J . Phys. Chem. 1991, 95, 1035-1040
1035
Ab Initio Examination of the Electronic Excitation Spectrum of CCH Antonios G,Kourest and Lawrence B. Harding* Theoretical Chemistry Group, Chemistry Division,Argonne National Laboratory, Argonne, Illinois 60439 (Received: March 13, 1990; In Final Form: July 21, 1990)
Large-scale MCSCF/MRSDCI calculations have been performed to examine the vertical electronic excitation spectrum of the ethynyl radical. Valence, Rydberg, and cationic states are calculated and discussed. The two observed UV transitions are discussed, and an assignment to the 8.9-eV transition observed by T. A. Cool is made. A value for the adiabatic ionization potential which is believed to be within f 0.1 eV of the true value is given, and its implication on the recent acetylene bond dissociation energy controvery is discussed. Comparison is made to an older study by Shih et al. and generally shows reasonable agreement with a few significant differences which are discussed.
1. introduction The ethynyl radical (CCH) plays a role in combustion processes as a reactive intermediate. It is thought to be a precursor in soot formation and has also been found to be among the most abundant species in interstellar space.'V2 Experimentally, it has been studied extensively by ESR,'*4 LMR? color center laser,@ matrix isolation infrared,lsl2 UV,I3 and microwave s p e c t r o ~ c o p y . ' ~ - More ~~ recently, diode laser ~pectroscopy'~ and time-resolved FTIRI8 studies have also been reported. In comparison, a surprisingly small number of theoretical studies on CCH have been The most extensive theoretical study to date is that of Shih et (SBP) in which the vertical excitation spectrum is calculated for some 49 of the lowest valence Rydberg and cationic states. Most of the studies, both theoretical and experimental, have focused on the low-lying A211+-X2Z+ transition. This transition lies in the 1R region, and the assignment of the spectrum has been complicated by perturbations between the A211 state and vibrationally excited states associated with the ground electronic potential surface. For this reason there is still some uncertainty over the energy of this lowest 211state. Stephens et al.9c have placed the origin of this transition at 0.47 eV, while Jacox et al.Ilb have reported evidence that the origin could be as low as 0.2 eV. Theoretical calculations are also not in complete agreement on the energy of this state. SBP22report a vertical excitation energy of 0.96 eV, significantly above that of several calculations including Hillier20(0.68 eV), Largo26(0.62 eV), and Thumme127(0.63 eV). However the adiabatic excitation energy reported by SBP,230.50 eV, is in reasonably good agreement with the results of several more recent calculations, including KraemerZS(0.45 eV) and T h i i m n ~ e (0.41 l ~ ~ eV), but significantly above the prediction of Fogarasi et al.,24who obtained an adiabatic excitation energy of 0.25 eV. Agreement between the theoretical calculations of SBP and the matrix isolation UV spectroscopy of Graham4J3is surprisingly poor. In the experimental studies two UV electronic transitions have been attributed to the CCH radical. The lowest consists of a vibrational progression ranging from 3.6 to 5.0 eV, peaking at 4.5 eV. This transition was originally assigned as either ( ~ U X ~ S U ~ ) ~(4a2n45a)X2Z+ ~Z+ or ( 4 ~ ~ n ~ 5 u n * ) 2 ~ Z (4a2r45a)X2Z+.The calculations of SBP placed both of these states at much higher energies, and they suggested the spin-forbidden transition (4a2n35a7r*)14Z+ (402r45a)X2Z+as an alternative assignment in that energy range. More recently, Graham et al." observed the second, higher energy progression originating at 6.4 eV and extending up to 7.7 eV. They have assigned this as ( 4 ~ 7 r ~ 5 0 ~ ) 3 ~ 2(402r45u)X2Z+ + and suggested that the previously observed transition at the lower energy must then be assigned as (4n2n350r*)22Z+ (4u2r45a)X2Z+ SBP predict vertical excitation energies to the 222+and 32Z+states of 7.3 and 9.6 cV, rcspcctivcly. Thus, for both states the calculations are
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'Current address: Allied Signal, Inc., Research and Technology, Math and Simulation Sciences Department, Des Plaines, IL 60017-5016.
2-3 eV above the experimental assignments. Resonance-enhanced multiphoton ionization (REMPI) spectroscopy of transient species is becoming a powerful tool in flame diagnostics. In order to make its application widespread, however, more spectroscopicdata are needed for the Rydberg states of flame radicals.28 Recently, mass-resolved (2 + 1) and (3 + 1) REMPI
( I ) Tucker, K. D.; Kutner, M. L.; Thaddeus, P. Astrophys. J . 1974, L I I S , 193. (2) Ziurys, L. M.; Saykally, R. J.; Plambeck, R.; Erickson, N. Astrophys. J . 1982, 94, 254. (3) Cochran, E. L.; Adtian, F. J.; Bowers, V. A. J. Chem. Phys. 1964, 40, 213. (4) Graham, W. R. M.; Dismuke, K. 1.; Weltner, W., Jr. J . Chem. Phys. 1974,60, 3817. (5) Saykally, R. J.; Veseth, L.; Evenson, K. M. J . Chem. Phys. 1984.80, 2247. (6) Carrick, P. G.; Pfeiffer, J.; Curl, R. F.; Koester, E.; Tittel, F. K.; Kasper, J. V. V. J . Chem. Phys. 1982, 76, 3336. (7) Carrick, P. G.; Merer, A. J.; Curl, R. F. J . Chem. Phys. 1983, 78, 3652. (8) Curl, R. F.; Carrick, P. G.; Merer, A. J. J . Chem. Phys. 1985,82,3479. (9) (a) Yan, W. B.; Hall, J. L.; Stephens, J. W.; Richnow, M. L.; Curl, R. F. J . Chem. Phys. 1987,86, 1657. (b) Yan, W. B.; Dane, C. B.; Zeitz, D.; Hall, J. L.; Curl, R. F. J. Mol. Spectrosc. 1987, 123,486. (c) Stephens, J. W.; Yan, W. B.; Richnow, M. L.; Solka, H.; Curl, R. F. J. Mol. Struct. 1988, 190, 41. (IO) Milligan, D. E.; Jacox, M. E.; Abouaf-Marguin, L. J. Chem. Phys. 1967, 46, 4562. ( 1 I ) (a) Jacox, M. E. Chem. Phys. 1975,7,424. (b) Jacox, M. E.; Olson, W. B. J. Chem. Phys. 1987,86, 3134. ( I 2) Shepherd, R. A.; Graham, W. R. M. J. Chem. Phys. 1987,86,2600. (13) Chang, K. W.; Graham, W. R. M. J. Chem. Phys. 1982, 76, 5238. (14) (a) Bogey, M.; Demuynck, C.; Destombes, J. L. Astron. Astrophys. 1985, LIS, 144. (b) Bogey, M.; Demuynck, C.; Destombes, J. L. Mol. Phys. 1989, 66, 955. (15) Sastry, K. V. L. N.; Helminger, P.; Charo, A,; Herbst, E.; DeLucia, F. C. Astrophys. J. 1981, L119, 251. (16) Gottlieb, C. A.; Gottlieb, E. W.; Thaddeus, P. Astrophys. J. 1983, 264, 740. (17) (a) Kanamori, H.;Seki, K.; Hirota, E. J. Chem. Phys. 1987,87,73. (b) Endo, Y.; Kanamori. H.; Hirota, E. Chem. Phys. Lett. 1989, 160, 280. (c) Kanamori, H.; Hirota, E. J. Chem. Phys. 1988,88.6699. (d) Kanamori, H.; Hirota, E. J. Chem. Phys. 1989, 89, 3962. (18) Fletcher, R. T.; Leone, S. R. J . Chem. Phys. 1989, 90, 871. (19) Barshun, J. Asrrophys. Leir. 1972, 12, 169. (20) Hillier, I. H.; Kendrick, J.; Guest, M. F. Mol. Phys. 1975, 30, 1133. (2 I ) So, S. P.; Richards, W. C. J. Chem. SOC.,Faraday Trans. 2 1975, 71, 660. (22) Shih, S.;Peyerimhoff, S. D.; Buenker, R. J. J . Mol. Spectrosc. 1977. 64, 167. (23) Shih, S.; Peyerimhoff, S. D.; Buenker, R. J. J. Mol. Specrrosc. 1979, 74, 124. (24) Fogarasi, G.; Boggs, J. E.; Pulay, P. Mol. Phys. 1983, SO, 139. (25) Kraemer, W. P.; Roos, B. 0.; Bunker, P. R.; Jensen, P. J. Mol. Spectrosc. 1986, 120, 236. (26) Largo, A.; Barrientos, C. Chem. Phys. 1989, 138, 291. (27) Thiimmel, H.; P e r k M.; Peyerimhoff, S. D.; Buenker, R. J. Z . Phys. D 1989, 13, 307. (28) Hudgens, J. W. In Adoances in Multi-photon Processes and Spectroscopy; Lin, S. H.. Ed.; World Scientific: Singapore, 1988; Vol. 4, p 171.
0022-3654/91/2095- I035%02.50/0 0 1991 American Chemical Society
Koures and Harding
1036 The Journal of Physical Chemistry, Vol. 95,No. 3, 1991
studies have been initiated which focus on the s and p Rydberg series of the ethynyl radical converging to the ground state of the cation, 311.29 In these studies, a careful search in the range from 216 to 500 nm expected to exhibit 3s and 3p Rydberg spectra yielded only a weak diffuse spectrum at 276 nm, which has been assigned to the ethynyl radical. In view of the current experimental interest on the Rydberg states of the ethynyl radical, we have reexamined the excitation spectrum of the radical. Our focus is on the 3s and 3p Rydberg states associated with the cation ground state. However, we have also examined some of the Rydberg states associated with the first excited state, 32-,of the cation. In addition to the vertical excitation energies of the Rydberg states, we will also report the excitation energies to a number of the valence states of the radical as well as the IPSto the lowest states of the cation. The importance of this work is that the present day state-of-the-art calculations may be compared with previous theoretical studies and recent experiments to put the excitation spectrum of the ethynyl radical on a more solid ground. The layout of this paper is as follows. In section 2, we discuss the computational details of the present calculations: basis sets, selection of active spaces, and MO bases for the CI calculations. I n section 3 we compare our results with those of previous theoretical and experimental studies. 2. Computational Details A multireference approach is used in all our calculations. Specifically, the molecular orbital coefficients were optimized by using the multiconfiguration self-consistent-field method (MCSCF),30and the correlation energy is calculated by using a multireference configuration interaction approach including all single and double excitations MRSDC1).31-32All the calculations were carried out using the COLUMBUS program package.33 Due to the symmetry restrictions of the integral codes, the calculations employ only C, and C, spatial symmetries for the linear and bent geometries, respectively. To carry out these calculations, we partition the orbital space into three segments: (i) a doubly occupied space, (ii) an active space, and (iii) a virtual space. In the MCSCF calculations the doubly occupied space consists of the la, 28, 3a, and 40 orbitals corresponding to the carbon 1s orbitals and the C-C and C-H a-bonding orbitals. The active space is defined to include the 50 orbital (a nonbonding sp hybrid orbital on the radical center) and the rx,rx*and 7rY, 7rY* orbitals. The virtual space consists of all the remaining orbitals. The MCSCF wave functions then include all configuration state functions (CSF's) that can be constructed by distributing five electrons (four for the cation) in these five active orbitals in all possible ways consistent with the spatial and spin symmetry of the required state(s). This is often referred to as a complete active space (CAS)34wave function. For the purpose of carrying out the MCSCF calculation to generate the optimum M O s for each state, the active orbitals are given "natural orbital resolution'' while the virtual orbitals are "Fock resolved". The MO's resulting from the MCSCF calculations described above are used as a basis for the MRSDCI calculations. The reference CSF's for the C1 calculations are generated in a manner similar to that described above, with two important differences. First, for the reference CSFs no spatial symmetry selection is used; Le., configurations of the wrong final symmetry are included in the reference list. This is necessary to ensure that the C1 energies are a smooth function of the bend angle, which lowers the symmetry from C,, to C,. Second, for calculations on Rydberg states, the valence orbitals are taken from an MCSCF calculation on the corresponding ion state. For these states the active space is (29) Cool,T.A. Private communication. (30) Shepard, R. Adu. Chem. Phys. 1987, 69, 63. (31) Kahn, L. R.;Hay, P. J.; Shavitt, 1. J . Chem. Phys. 1974, 61, 3530. (32) Blomberg, M.R.A.; Siegbahn, P. E. M. Chem. Phys. Lett. 1981,81. A
( 3 3 ) Shepard, R.; Shavitt, 1.; Pitzer, D. C.; Pepper, M.; Lischka, H.; Szalay. P. G.;Ahlrichs, R.; Brown, F. B.; Zhao, J. I n f . J . Quantum Chem. 1988, s22, 149. (34) Roos, B. 0.Ado. Chem. Phys. 1987, 69, 399.
T
s 2.
's
s *
-11
'
I
8 4
9 s *
0 -4
-8 -11 - 1 2 - 8 - 4
0
(4
4
8
Figure 1. Contour plots of the 3s and 3p Rydberg orbital amplitudes. The contour interval is 0.01. Positive contours are shown with solid lines, negative contours with dashed lines, and nodes with dotted lines.
augmented with additional (Rydberg) orbitals. The added Rydberg orbitals are the lowest "Fock-resolved" virtual orbitals from the MCSCF calculation on the corresponding ion. For the a-type Rydberg states, two such orbitals are added to the active space, the 60(3s) and 7a(3pZ) (see Figure 1). For the *-type Rydberg states, the active space is augmented with the 37r, (3px) and 37ry (3py) orbitals (see Figure I ) . Thus, for the valence states the active space is identical with the MCSCF active space described above, while for the Rydberg states the active space consists of seven orbitals, five valence orbitals taken from the active space of the corresponding ion, and two Rydberg orbitals taken from the virtual space of the ion. The reference CSF's for the CI calculations are then taken to be all possible ways of distributing five electrons (four for the ion states) among these active orbitals consistent with having the correct spin symmetry and with the restriction that at most one electron be allowed into the Rydberg orbitals. The MRSDCI calculations thus include all CSF's, of the correct symmetry, generated by taking all single and double
Electronic Excitation Spectrum of CCH
excitations, relative to these reference CSF's (with the restriction that the carbon Is orbitals are kept doubly occupied). To check the accuracy of using ion orbitals for CI calculations on Rydberg states, we made a comparison of the MRSDCI vertical excitation energies to the 411(3s) Rydberg state obtained using orbitals from ( I ) an MCSCF calculation which included the 3s orbital in the active space and (2) the cation orbital approach outlined above. The two calculations agreed to within 0.003 eV. The basis sets used in these calculations are the "correlation consistent" basis sets developed by Dunning.35 Most of the calculations reported here employ the polarized double-f basis set (DZP), consisting of (9s4pI d/4s I p) primitive Gaussians, contracted to [3s2pld/2slp]. This basis set is augmented with two s and one p Rydberg function centered on each of the carbons for a total of 43 functions. The exponents of these Rydberg functions are optimized for the carbon atom in its 3P(2s22p13s') and 3D(2sZp'3p1)states, for the s and p functions, respectively, using the correlation consistent procedure outlined by Dunning. The optimum exponents are 0.041 26 and 0.016 591 for the s and 0.022 25 for the p. In order to check the accuracy of the DZP calculations, selected states were also calculated with a polarized triple-f (TZP) basis set. The TZP basis set consists of (10s5p2dl f/Ss2pld)/[4~3p2dIf/3s2pld] functions augmented with two s Rydberg functions having exponents of 0.041 88 and 0.016 84 and one p Rydberg function with an exponent of 0.021 56 for a total of 84 functions. The Rydberg function exponents are obtained in a manner analogous to the double-f case described above. In the next section we present and discuss the MRSDCI vertical excitation energies obtained by the above prescription. We also report the energies corrected for higher order (quadruple) excitations using the normalized Davidson c o r r e ~ t i o nreferred ,~~ to here as DV2. This is defined as DV2 = (1 - ~ , , f 2 ) A / ~ , , f z (35) Dunning, Jr., T. H.J . Chem. Phys. 1989, 90, 1007. (36) Shavitt. 1.; Brown. F. B.: Burton, P.G. Inf. J . Quantum Chem. 1987, 31, 507.
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
where A = Ecl - Ercfand crcf2=
1037
re^:.
3. Results and Discussion Tables I, 11, and 111 contain all states calculated in this work, ordered by energy, starting from the ground state on up for the valence states, the Rydberg states, and ionic states, respectively. Along with each state, these tables list the type of transition (in parentheses) producing it, the dominant configuration(s) with associated weight(s) necessary for its description, cret,and the dimension of the CI matrix solved. These tables emphasize that the majority of the states of CCH require a multiconfigurational description. Tables IV, V, and VI contain the vertical excitation energies to the valence, Rydberg, and ion states, respectively, as calculated from the CI and CI + DV2 total energies. These tables also include the corresponding results from the SBP study as well as what is currently known experimentally. Table VI1 contains the optimized geometries for a few states of the radical and its cation. Table Vlll gives the term value for each Rydberg state (Le., its binding energy relative to the corresponding state of the ion), along with the value of the quantum defect (6). Finally, Table IX lists vertical and adiabatic ionization potentials to the 'I'I state, calculated with the DZP and TZP basis sets, including our theoretically estimated value and experimentally observed range of values. 3.1, ValenceStates. Examination of Table 1V shows that the agreement between the present study and that of SBP is reasonable for most of the valence states. The average difference is -0.3 eV with the present calculations giving generally lower excitation energies. These differences are probably due primarily to two important factors: (i) the basis set used here is larger then that used by SBP, and (ii) the present CI calculations utilize MO bases which are optimized for each state of interest. The values obtained for the geometry of the ground 22+state and first excited 211 state are in excellent agreement with exp e r i m e n ~ ~As . ' ~can be seen in Table VII, both states possess linear report from exgeometries. For the 2Z+state, Bogey et a1.14a*b perimental r, structures a C-C distance of 2.30 bohrs and a C-H
1038 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
8.27 8.12 8.8 I 8.46 8.1 1 9.60 6.4e "Numbers in parentheses reflect the TZP results. bThe DZP ground-state energy E,, is -76.395 985 hartrees and ECI+DV2 is -76.409 71 8 hartrees. Reference 22. Reference 4 and 13. Reference I 3. distance of I .97 bohrs. This compares well with our T Z P results of 2.30 and 2.00 bohrs for the C-C and C-H re distances, re2 1
22+
Koures and Harding
spectively. For the 211state the experimental data of Yan et al.9b yield rs distances of 2.44 and 2.00 bohrs for C-C and C-H, respectively. Our T Z P calculation gives C-C at 2.44 bohrs and C-H at 2.02 bohrs. Our best e imate of the A211 X2Z+ vertical excitation energy from the T P calculation is 0.67 eV. This compares very well with the previous calculations of Hillier et aLzoThiimmel et aI.,*' and Largo et a1.26but is significantly below the earlier SBP result.
F
+-
Electronic Excitation Spectrum of CCH
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 1039
TABLE Vi: Vertical Excitation Energies (in eV) to ionic States"*
state
CI
3n
1 1.28
32-
12.32 12.45
In
CI
+ DV2 11.37 12.42 12.54
SBPC 1 I .04 12.57 12.43
"For the )lI state, Ecl is -75.981 57 hartrees and ECI+DVz is -75.991 72 hartrees. bSee Table IV for the ground-state energy of the neutral species. e Reference 22. TABLE VII: Equilibrium Geometries of Various States'qb CCH(?P) CCH(*n) CCH+(311) CCH+OZ-)
R(CC) 2.33 (2.30) 2.48 (2.44) 2.42 (2.39) 2.63
R(CH) 2.04 (2.00) 2.05 (2.02) 2.07 (2.04) 2.09
"All of the above states were found to be linear. bNumbers in parentheses are TZP results. All distances are in bohrs. TABLE VIII: Term Values and Quantum Defects (6) for Rydberg States Corresponding to the First Two Ionic States" I l l ( 1 1.37 eV) )Z- (1 2.42 eV) term d term 6 o-type Rydberg 4n(3s) 3.32 (0.98) 42-(3s) 3.61 (1.06) states zn(3s) 3.20 (0.94) *2-(3s) 3.45 (1.01) 411(3p,) 2.90 (0.83) 42-(3p,) 3.23 (0.95) 2n(3pZ) 2.69 (0.75)
"-type Rydberg '2+(3p) 2.46 (0.65) states 2Z+(3p) 2.36 (0.60) 4A(3p) 2A(3p) 42-(3p) 2Z-(3p)
2.34 2.31 2.27 2.26
"All calculated from the CI
(0.59) (0.57) (0.55) (0.55)
+ DV2 vertical excitations.
TABLE IX: Calculated Vertical and Adiabatic Ionization Potentials for C2H and CzHz Cations Using DZP and TZP Basis Sets" vertical adiabatic C2H C2H2
DZP
TZP
DZP
TZP
observed
11.37 11.14
11.61 11.32
11.25 10.96
11.48 11.24
(11.51,6 11.6: 11.96d) 11.40e
"All results shown are obtained by using the CI + DV2 energies. Reference 38. Reference 39. Reference 40. Reference 41. With the TZP basis we calculate an adiabatic excitation energy of 0.44 eV. This is in good agreement with calculations of Kraemer et a1.25and Thummel et al.27 and the experimental assignment of Stephens et aI.% (Note that Kraemer et al. predict a zero-point correction of
