1640
J. Phys. Chem. 1992, 96, 1640-1648
-
constants. By contrast, a valence Rydberg transition of C2 as assumed by van de Burgt and Heaven36would place the upper Rydberg state at an extremely low energy (==4.0 eV), an assumption at variance with well-founded experimental results3' indicating that the lowest-lying Rydberg state of C2 lies above 8.0 eV.
Acknowledgment. Financial support by NSERC (Canada) is gratefully acknowledged. We also thank NSERC for a special grant to purchase and implement S U N workstations, on which the present calculations were carried out. Registry No. C,, 12070-15-4; C2+, 12595-79-8.
Structures and Energies of the Lowest Lying Singlet and Triplet States of C3H2 and C3F2. A Theoretical Study Voker Jonas, Marlis Bohme, and Gernot Frenking* Fachbereich Chemie, Universitat Marburg, Hans- Meenvein-Strasse, 0-3550Marburg. Germany (Received: July 25, 1991)
The theoretically predicted geometries for the propargylene, cyclopropenylidene, vinylidenecarbene, and cyclopropyne forms of C3H2 and C3F2 in their singlet and triplet states are reported at the MP2/6-31G(d) level of theory, using spin-restricted wave functions for the singlets and spin-unrestricted wave functions for the triplets. The calculated vibrational spectra for the different isomers have been calculated at HF/6-31G(d) and, in some cases, at MP2/6-31G(d). Improved total energies were calculated for C3H2at MP4/6-31 lG(2df) and for C3F2at MP4/6-31G(d) using the MP2/6-31G(d) optimized geometries. The relative stabilities of the C3H2isomers are predicted at MP4/6-31 lG(2df)//MP2/6-3lG(d) and for C3F2isomers at MP4/6-3 lG(d)//MP2/6-3 1G(d) corrected by zero-point energies, using spin-projected wave functions for the triplet states. To give an estimate for the accuracy of the calculated singlet-triplet gap, the energy differences between the lowest lying singlet and triplet states of CH2 and CF2 are calculated and compared with experimental values.
Introduction The study of C,H2 species is a challenge for theoretical and experimental chemists with many questions still being open. The first C3H2molecule identified by direct spectroscopic methods was triplet propargylene I t (Chart I), for which the ESR spectrum was published in 1965.l On the basis of the zero-field splitting parameters, a quasi-linear structure was postulated for It.' In spite of the observation of the IR spectra of I t and its deuterated isomers? it was very difficult to determine exactly the structure of triplet propargylene, Le., whether I t has a nonplanar C2geometry with two identical CC bonds or a planar C, structure with one short and one long CC bond. A recent analysis of the calculated and experimentally observed I R spectra suggests that I t has a C, equilibrium g e ~ m e t r y . ~ l t is not the global minimum on the C,H2 potential energy hypersurface. The energetically lowest lying isomer is singlet cyclopropenylidene 2s, which was prepared for the first time in 1984 by high-vacuum flash pyroly~is,~ 19 years after the preparation of the less stable species It. The interest in cyclopropenylidene rose considerably when it was discovered that 2s is the most abundant hydrocarbon identified in interstellar space.5 The third C3Hzisomer that has been detected experimentally is singlet vinylidenecarbene, 3se6 The preparation of 3s was achieved via photochemical conversion 2s It 39,which shows that interconversion among the three C3H2 isomers is possible.
--
(1) Bernheim, R. A.; Kempf, R. J.; Gramas, J. V.; Skell, P. S. J. Chem. Phys. 1965, 43, 196. (2) (a) Chi, F. K. Dissertation, Michigan State University, 1972. (b) Jacox, M.; Milligan, D. E. Chem. Phys. 1974, 4, 45. (3) Maier, G.; Reisenauer, H.-P.; Schwab, W.; Cirsky, P.; Spirko, V.; Hess Jr., B. A.; Schaad, L.J. J. Chem. Phys. 1989, 91, 4763. (4) Reisenauer, H.-P.; Maier, G.; Riemann, A,; Hoffmann, R. W. Angew. Chem. 1984, 96, 596;Angew. Chem., Int. Ed. Engl. 1984, 23, 641. ( 5 ) Thaddeus, P.; Vrtilek, J. M.; Gottlieb, C. A. Asrrophys. . . J . 1985, 299,
L63.
(6)Maier, G.; Reisenauer, H.-P.; Schwab, W.; CBrsky, P.; Hess Jr., B. A,; Schaad, L.J. J . Am. Chem. SOC.1987, 109, 5183.
0022-3654/92/2096- 1640$03.00/0
CHART I x-c===c=c X
/c/
x--c=c-c
\X
X /c=c\
X
X = H
1s
It
2s 2 t
X = F
5s
5t
6s
IDif t u o r o l p r o p o r g y t e n e
6t
IDif LuorolcycLopropenyLidene
x\
*/c=c=c X = H
3s
3t
4s
4t
X = F
7s
7t
8s
8t
(Dif1uoro)vinylidenecarbene
(Diftuoro)cyclopropyne
The infrared spectrum of 3s was compared with the theoretically predicted IR data, which confirmed that the newly detected isomer is the H2C=C=C species 3sS6 A number of theoretical studies have been devoted to C3H2 molecules, and the identification of experimentally observed species ~ * ~most ~~ has been aided by quantum mechanical c a l c ~ l a t i o n s . The complete theoretical study of the C3H2potential energy hypersurface is an early study by Hehre et al.,' who studied singlet and triplet states of eight different isomers using single determinant ab initio methods. More recent calculations by DeFrees and McLean* predict energies and geometries of Is, It, 2s, 39, and (7) Hehre, W. J.; Pople, J. A.; Lathan, W. A,; Radom, L.;Wasserman, E.; Wasserman, 2.R. J. Am. Chem. SOC.1976, 98, 4378. (8) DeFrees, D.J.; McLean, A. D.Astrophys. J . 1986, 308, L31.
0 1992 American Chemical Society
C3H2 and C3Fz
3t at a slightly higher level of theory (MP4/6-311++G(df, pd)//MP376-3lG(d)). A theoretical study by Copper and Murphyg using CASSCF wave functions focussed on the singlet species ls, 29, and 3s. Other theoretical work has been restricted to a particular C3H2 ~ p e c i e s . ~ - ~ , ~ J * ~ ~ The present status of theoretical research on the relative energies of C3H2 species is as follows: 2s is predicted as the global minimum on the C3H2 potential energy hypersurface, followed by 3s and then by lta8 1s is calculated not much higher in energy than It, while other C3H2isomers are significantly less stable and it may be difficult to detect them experimentally.* Singlet cyclopropyne 4s is not a minimum energy structure, but triplet cyclopropyne 4t is a local minimum.I3 In this paper we address questions on C3H2 species which are still open. First, we show calculated energy differences between singlet and triplet states which are the results of spin-projected wave functions for the triplet states. In some cases we found that spin contamination in the UHF wave function is very high, and the predicted singlet-triplet energy gaps are substantially different than those of previous studies*if spin-projected wave functions are used. Second, we studied the structure of the energetically lowest lying triplet state of cyclopropenylidene 2t, which is a difficult problem for theory. The energetically lowest lying triplet state of C, cyclopropenylidene is the 3A2state, which has three imaginary frequencies at the spin-restricted Hartree-Fock (ROHF) level of theory.llbvc Optimization at ROHF/3-21G without symmetry constraint yields an unusual nonplanar geometry with CIsymmetry, which exhibits three different CC bonds in the three-membered ring and a hydrogen atom bent by 46.4' out of the plane.Ilc It was speculated that the strange geometry was caused by the instability of the Hartree-Fock wave function and that a proper MCSCF calculation would probably yield a molecule with C, symmetry for the lowest lying triplet state of cyclopropenylidene. Although a full-scale MCSCF calculation of 2t is not possible for us, we performed a geometry optimization of 2t with inclusion of correlation energy. The focus of our present work, however, is the structures, relative energies and vibrational spectra of the fluorine substituted analogues C3F2 It is known that electronegativesubstitution of carbenes stabilizes the singlet state over the triplet state. For example, CF2 has a singlet ground state,14while CH2 has a triplet ground state.I5 Since most of the C3H2 isomers are carbenes, a strong shift toward stabilization of singlet states may be expected. Substitution of hydrogen by fluorine should show a marked effect on the calculated structures and energies and thus should help to understand the electronic structures of C3H2 and C3F2 isomers. We present our calculated results for the energetically lowest lying singlet and triplet states of difluoropropargylene (5s, St), difluorocyclopropenylidene(k,6t), difluorovinylidenecarbene (7s, 7t), and difluorocyclopropyne(8s,8t). To give an estimate for the accuracy of the theoretically predicted energy differences between singlet and triplet states, we also calculated the 'A, and 3Bl states of CH2 and CF2 and compared the results with experimental data. (9) Cooper, D. L.; Murphy, S. C. Astrophys. J . 1988, 333, 482. 110) la) Dvkstra. C. E.: Parsons. C. A,: Oates. C. L. J . Am. Chem. SOC. 1979, Z01,'19&2. (b) Kenney 111, J: W.; &nons, J.; Purvis, G. D.; Bartlett, R. J. Am. Chem. SOC.1978, 100, 6930. (1 1) (a) Shepard, R.; Banerjee, A,; Simons, J. J . Am. Chem. SOC.1979, 101, 6174. (b) Bofill, J. M.; Farris, J.; Olivella, S.; Sol& A.; Vilarrasa, J. J . Am. Chem. Soc. 1988. 110. 1694. IC) Lee.. T.:. Bunae. - . A.:. Schaefer 111. H. F. J. Am. Chem. Soc: 1985, 107, 137. (12) Fan, Q.;Pfeiffcr, G. V . Chem. Phys. Lett. 1989, 162, 472. (13) (a) Saxe, P.; Schaefer 111, H. F. J . Am. Chem. SOC.1980, 102, 3240. (b) Yamaguchi, Y.; Osamura, Y.; Fitzgerald, G.; Schaefer 111, H. F. J . Chem. Phys. 1983, 78, 1607. (14) (a) Bauschlicher Jr., C. W.; Schaefer 111, H. F.; Bagus, P. S. J. Am. Chem. Soc. 1977,99,7106. (b) Bauschlicher, C. W. J . Am. Chem. SOC.1980, 102,5492. (c) Koda, S. Chem. Phys. Lett. 1978,55,353. (d) Koda, S. Chem. Phys. 1982.66, 383. ( I 5 ) (a) Leopold, D. G.; Murray, K. K.; Stevens Miller, A. E.; Lineberger, W . C. J . Chem. Phys. 1985,83,4849. (b) Bunker, P. R.; Sears, T. J. J . Chem. PhyJ. 1985,83,4866. (c) Carter, E. A.; Goddard 111, W. A. J. Chem. Phys. 1987, 86, 862.
The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 1641 Theoretical Methods Most of the calculations have been camed out using the CONVEX versions of the program packages G A U S S I A N ~ Oand ' ~ CADPAC.~' At the first step, we optimized the geometries and calculated the vibrational frequencies and zero-point vibrational energies (ZPE) of 1s-8t at the Hartree-Fock level of theory using the basis sets 3-21G and 6-31G(d). Second, we optimized the geometries at 6-31G(d) with inclusion of correlation energy using M~rller-Plesset perturbation theory terminated at second order.20 This is denoted MP2/6-3 lG(d). Singlet states are calculated with spin-restricted wave functions, and triplet states are calculated using the UHF or UMP formalism. For some isomers we calculated the vibrational frequencies at MP2/6-31G(d) in order to determine if they are minima on the potential energy surface. Improved total energies were obtained using M~rller-Plesset theory fourth order (MP4) and the 6-311G(2df) basis set for C3H2 (6-31G(d) for C3F2) with the geometries optimized at MP2/6-31G(d). Thus, the highest level of theory used in this study for predicting relative energies of C3H2 isomers is PMP4/6-3 1lG(2df)//MP2/6-3 1G(d) + ZPE(HF/6-31G(d)). For C3F2 the highest level is PMP4/631G(d)//MP2/6-31G(d) ZPE(HF/6-31G(d)). The vibrational frequencies and ZPE data calculated at HF/6-31G(d) are scaled by 0.89, and the MP2/6-31G(d) values are scaled by 0.92.21 For the triplet states, the spin-projected wave functions are employedz2 to predict the singlet-triplet energy differences more reliably. They are denoted PMP4. MP2 calculations were performed with full core, MP3 and MP4 calculations were carried out with the frozen-core option. The geometry of the lowest lying triplet state of cyclopropenylidene2t was optimized with a CASSCF(6/6) and CASSCF(10/10) wave function using the STO-3G basis set. The wave function consists of 189 (29 700) configurational state functions (CSF) generated by an active space in which four (six) a-electrons and two (four) &electrons are distributed in six (ten) orbitals each. The CASSCF calculations were carried out using the program G A M E S S . ~ ~
+
Results and Discussion The calculated relative energiesz4for the lowest lying IAl and 3B, states of CH2 and CF2 are shown in Table I. The calculated relative energiesz4for the C3H2 isomers 1s-4t and the corresponding C3F2molecules 5s-8t are shown in Tables I1 and 111. The optimized geometries are exhibited in Table IV. The theoretically predicted vibrational frequencies and IR intensities are (16) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foreman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M. A.; Binkley, J. S.; Gonzalez, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, R. A,; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.;Pople, J. A. GAUSSIAN 90; Gaussian Inc.: Pittsburgh, PA, 1990. (17) Amos, R. D.; Rice, J. E. CADPAC: The Cambridge Analytical Derivatives Package, issue 4.0, Cambridge, 1987. (18) (a) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J. Am. Chem. Soc. 1980, 102,939. (b) Gordon, M. S.; Binkley, J. S.; Pople, J. A.; Pietro, W. J.; Hehre, W. J. J. Am. Chem. SOC.1982, 104, 2797. (c) Pietro, W. J.; Francl, M. M.; Hehre, W. J.; DeFrees, D. J.; Pople, J. A.; Binkley, J. S. J . Am. Chem. SOC. 1982, 104, 5039. (19) (a) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J . Chem. Phys. 1972, 56, 2257. (b) Francl, M. M.;Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. (c) Hariharan, P. C.; Pople, J. A. Chem. Phys. Lett. 1972, 66, 217. (20) (a) Mdler, C.; Plesset, M. S. Phys. Reu. 1934, 46, 618. (b) Binkley, J. S.; Pople, J. A. Int. J. Quantum Chem. 1975, 9S, 229. (21) (a) Hout, R. F.; Levi, B. A.; Hehre, W. J. J . Comput. Chem. 1982, 3, 234. (b) DeFrees, D. J.; McLean, A. D. J . Chem. Phys. 1985, 82, 333. (22) Schlegel, H. B. J . Chem. Phys. 1986, 84, 4530. (23) Dupuis, M.; Spangler, D.; Wendolowski, J. J. National Resource for Computations in Chemistry, University of California, Berkeley, Program QGOI. We used the modified version as described by: Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Jensen, J. H.; Koseki, S.; Gordon, M. S.; Nguyen, K. A,; Windus, T. L.; Elbert, S. T. QCPE Bull. 1990, 10, 52. (24) The calculated total energies for 2s are as follows (in hartrees): -1 13.9459 (HF/3-21G); -1 14.6203 (HF/6-31G(d)); -114.9834 (MP2/631G(d)); - 1 14.9878 (MP3/6-31G(d)); -1 15.0084 (MP4/6-31G(d)); -1 14.6231 (HF/6-311G(2df)); -115.1 153 (MP4/6-31IG(Zdf)). The calculated total energies for 6s are as follows (in hartrees): -310.5696 (HF/3-21G); -3 12.3057 (HF/6-3 IG(d)); -3 13.01 56 (MP2/6-3 IG(d)); -3 12.9990 (MP3/6-3 IG(d)); -3 13.0413 (MP4/6-31G(d)).
1642 The Journal of Physical Chemistry, Vol. 96, No. 4, 1992
Jonas et al.
TABLE I: Relative Energies Ed (kcal/mol), Geometries, Zero-Point Vibrational Energies ZPE (kcal/mol, Scaled by 0.89), and Eigenvalues of the S2Operator (S2)of CHI and CF2 HF/3-21G//HF/3-21G CH2 CHI CF2 CF2
+35.9 0.0 0.0 +27.7
'AI 'Bl ,AI
%
HF/6-3 IG(d)//HF/6-3 lG(d)
'c-x
excx
Ere1
1.102 1.071 1.321 1.337
104.6 131.3 104.0 120.0
+30.8 0.0 0.0 +32.5
Ere1
MP2/6-3lG(d)//MP2/6-31G(d) CH, CH; CF2 CF2
Ere1 +21.0 0.0 0.0 +52.0
'At 'Bl' 'AI 'B I
CH2 CH2 CF2 CF2
'AI 'BI 'AI 'BI
CH2 CH2 CF2 CF2
IAI 'Bl "I
rc-x
E,, (S2) +17.1 0.0 2.02 0.0 +56.1 2.01 MP4/6-31G(2df)// MP2/6-31G(d)
(S2)
CH2 CHI CF2 CF2
I.41 'Bl
'A, 'B I
+12.8 0.0 0.0 +57.8
2.02 2.01
+18.4 0.0 0.0 +51.6 PMP4/6-31G(d)// MP2/6-31G(d) Ere1 Ere: +17.8 +17.5 0.0 0.0 0.0 0.0 +55.7 +55.5 PMP4/6-3 IG(2df)// MP2/6-31G(d)
(S2)
2.01
oxcx
103.0 130.7 104.5 118.7
E,I
102.2 131.6 104.2 119.9
2.02
'c-x
1.097 1.07 1 1.283 1.304
MP3 /6-3 1G(d) . .,/ ,/MP2/6-3 1G(d) . ,
oxcx
1.109 1.077 1.313 1.327 MP4/6-3 lG(d)// MP2/6-31G(d)
E,,, +13.6 0.0 0.0 +58.2 MP4/6-311G(2df)// MP2/6-3 lG(d)
ZPE 4.4 4.2 10.0 10.3
Exi
Ere1
+14.4 0.0 0.0 +57.8 PMP4/6-31 1G(2df)// MP2/6-3 1G(d)
Ed +13.6 0.0 0.0 +57.1
E,-I' +13.3 0.0 0.0 +56.9
+14.1 0.0 0.0 +57.6 exP E,., +9.0a 0.0 0.0 +56.6b
'Reference 15a,b. bReference 14c,d. CEre,'= E,,, with inclusion of HF/6-31G(d) ZPE.
shown in Table V. Unless otherwise noted, relative stabilities for C3H2 are given at PMP4/6-31 lG(2df)//MP2/6-3lG(d) + ZPE(HF/6-31G(d)), and for C3F2 they are given at PMP4/63 1G(d)//MP2/6-3 1G(d) ZPE(HF/6-3 1G(d)). The geometries are always at MP2/6-31G(d). Relative Energies on IAl and 3BI States of CH2 and CF2. Methylene (CH,) has a 3B1ground state 9.0 kcal/mol lower in energy than the 'Al first excited ~ t a t e . The ~ ~ results ~ , ~ shown in Table I indicate a continuous decrease in the calculated singlet-triplet gap with increasing theoretical level. At the highest level of theory employed in our study, Le., PMP4/6-311G(2df)//MP2/6-31G(d) ZPE(HF/6-31G(d)), the 3B, state is predicted to be 13.3 kcal/mol lower than the IA, state. Thus, the remaining error is -4 kcal/mol favoring the triplet state too much. Unlike the calculated results for CH2,the theoretically predicted singlet-triplet gap for CF2 has practically converged at PMP4/6-31G(d)//MP2/6-31G(d) + ZPE(HF/6-31G(d) to the experimentally reported1&sdvalue of 56.6 kcal/mol for the IA, state to be much stable than the 3B1state. Further expansion of the basis set to PMP4/6-31 lG(2df)//MP2/6-3lG(d) + ZPE(HF/6-3 1G(d) does not change the energy difference significantly (Table I). Although a direct comparison with the C3X2 systems should be made with caution, we estimate that our calculated results for C3H2 may favor the triple states by perhaps -5 kcal/mol, while the results for C3F2should be more reliable. Relative Energies of C3H2and C,F2 Isomers. The calculated energies for the C3H2 isomers shown in Table I1 predict the singlet cyclopropenylidene 2s is the global minimum on the C3H2 potential energy hypersurface. This result is obtained after correlation contributions are included in the energy calculations. At the Hartree-Fock level, the triplet structure It is calculated as the most stable form (Table 11). The results at the MP2, MP3, and
+
+
MP4 level using the 6-31G(d) basis set predict a stability sequence 2s > 3s > It and relative energies (at MP4) of 0.0 kcal/mol (a), 13.1 kcal/mol (3s), 22.9 kcal/mol (It) if the spin-contaminated wave functions are employed. A comparison with the results reported by DeFrees and M c h n (DM)*and with those obtained at MP4/6-31 lG(2df) (Table 11) shows that the calculated energy differences among the different isomers change very little when further increasing the basis set. Because the energy differences among the two triplet forms lt(C3 and lt(C,) and the singlet form 1s is only 5 kcal/mol at MP4/6-311++G(df,pd), DM did not decide whether a singlet or triplet is the more stable propargylene species.8 However, the energy gap between the triplet and singlet species becomes much larger when spin-projectedwave functions are used. The differences between It and 1s are further increased when ZPE corrections are included. The triplet isomer It becomes stabilized relative to the singlet isomer 1s and is even more stable than 3s at PMP4/6-31 lG(2df)//MP2/6-31G(d). The stability sequence is 29 > It > 3s and the relative energies are 0.0 kcal/mol (29), 8.7 kcal/mol (It), 13.5 kcal/mol(3s), when ZPE corrections are made (Table 11). The C2 and C, forms of It are nearly isoenergetic at MP4/6-311G(2df) and differ slightly by 1.3 kcal/mol when corrections for ZPE and spin contaminations are made. A very careful analysis of the vibrational spectrum showed3 that It has a very flexible structure which makes it difficult to correlate the experimentally obtained IR data with calculations based on the harmonic approximation. Only when nonrigidity is taken into account an agreement between theory and experiment can be established which indicates that It probably has C, geometryU3The other isomers are much higher in energy, and it will be difficult to observe them experimentally, perhaps with the exception of 1s. The theoretically predicted relative stabilities of the C3F2 isomers show significant differences compared with the corresponding
C3H2 and C3F2
The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 1643
TABLE 11: Relative Energies Ed (kcal/mol), Zero-Point Vibrational Energies ZPE (kcal/mol, Scrled by 0.89), Number of I m ~ g i ~ r y Frequencies i, a d Eigenvalues of the S2Operator (S*) of C a 2 Isomers HF/3-21G// MP2/6-3 lG(d)// HF/3-21G HF/6-3 lG(d)//HF/6-3 1G(d) MP2/6-3 1G(d) En, i E,, ZPE i Ere1 i +43.7 0 +37.9 17.1 0 +32.6 0 0.0 15.3 0 +27.2 1" WC2) 0.0 1 +0.2 14.8 1 +27.0 Oa NC,) 0.0 0 +7.5 19.5 0 0.0 ZdC,) +34.1 0 +53.4 18.1 0 +52.9 WC1) +73.9 0 +25.5 18.8 0 +19.3 WC,) +30.7 0 +23.9 17.8 0 +54.8 YC,) +24.0 2 +91.8 17.8 2 +63.2 1 49(czu) +120.2 4t(C,.,) +94.4 0 +73.5 19.0 0 +69.1 MP4/6-3 lG(d)// PMP4/6-3 lG(d)// MP3/6-31G(d)//MP2/6-3 1G(d) MP2/6-31G(d) MP2/6-31G(d)
E,,,
Ere1 +33.0 +23.0 +23.0
WCS) NC2) WC,) WC,) Zt(CI)
WC,) 3t(C,) 4S(C,) 4t(C,)
+28.8 +22.9 +22.9
0.0
0.0
+53.4 +16.9 +51.0 +71.1 +70.0
+52.3 +13.1 +5 1.6 +60.8 +66.8
MP4/ HF/ 6-3 1lG(2df)//MP2/6-3lG(d)
ls(cJ) WC2) ZS(C2ll) WC,)
WC,) 3t(C,) 4S(C,) 4t(C,)
Ere1 +36.9 0.0 +o. 1 +6.9 +55.0 +25.6 +25.1 +91 .O +75.9
Ere, +26.6 +22.5 +22.6 0.0 +54.5 +14.2 +54.2 +61.5 +71.4
(S2) 2.37 2.35 2.40 2.03 2.03
(S2)
Ed
En:
2.38 2.36
+28.8 +13.0 +13.6
+26.4 +8.8 +lo.@
0.0 2.41
+51.4 +13.1 2.02 +42.5 +60.8 2.02 +65.9 PMP4/6-3 11G(2df)// MP2/6-31G(d) E I, E,( +26.6 +24.2 +12.9 +8.7 +13.6 1O.Ob
+
0.0 +53.5 +14.2 +45.3 +61.5 +70.4
0.0 +52.1 +13.5 +43.6 +59.8 +69.9
0.0 +50.0 +12.4 +40.8 +59.1 +65.4 othePc Ere, +26.8 +22.3 +21.7 0.0 +14.5 +54.1
"Reference 8. With MP2/6-31G(d) ZPE (15.9 kcal/mol, scaled by 0.92; from ref 8). CMP4/6-31l++G(df,pd)//MP3/6-3lG(d). with inclusion of HF/6-31G(d) ZPE.
dEn,' = E,,
TABLE III: Relative Energies Ed (kcal/mol), Zero-Point Vibrational Energies ZPE (kcal/mol, Scaled by 0.89), Number of Imaginary Frequencies i and Eigenvalues of the S2Operator (S2)of C g , Isomers
WCS) st(c2) St(CJ) WC,) WCI) 79(C,) 7t(C,) WC,) WC,)
SS(CS)
%c2) st(cJ) WC,)
Wc,) 79(C,) 7t(C,)
WG) WC,)
HF/3-21G// HF/3-21G Ere, +23.2 +2.2 +6.5 +18.8 +55.9 0.0 +6.3 +75.3 +64.4
i
0 0 1
0 0 0 0 1 0
MP3/6-3 lG(d)//MP2/6-3 1G(d) Ere, +27.3 +43.1 +42.6 0.0 +54.6 +2.0 +50.8 +34.9 +5 1.6
MP2/6-3 lG(d)// HF/6-3 lG(d)//HF/6-3 1G(d) MP2/6-31G(d) Ere1 ZPE i Ere, i +26.6 10.3 0 +26.9 0 +9.4 9.3 0 +49.5 0 +17.1 8.9 1 +46.1 0 11.6 0 0.0 0 0.0 +43.1 10.6 0 +56.1 11.0 0 +2.1 0 +2.3 +14.2" 9.3" 00 +57.0 0 +46.9 9.8 1 +27.1 1 +45.9 10.8 0 +52.7 MP4/6-3 lG(d)// MP2/6-3 1G(d) PMP4/6-3 lG(d)//MP2/6-3 1G(d) E,, (S2) Ere, Ere,' At +26.1 +26.1 +25.4 26.4 +47.0 2.46 +36.7 +35.4b +46.8 2.18 +42.1 +41 .9c +2.4 +2.4 +3.0 1.5 +57.2 2.44 +55.3 +54.9 0.0 0.0 0.0 17.4 +56.4 2.06 +46.8 +45.1 +29.6 +29.6 +28.4 17.8 +53.2 2.02 +52.5 +52.3
"C, symmetry. "Whti MP2/6-31G(d) ZPE (9.7 kcal/mol; scaled by 0.92). 'With MP2/6-31G(d) ZPE (10.8 kcal/mol; scaled by 0.92). dErc,' = Ere,with inclusion of HF/6-31G(d) ZPE. "Change in the singlet-triplet gap relative to the corresponding C3H2isomer.
C3H2 species (Table 11). As mentioned in the Introduction, substitution of hydrogen by fluorine in carbene-type structures
should yield energetically lower lying singlet states. The results are in agreement with the expectation. For all isomeric forms,
1644 The Journal of Physical Chemistry, Vol. 96, No. 4, 1992
Jonas et al.
TABLE I V Geometries of the Different Isomers of C f i 2 and C g 2 (First Line, HF/3-21C Optimized Geometry; Second Lme, HF/6-31G(d) Optimized Geometry; Third Line, MP2/6-31G(d) Optimized Geometry) RI
R3
R2
CP
R1 1s (X = H) 5s
(X = F)
R3
R2 1.371 1.377 1.370 1.433 1.441 1.437
1.209 1.208 1.237 1.184 1.186 1.224
R2 1.058 1.062 1.067 1.328 1.296 1.311
1.285 1.290 1.266 1.290 1.306 1.278
St(C2) (X = F)
R4 1.091 1.088 1.101 1.345 1.301 1.332
1.052 1.057 1.068 1.288 1.260 1.283
R1 lt(C2) (X = H)
"
A2
A I
R3
A1 180.4 180.5 167.8 178.7 178.8 174.8
A3
A2 185.0 184.3 191.8 188.2 188.2 198.3
A1 172.1 169.4 174.9 162.8 154.0 163.5
113.3 110.3 111.2 108.6 107.8 107.6
T1
A2 154.1 149.7 162.5 138.9 134.6 137.4
-141.8 -144.3 -141.3 -136.3 -139.9 -136.4
R2
R1
x-c-c-c
CP
w u L\R4 A1
R1 lt(C,) (X = H) 5t(C,) (X = F)
R2 1.301 1.290 1.307 1.340 1.359 1.391
1.264 1.290 1.233 1.217 1.215 1.191
A2
A3
R3 1.054 1.061 1.065 1.301 1.270 1.283
R1/&\
R4 1.060 1.062 1.072 1.341 1.308 1.328
A1 179.1 151.8 178.3 181.0 177.7 179.9
A3
A2 185.5 192.9 184.7 187.2 190.9 181.6
148.7 151.8 146.6 132.7 128.6 125.0
C2"
"/c.l
