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4.1 Heats of Formation

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

  1. An Algorithm for Estimating Heats of Reaction
    J. Gasteiger
    Comput. Chem.
    2, 85-88 (1978)
  2. Automatic Estimation of Heats of Atomization and Heats of Reaction
    J. Gasteiger
    Tetrahedron
    35, 1419-1426 (1979)
  3. Critical Evaluation of Additivity Schemes for Estimating Heats of Atomization
    J. Gasteiger, P. Jacob, U. Strauß
    Tetrahedron
    35, 139-146 (1979)
  4. Automatic Estimation of Ring Strain Energies
    J. Gasteiger, O. Dammer
    Tetrahedron
    34, 2939-2945 (1978)

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