J . Phys. Chem. 1987,91,4455-4459 of random matrix ensembles as basic statistical models. Considerable effort, e.g., has been devoted to the study of the hydrogen atom in a magnetic field. Numerical calculations show that the spectrum evolves from regular to WE-type behavior for increasing field This is a promising example since it is also a candidate for a direct experimental verification. Analogous findings come from the study of the quasi-energies of systems with time-dependent periodic perturbation^.^^-^^ Other interesting studies are treating systems where the Hamiltonian does not admit nontrivial real representations, so that not the GOE, but the Gaussian unitary ensemble, CUE, of complex Hermitian random matrices, becomes appropriate.8 This may, e.g., be accomplished by introducing a suitable electromagnetic field. The resulting spectral s t a t i s t i ~ s ~are l - ~in ~ good agreement with the CUE. For a discussion of the applicability of G O E or C U E see ref 84. The investigation of statistical properties of energy levels is a developing field. In spite of all evidence for the presence of random matrix-type fluctuations in complex spectra, a rigorous mathematical proof is lacking. We also mention another point that needs clarification theoretically, namely the influence of the number of degrees of freedom on spectral statistics. Systems withf= 2 (74) Wintgen, D.; Friedrich, H. Phys. Rev. Lett. 1986, 57, 571. (75) Delande, D.; Gay, J. C. Phys. Rev.Lett. 1986, 57, 2006. (76) Wunner, G.; Woelk, U.; Zech, I.; Zeller, G.; Ertl, T.; Geyer, F.; Schweizer, W., Ruder, H. Phys. Rev. Lett. 1986, 57, 3261. (77) Haake, F.; Kus,M.; Scharf, R. 2.Phys. E 1987, 65, 381. (78) Izrailev, F. M. Phys. Rev.Lett. 1986, 56, 541. (79) Jose, J. V.; Cordery, R. Phys. Rev.Lett. 1986, 56, 290. (80) Frahm, H.; Mikeska, H. J. 2.Phys. E 1986, 65, 249. (81) Seligman, T. H.; Verbaarschot, J. J. M. Phys. Lett. l985,108A, 183. (82) Berry, M. V.; Robnik, M. J . Phys. A 1986, 19, 649. (83) Berry, M. V.; Robnik, M. J . Phys. A 1986, 19, 669. (84) Robnik, M. In ref 73.
4455
degrees of freedom are exceptional in that for medium coupling strength there are several independent chaotic subregions in phase space. For f > 2 all chaotic regions are connected48 (”Arnold diffusion”); however, the time scale of diffusion between weakly connected irregular regions can be very large and it is not entirely clear how this will be reflected in the corresponding spectral statistics. In molecular physics it is still desirable to obtain high-quality spectra in order to demonstrate clearly the underlying statistical properties. The existence of random matrix type fluctuations in molecular spectra cannot be doubted since apart from experimental evidence even the most simple theoretical models such as coupled oscillators can exhibit this behavior. Good data, however, are needed in order to see what one can learn about specific molecular properties by a statistical analysis of the spectrum. Remember, e.g., the analysis of atomic spectra in section 3, which could demonstrate the existence of a good quantum number by analyzing the spacing distribution. Generally, irregular fluctuations show that apart from energy no further good quantum numbers exist, which could serve to interpret the spectrum. Whether further molecular properties, such as, e.g., underlying coupling mechanisms or fast intramolecular energy transfer, have impact on spectral statistics needs thorough investigation of suitable spectra. We finally hope to have demonstrated the usefulness of a statistical description of spectra. From a practical standpoint the analysis of statistical properties of energy levels is a particularly suitable approach to characterize energy spectra when traditional ways of interpretation are inappropriate, and generally allows insights into the nature of the underlying system. From a more theoretical point of view energy level statistics provide an interesting bridge between classical mechanics and the semiclassical limit.
ARTICLES Theoretical Studies on the Ground State and Low-Lying Doublet Excited States of the Propargyi Radical H. Honjou, M. Yoshimine, and J. Pacansky* IBM Almaden Research Center, Sag Jose, California 95120 (Received: December 12, 1985) The molecular geometries and electronic structures for the ground state and the two lowest-lying doublet excited states of the propargyl radical, CH,CCH, have been calculated by an ab-initio multiconfigurationself-consistent field (MCSCF) method. The vibrational frequencies were also calculated for the ground state by using a single configuration SCF method with a 4-31Gbasis set. 1. Introduction
The C3H3radical was detected by Farmer and Lossing’ in 1955 by a mass spectrometric study on the thermal decomposition of propargyl iodide. Since then a number of experimental studies have provided evidence that the most stable structure for the ground state of the C3H3radical is essentially the propargyl radical structure (H2CC=CH).Z-5 Theoretical calculations are in agreement with this structural assessment.6-8
The propargyl radical is one of the simplest conjugated systems having three centers and three electrons contained in an out-ofplane r network. In addition, the radical has an in-plane r molecular orbital. We show in Figure 1 a computer drawing for the ground state of the propargyl radical in order to introduce the nomenclature used in this report for the different molecular (6) Baird, N. Colin; Gupta, R. R.; Taylor, K. F. J . Am. Chem. SOC.1979, 101, 4531.
(1) Farmer, J. B.; Lossing, F. P. Can.J . Chem. 1955, 33, 861. (2) Ramsay, D. A,; Thistlethwaite, P. Can.J . Phys. 1966, 44, 1381. (3) Jacox, M. E.; Milligan, D. E. Chem. Phys. 1974, 4, 45. (4) Oakes, J. M.; Ellison, G. B. J. Am. Chem. Soc. 1983, 105, 2970,. (5) Collin, J.; Lossing, F. P. Can.J . Chem. 1957, 35, 778.
(7) (a) Henchliffe, A. J . Mol. Struct. 1977, 36, 162. (b) Ibid. 1977, 37, 295. (8) (a) Bernardi, F.; Camaggi, C. M.; Tiecco, M. J . Chem. Soc., Perkin Trans.2, 1974, 518. (b) Bernardi, F.; Epiotis, N. D.; Cherry, W.; Schlegel, H. B.; Whangbo, M. H.; Wolfe, S. J. Am. Chem. SOC.1976, 98, 469.
0022-3654/87/2091-4455%01.50/0 0 1987 American Chemical Society
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The Journal of Physical Chemistry, Vol. 91, No. 17, 1987
H‘2q
Honjou et al. H12
n
V
t
d
H11
1~20,
r 7
d
H11
L2A
d
Hll
Lz 2-IA
Figure 2. The calculated geometries for the 1-2B,ground state and the 1-2A” and 2-2A’ excited electronic states of the propargyl radical. Figure 1. A description of the geometry of the ground electronic state of the propargyl radical illustrating the Cartesian axis relative to the molecular frame, the ?r molecular orbitals, and the half-filled C2p,orbital on C’.
orbitals. As shown at the top of Figure 1, the molecular framework has one plane of symmetry which is taken as the YZ plane. The C C single bond is located between the C1C2atoms while the C C triple bond is between the C2C3atoms. The orientation of the in-plane a molecular orbital, ry,is shown by the second drawing in Figure 1 while the orientation of the out-of-plane T molecular orbital, a,, is illustrated at the bottom. Figure 1 also shows the half-filled CZprorbital, which is on C’, that along with the a, molecular orbital forms the conjugated A system. Henceforth, Figure 1 should be referred to for the designation of the molecular orbitals, and the Cartesian axes relative to the molecular frame. It is well-known that configuration mixing among different *-electron arrangements are important for obtaining realistic geometries of such systems. Baird6 et al. demonstrated this importance for several radicals including the propargyl radical, by using the ab-initio restricted Hartree-Fock molecular orbital (RHF-MO) method and the configuration interaction (CI) method among a-electron configurations with an STO-3G basis set. Recent extensive MCSCF-CI calculations9 on vinylmethylene (H2CCHCH) are another pertinent example; these results, in which full *-electron configuration mixing was taken into account, yielded a resonance structure having almost equal C-C bond distances for the 3A” ground-state optimal geometry, while the single configuration SCF method gave a vinylcarbene structure. For the CHzCCH radical, previous theoretical calculations were restricted to the single configuration S C F level. The C I calculation,6 which is the only calculation beyond the single configuration S C F level reported thus far, only involved the out-of-plane r,, C2p,space although there are nearly degenerate in-plane a) orbitals in the propargyl radical triple bond (at the R H F level using a 4-3 1G basis set, the orbital energies are -0.429 (a,) and -0.389 au (T,) for the propargyl radical). Furthermore, the previous calculation was only for the ground state. As shown by Ramsay and Thistlethwaite,* vibrational bands are found in the ultraviolet absorption spectrum of the gas-phase propargyl radical. Ramsay et al. assigned the lower state of the band system to the ground state of the propargyl radical; this was subsequently confirmed by Jacox and Milligan3 by vacuum ultraviolet photolysis of methylacethylene in rare gas matrices. (9) Honjou, N.;Pacansky, J.;Yoshimine, M. J . Am. Chem. SOC.1984, 106, 5361.
Of particular interest is that the lowest two doublet excited states are expected to be closely situated to each other around the vertical excitation region of the ground state. This is because these excited states may correspond to one-electron excitations from the triple bond, Le., the out-of-plane a, or in-plane xu orbitals, into the singly occupied Czp,orbital on C1 (see Figure 1); configuration mixing would be important for these excited states. One of the goals of the present study is to obtain information for the molecular structures, electronic structures, and energy levels of the three lowest-lying doublet states of the CH2CCH radical including the ground state by the ab-initio multiconfiguration self-consistent field (MCSCF) method. No theoretical data have been reported for the vibrational frequencies of the propargyl radical. We obtained the harmonic vibrational frequencies using the ab-initio single configuration S C F method and have compared the experimental infrared spectrum with the computed data. The method of calculation is described in section 2. The results and discussions are given in section 3. 2. Computational Details Multiconfiguration self-consistent field (MCSCF) wave functions were obtained for the ground and two lowest excited doublet states of the propargyl radical. The configurations included in the MCSCF wave functions were generated by distributing the five electrons among the five outer-valence orbitals: e.g., for a C2, symmetry, three bl orbitals comprising the outof-plane a, and the Czp, orbital, and the two b2 orbitals forming the in-plane irYmolecular orbital (see Figure 1). The geometry optimizations were performed for the low-lying three doublet states by using the MCSCF method with a 4-31G basis set.I0 For the lowest doublet state (the ground state), the geometry optimizations were also carried out by using a single configuration self-consistent field (SCF) method with 4-31G basis set and the double j- plus polarization (DZP)basis set, which was constructed from atomic basis sets of van Duijnevelt,]’ C(9sSp) and H(5s); the d functions” had exponents of 0.7327; the p functions” on H had an exponent of 0.9. The force constant matrix was calculated for the ground state by computing the first derivatives of the SCF energies with respect to nuclear coordinates analytically and the second derivatives by finite differences. The computer program used in this work was GAMESS. I *
(10)Hehre, W. J.; Radom, L.; Schleyer, P. R.; Pople, J. A. Ab-Initio Molecular Orbital Theory; Wiley: New York, 1986. (1 1) Van Duijnevelt, F. B. IBM report RJ945, 1971. (12)GAMESS, Dupius, M.; Wendoloski, J. J.; Spangler, D Natl. Res. Comput Chem. Software Catalog. ’980, 1, QGO1.
The Journal of Physical Chemistry, Vol. 91, No. 17, 1987 4457
Theoretical Study of the Propargyl Radical TABLE I: Molecular Orbital Energies for the *BI Ground Electronic State of the Propargyl Radical and Results for Restricted Hartree-Fock Calculations (Basis: DZP) at the Optimized Geometry MO energy, MO (symmetry C2J hartree la1 -1 1.265018 2a1 -11.252291 3a1 -1 1.239 91 1 4a I -1.058 188 5a1 -0.938 923 6a I -0.725 181 7a1 -0.641 612 1b2 -0.619810 1bl -0.432 319 2bZ -0.396 778 2bl -0.364026
2-’6,
qualitative description
l-zA,,
(Opt. Geom.)
(Opt. Geom.)
in-plane C1 (2s + 2pJ out-of-plane ?T, in-plane rY half-filled C’ (2p,)
4
40
3. Results and Discussions Before consulting the quantitative aspects of the results it is pertinent to provide a qualitative description of the three electronic states studied. The ground state contains a pair of electrons in the in-plane ayand out-of-plane rxorbitals, respectively, and one electron in the C2,,, orbital on C’. As shown in Figure 2 the groundstate has a C, symmetry with the molecular frame in the YZ plane. Two excited states were generated by promotion of an electron from the in-plane ayorbital or the nearly degenerate out-of-plane axorbital. Also as shown in Figure 2 the net consequence of the excitations on the molecular geometry is to remove the C, symmetry; in the excited state the molecular frame distorts out of the YZ plane, but since it is symmetrical to the XY plane, a C, symmetry is retained. With respect to this latter plane, the 2A’state results by excitation of an electron from the ?r, molecular orbital to the half-filled C2p,orbital; a 2A” state results via promotion of a electron from the ayorbital. The change in symmetry generates some confustion because the in-pland and out-of-plane r molecular orbitals in C2, are the out-of-plane a molecular orbitals in the C, symmetry; as stated above this is due to the fact that the molecular frame distorts out of the YZ plane (Figure 2). Tables I and I1 list the molecular orbital energies, optimized geometrical parameters, and the total energies. Computer drawings of the optimized structures are in Figure 2. The potential energy surfaces are depicted schematically in Figure 3. 3.1. The *B, Ground State. While the experimental observations indicate that the ground state for the C3H3system has the propargyl radical structure, no empirical structural parameters are available. We obtained the optimized structural parameters for the ground electronic state of this radical using the single configuration S C F method with the 4-31G basis set and with a double {plus polarization basis set, and the MCSCF method with the 4-31G basis set. The results are given in Table I1 along with
23.1 /-
’
15.0 / ,T,/’ 1- A /
E,/
0
1-’6, (Opt. Geom.)
Figure 3. The relative energies of the ground and first two excited electronic states of the propargyl radical: first column, relative energies calculated at the 1-2Bl optimized geometry; second column, relative energies calculated at the 2-2A‘optimized geometry; third column, relative energies calculated at the 1-2A” optimized geometry.
the previous results which were obtained by the following methods: INDO,’ unrestricted Hartree-Fock (UHF) with a 4-31G basis set,8a and a a-CI with a STO-3G basis set.6 The following results are obtained from the present calculations: (1) A useful starting point is the SCF(DZP) molecular orbital energy listed in Table I where the molecular orbitals are listed according to their symmetry (C,) and total energy, and also a qualitative description is given for the pertinent valence orbitals. The molecular orbitals from l a l to 7al are those containing the C(ls), H(ls), and C(2s) and C(2p) orbitals essentially not involved with the a-bonding valence electrons. Of the three molecular orbitals of interest here the lbl, the out-of-plane a, orbital, has the lowest energy. The 2b2, the in-plane ayorbital, is slightly higher in energy with the 2bl, the half-filled C2p,orbital on C1, being the highest. (2) Both the S C F and MCSCF calculations show that the ground state has the propargyl radical structure. The structural parameters optimized by both S C F (restricted Hartree-Fcck) and MCSCF methods are similar to those given by the previous calculations. (3) The very small difference between the S C F (4-31G) and the SCF (DZP) geometries indicates a small polarization basis
TABLE II: Optimized Structures and Total Energies of the Lowest Three Doublet States of the CHICCH Radical
12-BIC R H F (4-31G) R H F (DZP) MCSCF (4-3 lG) 1-2A” C R H F (4-31G) MCSCF (4-31G) 2-2A’C MCSCF (4-31G)
C1-C2
distance, A CI-HII Cz-C3 C1-HZZ
1.405 1.419 1.394
1.196 1.196 1.223
1.069 1.073 1.070
1.05 1 1.059 1.051
120.7 120.6 120.9
180.0 180.0 180.0
180.0 180.0 180.0
1.295 1.318
1.366 1.370
1.072 1.072
1.087 1.085
121.1 121.0
174.2 168.0
115.7 117.3
90.0 91.3
-1 14.980 998 -1 15.026 792
1.425
1.324
1.070
1.07 1
120.4
153.1
129.4
94.7
-155.021 368
120 180.0 180
180 180.0 120
angles, deg LH”C1C2 C3-H31 LHIZC’CZ Present Results
LC1CzC3
LC2C3HHII LH”C1CZC3
total energy, au
-1 15.076 105 -115.262043 -115.15201 1
Previous Results l-2Bl
IN DO^ UHFd CI (STO-3G)‘
1.382 1.401 1.43
1.225 1.213 1.21
1.08 1.08 1.105
1.08 1.066 1.000
120 119.53 120
-1 15.091 41 -1 13.882 3
ODihedral angle between the HI1 plane and the C1C2C3plane. *See ref 7a. ‘The molecular plane is ( y z ) in C,, symmetry. The reflection plane ( x z ) in C,. dReference 7b. CReference6.
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The Journal of Physical Chemistry, Vol. 91, No. 17, 1987
set effect exists in the propargyl radical structure at the single configuration level. (4) The difference between the SCF (4-31G) and the MCSCF (4-3 1G) geometries shows that the configuration mixing effect enhances the out-of-plane ?r, bond conjugation with the half-filled Czp,orbital. The C1-C2 bond length decreases by 0.01 8,to 1.394 8, and the C2-C3bond length increases by 0.03 8, to 1.223 8, for the MCSCF results. (5) The hybridization on both the C2center and the C3center is sp. The C2-C3 triple bond length of 1.223 8,is a little longer than the acetylene triple bond length, 1.203 This may be explained by delocalization of the lowest energy K, orbital electrons into the C1-C2 bond. (6) The hybridization on the C’ center is sp2. The C1-C2 distance of 1.394 8,is much longer than the sp2-sp bond distance of allene, 1.308 and shorter than the sp3-sp bond distance of 1.459 8, for methylacetylene. (7) The MCSCF (DZP) wave function in the natural orbital CI expansion, which was calculated at the SCF (DZP) optimized geometry, showed that the X *BI state is described mainly by a single configuration of 2b:lb!2bi, weighted by 92.4%. The configuration with the next largest weight (1.7%) is 2b;lb:2b;3bi. Since this configuration corresponds to an in-plane rYto K,,* excitation it provides a rationale for the small geometrical parameter differences between the single configuration S C F and the MCSCF results. 3.2. The Excited Doublet States. 3.2.1. The 1-2B2and 2-2Bl States. As discussed in section 3.1, the ground electronic state of the propargyl radical has as the dominant configuration 2bilb:2bt3by3b;. The indicated five orbitals are the outermost valence obitals and they may be described as bonding (2b2 and lb,) and antibonding (3bl and 3b2) orbitals of propargyl triple bond and a nonbonding 2bl orbital. They are composed of the carbon 2p, (b, symmetry) and 2pY(b2 symmetry) orbitals. The low-lying valence states are expected to be described dominantly by the electron configurations which are generated by distributing five electrons among the five outer valence orbitals. Only the ’B, and 2B2symmetry configuration state functions arise from such , symmetry. We carried out the calculations configurations in C for the lowest 2B, excited state (2-*B1)and the lowest 2B2excited state (1-2B2). The 22Bl state is the result of excitation of an electron from the out-of-plane r, to the half-filled C12p,and the 12B2results from the in-plane rYto C12px excitation. First an MCSCF (4-3 1G) calculation was performed for the 22B, and 12B2at the SCF (4-31G) optimized geometry of the 1-2B1 state. The vertical excitation energy for the dipole forbidden 1-2B2 state is 102 kcal/mol. Only 3 kcal/mol above this state, the dipole-allowed 2-2Bl state is situated. This energy, 105 kcal/mol, is close to the energy region of the band system, 82.9-98.5 kcal/mol, which was observed2 during the flash photolysis of a series of compounds XCH2C=CH, where X = H, C1, Br, CH,, C2H5,or C,H,. The MCSCF wave functions in the natural orbital expansion showed that a single configuration description is not appropriate for both of the excited states. Two configurations contribute ap reciably to the 1-2B2state’s MCSCF wave function; these are 3 b ~ There are four dom2b21b:2b: (86%) and 2 b ~ l b ~ 2 b ~(11%). inant configurations in the 2-2B, state’s wave function; they are 2b21b’2b2 (69%), 2b:lbi2b73b: (8%), 2b;lby2b:3bi (7%), and 2b21b,2b,3b~ l A b (6%). These results suggest that a multireference large-scale (at least single-double electron excitations level) CI would be desirable for obtaining more accurate excitation energies. With respect to the ground-state dominant configuration 2bilb:2bi, the dominant configurations of the 1-2B2and 2-2B1 states correspond to the one electron transitions from triple bond orbitals (2b2 or l b l , Le., the in-plane T,, and out-of-plane K, orbitals) to the nonbonding half-filled 2bl orbital on atom C’. This
P
(13) For, example see, Pople, J. A. Mod. Theor. Chem. 1977, 4 , 1 , and references therein,. (14) Herzberg, G. Molecular Spectra and Molecular Structure, II, Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand: New York, 1945.
Honjou et al. may explain the near degeneracy of the l-2B2and the 2-2B1states. We have also calculated the MCSCF excitation energies by using the DZP basis set a t the 1-2B, ground electronic state geometry optimized by the MCSCF (4-31G) method. It was found that the MCSCF (DZP) excitation energies are almost identical with the MCSCF (4-3 1G) excitation energies; the differences are at most 2 kcal/mol. We chose the MCSCF (4-3 1G) method for the calculations of the CH2CCH excited-state surfaces. 3.2.2. Potential Surface Minima of the Doublet Excited States. Ramsay and Thistlethwaite2 found a relatively strong band at 86.04 kcal/mol in their observed electronic absorption spectrum and tentatively assigned it to the (0-0)band system arising from the excitation of the propargyl radical. Since some vibrational progressions were found in the spectrum, a potential well minimum for a doublet excited state might be expected to be situated closely around the Franck-Condon region of the ground-state equilibrium geometry. The dipole-allowed transition to the 2-2B1state is a candidate; however, no stable minimum was found in C, symmetry for this state. Therefore, the geometry was optimized for the two excited states in contention and MCSCF calculations were performed for the ground and the excited states at each of the excited-state geometries. The results of the geometry optimization are shown in Figure 2 and the total energies relative to the ground electronic state are contained in Figure 3. As shown in Figure 2 a lower C,symmetry is found for the excited states. By lowering , to C, the 2-2B, state (see Figure 3) corthe symmetry from C relates adiabatically to the 2-2A’ state, and the l-2B2state correlates adiabatically to the 1-2Af’state; the ground electronic state is 1-2A’at the C, symmetry. The calculation for the 2-2A’ state yielded a stable minimum (see Figure 3) lying 82 kcal/mol above the ground state, X-2Bl. At this geometry, the 1-2A” excited surface is situated at 7 kcal/mol above. The 1-2Af’excited-state state has a potential surface minimum at 79 kcal/mol above the ground state X-2B,. This minimum is 3 kcal/mol lower than the 2-2A’ state’s minimum. If the 1-2A” state minimum is the lowest minimum among the doublet excited state’s minima, it might be more possible that the fluorescence occurs from this minimum rather than the 2-2A’ state minimum, by going through internal conversion. The optimized geometrical parameters of the l-2A” and 2-2A‘ excited states are given in Table I from which the following observations may be drawn. (1) The optimized geometry for the 1-2A” state closely resembles an allenyl radical structure. The C’C2C3bond angle is 168”, which is close to linear. The C1-C2 distance of 1.3 18 8, is almost the same length as the C-C bond (sp2-sp) distance of 1.308 8,in allene.14 The C2-C3 distance of 1.370 8,is, however, much larger than the allene double bond length, since the C2-C3K,, orbital is a singly occupied orbital. We may say that the hybridization on the C’ and C3 centers is almost sp2 and that of the C2 center is approximately sp. (2) On the 2-2A‘ state, the hybridization of the C’ and C3 centers are almost sp2 and that on the C2 center is intermediate between sp and sp2. This observation is deduced from the following structural data: (a) The C1C2C3angle of 153’ is midway between 180” (sp hybridization on C2 center) and 120” (sp2 h bridization on C2 center). (b) The C2-C3 bond distance of 1.324 is between the allene double bond (sp-sp2) distance, 1.308 & I 4 and the ethylene double bond (sp2-sp2)distance, 1.338 A.14 (c) The C’-C2 distance of 1.425 8, is very close to the averaged value of ethylene double bond (sp2-sp2) distance, 1.338 A and butadiene central C-C single bond (sp2-sp2) distance, 1.483 .&I3 A plausible reason for the intermediate sp and sp2 hybridization on the C2 center is the delocalization of rYelectron on the C’-C2-C3 plane. 3.3. Vibrational Analysis of the Propargyl Radical. Jacox and Milligan3 reported the infrared absorption of all of the C3H, species with n C 4 via a matrix-isolation study of the vacuumultraviolet photolysis of allene and methylacetylene. They suggested that the absorptions at 484, 548,688, and 3310 cm-’, which appear upon photolysk, are due to the C3H3radical. Although the 548-cm-I band was not assigned, nevertheless the 484-cm-’ feature was attributed to a CCC skeleton mode because it did not
w
The Journal of Physical Chemistry, Vol. 91, No. 17, 1987 4459
Theoretical Study of the Propargyl Radical TABLE III: Normal-Made Vibrational Frequencies (cm-') vibrational frea, cm-I group
mode stretch stretch stretch stretch scissor rock stretch bend bend wag bend bend
symmetry a1 b2 a1 a, a1 b2 a1 b2 bl bl b, b2
calcd 3665 345 1 3345 2342 1606 1160 1072 875 852 568 443 406
obsd 3310
cf. 3429' 3106* 3010b 2150"
688
930' 642"
548 483
54OC 336d
bPropylene, ref 15. a Methylacetylene, ref 14, infrared spectra. cEthyl radical, ref 16 and 17. "Methylacetylene, ref 14,Raman spectra.
shift when deuteriated allene or methylacetylene was photolyzed. Also, a reasonable assignment for the 33 10-cm-' feature was the stretching of the acetylenic CH bond; a bond angle bending motion of the acetylenic C C H group was assigned to the 688-cm-' absorption. In order to elucidate the interpretation of the experimentally observed spectrum, a theoretical analysis of the harmonic frequencies was performed. The geometry was optimized and the harmonic frequencies were determinedI2 by using restricted open-shell Hartree-Fock calculations with a 4-31G basis set. The calculated harmonic frequencies and the experimental results of Jacox and Milligan are listed in Table 111. As usual the computed harmonic frequencies are about 10% higher than the observed values. A number of calculated frequencies for the propargyl radical agree with those characteristically observed for functional groups. These are the acetylenic CH stretching and bending frequency, the olefinic CH stretching frequencies, and the CC triple and single bond stretching frequencies. Very good agreement is obtained between the computed and the observed stretching frequencies when the former values are lowered by 10%. For example, the observed and adjusted theoretical frequencies for the acetylenic and olefinic C H stretching frequencies are 3429 (methyla ~ e t y l e n e ' ~ - '3400 ~ ) , cm-'; and 3086, 301 5 (pr~pylene'~.'~), 3 106, 3010 cm-I, respectively. A similar comparison is also found for the C C triplet bond stretching frequency, 21 50 (methyla ~ e t y l e n e l ~ ~965 ' ~ ) ,cm-', and the C C single bond stretching frequency, 930 (methyla~etylene'~~'~), 965 cm-I. The good
-
(15) Sverdlov, L.M.;Kovner, M. A.; Krainov, E. P. Vibrational Spectra of Polyatomic Molecules; Wiley: New York, 1970.
agreement between the theoretical stretching frequencies and the observed characteristic frequencies suggests that the CH and C C bonds in the propargyl radical closely resemble those in methylacetylene and propylene. This view is in concurrence with the assignment of the 3310-cm-' band to the acetylenic C H stretch by Milligan and Jacox? On this basis the band at 688 cm-' should be assigned to the out-of-plane deformation of the acetylenic C H bond; the frequencies of these motions appear in this region. Among the four bands which were observed in the IR spectra, the 483-cm-' band was assigned to the CCC skeletal deformation because it shifted very little as deuterium was substituted in the parent molecule.5 The calculated CCC bending vibrational frequencies are 443 cm-l for the out-of-plane mode and 406 cm-I for the in-plane mode. In the photoelectron spectra of CH,=C=CHand CD2= C=CH-, a single active vibration was observed. This mode had a frequency of 510 cm-' and was assigned as an out-of-plane bend of the acetylenic hydrogen of the propargyl radical by Oakes and E l l i ~ o n .Comparing ~ with the 688 cm-' of the C-H deformation frequency which was assigned by Jacox and Milligan, and the 875, 852 cm-' calculated frequencies, the 510 cm-' value is rather low. A reasonable assignment for the band observed by Oakes and Ellison and the 548-cm-' absorption reported by Milligan and Jacox is the out-of-plane deformation of the methylene group. This mode is observed a t 540 cm-l in the ethyl and is calculated at 500 cm-l by using similar S C F methods.I6 This mode for the propargyl radical is calculated at 568 cm-I. The slightly higher frequency may be a reflection of a small amount of T bonding in the C'-C2 bond.
4. Conclusion The molecular geometries and the electronic structures have been predicted by an ab-initio MCSCF method for the ground state and the lowest-lying doublet excited states of CHICCH radical. The l-,A" excited state has an equilibrium geometry similar to an allylic radical structure. Strong configuration mixing was found in the electronic structures of the doublet excited states, especially in the 2-2A' state. At the vertical excitation region of the l-,B1 state equilibrium geometry, the energy levels of the l-,A" and 2-2A' excited states are nearly degenerate. The separation is only about 1 kcal/mol at the MCSCF (4-31G) level. The vibrational frequencies have been calculated for the propargyl radical by an ab-initio single configuration S C F method and a vibrational analysis was performed. The overall agreement between the theoretical and the experimental values are fairly good. Registry No. CH2CCH,2932-78-7. (16) Pacansky, J.; Dupuis, M. J . Am. Chem. SOC.1982, 104, 415. (17) Pacansky, J.; Schrader, B. J . Chem. Phys. 1983, 78, 1033.
