost) degenerate, but the effect is small whenever the energy difference with the next state is large compared to the vibrational frequencies.

THERMO {P=pressure} {T=temp1 {temp2}} {nT=nT}

pressure

The Pressure in atmospheres. Default value: 1.0. A zero or negative pressure is adjusted by the program to a (very) small number 1e-4

temp1,temp2

The endpoints of the Temperature range (in K), for which the results are computed. By default only room temperature is considered (298.15 K).
If the option T= is used and only one value supplied (temp1), then temp2 is assumed to be equal to temp1.
A zero or negative temparture is adjusted by the program to a (very) small number 1e-4

nT

The number of steps by which the temperature interval is scanned. By default it is computed by the program from the temperature range (temp1, temp2), such that the step size is as close as possible to 10 K. Note that the number of temperatures for which the calculations are done is one more than the number of temperature steps.

The thermal analysis is based on the temperature dependent partition function. The energy of a (non-linear) molecule is

E/NkT = 3/2 + 3/2 + ∑_j^3N-6[ hν_j/(2kT) + hν_j/kT(e^hν_j/(kT-1)) ] - D/kT   (5.1.2)

The summation is over all harmonic ν_j, h is Planck's constant and D is the dissociation energy

D = D₀ + ∑_j hν_j/2   (5.1.3)