Calculation of heat of formation

The heat of formation is defined as:

ΔH_f = E_elect + E_nuc - E_isol + E_atom + E_bits

where E_elect is the electronic energy, E_nuc is the nuclear-nuclear repulsion energy, -E_isol is the energy required to strip all the valence electrons off all the atoms in the system, E_atom is the total heat of atomization of all the atoms in the system, and E_bits is the energy from hydrogen bonds and dispersion. These energies can be printed by adding keyword DISP. 

Solvation effects

If EPS=n.nn is also present, then solvation effects are modeled.  The energy due to the stabilization of the system as a result of the solvent is printed on the line "DIELECTRIC ENERGY".  The destabilization of the solvent due to the system is not printed.  Energies due to solvation are present in the terms E_elect and E_nuc, that is, the solvation terms are included in these two quantities, and cannot be separated from them. Thus, the E_elect and E_enuc terms for a solvated system, E_elect(solvated) and E_enuc(solvated) should be thought of as:

E_elect(solvated) = E_elect + (some solvation terms)

and

E_enuc(solvated) = E_enuc + (some other solvation terms)

The easiest way to calculate the solvation energy would be to calculate the solvated system, then, in a separate job and using the final geometry from the solvated calculation, do a 1SCF calculation but without solvation, then take the difference in heats of formation.

An alternative would be to calculate the heat of formation using solvent, and in a separate job, run the same calculation but without solvent.  The solvent effect would then be obtained by taking the difference in the two heats of formation.

 Because the "TOTAL ENERGY" includes E_elect and E_nuc, that term also includes the solvation effects.

Single atom

For a single atom, there is no nuclear term, therefore:

ΔH_f = E_elect  - E_isol + E_atom

But E_elect = E_isol for an isolated atom, therefore

ΔH_f =  E_atom

where E_atom is the experimental heat of formation of the isolated atom from the element in its standard state. For example, in nitrogen this is half the heat required to break a N₂ molecule into its separated atoms. Isolated nitrogen atoms have the configuration 1s² 2s² 2p³, and the state 4S_u, i.e. quartet S. Experimentally, this energy is 113 kcal/mol.  This means that all semiempirical methods predict the heats of formation of isolated atoms with a zero error, except in those few instances when the predicted ground state is incorrect.