# The NIST Structures and Properties Group Additivity Model

The Structures and Properties software fully implements Benson's Group Additivity method[1,2, 3] for estimating gas phase enthalpies of formation, entropies and heat capacities. The implementation includes a variety of corrections, including ring strain, symmetry and non-nearest neighbor effects such as cis, gauche and ortho interactions. Benson's group values are used except when more recent data call for significant changes or where it was necessary to compensate for differences in computed symmetry numbers (discussed below). Some entropy and heat capacity group values missing from Benson's tables are taken from the DIPPR Data Evaluation Handbook[4].

Based primarily on more recently reported data, about 30 new groups have been assigned enthalpy of formation values and nearly 40 new ring corrections were added[5]. The principal source of experimental data for the new groups and ring corrections was "Thermochemical Data of Organic Compounds"[6]. The treatment of symmetry and equivalent isomers is generally the same as Benson's, but differs in some respects, as discussed later in this section.

For flexible ring systems and trivalent nitrogen compounds the program occasionally gives values different from those recommended by Benson. This is done intentionally to predict more reliably entropies of ring systems for which no data exists, although agreement for a limited number of known compounds (some substituted cyclohexanes) may be slightly degraded. The rationale for our choice of symmetry numbers is given below.

Benson's "whole molecule" corrections to the entropy for symmetry (σ) and for numbers of equivalent optical isomers (n) require an understanding of the molecular conformation, which often is not available. Therefore, such corrections can be difficult to apply, especially for flexible, cyclic molecules.

For rigid molecules, the entropy correction is -Rln(σ/n), where σ is the number of equivalent orientations of the molecule and n is the number of distinguishable, but equally stable optical isomers. A minor complexity arises when there are equivalent stereocenters. In this case, isomeric molecules with different optical isomers (diastereomers) may have different rotational symmetry numbers. The program distinguishes diastereomers and sets n=2 if a molecule and its mirror image are not superimposable. Free rotation around single bonds and rapid conformational inversion are assumed.

Corrections arising from simple internal rotation are also straightforward; here the internal rotation symmetry number is used.

Problems arise for highly hindered rotations, inversion (as in ammonia) and ring puckering modes. If barriers are sufficiently high, Benson uses the most stable conformer in calculating symmetry numbers. Hence cyclobutane and cyclopentane, because of rapid conformational change, are assigned symmetry numbers as if they were planar (8 and 10). But cyclohexane and cycloheptane are assigned values of 6 and 1, reflecting the symmetry of the conformer presumed to be most stable. Also ammonia is assigned a value of 3 because its inversion is slower than its rotation.

A major practical problem arises in the application of these corrections. There is no way to predict these barriers in complex molecules or to estimate the stabilities of the various conformers to a useful level of accuracy. Moreover, for substituted rings larger than cyclohexane little reliable information on conformations is available. Note that ring corrections are really used for estimates of SUBSTITUTED compounds; the entropy for the unsubstituted ring is generally the source of the correction.

A theoretical problem also exists. By using rigid conformers to assign symmetry numbers, the effective indistinguishability of H-atoms in molecules such as cyclohexane and cycloheptane are not properly accounted for. We illustrate this with a hypothetical disproportionation reaction:

cyclo-C_{3}H_{5}D + cyclo-C_{7}H_{14} =
cyclo-C_{3}H_{6} + cyclo-C_{7}H_{13}D

symmetry numbers | ||||
---|---|---|---|---|

Benson | 1 | 1 | 6 | 1 |

S&P | 1 | 14 | 6 | 1 |

Using Benson's symmetry corrections, the equilibrium constant is predicted to be 1/6. On a purely statistical basis, however, all H-atom positions are equivalent and the ratio should be 14/6 = 2 1/3.

On the other hand, Benson's correction for cyclohexane (6 instead of a statistical value of 12) predicts entropies of substituted cyclohexanes exceptionally well. This appears to be due to the preference of alkyl substitution at only half of the positions in cyclohexane (the equatorial positions). This factor, however, is really a consequence of steric interactions and should not be built into symmetry corrections.

For these reasons, the program calculates symmetry corrections assuming facile interconversion of conformers (and inversion of amines). Simply stated, the estimation calculations of the program assume monocyclic rings and amines to be flat. Group values which were based on molecules for which Benson used different data from that which we used were adjusted to preserve predictive accuracy.

It is important to note, however, that in almost all cases the differences in symmetry numbers used here and those used by Benson result in estimated data values that differ by no more than a factor of Rln2, and often differ not at all. This variation is virtually always smaller than uncertainties arising from estimates of enthalpies of formation.

- S.W. Benson, "Thermochemical Kinetics, 2nd Ed.", John Wiley & Sons, New York, 1976.
- R.C. Reid, J.M., Prausnitz and B.E. Poling "The Properties of Gases and Liquids, 4th Ed.", McGraw-Hill Book Company, 1987.
- W.J. Lyman, W.F. Reehl and D.H. Rosenblatt, "Handbook of Chemical Property Estimation Methods. Environmental Behavior of Environmental Compounds", McGraw-Hill Book Company, 1982.
- AIChE Design Institute for Physical Property Project, Property Estimation Handbook, American Institute of Chemical Engineers, 1987.
- NIST Standard Reference Database 25: NIST Structures and Properties Database and Estimation Program, software by Stephen E. Stein, Johannes M. Rukkers, and Robert L. Brown, 1991.
- J.B. Pedley, R.D. Naylor and S.P. Rylance, "Thermochemical Data of Organic Compounds", Chapman and Hall, 1986.