Charles F. Cooper' University of Missourl-Rolla Roila, MO 65401
Quantitative Hydrocarbon Energies From the PMO Method
Applications of Dewar's perturbational molecular orbital (PMO) method (I) have been reviewed previously in this Journal (2.31 and have dealt nrimarilv with the aualitative ruther I han any pnssil~lcquantitntive applicatims, no doubt 1,) dent~msrratethat the 1'110 method is a viable alterttative to the still more widely used resonance theory. That the method can be used, however, to calculate quantitative heats of atomizations of conjugated hydrocarbons has recently been shown (4). Such calculations not only can further demonstrate the power of the PMO technique itself, but also hopefully will stimulate interest in more sophisticated molecular orbital techniques and quantum mechanical applications. To take full advantage of the simplicity of the original PMO method it must be realized that the PMO resonance energy is merely a summation of 1st order perturbational terms of rine closure. Unlike other MO methods. this extra enerev of stahization (or destabilization) can be calculated direct& by PMO techniaues. Bond enereies can then he summed to oble possrsi tain a hyl~otlleticalenrrpy which tht: m o l e r ~ ~would i t the rrwn;tnce enrrys (H.C:.) w r i . Yero. ;and by addinr the resonance energy calcdated earlier to this ad&tive energy, the total heat of atomization can be computed. Large molecules will have rather complex resonance energies whLh must he derived from simoler monocvclic comoounds. Once a complex non-additive energy hasbeen evaiuated, however, it in turn can he used further to form the basis of even larger and more complex molecules. The technique is outlined becow and parameters are provided in Table 1.Several examples will subsequently be provided for clarification. Also, it will be assumed that the reader is familiar with the PMO method, or if not, can readily familiarize himself with the technique by consulting the references cited. (1) The molecule should be first evaluated by qualitative PMO ring analysis to determine how many, if any, aromatic, nonaromatic,and anti-aromatic portions are present. Any aromatic or anti-aromatic portions will have non-additive energies, but non-aromatic energies (R.E. = 0) can be calculated by merely summing the energies provided in Table 1for the correct number of double and single bonds.
Table 1. Data for Calculatlna Heats of Atomization Bond C=C C-C C-H
Energy (eV)
(conjugated) Alternative Parametersa
C-C C-H
~~~
Figure 1. Benzene. 568 / Journal of Chemical Education
4.7409 4.6375 8 = 0.8673 eV in all cases
Use of these parameters eliminates the need for assignment of single and double carbon carbon bonds when calculating reference structure energids. It is a theoretically justifiable method (9).
Figure 2. Napthalene
1 Present address: Department of Chemistry, University of Minnesota. Minnea~olis.MN 55455. ~i'nimizine'fi~ae'isalso chosen for ealculatine a r* transitions and rl~c trcm ~ I I O I ! I V + and i ~ n thia g methwl uiiorming thr R.S pair rhrreiorr rrr.dins ~ m r i ~ t e nnriynell 8% hemy thr m w throretic~ll) iustifiahle mode (8).
-
5.5409 4.3409 4.4375
-
Figure 3. Phenanthrene and anthracene.
Table 2.
Compound
Carbon Bonds (0:Double bond S: Single Bond)
Total Energies for Conlugated Hydrocarbons PMO R.E. (Bunits)
Benzene
6H
Napthalene
8H
Strain Energy (ev)
PMO
IOH 10H 1OH 12H
12H
Chrysene
12H
1.3-Buiadiene
6H 12H 10H
Stilbene Biphenyl Biphenylene
8H
Acenapthylene
8H
Fluaranthene
10H
8H
Cyclobutadiene
4H
Fulvene
6H
Pentalene
6H
8H
Experimental values are those listed in references (5)and (6).
(2) If the s energy of the molecule is "on-additive, the R, S division .~ this will involve is determined to provide the minimum 6 E ~ sUsually two, three, or possibly mare points of union. The compound is then examined t o see if partial union along the same lines can form an acyclicsystem whose energy can he calculated from the union of two even alternate hydrocarbons a t one point of union. (3) If more than oneacyclieprecursor appears to beavailable from the above stipulations, the one providing minimum 6ERs of ring closure is chosen. In addition only the ring through which the R, S division is made should have its aromatic character altered in this precursor. ( 4 ) The acyclic structure's r energy is merely the sum of appropriate even alternate energies plus the required number of conjugated "single" bonds. Usually even-alternate systems are united a t one point of union to form the acyclic precursor, but in some cases union at more than one point is acceptable if it can be proven that the ring thus formed is non-aromatic by PMO ring analysis. (51 If it is evident that the acyclic precursor itself contains nonadditive portions, the resonance energies of these portions should be calculated as if they were separate molecules. (6) In the case of anti-aromatic compounds which often have several 6 E ~values s equal to zero, the R,S pair is chosen such that the resonance energy is the least negative. (7) If ~ E R cannot S be minimized to meet the above criteria, the energy of the compound may be calculable from an isomer whose nlrrr.tr K,S pair ic identical w e thr anthrscene exnrnpk I,elow.. If thw IS n
