The heat of formation can be calculated for neutral molecules, radicals, cations, and radical cations in the gas phase at 25 degree C.
Heats of formation are estimated from additive contributions of substructures in a molecule.
Figure 1. Calculation of
The substructures and the values of their contribution to the heat of formation are contained in tables in the program.
The accuracy of an additivity scheme for the estimation of molecular properties is strongly dependent on the number of parameters selected, i.e., on the maximum size of the substructures considered in the approach. With increasing number of parameters the accuracy for reproducing known data increases. However, the predictive power will go down as substructures might be present in structures with unknown properties that have not yet been parameterized. This is actually a trade-off between accuracy and predictive ability. A scheme was chosen that works with substructures consisting of two, three, or four atoms thus covering the interaction of atoms over one, two, or three bonds (1,2-,1,3-,and 1,4-interactions).
In order to keep the number of parameters within reasonable limits, substructures for 1.4 interactions (A-B-C-D) are taken only, when the central bond is a double bond (B=C).
The numerical value (parameter) for the contribution of a substructure were obtained by a statistical analysis (multilinear regression analysis) of experimental heats of formation. These data are contained in a database that can be updated and the entire scheme can easily be reparameterized when new experimental data have been added to the knowledge base.
Figure 2. Generation of the knowledge base
Interactions involving hydrogen atoms are only taken for bonds (A-H). For larger substructures they have been set to zero. This is done to allow the determination of parameters by multi-linear regression analysis. Otherwise, the system becomes over-determined and the set of linear equations is linearly dependent and cannot be solved.
Cyclic structures, in particular small rings and aromatic systems, strongly influence heats of formation and therefore additional parameters for strain energies and aromatic delocalization energies must be considered.
For radicals additional atomic parameters for the radical center (A.) have to be determined.
Values calculated
(DELTAHF): standard heat of formation
(STABIL): aromatic resonance stabilisation energy
(STRAIN): ring strain energy
Example
Calculation of the heat of formation of 2-propanol
No. of occurrences |
substructure |
contribution in kJ/mol |
7 |
C - H |
415,97 |
2 |
C - C |
332,82 |
1 |
O - H |
463,48 |
1 |
O - C |
326,22 |
1 |
C - C - C |
9,69 |
2 |
O - C - C |
23,53 |
1 |
O - C (- C) - C |
-6,28 |
= 4417.63 kJ/mol |
of atomization energy of elements = 4146.10 kJ/mol
Results
Some examples for experimental and calculated heats of formation are presented in Table 4.
Compound |
composition |
deviation | ||
2-methylpropane |
C4H10 |
-134.2 |
-134.4 |
-0.2 |
2-methylpropene |
C4H8 |
-16.9 |
-14.9 |
2.0 |
diethylamine |
C4H11N |
-72.5 |
-76.7 |
-4.2 |
benzene |
C6H6 |
82.6 |
77.2 |
-5.4 |
ethanol |
C2H6O |
-235.2 |
-233.5 |
1.7 |
propanoic acid |
C3H6O2 |
-453.5 |
-457.4 |
3.9 |
tert-butyl radical |
C4H9 |
37.6 |
37.4 |
-1.7 |
Table 4. Examples for calculated and observed heats of formation (all data are given in kJ/mol)
Altogether, approximately 800 organic compounds and 180 radicals have been studied. A short overview of some of the classes of compounds that have been studied, together with the root mean square (RMS) between experimental and calculated heats of formation is given in Table 5.
class of compounds |
No. of compounds |
RMS |
alkanes |
61 |
6.9 |
alkenes |
64 |
3.8 |
alcohols |
34 |
11.3 |
carboxylic acids |
26 |
8.9 |
esters |
36 |
9.4 |
ethers |
41 |
8.2 |
nitro-compounds and amines |
87 |
11.2 |
halogen compounds |
153 |
6.2 |
cycloalkanes and aromatic compounds |
136 |
8.1 |
acyclic carbon hydrogen radicals |
32 |
5.0 |
hetero atom containing radicals |
23 |
7.5 |
Table 5. Classes of organic compounds and root main square errors (RMS in kJ/mol)
Scope and Limitations
Presently, the method has been parameterized for
Parameters are available for molecules containing C, H, O, N, S, P, F, Cl, Br, I atoms.
Applications
The enthalpy inherent in a compound is a fundamental factor determining its stability and chemical behaviour. Its experimental determination is tedious and time-consuming. Thus, an estimation scheme is very valuable.
The values of the heats of formation of starting materials (SM) and products (P) of a reaction can be used to calculate the heat of reaction.
Thus, the thermochemistry of a process, whether it is exothermic or endothermic, can be determined.
References