J. Phys. Chem. 1991, 95,6905-6908
6905
Ab Inltio Theoretical Study of the HC2 -t CO Reaction and the HC2C0 Radical Zdenko A. Tomagit and Gustavo E. Scuseria* Department of Chemistry and Rice Quantum Institute, Rice University, Houston, Texas 77251 - 1892 (Received: February 12, 1991)
The ethynyl radical, carbon monoxide, and their product (HC,CO) have been studied at the self-consistent field (SCF), configuration interaction, and coupled cluster correlation level including all single and double excitations (CISD and CCSD, respectively). The basis sets employed were of double {plus polarization (DZP) and triple {plus double polarization (TZ2P) quality. The geometries were optimized at both the SCF and CISD levels of theory. The energetics of the reaction were also studied by employing the open-shell coupled cluster method. A nonlinear HCzCOproduct was found to be a minimum while the linear HC2C0structure proved to be a stationary point with two imaginary frequencies. Our best theoretical prediction after correction for basis set superposition error and zero-point vibrational energy yields for HCzCO a binding energy of 20.0 kcal/mol with a very small (0.8 kcal/mol) activation barrier. Vibrational frequencies are also presented.
Introduction The ethynyl radical (HC,) importance stems from its intermediary role in a number of environments. It figures prominently as a precursor in the soot formation of combustion processes' and has been detected in interstellar space2 Lander et ala3studied the kinetics of its reactions with simple hydrocarbons, carbon monoxide, oxygen, and deuterium. They found not only hydrogen abstraction but also two different mechanisms of forming carbon monoxide (in the reaction with oxygen). In a recent paper, Lander, Unfried, Glass, and Curl' obtained a third-order rate constant for the reaction of HC2 with CO. Their results seemed to indicate the presence of an HC2C0 complex under the experimental conditions. The ethynyl radical has also been the focus of recent experimental studies concerning its photodissociation? vibrational properties?S6 and reaction with alkynes.' The electron affinity of HC2 has also received considerable attention both from the theoretical and experimental viewpoints.* In this paper, we have studied the reaction of HC2 with CO and explored the HC2C0 potential energy surface employing high quality ab initio methods and large basis sets.
Theoretical Approach The smallest of the basis sets employed in this study is the standard Huzinaga-Dunning double { Ius polarization (DZP) basis set C, N(9sSp/4s2p), H(4s/2s)?J The scaling factor for the hydrogen primitive Gaussian s functions was (1 .2)2 = 1.44. Polarization function orbital exponents were q ( C ) = 0.75, ad(N) = 0.80, and a,(H) = 1.OO. The triple { (TZ) basis sets are based on the Hu~inaga-Dunning~J'C, N( 1Os6p/5s3p), H(Ss/3s) contraction scheme. The TZP (triple {plus polarization) polarization function orbital exponents were the same as for the DZP set. The TZ2P basis set consists of the T Z set with the addition of two sets of polarization functions. The polarization function exponents for this basis were chosen as ap(H) = 1.40,0.25 and ad(C,N) = 1.50,0.35. Proper sets of five d functions were included as polarization functions with the TZ2P basis sets while all six Cartesian components were kept with the smaller DZP basis set.
!
(1) Report 1988, DOE/ER/13508-2, Order No. DE88Ok457, Energy Research Abstract [13], Abstract No. 15525, 1988. (2) Brown, P. D.; Charnley, S.B.; Millar, T. J. Astrophys. Space Sci. Ubr. 1 9 0 , 116,263. (3) Lander, D. R.; Unfried, K. G.; Stephens, J. W.; Glass, G. P.; Curl, R. F. J . Phys. Chem. 1989,93,4109. (4) Lander, D. R.; Unfricd. K. G.; Glass, G. P.; Curl, R. F. J. Phys. Chem. 1990,94,7759. (5) Fletcher, T. R.; Leone, S. P. J . Chcm. Phys. 1989, 90,871. (6) Brown, J. M.;Erenson, K. M. J. Mol. Spcctrosc. 1988, 131, 161. (7) Brachhold, H.; Alkmade, K.; Hormann, K. H. Bcr. Bunsen-Ges., Phys. Chcm. 1988, 92,916. (8) Lima, E. G.; Canuto, S. In?. J . Quanrum Chcm., Quanrum Chem. Symp. le,22. 199, and references therein. (9) Huzinaga, S . J . Chem. Phys. 1965.42, 1293. (IO) Dunning, T. H. J . Chem. Phys. 1970, 53, 2823. (11) Dunning, T. H. J . Chcm. Phys. 1971, 55, 716.
Electron correlation effects were based upon configuration interaction'? and coupled cluster13theory including all single and double excitations (CISD and CCSD, respectively). The effect of triple excitations was also included by addition of a perturbative correction to CCSD. The recently proposed CCSD(T) method'' has been employed in several s t u d i e ~ ' ~with ' ' great success and proven to be a reliable, cost-effective technique for inclusion of triple excitations.I8 Geometry optimizations for all species studied in this work were carried out by employing analytic gradient techniques at the restricted Hartree-Fock SCF19 and CISD20levels of theory. In all correlated calculations the four innermost orbitals were kept frozen (inactive) and the four highest virtuals were deleted. Harmonic vibrational frequencies and infrared intensities were evaluated at the SCF level of theory employing analytic second derivative methods12while CISD frequencies were obtained by finite difference of analytic first derivatives. The open-shell coupled cluster calculations were carried out using a recently developed CCSD and CCSD(T) program that is based on restricted Hartree-Fock references. In all HC2C0 calculations symmetry was restricted to the C, point group while the C, point group was used for carbon monoxide, the ethynyl radical, and linear HC2C0. The number of single and double excitation amplitudes for HCzCO at the CCSD level of theory with the DZP and TZ2P bases were 449 547 and 547 838, respectively. All calculations were carried out on the NEC SX2-400 supercomputer at HARC (Houston Advanced Research Center) employing previously developed p r o g r a m ~ . ' ~ J ~ J ~ ~ ~ ~
Results and Discussion Four stationary points at the SCF and CISD levels of theory were located on the HC30 potential energy surface. yPropynonyl" (Figure 1) and cyclopropenonyl (Figure 2) correspond to minima. (12) Saxe, P.; Fox, D. J.; Schaefer, H. F.; Handy, N. C. J. Chcm. Phys. 1982, 77, 5584. (13) Scuseria, G. E.; Jansscn, C. L.; Schaefer, H. F. J . Chem. Phys. 1988, 89. - - , 1382. . - - -. (14) Raghavachari, K.; Trucks, G. W.; Pople, J. A,; Head-Gordon, M. Chem. Phys. Lett. 1989,157,419. ( I S ) Lee, T. J.; Scuseria, G. E. J . Chem. Phys. 1990, 93, 489. (16) Lee, T. J.; Rendell, A. P.; Taylor, P. R. J. Chem. Phys. 1990, 93, 6636. (17) Scuseria, G. E. J . Chem. Phys. 1991, 94, 442. (18) Scuseria, G. E.; Lee,T. J. J. Chem. Phys. 1990, 93, 5851. (19) Brooks, B. R.; Laidig, W. D.; Saxe, P.; Goddard, J. D.; Yamaguchi, Y.; Schaefer. H. F. J . Chem. Phys. 1980, 72,4652. (20) Rice, J. E.; Amos, R. D.; Handy, N. C.; Lee, T. J.; Schaefer, H. F. J . Chem. Phys. 1986,85,963. (21) Saxe, P.; Yamaguchi, Y.; Schaefer, H. F. J . Chem. Phys. 1982, 77, 5647. (22) Scuseria, G. E. Chem. Phys. kr?. 1991, 176, 27.
, ,12095-6905502.50/0 .. .. ., - 0 1991 American Chemical Society 0022-3654191 ~~~
~
6906 The Journal of Physical Chemistry, Vol. 95, No. 18, 1991
TomaSiC and Scuseria
TABLE I: Vibratiwl Frqucacies (em-') witb IR Latcsdtkr ( W d )(in Parenthesea) md Zero-Point V i h t k m l lkrgiea for the Bent ('PIOPYW~YI"~Finun 1) md CYCUC (Cy~lopropca~l, F i p ~ n2) HC2CO Stnrcture~ 'propynon yl" 'propynon yl" 'propynon y I" cyclopropenonyl DZP-SCF TZ2P-SCF DZP-CISD DZP-SCF v,(a') 3409 (1 1) 3413 (3) 3442 (16) 3386 (12) da') 2392 (2245) 2374 (2214) 2305 (1360) 2051 (1574) YAa') 1909 (76) 1758 (107) 1719 (73) 1901 ( 8 5 ) 1041 (4) y4(a') 1046 (9) lo02 (4) 1103 (110) 4a") 915 (63) 890 (60) 685 (72) 856 (74) Y6W) 743 (86) 667 (92) 738 (67) 987 (33) 378 (15 ) 4a') 539 (37) 544 (29) 780 (72) da") 284 (7) 241 (11) 265 (9) 604 (1) da') 158 (23) 136 (19) 199 (12) 560 (16) ZPVE cm-l 5698 5637 5324 6051 kcal/mol 16.3 16.1 15.2 17.3 TABLE 11: Vibrational Frequencies (cm-I) with IR Intensities (km/ml) (in hmtbeses) a d Zero-Pdnt Vibrational Energies for the Linear HC2C0 Structure DZP-SCF TZ2P-SCF DZP-CISD 3607 (96) 3567 (81) vl(al) 3623 (105) 2365 (924) 2302 (794) 4%) 2375 (951) 1901 (82) 1843 (24) 1883 (68) u3(al) 958 (9) 959 (2) udal) 949 (11) 926 (13) 813 (23) udbz) 921 (IS) 691 (44) 621 (28) u6(b2) 665 (50) 333 (9) 282 (9) u7(bl) 325 (16) 214 (1) 227 ( I ) 235 (1) db2) 242i (64) 303i (24) u9(bl) 2441 (103) 31 li (40) 502i (71) u,o(b,) 378i (4) ZPVE cm-' 5485 5507 5300 kcal/mol 15.7 15.7 15.2 05
05 cyclopropenonyl radical H1C2 C2C3 c3c4
c2cs
C405
I
HlC2C3
c3
c2c3c4
d
c4c2c3 05C4C3 05C4C2
'propynonyl" radical
SCF DZP
CISD DZP
SCF TZ2P
H 1CZ C2C3 c301 C405
1.075 1.278 1.296 1.147
1.075 1.271 1.311 1.168
1.070 1.264 1.287 1.135
n 1c2c3 c2c3c4 c3c4c5
136.2 155.5 173.3
139.1 158.8 171.5
137.1 159.1 174.7
Figure 1. 'Propynonyl" radical (HCzCO) optimized geometries (bond lengths in A, bond angles in deg). This structure was found to be a minimum at all three levels of theory. The corresponding vibrational frequenciesare reported in Table I.
These two radical isomers were found to have C,symmetry. The third structure is a transition state for the HC2 CO addition (Figure 3). The fourth structure is linear (Figure 4) and has two imaginary frequencies whose normal modes correspond to bending motion. The first three structures are 2A' states, while the fourth one is a *Bt state. The IR vibrational frequencies with the corresponding infrared intensities at the DZP-SCF, TZZP-SCF, and DZP-CISD levels of theory are reported in Tables 1-111. The
+
DZP TZ2P
DZP SCF
CISD
SCF
1.077 1.337 1.461 1.461 1.185
1.073 1.319 1.431 1.452 1.174
1.068 1.308 1.429 1.450 l.lG2
153.9 62.8 62.8 156.1 149.4
152.2 63.6 62.0 155.2 150.3
152.2 63.8 62.2 155.6 150.4
Flgcpe2. C lclopropenonylradical (HCzCO)o p t i d geometries (bond lengths in , bond angles in deg). This structure was found to be a minimum at all three levels of theory. The corresponding vibrational frequencies at the DZP-SCF level only are reported in Table I.
TABLE 111: H C g O Tnari*Strte Vibntiolul Frequencies (em-') witb IR Intensities (km/mol) (in Pareatkses) md Ztro-Poiat Vibrational Enemies transition-state radical DZP-SCF
3628 (69) 2370 (323) 2204 (22)
763 (41) 780 (37) 315 (4) 102 (9) 102 ( 5 ) 54% (4) 5132 14.7 calculated equilibrium geometries for these structures are presented in Figures 1-4.
The HC2
+ CO Reaction and the HCzCO Radical
The Journal of Physical Chemistry, Vol. 95, No. 18, 1991 6901
TABLE IV: Total h e r g l d for HCICO As Predicted by the SCF, CISD (with rad witbout Ihridsos's Correction +Q),CCSD, rad CCSD(T) Metkde U8ing V8rlolg Bmis scb method/optimized geometry
'prop ynon y I" (Figure 1)
cyclopropenony I (Figure 2) DZP Basis
transition state (Figure 3)
linear structure (Figure 4)
0.93519 0.41039 0.47539 0.48595 0.51287
0.92052 0.39906 0.46301 0.47 1 1 1 0.49727
0.88951 0.35935 0.42510 0.43798 0.46081
0.93014 0.40651 0.47101 0.48042 0.50583
SCF/SCF CISD/CISD CISD+Q/CISD CCSD/CISD CCSD(T)/CISD SCF/SCF CCSD/DZP-CISD CCSD(T)/DZP-CISD 4Energiesare reported in hartrecs as -(E
TZ2P Basis 0.96887 0.58200 0.61807
0.94990
0.96509 0.57798 0.61263
+ 188) for the SCF method and -(E + 189) for all correlated methods. TABLE V: Relative Energies (in LcaVmol) of Different HClCO Isomers As Predicted by the SCF, CISD (with md witbout Davidsoa's Correction +Q),CCSD, rad CCSD(T) Methods Ushg V8rioucl Basis sets*
binding activation energy barrier
method/optimized geometry
Eop-Ep
El-Ep
&-E,
EU-Er
18.3 29.4 30.3 29.7 33.6
10.4 2.6 1.2 0.4 -0.9
DZP Basis
_.--
SCF/SCF CISD/CISD CISD+Q/CISD CCSD/CISD CCSD(T)/CISD
c4
HlC2 C2C3 c3c4 C405
DZP SCF
DZP CISD
1.194 1.064 1.212 1.064 2.055 2.216 1.118 1.136
HlC2C3
05C4C3
177.6 170.6 125.7
177.1 176.0 126.0
c2c3c405 H LC2C3C4
180.0 180.0
180.0 180.0
c2c3cA
Figure 3. HCICO transition-state geometry (bond lengths in A, bond angles in deg) for the HCz + CO reaction.
H1
C2
C3
05
C4
'propynonyl" radical
DZP SCF
DZP CISD
TZ2P SCF
H 1C2 C2c3 c3c4 '305
1.059 1.223 1.319 1.159
1.063 1.242 1.317 1.177
1.053 1.212 1.311 1.146
3.2 2.4 2.8 3.5 4.4
TZ2P Basis SCF/SCF 11.9 2.4 16.4 CCSD/DZP-CISD 13.9 2.5 30.0 CCSD(T)/DZP-CISD 3.4 33.9 Op = 'propynonyl", cp = cyclopropenonyl, I = linear structure, ts = transition state for the HCz + CO reaction, r = HCz + CO reactants.
H1 transition s l a k radical
9.2 7.1 7.8 9.3 9.8
R@Jn4. Linear 'propynonyl" radical (HCzCO) optimized geometries (bond lengths in A)* structure has two imaginary frWenciesat all three levels of theory. The corresponding vibrational frequencies are reported in Table 11.
Our predictions at the DZP-SCF, TZ2P-SCF, and DZP-CISD levels of theory indicate that HCzCO is nonlinear, defies a classical localized bond description in terms of formal CC triple and CO double bonds, and is probably better represented by an intermediate structure between propynonyl ( H C E P C C . 4 ) and the corresponding cumulene radical ( H C ' - C = C 4 ) . At the DZP-CISD level the CICt bond length (1.271 A) is slightly shorter than the typical carbon-carbon double bond. Basis set improvements are likely to shorten this bond length to somewhere in between a typical double and triple bond (1.28-1 -20 A). The
C3C4bond length at the DZP-CISD level of theory (1.3 1 1 A) is certainly longer than the typical double bond. It is evident that the predicted HCzCO equilibrium geometry does not correspond to a classical structure. The magnitudes of the dipole moment for the 'propynonyl" radical at the DZP-SCF, TZ2P-SCF, and DZP-CISD level of theory are 1.942, 1.835, and 1.555 D, respectively. On the other hand, the calculated dipole moments for the cyclopropenonyl radical are much larger: 3.475 and 2.968 D at the DZP-SCF and TZ2P-SCF levels, respectively. The geometry of the transition state for the addition reaction between ethynyl radical and carbon monoxide (Figure 3) suggests that the approximate sp-hybridized orbital with an unpaired electron attacks an sp2 hybrid orbital on carbon monoxide. The ethynyl moiety is however already beginning to bend although it remains close to the classical propynonyl radical structure. The total energies of the species studied in this work are presented in Table IV, and relative energies are shown in Table V. The designations in the tint column are as follows: the symbol to the left of slash indicates the particular method employed to calculate the energy while the symbol to the right of slash indicates the method used to optimize the geometry. Since the CISD method is not size extensive, supermoleculeaggregates (ethynyl radical and carbon monoxide moieties separated by 200 bohn)
were used in product/reactants energy comparisons. With all methods and basis sets employed in this work, the extended "propynonyl" radical is predicted to be more stable than the cyclic isomer. At the DZP-CCSD(T) level of theory, the energetic difference is 9.8 kcal/mol with triple excitations contributing only 0.5 kcal/mol. Extending the basis set from DZP to TZ2P makes this difference even bigger. At the TZ2P-CCSD level of theory "propynonyl" is 13.9 kcal/mol more stable than the cyclic structure. The binding energy of "propynonyl" is predicted to be 33.6 and 33.9 kcal/mol at the CCSD(T) level of theory employing the DZP and TZ2P basis sets, respectively. However, these predictions are
6908
J. Phys. Chem. 1991, 95,6908-6912
substantially modified after correction for basis set superposition error (BSSE). Employing the counterpoise method in the presence of the full ghost basis, the binding energy is reduced to 20.1 and 24.0 kcal/mol at the DZP-CCSD and DZP-CCSD(T) levels of theory, respectively. Applying this DZP-CCSD-derived correction (9.6 kcal/mol) to our best theoretical prediction at the TZ2PCCSD(T) level of theory (33.9 kcal/mol), an estimate of 24.3 kcal/mol is obtained. The barrier for the addition reaction of HC2 + CO (Table V) becomes smaller with increasing correlation effects. The effect of triple excitations is to reduce the reaction barrier to -0.9 kcal/mol, and to increase the binding energy to 33.6 kcal/mol. As expected, the reverse reaction from "propynonyl" to ethynyl radical and carbon monoxide has a large barrier of -30 kcal/mol (see Table V). The zero-point vibrational energy correction (ZPVE) determined at the DZP-SCF level of theory decreases the binding energy of the cyclopropenonyl radical by 4.3 kcal/mol. Including the DZP-SCF ZPVE correction, the 'propynonyl" binding energy is decreased by 3.3 kcal/mol and the activation barrier for the HC2 CO reaction is increased by 1.7 kcal/mol.
+
Conclusions
The product of carbon monoxide and ethynyl radical addition reaction is a nonlinear molecule with a highly delocalized unpaired electron. Its structure is somewhere between propynonyl and the corresponding cumulene radical. Our calculations indicate that the linear HC2C0structure is a stationary point in the potential
energy surface with two imaginary frequencies. At all levels of theory investigated in this work, the nonlinear structure is favored over the linear HC2C0 by 3-4 kcal/mol (see Table V). Correlation effects are found to be of the utmost importance for the activation barrier of the addition reaction. It is unlikely that reoptimization of all predicted structures at the CCSD level of theory will change our main energy conclusions. The contribution of triple excitations stabilizes the "propynonyl" radical relative to ethynyl radical and carbon monoxide. It also reversa the sign of the reaction barrier; Le., the reaction essentially proceeds without an activation barrier and makes the reverse reaction even more unfavorable. Our best theoretical prediction of 0.8 kcal/mol after BSSE and ZPVE corrections for the activation bamer is in line with the usual expectations for radical reaction barriers. The best theoretical estimate for the energy stabilization of the "propynonyl" radical relative to the reactants is 20.0 kcal/mol, after BSSE and ZPVE corrections. Our calculations indicate that the cyclopropenonyl isomer is energetically higher than the "propynonyl" radical.
Acknowledgment. We are thankful to Professor Robert Curl for helpful discussions. Acknowledgement is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. The authors gratefully acknowledge computer time on the NEC-SX2 supercomputer at HARC (Houston Advanced Research Center). Registry No. Ethynyl radical, 2122-48-7; carbon monoxide, 630-08-0; propynonyl radical, 134389-55-2;cyclopropenonyl radical, 135312-12-8.
Electron Correlation Effects on the Calculated Dlpole Moments of Fulvene and Cyclopentadiene Eric S.Replogle," Gary W.Trucks,1band Stuart W . Staley**l' Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, and AT& T Bell Laboratories, Murray Hill, New Jersey 07974 (Received: March 13, 1991)
The dipole moments of fulvene and 1,3-cyclopentadieneare calculated by ab initio molecular orbital theory. The dipole moment of cyclopentadiene can be accurately calculated by Hartree-Fock theory with large basis sets, but it is necessary to include the effects of higher order (MP4 or QCI) electron correlation to accurately reproduce the experimedtal result for fulvene. The MP2 correction to the HartretFock dipole moment of fulvene causes a greater discrepancy with the experimental result. It is shown that these results are primarily a consequence of how the electron correlation method corrects the T component of the dipole moment.
Fulvene (1) is a nonaltemant hydrocarbon that is often viewed as a relatively polar molecule.2 This view is generally rationalized on the basis of a significant contribution from resonance form le, in which r-electron density is transferred from the exocyclic bond to an "aromatic" five-membered ring. The perceived exceptional importance of the latter representation probably derives in part from an early estimate and measurement (in benzene) of the dipole moment of 1 of 1.2) and 1,l D,' respectively. Subsequently, the dipole moment of 1 was determined by microwave spectroscopy to be 0.42 D', demonstrating that 1 is actually no more polar than 1,3-cyclopentadiene(2)6 in the gas phase. The dipole moment ~ _ _ _ ~ ~ _ _ _ _ _ _____ _ _ _
.
_
_
of fulvene has been difficult to reproduce on the basis of ab initio molecular orbital models,' although semiempirical calculations limited to r electrons have given reasonable values6and a recent semiempirical calculation closely reproduced the dipole moment, but not the structure, of fulvene? 1
4
1
la
~
( I ) (a) Carnegie Mellon Univenit (b) ATdtT Bell Laboratories. Current address: Lorentzian, Inc., Norti Haven, CT 06743 (2) (a) Yatcs, P.Adu. Alkyclic Chem. 1968,2,59. (b) Mulliken, R. S . In M&mHIII Encyclopedia of Chemistor.Parker, S. P.;Ed.;Mdjraw-Hill: New York, 1982; -215; (3) Wheland, W.; Mann, D. E. J. Chcm. Phys. 1949, 17, 264. (4) Thicc, J.: Wiemann. J. Bull. Soc. Chim. Fr. 1956. 177. (5) Baron, P;D.; Brown, R. D.; Burden, F. R.; Domaille, P. J.; Kent, J. E. 1. Mol. Spcctrosc. 1972, 43, 401. (6)Scharpen, L. H.;Laurie, V. W. J. Chcm. Phys. 1%5,13, 2765.
d.
0022-3654/91/2095-6908$02.50/0
4
2
3
(7) (a) Praud, L.; Millie, P.;Berthier, 0 . Theor. Chim. Acta 1%8,11,169. (b) Rancurel, P.;Huron, B.; Praud, L.; Malrieu, J. P.;Berthier, G. J. Mol. Spectmc. 1976,60,259. (c) Kollmar, H.J. Am. Chem. Soc. 1979,101,4832. (d) de Brouckhe, G.; Berthier, 0. Mol. Phys. 1982,47,209. ( 8 ) (a) Straub, P.A.; Mueche, D.; Heilbronncr, E.Hefu. Chim. Acta. 1% 19, 517. (b) GrOndler, W. Z . Chcm. 1979, 19, 266.
0 1991 American Chemical Society
