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457265 Demonstration of the Equivalence of Ring-Additivity and Group-Contribution Methods for Properties of Unsubstituted Polycyclic Aromatic Hydrocarbons (PAH)

In the present work, a new ring-additivity method for the estimation of pure-component properties of unsubstituted benzenoid PAH (polycyclic aromatic hydrocarbons containing only 6-membered rings, also called PAH6) is shown to be equivalent to all other known group-additivity/group-contribution estimation methods against which direct comparisons can be made.

There are only 12 ring groups for PAH6. The original notation of Gutman and Cyvin [1] uses the letter L, A, or P followed by the number of rings with which it is fused (from 1 to 6). For the cases of being fused with 1, 5, and 6 rings, there is no ambiguity, so they are only labeled with L; for 2, 3, or 4 rings, there are three possible configurations. Their simplified numbering scheme [2] only uses the numbers 1 through 12. In previous work [3], a nomenclature was developed using H to denote a 6-sided central ring, followed by the number of rings fused to it; for the cases of 2-4 rings fused to the central ring, this is followed by a dash then a number indicating the location of the rings. The notation is designed to facilitate computer implementation of the ring additivity method.

There is are a great many group-contribution (GC) methods for determining pure-component properties. The majority of those for critical properties only use two groups ACH and AC (or an atom-additivity method which can be converted to these groups, such as in Wilson and Jasperson), such as those of Joback, Forman and Thodos, Somayajulu, Constantinou and Gani, and Nannoolal _{x}H_{y}, # ACH groups = y, #AC groups = x-y. The number of rings n = 1 + (#AC/2).

Avaullée

Each of the 12 ring groups is the following sum of the contributions of the ACH, ACp, and ACi groups: #ACH + #ACp/2 + #ACi/3, plus additional groups specific to the estimation technique. Each of the 12 groups then is the equivalent to anywhere from 2 to 5 ACH and AC groups. In this manner, the ring groups are directly equivalent to all of the above-cited GC methods.

The sets of groups which have been developed to estimate thermochemical properties of PAH (ΔH, S, Cp) are significantly more detailed than those in the methods used above. The method of Benson (exemplified here by Stein

For the PAH6 ring groups to accommodate any of the additional levels of complexity in splitting the AC groups into groups besides ACp and ACi, the types and locations of rings fused to a given ring group must be considered. Otherwise, some of the atom locations have ambiguous as group assignments as follows: (1) AC1 or AC2, (2) AC2 or AC3p, or (3) AC3i1 or AC3i2. This refinement has been done with little increase in computational difficulty, again leading to a a one-to-one correspondence between the new ring-additivity method and these more detailed group-contribution methods.

On the surface, it might seem to be adding an unnecessary level of complexity to group contribution methods by switching to groups consisting of entire rings, especially given the decades-long use of the approaches for PAH6. However, GC methods have had limited success in predicting properties for PAH containing both 5- and 6-membered rings (PAH5/6), especially for those with curvature induced by internal 5-membered rings [13,14].

A ring-additivity method for PAH5/6 (those containing both 5- and 6-membered rings) and fullerenes (closed-cage all-carbon molecules containing both 5- and 6-membered rings) might prove more successful in predicting the properties of those molecules than previous GC methods, since the ring groups would include much more information about the types of curvature produced by the proximity of atoms at the junction of two 6-membered rings and one 5-membered ring.

However, even if only those PAH5/6 and fullerene structures are considered which obey the "isolated pentagon rule" (IPR), 50 new ring-additivity groups will need to be added to the 12 PAH6 ring groups to describe these compounds [3]. It was therefore thought prudent to first explore the feasibility of using the simpler PAH6 ring additivity method. The current work demonstrates how theoretically sound and readily applicable this method is to benzenoid PAH. Even though the equivalence between the new PAH6 ring additivity method has been demonstrated, further testing is in progress to see if new insights can be gained by its implementation. Development of the PAH5/6 ring additivity method is also underway.

Furthermore, the current PAH6 ring groups can serve as an excellent starting point for developing groups for substituted PAH6, since the rings will carry information about the bonding environment at the location of the substituents. Further work along these lines is warranted.

References:

[1] Gutman, I.; Cyvin, S.J. (1989) "Introduction to the Theory of Benzenoid Hydrocarbons", Springer-Verlag, New York.

[2] Gutman, I.; Furtula, B.; Radenković, S. (2004) "Relation between Pauling and Coulson Bond Orders in Benzenoid Hydrocarbons, *Z.Naturforsch.*, **59a**, 699-704.

[3] Pope, C. (2015) "Estimation of Diffusion Coefficients of Polycyclic Aromatic Hydrocarbons (PAH) and Fullerenes", poster presented at the American Institute of Chemical Engineers Annual Meeting, November 2015, Salt Lake City, UT. See also references cited therein.

[4] Pope, C.J. "Estimation of Normal Boiling Point, Critical Properties, and Lennard-Jones ---Parameters for Polycyclic Aromatic Hydrocarbons and Fullerenes", poster presented at the American Institute of Chemical Engineers Annual Meeting, November 2013, San Francisco, CA. See also references cited therein.

[5] Avaullée, L.; Trassy, L; Neau, E.; Jaubert, J.N. (1997) "Thermodynamic modeling for petroleum fluids I. Equation of state and group contribution for the estimation of thermodynamic parameters of heavy hydrocarbons", *Fluid Phase Equil.*, **139**:155-170.

[6] Dias, J.R. (1987) "Handbook of Polycyclic Hydrocarbons Part A: Benzenoid Hydrocarbons", Elsevier, New York, pp. 122-123.

[7] Marrero, J.; Gani, R. (2001) "Group-contribution based estimation of pure component properties", *Fluid Phase Equil.*, **183–184**:183–208.

[8] Stein, S.E.; Golden, D.M.; Benson, S.W. (1977) "Predictive Scheme for Thermochemical Properties of Polycyclic Aromatic Hydrocarbons", *J.Phys.Chem.*, **81**:314-317.

[9] Herndon, W. C.; Nowak, P. C.; Connor, D. A.; Lin, P. (1992) "Empirical Model Calculations for Thermodynamic and Structural Properties of Condensed Polycyclic Aromatic Hydrocarbons", *J.Am.Chem.Soc.*, **114**:41−47.

[10] Moiseeva, N.F.; Dorofeeva, O.V.; Jorish, V.S. (1989) "Development of Benson Group Additivity Method for Estimation of Ideal Gas Thermodynamic Properties of Polycyclic Aromatic Hydrocarbons", *Thermochim.Acta*, **153**:77−85.

[11] Steele, W.V.; Chirico, R.D.; Nguyen,A.; Hossenlopp, I.A.; Smith, N.K. (1990) "Determination of Ideal-Gas Enthalpies of Formation for Key Compounds", *AIChE Symp.Ser.*, **86**:138−154.

[12] Cohen, N. (1996) "Revised Group Additivity Values for Enthalpies of Formation (at 298 K) of Carbon-Hydrogen and Carbon-Hydrogen-Oxygen Compounds", *J.Phys.Chem.Ref.Data*, **25**:1411−1481.

[13] Pope, C.J.; Howard, J.B. (1995) "Thermochemical Properties of Curved PAH and Fullerenes: A Group Additivity Method Compared with MM3(92) and MOPAC Predictions", *J.Phys.Chem.*, **99**:4306−4316.

[14] Allison, T.C.; Burgess, D.R., Jr. (2015) "First-Principles Prediction of Enthalpies of Formation for Polycyclic Aromatic Hydrocarbons and Derivatives", *J.Phys.Chem.A*, **119**:11329-11365.

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