(231v) Application of the Marrero and Pardillo Property Estimation Method to Unsubstituted Polycyclic Aromatic Hydrocarbons (PAH) and Fullerenes

The chief problem in applying the Marrero and Pardillo (MP) property estimation method [1,2] to PAH and fullerenes is that due to the presence of resonance structures there are multiple possible ways to define the structure of the molecule, leading to multiple numerical values for predictions of each property estimated.  An approach has been developed for use of the MP method on unsubstituted PAH and fullerenes.  From structural considerations, the number of possible configurations of bonds which need to be considered is decreased dramatically, making the problem tractable.  The method leads to ranges of predicted values for the normal boiling point (T_b), critical temperature (T_c), critical pressure (P_c), and critical volume (V_c) for each molecule.  The fractional ranges of values are less than 0.7% for T_b, 2.0% for T_c (except for the largest kata-condensed acenes considered, for which the range is less than 10%), 10.0% for P_c (except for the largest zig-zag kata-condensed acenes), and 2.2% for V_c.  While these ranges might be larger than desirable, the present work points towards possible improvement of the MP method.  Considerations for using the method on substituted PAH are discussed.

DISCUSSION

The Marrero and Pardillo property estimation method [1,2] is unique among group contribution (GC) based schemes in that it is a "group-interaction contribution (GIC)" [1] approach.  Each pair of groups connected by a covalent bond, as well as the bond order (single, double, triple), defines a unique group interaction:  in effect, it is a bond additivity method.

With the exception of the atom additivity method by Wilson and Jasperson [2], other commonly-used techniques [2-13] count multivalent atoms as the main type of group, often with additional corrections for other features which can usually be discerned by inspection of the molecular structure, such as whether the atom is a part of a ring, size and arrangement of rings, interactions between groups, and so on.

All of the PAH considered have the maximum number of conjugated non-adjacent double bonds possible, with all the carbon atoms being sp² hybridized. In that sense, all the carbon atoms are involved in an extended aromatic π-bond structure.  There are also no structures containing a biphenyl-type sigma bond around which rotation can occur.

Four series of unsubstituted PAH are considered in the present work:

(1) linear acenes:  kata-condensed benzenoid PAH with 1 to 23 aromatic rings (C_2+4nH_4+2n).  The first four compounds beyond benzene in this series are naphthalene, anthracene, tetracene, and pentacene.

(2) zig-zag acenes:  kata-condensed benzenoid PAH with 1 to 23 aromatic rings (C_2+4nH_4+2n).  The first four compounds beyond benzene in this series are naphthalene, phenanthrene, chrysene, and picene.

(3) peri-condensed PAH:  benzenoid PAH which have tightly packed ring structures (like chicken wire), extending from benzene to circumcircumcoronene (C₉₆H₂₄ -- 37 aromatic rings, 1177 amu), including the first ten compounds in the one-isomer series of Dias [14].  This series of PAH is representative of those found under combustion conditions.

(4) the fullerene formation mechanism (FFM) series:  PAH containing both 5- and 6- membered rings (PAH5/6), starting with acenaphthalene (C₁₂H₈) and extending to the fullerene C₆₀, which have been previously proposed as intermediates in the formation of C₆₀ in flames [15]. The majority of the PAH in the FFM series have the most condensed structures possible for PAH5/6 [16]; all of the structures obey the "isolated pentagon rule" [17].

Polycyclic aromatic hydrocarbons (PAH) always have multiple resonance (Kekulé) structures.  (Otherwise, by definition, they would not be aromatic.)  Therefore, in the general case, there would not be a unique set of numbers of group interactions which could fully describe a PAH; there would be multiple numerical values for the resulting sum of the GIC values, yielding different values for the estimated properties.  In the most extreme conceivable case, the number of values for the predicted properties for a given PAH could be as many as K, the number of possible Kekulé structures, which can be exceedingly large.  The values of K for the largest PAH in the given series are:  (1) 24; (2) unknown [but can be calculated by methods described in reference 18]; (3) 232,848 [14]; (4) 12,500 [19].  Clearly, there is a need to simplify application of the MP method to PAH if there is any hope of using it.

For the PAH considered, only six types of group interactions exist.  In the numbering and notation of reference 1, followed by the notation used here, they are:

#141      =C< [r] & =C< [r]               G01

#139      >C[=] [r] & >C[=] [r]        G02

#134      =CH- [r] & =C< [r]             G11

#131      -CH[=] [r] & >C[=] [r]      G12

#133      =CH- [r] & =CH- [r]           G21

#130      -CH[=] [r] & -CH[=] [r]    G22

The total number of group interactions (= the number of bound pairs of carbon atoms) for a given PAH of the kinds considered with an empirical formula of C_xH_y would be (3x-y)/2.  From the properties of benzenoid PAH, two more relations linking the relative numbers of group interactions can be found [18].  Since all the C-atoms are sp², the total number of group interactions involving double bonds (G02+G12+G22) would be equal to x/2.  An additional relation for bonds on the periphery was found in the present work.  Therefore, the problem of finding how many group interactions of each type are contained in a given benzenoid PAH reduces to a linear algebra problem of five equations in six unknowns.  The required inputs are the empirical formula (x, y) and b, which is the number of pairs of linked C atoms on the periphery of the PAH.  The value of b is related to the number of bay, cove, and fjord structures [18] in the molecule.

The group G22 (a double bond between two -CH= groups) is chosen as the independent variable for convenience.  From structural considerations, upper and lower bounds for the number of G22 contributions can be determined by inspection.  For example, there are only 6 bonded pairs of =CH- groups in circumcircumcoronene (C₉₆H₂₄), making the conceivable range of values for G22 zero to 6.  A slightly more detailed analysis of the possible of arrangements of double bonds on the periphery further delimits the range by showing that the minimum possible number of G22 groups interactions is 3.  There are only four possible solutions -- a lot fewer than 232,848!  Similar treatment of all the benzenoid PAH considered yields similarly tractable results.  The only difference in extending the method to PAH5/6 is that the number of 5-membered-rings is also an input.  The quality of the results is briefly described in the summary above.

REFERENCES

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