J . Phys. Chem. 1989, 93, 139-144 to explain. However, if this deuterium is located on the water molecule, then isotopic mode mixing17J8 in the asymmetrical complex could account for the observed behavior. The transition frequency is the same when both two and three deuteriums are present, and its shift, relative to the fully protonated complex, corresponds to a nearly pure hydrogen motion. This suggests that when two deuteriums are present in the complex, both are bonded directly to the water. This again is consistent with the isotopic shifts of the stretching vibration.
Conclusions Measurements of the effects of isotopic substitution on the radiationless decay of the vibrationless level of the phenol SI state (17) Wiberg, K. B.; Walters, V. A.; Wong, K. N.; Colson, S. D. J . Phys. Chem. 1984. 88. 6067. ( 1 8) Rava, R: P.; Philis, J. G.; Krogh-Jespersen, K.; Goodman, L. J. Chem. Phys. 1983, 79, 4664.
139
show a dramatic reduction in the rate of internal conversion and a lesser reduction in the rate of intersystem crossing. Similar but smaller changes are observed upon hydrogen bonding of water to the OH hydrogen. It is likely that these two effects have the same origin, namely, reduction in the effectiveness of the O H stretching mode as an acceptor mode for radiationless transitions. The low-frequency, phenol-water "complex" modes are discussed in terms of the effects of substitution. Successive isotopic substitution is found to first replace the water hydrogens and then that of the phenol OH. Isotopic shifts are used to confirm the assignments of the lowest two observed modes in phenol-HzO (156 cm-' for the totally symmetric hydrogen bond stretch and 121 cm-I for a totally symmetric hydrogen wagging mode). Some isotopic species also show Fermi resonances, which are analyzed.
Acknowledgment. This research was supported by the National Institutes of Health. Registry No. HzO, 7732-18-5; D2,7782-39-0; phenol, 108-95-2.
Structure and Properties of C,H,+ Cations Alan Cameron, Jerzy Leszczynski, Michael C. Zerner,* Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 3261 1
and Brian Weiner Department of Physics, Penn State University, Dubois, Pennsylvania 15801 (Received: April 25, 1988)
Two possible mechanisms have been suggested for the formation of soot in fuel-rich flames and exhausts. One of these involves precursors that are small radicals, the other small carbocations. We begin here a quantum chemical study of the latter mechanism with an examination of the isomers of C3H3+, an ion observed in abundance in sooting flames. We uncover four stable singlet structures and suggest that structures computed stable at lower levels of theory are artifacts of those calculations. We calculate that the cyclic isomer is most stable, followed by the linear propargyl cation with an estimated heat of formation 27.7 kcal/mol greater. In order to characterize these tautomers for possible identification in sooting environmentswe calculate their vibrational and electronic spectra.
Introduction Two possible mechanism have been proposed for the formation of soot in fuel-rich flames. One mechanism invokes radical reactions, the other ion/molecule reactions involving small ions. The latter mechanism has been advanced by the observation that C3H3+ is the most intense ion observed in sooting flames'V2 and motivates this theoretical study along with experimental studies of ion/ molecule reactions involving small hydrocarbon ions using Fourier transform ion cyclotron resonance techniques3 A good characterization of possible C3H3+tautomers would be helpful in identifying their presence in sooting flames. The presence of such species is experimentally determined through mass spectroscopic techniques and the techniques presently being used cannot distinguish isomeric structures unambiguously. In the ion/molecule soot formation scheme condensation and condensation-elimination reactions of C3H3+with acetylene and polyacetylenes are postulated to occur rapidly with eventual formation of polycyclic aromatic hydrocarbon ions of mass 500-1000 d a l t o n ~ .Various ~ ~ ~ mass spectrometric studies suggest ( I ) Goodings, J. M.; Bohme, D. K.; Ng, C. W. Combust. Name 1979,36, 27. (2) Olson, D. B.; Calcote, H. F. Symp. (hit.) Combust., [Proc.] 1981, lath, 453. (3) See, for example: Ozturk, F.; Baykut, G.; Moini, M.; Eyler, J. R., J . Phys. Chem. 1987, 91, 4360. (4) Calcote, H. F. Combust. Flame 1981, 42, 215. (5) Olson, D. B.; Calcote, H. F. In Particulate Carbon Formation during Combustion; Siegler, D. C., Smith, G. W., Eds.; Plenum: New York, 1981.
0022-3654/89/2093-0139$01,50/0
that C3H3+possesses reactive and nonreactive components. The most stable form of C3H3+,the cyclopropenyliumcation (I), Figure 1, is relatively unreactive toward acetylene and polyacetylenes as well as toward other small hydrocarbon^.^^^ The propargylium cation (11) is considerably more reactive toward C2H2and leads to the formation of C5H3+and C5H5+ions, both with reactive and unreactive components. The propargylium cation (11) is believed to lie some 25 kcal/mo17 higher in energy than the cyclopropenylium cation (I), but this species, as well as others potentially important, might be formed under the reaction conditions observed in sooting flames. We thus embark in this study to uncover possibly reactive species of C3H3+. Studies of larger ions suggested by the ion/molecule soot formation mechanism, C5H3+ and CSHS+,for example, are under way. Carbocations such as C3H3+have been of interest for some time. Cyclopropenylium ions represent the first members of the 2 4n aromatic series and as such have been the object of much theoretical discussion. A rather complete study of the relative stability of many C3H3+structures has been reported by Radom, Hariharan, Pople, and Schleyer.8 Although some of these earlier calculations are of somewhat lesser accuracy than those we report here, in general we agree with their ordering of stabilities and their
+
(6) Symth, K. C.; Lias, S.G.; Auslons, P. Combust. Sci. Technol. 1982, 28, 147.
(7) Lossing, F. P. Can. J. Chem. 1972, 50, 3973. (8) (a) Radom, L.; Hariharan, P. C.; Psple, J. A.; Schleyer, P. v. R. J . Am. Chem. SOC.1976,98, 10. (b) See also: Raghavachari, K.; Whiteside, R. A.; Pople, J. A.; Schleyer, P. v. R. J. Am. Chem. SOC.1981, 103, 5649.
0 1989 American Chemical Society
140 The Journal of Physical Chemistry, Vol. 93, No. I , 1989 TABLE I: Relative Stabilities of C&+
Cameron et al.
Isomers ( a ~ ) ~
I (cyclic (CH),)
I1 (H2-C-C-CH) 0.0564
STO-3G
-1 13.6203'
3-21G
-1 14.3294'
0.0201
6-31GL 6-31G**h
-1 15.0070' -1 15.0133'
0.0559 0.0564
+MP2
-1 15.3494'
0.0526
+MP4
-1 IS.4081'
0.0460
Radom et al.' exptf
0.0548 0.040 f 0.01
IV (HZC-CH-C) s4 (7-1'
111 (H3-C-C-C) s4
0.2900 [0.1831]' 0.2819 [O. 1705Ic [0.1928]' 0.3160 [O. 19351' 0.3253 [0.1873]' 0.2949 [0.1 61 [0.1753]'
(0.1680)
V (cyclic H2CCCH)
(0.1136)
0.1110
0.2049
(0.11 17)
0.0820
0.1991
(0.1413)
0.1104 0.1111
0.20908 0.2236'
0.1283
0.2659
0.1153
0.2261
0.1109
0.2039
1 au = 627.5 kcal/mol. S = singlet, (T) = triplet. 'Calculated total energies. CComplex calculation. dEstimated. "Reference 7. g6-31G1//3-21G. h6-31G**//6-31G*. '6-31G**//3-21G. C3H3PI.
TABLE 11: The Calculated Geometries of the Cyclopropenylium Ion, I, Figure 1 CH, A
cc, A
CCC, deg
INDO
STO-3G
3-21G
6-31G*
1.087 1.386 60
1.095 1.377 60
1.062 1.361 60
1.072 1.349 60
structures, with one exception as discussed later.
Methods The initial structures of this study were obtained through INDO calculation^.^ These geometries were then refined by using the STO-3G, then 3-21G, and finally 6-31G* basis sets advocated by Pople.lo The use of this larger basis set has been prompted by our observation that stable minima at the 3-21G level can become "unstable" transition states at a higher level of calculation. Such a case will occur here. A Broyden-Fletcher-GoldfarbShanno quasi-Newton update procedure was used to obtain all structures",12 with no constrained degrees of freedom. The ab initio calculations were performed with the GAUSSIAN 82 programl3 suitably modified with this search algorithm. All calculations begin with structures of no symmetry; when symmetry was obtained it was as a result of the geometry search. The geometries believed most accurate are those obtained from the 6-31G* calculation, although all the calculated structures are reported for comparisons. Vibrational frequencies were calculated by using both the 3-21G geometries and wave functions and the 6-31G* geometries and wave f ~ n c t i o n s , and ' ~ they are unscaled. When comparing with experiment multiplication by a factor of 0.85 has been found to greatly improve predictions. At optimized 6-3 lG* structures single-point 6-31G** SCF calculations were performed and then corrected through fourth-order in Mdler-Plesset RayleighSchrodinger perturbation theory but leaving the core "electrons" ~ncorre1ated.l~The best calculations on the relative energy of these structures are thus characterized by MP4/6-3 1G**//631G*. The electronic spectra of these optimized structures were estimated by using the INDO-CI spectroscopic (9) Bacon, A. D.; Zerner, M. C. Theor. Chim. Acta 1979, 53, 21. (IO) See, for example: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab-Initio Molecular Orbital Theory; Wiley: New York, 1986. (11) Head, J. D.; Zerner, M. C. Chem. Phys. Lett. 1986, 131, 359. (12) Head, J. D.; Zerner, M. C. Inf. J . Quantum Chem. 1988, 33, 177. (13) Binkley, J. S.; Frisch, M. J.; Defrees, D. J.; Raghavachari, K.; Whiteside, R. A.; Schlegel, H. B.; Fulder, E. M.; Pople, J. A,, Carnegie Mellon University, Pittsburgh, PA 15213. (14) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Int. J. Quantum Chem. 1979, 13, 225. (15) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Inr. J . Quantum Chem. 1978, 14, 545. (16) Ridley, J. E.; Zerner, M. C. Theor. Chim. Acta 1973, 32, 111. (17) Zerner, M . C.; Loew, G . H.; Kirchner, R. F.; Muller-Westerhoff, U. f.J. Am. Chem. SOC.1980, 102, 589.
8. /Reference
nH6
1.072
WH5
Figure 1. Optimized structure (6-31G*) of cyclopropenyl cation (I). C3H3PII.
H5n
HB"
Figure 2. Optimized structure (6-31G*) of propargylium cation (11). C3H3PnI.
H4n
H B "
Figure 3. Optimized structure (6-31G*) of 1-propenyl cation (111). The numbers in brackets are for the triplet.
Results The relative energies obtained for five structures are summarized in Table I. A summary of calculated geometries is given in Figures 1-5 and Tables I1 and VI. As expected, all calculations
Structure and Properties of C3H3+Cations
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 141
C3H3PIV
TABLE I11 The Calculated Geometries of the Propargytium Ion 11, Figure 2
Cl-C2, A C2-C3, A C3-H4, Cl-H5, A H5-Cl-C2, deg
INDO 1.407
STO-3G 1.360
3-21G 1.334
6-31G* 1.342
1.341
1.214 1.091
1.213
1.214
1.061
1.067
1.109 121.1
1.078
1.078
120.5
120.5
1.079 1.091 123.0
TABLE I V The Calculated Geometries of the 1-Propynyl Cation, 111, Figure 3
Cl-C2, A C2-C3, A Cl-H, A H-Cl-C2,
Figure 4. Optimized structure (6-31G*) of prop-2-en-l-yl-3-ylidine
singlet INDO" 3-21Gb 6-31Gb INDOd 1.382 1.418 1.434 1.430 1.242 1.357 1.359 1.272 1.110 1.095 1.091 1.11 110.2 110.2 109.2 108.9
tripletC 3-21G 6-31G* 1.435 1.445 1.267 1.257 1.082 1.082 112.3 111.7
deg
cation (IV).
Two-determinant ROHF optimization. Complex orbital optimization. CUHFcalculations. d A slight break in symmetry.
C3H3PV.
TABLE V The Calculated Geometries of the Prop-2-en- 1-yl-3-ylidine Cation, IV, Figure 4
H5nH6
~
Cl
c2
Figure 5. Optimized structure (3-21G) of cyclopropl-yl-2-ylidinecation (V). Note this structure opens to that of Figure 4 with the 6-31G* basis.
predict the cyclopropenylium ion (I) lowest in energy followed by the propargylium cation (11). The best estimate of the difference in energy between those two structures is 28.9 kcal/mol, in reasonable agreement with the HF16-31G* value of 34.4 kcal/mol calculated by Radom et a1.8aand a 3 1.1 kcal/mol MP4 value estimated by Raghavachari et a1.8busing a 6-31G**//63 lG* level of theory. Correction for zero-point vibrational energy reduces this value to 27.7 kcal/mol, to be compared with an experimental estimate of 25 f 4 kcal/mol.' Structure IV, the prop2-en- 1-yl-3-ylidine cation is calculated next higher in energy, some 72.4 kcal/mol higher than the cyclopropenylium ion, a value reduced to 70.9 kcal/mol when corrected through inclusion of 0.85 times the zero-point vibrational energy. Structure 111, the 1-propynyl cation, possesses C3, symmetry and a pair of degenerate ?r-like orbitals sharing two electrons. Such a situation gives rise to a triplet and three singlets. The lowest energy singlet is calculated by using complex orbitals and is estimated to lie some 101 kcal/mol higher in energy than the cyclopropenylium cation reference. The optimized triplet structure lies at considerably lower energy than the corresponding singlets. This structure is predicted to lie 89 kcal/mol above the cyclopropenylium ion reference, but higher in energy than either of the singlet structures I1 and IV. Comparisons between states of different multiplicities such as we have made here for structure 111 are notoriously difficult for all but the most exacting a b initio theories, as these calculations tend to overstabilize triplet-state energies relative to singlets. Considering the partially filled degenerate orbitals of I11
3t**
-3t qb
3 . t t3- -I-+ t t *c
Jrd
**
*f
the use of complex orbitals approximates the (1/21/2)(+a - +b)
CFC2,A C2-C3, A H5-C1, A H6-C1, 8, H3-C2, 8, H5-CI-H6, H5-CI-C2, Cl-C2-H3, Cl-C2-C4,
deg deg deg deg
STO-3G
3-21G
1.377 1.396
1.372 1.347 1.074
1.102 1.102 1.090 116.9 121.2
123.6 115.8
1.08 1 117.3
120.3 122.9 118.0
1.346 1.077
1.078 1.078 117.0 120.9 125.9 108.0
component of the 'E (the other component is ( 1/21/2)(+c- +d)). The 3A2state is estimated by a U H F calculation on +e the (the other components are +f and (1 /21/2)(+c + +&). Our calculated energy difference between these two states is likely too large. The INDO/S-CI method, however, has been found quite reliable in estimating these differences at fixed geometries. These calculations, performed at the optimized triplet geometry, suggest that the 3A2 state lies only 11 kcal/mol lower than the 'E state and that the 'A, state (1/21/2)(+a +J) lies 11 kcal/mol higher in energy that the 'E. The difference between the ab initio S C F IE - 3A2energy of 32 kcal/mol and that of 11 kcal/mol estimated by the INDO/S calculations corresponds closely to the observation that ab initio calculations of this type tend to artificially favor triplets by about 20 kcal/mol. The cyclic structure V, the cycloprop- 1-yl-2-ylidine cation, is estimated to lie 142.9 kcal/mol above the reference compound I at the 3-21G level. At the 6-31G* level, structure V is not stable and opens to become structure IV. This finding is in contrast to previous studie$ with the inclusion of polarization functions the cyclic form V opens to IV, but the angle that has opened, ClC2C4 of Figure 4, has decreased with this better basis from 118' (3-21G) to 108' (6-31G*), Table V. Structure V has two a-like electrons (a"). A near-lying state with four a-like electrons also is unstable, leading back to the propargylium cation, 11. Other structures have been examined by Radom et aL8 but those are all predicted less stable than those we report here. Although these latter calculations are reported at the Hartree-Fock level, we note from Table I that the use of a slightly better basis set and the inclusion of a fourth-order perturbation theory does not effect the differences in energies by more than about 10%. Note, however, that differences calculated at second order deviate more from the fourth-order results than do the Hartree-Fock differences themselves. The inclusion of polarization functions in the 6-3 1G** calculations preferentially stabilizes the cyclopropenylylium cation (I) and destabilizes structure V. Table I1 and Figure 1 summarize the calculated geometry of cyclopropenylium cation. As is usual, the better basis set, 6-31G*
+
'
1.076
6-31G* 1.378
142
Cameron et al.
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989
although both valence bond structures are present in both calculations. Table IV and Figure 3 summarize the calculated structure of the 1-propynyl cation. The singlet structure is best described as
TABLE VI: The Calculated Geometries of the Cycloprop-1-yl-2-ylidine Cation, V, Figure V INDO STO-3G 3-21G 6-31G* STO-3G' 1.438 b 1.456 Cl-C2, A b 1.478 1.754 b 1.641 C2-C3, A b 1.700 1.465 b 1.530 Cl-C3, b b 1.507 1.076 b 1.104 b 1.112 H3-C2, A 1.098 b 1.109 b 1.102 H5-C1, 8, Cl-CZ-C3,deg b 56.1 53.5 b 58.8 b 54.6 b 54.5 52.1 CZ-C3-Cl,deg 69.4 74.4 66.6 C3-Cl-C2, deg 126.5 145.1 H3-C2-C1, deg 123.9
'From ref
H
\
H-C-C=C:
/
H
with the C-C single bond shortened by hyperconjugation H+
8. *Not stable
H-C
yields shorter bond lengths then does the minimum basis set STO-3G. The INDO results are in good accord. Table I11 and Figure 2 compare the calculations for the propargylium cation. The I N D O and ab initio results suggest different bonding schemes for this ion
/ H
H
H
vs
H
\ H-C-C?C*
H
\C=C=C+-H
=C=C:
The triplet, however, is best described as
ab initio
INDO
+
\
H-C=C=C:
H*
/C * - C C C - H
H+
Table V and Figure 4 give the calculated geometries of the prop-2-en-l-yl-3-ylidinecation (IV). There is a considerable
TABLE VII: Calculated Vibrational Frequencies Using 3-21G Optimized Structures and Wave Functions and 6-31C* Optimized Structures and Wave Functions, in em-'
a2" e'
907.9 1041.8
842.5 1029.2
a3 27
00 6
e"
1136.2
1099.6
00
00
ai e'
1209.2 1373.6
1 164.0 1418.3
00 74
00 04
e'
a,'
1702.3 3466.0
1795.2 3467.5
00 86
53 28
al'
3519.1
3518.5
00
91
0.048
0.0486
Eo, au
351.7 396.4 842.0 1089.1 1182.9 1222.8 1281.5 1613.0 2216.5 3275.2 3380.2 3535.8
280.3 364.2 741.6 1023.9 1131.5 1216.6 1265.1 1611.1 2194.9 3331.1 3443.3 3569.5
0.0464
0.0460
111 (singlet)
I11 (triplet)
e
3-21G 519.1 820.4 1266.4 1560.0 1616.9
6-31G* 306.2 885.7 913.8 1499.2 1484.9
a1 a,
2427.4 3201.9
1814.7 3137.1
49 5 125
I(R) 0 0 0 0 0 0 0 0
e
3296.4
3223.9
55
2
EO,au
0.0488
0.0440
e a,
e a1
00 03 01 01 00 57 00 02 28 101 58 47
45 25 74 02 01 77 06 03 816 16 45 75
Z(IN 5 49 36 24
WR)
a1 e
3-21G 480.9 839.9 1171.1 1542.9 1549.1
41 74 10 76 106
I(R) 79 1 03 2096 103 713
a1 a,
1765.3 3110.2
17 171
1414 166
e
3187.5
38
07
e a1
e
IV a' a" a" a' a' a" a' a' a' a' a' a'
3-21G 337.0 521.9 1024.4 1091.3 1256.0 1298.0 1358.4 1649.3 1699.3 3280.8 3303.3 3409.6
6-31G* 254.6 463.7 996.1 1013.4 1251.4 1265.1 1383.3 1648.4 1685.7 3333.2 3372.8 3444.9
Eo,au
0.046 1
0.0458
V
I(IR)
I(R)
09 11 65 09 13 10 94 254 264 21 61 40
07 02 00 02 11 01 29 15 04 52 63 40
a" a' a a' a" a' a' a' a' a' a" a'
3-21G 157.2 417.5 630.9 935.1 1003.7 1051.3 1194.2 1311.2 1333.0 3087.6 3114.2 3342.5 0.0400
"Not a stable structure, see text. bNumerical force constants. 'The IR intensities are in units of km/mol and the Raman intensity (R) is in A4/amu.
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 143
Structure and Properties of C3H3+Cations TABLE VIII: Calculated Electronic Spectra of C&+ (1000 cm-I) I this work ref 19b ]Al''
56.1 60.6 60.6 64.4 (0.166)' 64.4 (0.166) 62.2 (0.003)
IE''
E' IA
/I
1A It IEff 'A? E'
I1 this work 69.0 71.0 71.0 71.0 84.7 84.7
IA2 'A'
I.42 IBI
'AI 'A2
ref 20
17.9 41 .O (0.092)
18.8 42.2 (0.154)
49.4 52.4 59.6 (0.003) 59.8 (0.807) 14.8
60.1 66.2 (0.000) 73.0 (0.009) 73.8 (0.787)
I11 singlet (IE) 3.8
lA2 'A1
triplet ('A,) 14.4 (0.004) 14.4 (0.004)
'E
IE
18.4 19.6 (0.008) 19.6 (0.008)
'E
23.0 (0.000) 23.0 (0.000)
'E
46.0 (0.000) 46.0 (0.000)
'Al
23.3
'E
39.5 (0.004) 39.5 (0.004)
49.0 (0.000) 58.9 (1.620) -3.8
'A2
IV
V
31.7 (0.019) 35.6 (0.001)
'All
24.7 (0.000) 33.9 (0.024)
35.6 (0.001)
lA//
43.8 (0.030)
44.7 (0.461) 56.1 (0.021)
lA// 1A'
49.9 (0.003) 57.3 (0.114)
65.4 (0.000)
!A'
67.9 (0.180)
66.8 (0.097) 20.3
'All
17.4
45.3 (0.405) 3.8 3.8
'A2
IE
#The numbers in parentheses are oscillator strengths. bEstimated from Figure 6 of ref 19. shortening of the C2-C4 bond when the better basis set is employed, implying a more important role to H,
H
\ +
C , -C$. H
/
+H
H\
than
\ ,,C=ch H
+
/ C:
Table VI and Figure 5 present a summary of our findings for the cycloprop-1-ylidine cation, V. The structure of the figure is that obtained with the 3-21G basis set. As mentioned, this ion (IV) with the structure opens to the prop-2-en-l-yl-3-ylidine better basis. Experimental estimates for the heat of formation of the cyclopropenylium ion range from 256 to 258 kcal/mol with an estimated error of f 3 kcal/m01.~,~*Table I can then be used to estimate the heats of formation of other tautomers of this series. The vibrational frequencies we obtain for these lowest lying conformers of C3H3+are reported in Table VII. They are unscaled and we again remark that multiplication of these frequencies by a factor of about 0.85 often gives better results when compared with experiment. Of interest is the observation that lower frequency modes are most affected by the better basis and are generally decreased. The cyclopropenylium ion (I) has no low-lying frequencies, distinguishing it from the other less stable structures of this study. We note the very low frequency of structure V at the 3-21G level leading to ring opening at the 6-31G* level. The calculated UV-visible spectra of six species are presented in Table VIII. The 3-21G optimized geometries were assumed for INDO/S-CI calculations.'6~17This method has been found accurate for a great many hydrocarbons, and especially so for positively charged species where diffuse states are not important. For comparisons, results of calculations by Tokada and Ohno for the cyclopropenylium ion (I)2o and by Eyler, Oddershede, Sabin, Diercksen, and Gruner for propargylium ion (11)21are included. The former calculations are an ab initio SCF-CI calculation but (18) This is an observation that we have made for many systems; see, for example: Larsson, S.;Staahl, K.; Zerner, M. C. Inorg. Chem. 1986, 25, 3033. (19) Holmes, J. L.; Lassing, F. P. Can. J . Chem. 1979, 57, 249. (20) Takada, T.; Ohno, K. Bull. Chem. SOC.Jpn. 1979, 52, 334. (21) Eyler, J. R.; Oddershede,J.; Sabin, J. R.; Diercksen, G. H. F.; Gruner, N . J . Phys. Chem. 1984.88, 3121.
employ a rather small basis set for this purpose. Our results differ considerably from those of Takado and Ohno. The results reported by Eyler et al. on the propargylium cation (11) are from good basis set polarization-propagator methodology.22 The lower two excitation energies they obtain are in remarkable agreement with the INDO/S-CI results. Other states they calculate are 10000-15000 in-' higher in energy than those we obtain, but the ordering and estimated oscillator strengths are again in good accord. Of some interest in the formation of soot is the interconversion of the propargylium cation to the cyclopropenylium cation. The former can form an encounter complex with acetylene and disproportionate back to either the cyclic or linear C3H3+. The cyclic isomer does not appear to react with acetylene, from evidence obtained from deuterium-exchange reaction^.^^^^^ There is no evidence that cyclopropenylium cation tautomerizes to propargylium cation in the absence of an encounter complex with a neutral molecule. In keeping with this we have not been able to find a transition-state geometry linking the two structures, and from constrained optimization calculations we estimate a transition energy of at least 60 kcal/mol.
Discussion We have examined several stable structures of C3H3+and report on the five most stable structures that we have uncovered. The cyclic form, the cyclopropenylium cation, is lowest in energy, followed by the linear propargylium ion, [H2CCCH]+,calculated to lie some 27.7 kcal/mol higher in energy, in reasonable agreement with an experimental estimate of 25 f 4 kcal/mol. Other structures reported are calculated at least 25 kcal/mol higher in energy then the propargylium ion. All of the structures we report, however, have reasonably high vibrational frequencies, suggesting all but this structure are resistant to interconversion. Structure V, cycloprop- 1-yl-2-ylidine cation [H2CCCH]+, we predict is not stable, either with two or four r-type electrons. Under the conditions in which we are interested, sooting flames, (22) Oddershede, J. Adu. Quantum Chem. 1978, 1 1 , 275. (23) Wiseman, F.; Ozturk, F.; Eyler, J. R.; Zerner, M. C., to be submitted for publication. (24) Ozturk, F.; Moini, M.; Brill, F.; Eykr, J. R.; Buckley, T.; Lias, S.G . ; Ausloos, P. J., submitted for publication.
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J. Phys. Chem. 1989, 93, 144-149
some, or even all, structures might be observed. In addition, the lowest energy conformer might not be the most abundant, or the most reactive with C2H2or C4H2,to form higher molecular mass precursors of soot. Indeed, as mentioned earlier, the most stable cyclic form is relatively unreactive with C2H2and C4H2,much less so then the propargylium f ~ r m . ~ ? ~ In attempts to locate various species present in flames, or in models of these flames simulated in ion cyclotron resonance exp e r i m e n t ~ ,we ~ have calculated IR frequencies and electronic transition energies. Especially of interest are those species with low-lying allowed electronic transitions below about 40 000 cm-I. Such states might be excited through modern laser techniques and observed through laser-induced fluorescence or through ex-
citation of those ions using afterglow techniques. Above 40 000 cm-' interference from other species, especially aromatics, might be expected.
Acknowledgment. This work was sponsored in part through a research grant from the United States Air Force (Tyndall). This research was also supported in part by the Florida State University through time granted on its Cyber 205 supercomputer, and through a computer grant through the Office of Naval Research. We particularly thank John Eyler (Florida) and Lt. Floyd Wiseman (Tyndall) for useful and stimulating discussion. Registry No. I, 26810-74-2; 11, 21540-27-2; 111, 24858-94-4; IV, 57358-45-9;V, 117067-78-4.
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Photophysical Consequences of External Perturbations on the Emissive (n,,3s) Rydberg State of Saturated Amines Arthur M. Halpern* and Ali Taaghol Department of Chemistry, Northeastern University, Boston, Massachusetts 021 15 (Received: April 25, 1988; In Final Form: July 6. 1988)
Absorptive and emissive transitions between the ground and lowest excited 3s Rydberg state of the saturated amine 1azabicyclo[2.2.2]octane (ABCO) were studied as a function of collisional perturbations by He, Ar, Xe, SF6,dimethyl ether (DME), and methylcyclohexane (MCH). The fluorescence lifetime of ABCO decreases sharply between 0 and ca. 50 Torr of perturber pressure and levels off at several hundred Torr. The fluorescence quantum efficiency also shows an abrupt decrease followed by a leveling off to a constant value well below 1 atm. Absorption spectra of ABCO are observed to be generally unaffected by the presence of these perturbers up to 1 atm. No evidence is found for an external heavy-atom effect in Xe quenching. SF6 quenches ABCO fluorescence at the gas kinetic rate. These effects are interpreted with a model in which excited ABCO and the perturber reversibly form a loosely bound, emissive excited complex. This model includes a step describing quenching collisions between excited ABCO and a perturber. Equilibrium constants for the excited complexes are found to be 25.4, 27.1, 34.9, 27.2, and 45.6 atm-' for the respective perturbers. Dissociation rate constants are estimated from gas kinetic formation rate constants. The data show that the most significant change in the ABCO*-perturber systems occurs for the nonradiative decay channel, suggested to be an electron-transfer-inducedinternal conversion. There are slight increases in the radiative rate constants of the ABCO*-noble gas complexes, while little change is noted for the DME and MCH complexes. The nonradiative rate constant for the ABCO*-MCH complex is about 0.44 that of ABCO* in cyclohexane solution; the 1/ n 2 normalized radiative rate constants are virtually identical. The lifetime of trimethylamine was found to be nearly independent of perturber pressure (He or 2-methylbutane) up to 1 atm. This insensitivity is interpreted as steric interference in forming the complex between the planar excited state and the perturber. The results suggest that the (nN,3s) Rydberg state of amines may have appreciable conjugate valence character.
Introduction The influence of the medium on the potential energy hypersurfaces of ground and electronically excited molecules and, hence, the effects of environment on absorption and emission spectra have been of fundamental concern in molecular spectroscopy for many years. The solvent medium often plays a determining role, for example, in the relative ordering of the h a * ) and (a,**)states, both singlet and triplet, in N-heteroaromatic molecules.' In another context, currently receiving wide attention, molecules capable of achieving appreciable excited-state charge-transfer character consequent to conformational changes manifest profound solvent effects on emissive properties2 In this instance, the solvolytic properties of the excited molecule must be considered in the time domain because electronic state energetics depend on the dynamical coordination of both molecular conformations and solvent reorganization. In these examples of medium effects on
molecular spectroscopy and photophysics, electrostatic, hence energetic, consequences of particular molecular electronic states and their geometries can be considered in terms of intravalence excitations, Le., electronic configurations involving electrons within the valence shell (e.g., n = 2 for first-row elements). In considering extravalence, or Rydberg, states whose description requires the inclusion of atomic orbitals of higher principal quantum numbers, another sort of consideration must be made regarding the energetics of environmental interaction^.^ This issue stems from the much higher polarizability of excited Rydberg states as compared with intravalence states. For example, the polarizibility of the (n,3s) state of acetone has been estimated to be 450 A3; this contrasts with a ground-state value of 6.4 A3.4 In other cases where the polarizibilities of Rydberg states have been determined, values of several hundred cubic angstroms are found (for states terminating in 3s orbitals) and reflect the large
(1) (a) Liptay, W. Angew. Chem., Int. Ed. Engl. 1%9,8, 177. (b) Amos, A. T.;Burrows, B. L. Adu. Quantum Chem. 1973, 7, 289. (2) (a) Grabowski, Z. R.; Rotkiewicz, K.;Siemiarczuk, A.; Cowley, D. J.; Gaumann, W. N o w . J. Chim. 1979, 3,443. (b) Rettig, W. Angew. Chem., I n t . Ed. Engl. 1986, 25, 971.
(3) (a) Robin, M. B. Higher Excited States of Polyatomic Molecules; Academic: New York, 1974; Vol. 1, pp 208-229. (b) Runau, R.; Peyerimhoff, S. D.; Buenker, R. J. J. Mol. Spectrosc. 1977,68, 253; Avouris, P.; Rossi, A. J. Phys. Chem. 1981, 85, 2340. (4) Causley, G.C.; Russell, B. R. J. Am. Chem. SOC.1979, 101, 5573.
0022-3654/89/2093-0144$01.50/0
0 1989 American Chemical Society
