J. Phys. Chem. 1990, 94, 6637-6641 nm has a geometry such that the two sublevels separated by 2E are contaminated with equal amounts of singlet character and therefore they both have the same total decay rates. For that conformer, the mixing of these two sublevels under a weak magnetic field will not alter the fluorescence decay curve.
Conclusion The fluorescence spectra of 31- and '2-NPCs dispersed in liquid and solid solutions have been studied as a function of temperature, concentration, host and sample history by laser flash photolysis and conventional spectroscopy. The data show that the spectroscopic properties of these carbenes are mainly controlled by the naphthalene chromophore. In particular, the high-resolution fluorescence spectra of 32-NPC in Shpolskii matrices at 15 K can be analyzed by using the modes and ground-state frequencies of the naphthalene molecule. This is another application of the method of isodynamic molecules, first established for benzyl type radicals20 and then used to analyze the fluorescence spectra of m-xylylene biradicals and jDPC. As for 3DPC in Shpolskii matrices, the fluorescence spectra of '1- and '2-NPCs in the same host present broad and sharp spectra. The broad spectra are (20) Grajcar, L.; Leach, S. J . Chim. Phys. Phys.-Chim. Biol. 1964, 61, 1523.
6637
assumed to be due to carbenes located in particular matrix sites where their geometry may change upon excitation. Such spectra appear when the carbene contains two aromatic groups that are mobile with respect to each other. They are absent in the fluorescence spectra of dibenzocycloheptadienylidene where the two benzene rings are linked by an ethano bridge. The sharp bands may correspond to carbenes trapped in sites in which little geometric change is possible upon excitation. The decays of 32-NPC measured on the two sharp fluorescence origins at 588.7 and 600.1 nm are similar. In the presence of a 220-G magnetic field, however, the decay measured at 600.1 nm is altered while that measured at 588.7 nm remains unchanged. In both cases, the decays are attributed to the fluorescence from independent TI sublevels at a rate faster than the rate of spinlattice relaxation. The emissions starting at 588.7 and 600.1 nm are tentatively assigned to the syn and anti conformers of 2-NPC. In the conformer that fluorescences at 600.1 nm, the decay is altered because the weak magnetic field mixes the two sublevels, separated by 2E, which decay with different total rates. In the conformer that emits at 588.7 nm, the decay remains unchanged because the field mixes two sublevels that probably decay with the same total rate. Registry NO. 1, 841-86-1; 2, 1029-73-8; I-NPC, 1151 10-18-4; 2-NPC, 54031-13-9.
Ab Initio Heats of Formation of Medium-Sized Hydrocarbons. 12. 6-316" Studies of the Benzenoid Aromatics Rosalie C. Peck, Jerome M. Schulman,* and Raymond L. Disch Department of Chemistry, Queens College, City University of New York, Flushing, New York 11367 (Received: January 8, 1990; In Final Form: March 15, 1990)
The geometries and energies of 16 aromatic hydrocarbons are obtained from ab initio molecular orbital calculations at the 6-31G* SCF level. The energies are used to derive group equivalents that enable calculation of accurate heats of formation. Several applications of the group equivalents are described.
Ab initio molecular orbital theory provides an important and practicable framework for the study of molecular thermochemistry. Recent work has shown the feasibility of extending this method to the benzenoid aromatics in order to provide accurate heats of formation using the ab initio total energies and two types of newly derived aromatic group equivalents.' The previous study was based upon geometries optimized in the minimal STO-3G basis set.* In this paper we present optimized 6-31G*2 S C F geometries and energies of 16 aromatic hydrocarbons. New aromatic group equivalents are obtained for the 6-31G* basis set and several new applications of the method are described.
Geometries The geometries of the molecules shown in Chart I were optimized at the 6-31G* S C F level in the symmetries described in our earlier study.' The 6-3 lG*CC and CH bond lengths are given in Table I. The rms deviation from experiment for 101 CC bond lengths is 0.016 A, compared with 0.019 8, at the STO-3G level. Cartesian coordinates for the molecules are given in the supplementary material. All of the molecules except 3,4-benzophenanthrene and corannulene are planar. Values for the seven independent dihedral angles of benzophenanthrene in C2symmetry (Figure 1) are given ( I ) Schulman, J. M.; Peck, R. C.; Disch, R. L. J . Am. Chem. SOC.1989,
in Table 11. The experimental angles, obtained by X-ray diff r a ~ t i o n show , ~ significant distortions of the structure from C2 symmetry, due perhaps to thermal effects or packing forces. The 6-31G* angles differ from the averages of their counterpartsvalues that should be equal in C2 symmetry-by less than 2'. It is interesting that even with its nonplanar structure, benzophenanthrene has a AHf' only 7 kcal/mol greater than that of chrysene. The bond lengths and angles of corannulene in its bowl-shaped C,, form (Figure 2) are in good agreement with the experimental X-ray values4 The angles A, B, C, and D (indicated in Figure 2) describing the deviation of its carbon skeleton from planarity are calculated (and measured4) to be 10.0 (10.4)', 25.5 (26.8)', 21.1 (22.4)', and 12.0 (11.6)'. In optimizing the geometry of acenaphthene, we assumed a C , structure. This assumption is supported by S C F calculation of structures slightly distorted from C , symmetry according to the lowest frequency (a2)coordinate, which is predominantly twisting of the methylene groups. At the STO-3G level, there is a small increase in energy; at the 3-21G2 level, there is no significant change. Thus the energetic consequences of the twisting of the methylene carbons out of plane are insignificant. A C , structure was also found in a recent neutron diffraction study in the solid (3) Hirshfeld, F. L.; Sandler, S.; Schmidt, G. M. J. J . Chem. SOC.1963,
111, 5675.
2108.
(2) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A . A6 lnirio Molecular Orbird Theory; John Wiley and Sons: New York, 1986.
(4) (a) Barth, W. E.; Lawton, R.G. J . Am. Chem. SOC.1971, 93, 1730. (b) Hanson, J. C.; Nordman, C. E. Acra Crysrallogr. 1976, B32, 1147.
0022-3654190J 2094-6631$02.50/0
0 1990 American Chemical Society
6638 The Journal of Physical Chemistry, Vol. 94, No. 17, 1990 TABLE I: CC Bond Lengths molecule bond benzene a naphthalene a b C
d a b
azulene
C
d e f a b
biphenylene
C
acenaphth yleneb
d e a b C
d e f g
acenaph thene'
h a b C
d e f g
h a b
anthracene
C
phenanthrene
d e a b C
d e f g
h I
pyrene
a b C
d e
f
Peck e t al.
(A) STO-3G 1.387 1.425 1.353 1.432 1.405 1.391 1.396 1.392 1.389 1.391 1.502 1.426 1.367 1.353 1.426 1.516 1.331 1.495 1.357 1.435 1.360 1.436 1.377 1.421 1.567 1.532 1.354 1.432 1.359 1.433 1.388 1.418 1.444 1.341 I .451 1.425 1.393 1.409 1.364 1.418 I .402 1.473 1.334 1.454 1.417 I .363 1.385 1.395 1.462 1.333 1.413 1.446
6-31G" experiment" 1.386 1.399 1.416 1.412 1.358 1.371 1.420 1.422 1.409 1.420 1.393 1.399 1.395 1.418 1.385 1.383 1.387 1.406 1.388 1.403 1.485 1 ,501 1.417 1.419 1.373 1.385 1.357 1.372 1.413 1.426 1.508 1.514 1.340 1.395 1.466 1.480 1.360 1.381 1.424 1.427 1.382 1.366 1.425 1.433 1.378 1.386 1.410 1.441 1.562 1.567 1.519 1.501 1.359 1.375 1.423 1.423 1.365 1.382 1.421 1.421 1.392 1.391 1.416 1.408 1.432 I ,418 1.347 1.375 I .444 1.436 1.424 1.433 1.405 1.389 1.394 1.402 1.384 1.367 I ,411 1.409 1.404 1.420 1.461 1.465 1.350 1.339 1.440 1.453 1.409 1.423 1.365 1.386 1.384 1.395 1.391 1.406 1.446 1.438 1.339 1.367 1.411 1.425 1.432 1.430
molecule triphenylene
bond a b C
chrysene
d e a b C
3.4-benzophenanthrene
d e f g h i j k a b C
d e f g
h I
j
k
tetracene
a b C
d e f perylene
g
a b C
d e
f corannulene
g
a b C
coronened
d a b C
d
STO-3G 1.398 1.369 1.411 1.402 1.485 1.414 1.360 1.425 1.402 1.464 1.340 1.442 1.422 1.358 1.446 1.390 1.414 1.360 1.427 1.407 1.470 1.338 1.444 1.423 1.359 1.445 1.389 1.454 1.336 1.460 1.442 1.371 1.416 1.427 1.353 1.417 1.367 1.440 1.410 1.427 1.499 1.363 1.462 1.361 1.423 1.349 1.437 1.396 1.438
6-31G* exDeriment' 1.392 1.397 1.381 1.369 1.407 1.410 1.413 1.401 1.472 1.458 1.394 1.406 1.381 1.364 1.409 1.417 1.404 1.407 1.453 1.468 1.369 1.344 1.421 1.429 1.428 1.412 1.362 1.363 1.428 1.434 1.392 1.401 1.409 1.406 1.378 1.365 1.419 1.433 1.431 1.409 1.446 1.459 1.342 1.342 1.443 1.431 1.391 1.412 1.374 1.363 1.432 1.430 1.412 1.391 1.459 1.441 1.381 1.342 1.420 1.444 1.438 1.420 1.374 1.390 1.404 1.408 1.427 1.460 1.370 1.356 1.418 1.407 1.397 1.370 1.425 1.430 1.413 1.424 1.400 1.416 I .471 1.486 1.402 1.370 1.440 1.451 1.391 1.361 1.413 1.413 1.353 1.362 1.424 1.444 1.397 1.381 1.426 1.438
'Except
for acenaphthylene, acenaphthene, and coronene, the experimental values are given by Kao, J.; Allinger, N . L. J . A m . Chem. SOC.1977, 99, 975. bWood, R. A.; Welberry, T. R.; Rae, A. D. J . Chem. SOC.,Perkin Trans. 2 1985, 451. CReference 5. dThe experimental values were obtained by X-ray diffraction: Roberston, J. M.; White, J. G.J . Chem. SOC.1945, 607. The electron-diffraction values of bond lengths a-d are 1.385,1.415,1.430,and 1.430A, respectively: Bastiansen, 0.;Skancke, P. N. Adu. Chem. Phys. 1961, 3, 323.
9
TABLE 11: Dihedral Angles of 3,4-Benzophenanthrene (Degrees) angle 1 ZC-l -2-3
1-2-3-4 2-3-4-4a 3-4-4a-5 6-6a-12b-12c 6a-12b-12c-I 12b-I2~-I-2
'Determined
STO-3G
6-31G*
-0.4 -3.3 1.9 -172.7
-0.1
-11.1
-161.3 179.9
Q
experiment'
-3.6 1.5 -172.5 -1 1.3 -161.2 -179.8
-0.8 -4.1 2.2 -I 72.5 -10.0
-161.4 -177.9
from the Cartesian coordinates of ref 3.
state.' Acenaphthene has a dipole m o m e n t of 0.80 D directed toward t h e methylene groups, consistent with t h e presence of hyperconjugation. ( 5 ) Hazell, A. C.; Hazell, R. G.;Nsrskov-Lauritsen, L.; Briant, C. E.; Jones, D.W . Aria Cryslallogr. 1986, C42, 690.
Figure 1. Perspective drawing of 3,4-benzophenanthrene optimized in the 6-31GS basis.
Energies, T h e 6-31G* SCF energies of the 16 aromatic hydrocarbons a r e given in T a b l e 111. T w o a r o m a t i c group equivalents, denoted GE[=C,
