## Calculation of heat of formation

The heat of formation is defined as:

ΔHf = Eelect + Enuc - Eisol + Eatom + Ebits

where Eelect is the electronic energy, Enuc is the nuclear-nuclear repulsion energy, -Eisol is the energy required to strip all the valence electrons off all the atoms in the system, Eatom is the total heat of atomization of all the atoms in the system, and Ebits 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 Eelect and Enuc, that is, the solvation terms are included in these two quantities, and cannot be separated from them. Thus, the Eelect and Eenuc terms for a solvated system, Eelect(solvated) and Eenuc(solvated) should be thought of as:

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

and

Eenuc(solvated) = Eenuc + (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 Eelect and Enuc, that term also includes the solvation effects.

#### Single atom

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

ΔHf = Eelect  - Eisol + Eatom

But Eelect = Eisol for an isolated atom, therefore

ΔHf =  Eatom

where Eatom 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 4Su, 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.