J . Phys. Chem. 1991, 95, 8352-8363
8352
Ab InRio Thermochemistry for Unsaturated C2 Hydrocarbonst Christine J. Wu and Emily A. Carter* Department of Chemistry and Biochemistry, University of California, Los Angeles. California 90024- I569 (Received: January 31, 1991)
The first systematic study of the sequential bond dissociation energies for ethylene and acetylene, using generalized valence bond (GVB) theory and the correlation-consistentconfiguration interaction (CCCI) method is presented. The ab initio GVB/CCCI sequential C-H bond strenghts in ethylene and acetylene are: Do(H2CCH-H) = 109.5 (1 10.9 2) kcal/mol, Do(H2CC-H) = 70.8 (74.4 f 3) kcal/mol, Do(HCCH-H) = 37.1 (40.0 f 3) kcal/mol, Do(CCH-H) = 86.3 (91.3 f 5 ) kcal/mol, Do(HCC-H) = 129.7 (131.1 f 2) kcal/mol, and Do(CC-H) = 95.6 (102.5 3) kcal/mol. The values in parentheses represent our best estimates for the actual bond strengths, taking into account known systematic and random errors. New predictions for C - C double bond strengths are Do(H2C=CH) = 162.5 (168.2 f 6) kcal/mol and D0(H2C=C) = 149.5 (155.5 f 5) kcal/mol, while predictions for c=--C triple bond strengths are: Do(HC=C) = 160.4 (168.9 f 13) kcal/mol and Do(CqL) = 134.7 (129.2 15) kcal/mol. The adiabatic singlet-triplet splittings for HCCH and H2CC, the 211--%+ splitting in HCC, the ?Z2:-'Z; splitting in C2,and the isomerizationenergy for the conversion of H2CC(IAI)to HC=CH('Zi) are predicted to be 83.9, 48.1 f 2.5, 14.8, 42.2, and -44.3 kcal/mol, respectively. GVB-PP (perfect pairing) equilibrium geometries and harmonic vibrational frequencies of the above species are also presented. The qualitative trends in adiabatic bond strengths can be well rationalized in terms of two simple quantities: intrinsic (diabatic) bond strengths and final-state relaxation effects.
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I. Introduction Knowledge of the thermochemistryof unsaturated hydrocarbons is essential for understanding a wide variety of chemical processes, including combustion, catalysis, and more recently, diamond film growth. Among the most important quantities are the chemical bond dissociation energies of the C2 hydrocarbons, ethylene and acetylene.' Determination of the bond strengths in these two species has attracted the attention of both experimental and theoretical groups in recent years, focusing particularly on the first CH bond strengths in ethylene and acetylene. Despite numerous studies, these values remain a subject of controversy. While most values for D,(CH,CH-H) hovered around 108 kcal/mol for a number of years,' recent observation of the threshold energies for H+ formation by synchrotron radiation led Lee and co-workers2to report that Do(CH2CH-H) might be as high as 116.7 f 1.2 kcal/mol, remarkably higher than other reported By contrast, the most recent experimental value for Do(CH2CH-H) is 109.7 f 0.8 kcal/mol, obtained by Ervin et ai.' from gas-phase acidity and electron affinity measurements. Similar disagreement exists for the experimental values of the first CH bond strength in acetylene, which generally fall into two groups: 127 or 132 kcal/mol. Recently, Green et a1.8 reported a convincing new determination of an upper bound on Do(HCCH) of 126.647 kcal/mol, 5 kcal/mol lower than the consensus upper bound derived from six other experimental measurements,u*e12including Ervin et ale's recent value of Do(HCC-H) = 131.3 f 0.7 kcal/moL3 Green et al.'s upper bound agrees very well with Segall et ala's report of Do(HCC-H) = 127 f 1.5 kcal/mol, determined from acetylene pyrolysis kinetics.'' In order to help determine the first CH bond strengths in ethylene and acetylene, a number of ab initio calculations at different levels have been perf~rmed,'~''but few of the calculations included high levels of electron correlation in a systematic manner. The first high level ab initio calculations were reported by Curtiss and Pople using unrestricted Hartree-Fock with Moller-Plesset perturbation theory through fourth order (UHF/MP4). They predicted Do(H2CCH-H) = 110.2 and Do(HCC-H) = 133.4 kcal/mol." Very recently, configuration interaction (CI) calculations extrapolated to the complete basis set limit were carried out by Montgomery and Petersson,lSLwho predicted Do(HCC-H) to be 131.54 f 0.45 kcal/mol. At the same time, both the current authorsIsb and Bauschlicher et a1.I" cal-
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'This paper is dedicated to the memory of Professor Richard B. Bematein. our esteemed colleague whose scientific contributions and selfless leadership is sorely missed.
culated Do(HCC-H) to be 129.7 and 130.1 f 1.0 kcal/mol, respectively, by using multireference CI techniques. Ervin et al.' recently reported experimental measurements leading to estimates of other bond strengths in ethylene and acetylene, obtained by measuring the gas-phase acidities of acetylene, ethylene, and vinyl radical (the latter bracketed to within 5 kcalfmol) and the electron affinities of ethynyl, vinyl, and vinylidene. By employing current literature values for the heats of formation of C, C2, CH, and CH2, they derived from thermochemical cycles the other CH and C - C bond strengths in ethylene and acetylene: Do(H2CC-H) = 81.0 f 3.5, Do(HCCH-H) = 33.6 f 0.8, Do(H-HCC) = 83.9 f 4.2, Do(H - . . >
L~nyarocaroons
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8353
referred to as RCI*SD-). Additionally, single excitations from all valence orbitals are included (RCI*Q), which describe orbital shape and hybridization changes important along a chemical reaction path. Thus the total CCCI wave function, RCI*[SDw Sval],includes all of the dominant electron correlations dictated by the physics of the problem. Also, this method accounts for electron correlation in a consistent manner for the initial and final states for any general chemical process. The degree of electron correlation that is included in the calculations may generally be listed in the following order: GVB-PP < GVB-RCI < GVBRCI*SDw < CCCI(GVB-RCI*[Sb + SJ). We have found that CCCI yields high accuracy for single-bond strengths (-2 kcal/mol error) and reasonable accuracy for doublebond strengths (-6 kcal/mol error), but it severely underestimates the strengths of triple bonds.19* This is due to the need for simultaneous correlation of more than one breaking bond (Le,, inclusion of triple and quadruple excitations) in order to describe triple-bond breaking accurately. Thus we expect (and find) good agreement with experiment for all cases except those involving triple-bond breaking or weakening (e.g., H-C=C C I C H, HCCH 2CH, and HCC CH + C). Calculation of an adiabatic bond strength is achieved via use of the CCCI method on each step of a convenient but arbitrary thermodynamic cycle constructed for the bond dissociation proWe define an adiabatic bond strength to be the energy to go from the ground-state molecule to ground-state fragments, each in their equilibrium geometries. A diabatic bond strength is defined to be the energy to break a bond, dissociating to selected excited states of the fragments. We emphasize that the diabatic 11. Calculational Details bond strength is not exactly a "vertical" bond strength, since we A. GVB Wave Functions. GVB-PP wave functions were used allow the fragments to relax to their optimum geometries at each as starting points for the CCCI calculation^.^^ In the GVB-PP stage in the cycle. By taking advantage of the path independence calculations, the breaking bond is always correlated with two of thermodynamiccycles, we can leam about various contributions natural orbitals per pair of electrons, maintaining the correct to the bond strength (vide infra). For instance, the a-CH bond functional form for proper dissociation. All other electrons that of vinyl radical can be broken diabatically to form the 3B2excited are not directly involved in the dissociation process are either state of vinylidene, which then can relax to the 'Al ground state treated in the same manner (i.e., the GVB-PP level) or at the of H2CC. The diabatic dissociation energy is calculated by CCCI, HartretFock (HF) level. In order to explore the robustness of while the electronic relaxation is calculated at the RCI*SD,i, the CCCI expansion (vide infra) beyond our previous ~ o r k , ' ~ , ~ level,Igb ~ where SD* indicates single and double excitations from we present a comparison of results from several different CI the carbon lone pair involved in the deexcitation. In general, we expansions. Three types of multconfiguration-self-consistent-field always correlate the pair involved in the electronic transition as (MCSCF) wave functions were used as zeroth-order wave a GVB pair (GVB(1/2)), and we also examine the effect of functions for a CI: (i) GVB(6/12)-PP, where each of the six correlating neighboring bonds as GVB pairs or all bonds as GVB valence electron pairs are correlated with one correlating (or second pairs. This level of electron correlation was shown to provide natural) orbital: (ii) GVB(N/UV)-PP, where only nearest-neighbor accurate predictions of electronic excitations energies.'9b By bond pairs of the breaking bond and the breaking bond are treated subtracting the electronic relaxation energy from the diabatic at the GVB-PP level (Le., N < 6); and (iii) GVB(M/2M)-PP, dissociation energy, we obtained the adiabatic bond dissociation where only the M breaking-bond pairs are treated at the GVB-PP energy. In principle, use of this two-step cycle can provide a more level. The latter wave function was used in all previous CCCI accurate approach to calculating bond energies, since the energy studies.I9" The present calculationsindicate that correlating bond differences are always between electronic states that have similar pairs other than those of the breaking bond is unnecessary at the orbital character and hence similar correlation requirements. For CCCI level (our highest level of electron correlation), further example, the 3B2vinylidene excited state has two unpaired electrons substantiating our earlier work. in orbitals that are very similar to the same orbitals in vinyl radical. B. Cl Calculations and Strategies. Our multireference starting Thus, differential correlation problems are kept to a minimum point for the CCCI calculations is the GVB-RCI (restricted CI) by dissociating to the excited state and then relaxing to the ground wave function, where all three possible spatial configurations state. One other advantage of dissociating to a diabatic limit first ( ~ ~ n d i ~ ~ ~ n o n d i ~ ~ ! n ,&bonding) i ~ n ~ i " 6 ,for each GVB pair are alis that this cycle provides an upper bound to the activation energy lowed. This wave function includes the dominant interpair required for bond formation/cleavage, useful quantities for uncorrelations, in addition to the intrapair correlations already inderstanding reaction mechanisms. The only drawback to concluded in the GVB-PP description. Within the RCI reference structing such a cycle is the propagation of errors due to the space, the CCCI technique allows full correlation of each electron calculation of more than one quantity to arrive at a bond energy. pair involved in the process of interest (i.e., all single and double Such errors are discussed below. excitations from the breaking bond to all other orbitals are allowed, Another important multireference CI we employ here is called GVB-CI(N/2N), where N is the number of the GVB pairs. This (18) Bobrowicz. F. W.; Goddard, W. A., 111. In Method of Electronic is a full CI within the GVB valence orbitals, essentially a complete Srrucrun Throry; Schaefer, H . F., Ed.;Plenum: N m York, 1977; pp 79-127. active space (CAS) CI. This GVB-CI wave function allows for (19) (a) Carter, E. A.; Goddard, W. A., 111. J. Chem. Phys. 1988, 88, a proper description of a process involving simultaneous changes 1752. (b) Carter, E. A.; Goddard,W.A., 111. J. Chem. Phys. 1988,88,3132. (20) (a) Carter, E. A.; Goddard, W. A., 111. J . Phys. Chem. 1984, 88, in the shapes of many orbitals, such as in an isomerization pro1485. (b) Carter, E. A.; Goddard, W. A,, 111. J. Am. Chem. Soc. 1987,109, cess.20b*cHowever, we find that this level of CI is sufficient for 579. (c) Carter, E. A.; Goddard, W. A., 111. Organometallics 1988, 7,675. describing bond breaking, as are all valence level CI calculations. (d) Carter, E. A.; Goddard. W. A., 111. J . Phys. Chem. 1988,92, 2109. (e) Thus, for bond breaking, we report the results of the GVB-CI Carter, E. A.; Goddard, W. A., 111. J . Am. Chem. Soc. 1988.110,4077. (f) Carter, E. A.; Goddard, W. A., 111. Surf. Sci. 1989, 209, 243. calculations only to further emphasize its inadequacy and do not
Up to this point, almost all of the ab initio calculations have focused on the first C H bond strengths of ethylene and acetylene."-'' Curtiss and Pople reported Do(HCCH-H) = 32.8 by UHF/MP4 calculations~'and Bauschlicher and Langhofflsdhave recently calculated Do(C2-H) to be 112.4 f 2.0 kcal/mol. Calculations for other bond strengths in ethylene and acetylene, including high levels of electron correlation,have not been reported. A comprehensive and systematic theoretical study of all of the bond strengths in ethylene and acetylene would supply a standard for experimental studies with which to compare, as well as provide important insights into the trends in the thermochemistry of ethylene and acetylene. In this paper, we report the first such comprehensive of all of the sequential bond dissociation energies in ethylene and acetylene calculated by ab initio Generalized Valence Bond (GVB)l8 and Correlation-Consistent Configuration Interaction (CCCI)I9 theory, a method developed for calculating accurate dissociation energies for single and double bonds. It has a demonstrated accuracy for bond energies of 1-8 kcal/mol in both organic and transition-metal-containing molecules.20 We also report five adiabatic electronic excitation energies/isomerization energies for C2-containingspecies (vide infra). The equilibrium geometries and harmonic vibrational frequencies of all molecular species were predicted at the GVB(6/12)-PP (or equivalent) level (PP = perfect pairing). We note that a preliminary communication of this work appeared recently;'sb some of the values reported in that work are in error. The values reported in this paper should supersede those values in all cases.
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8354 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991
species CzHdIAi)
geometries'
= 1.356A r,(HC)= 1.085 A LHCH = 116.9' r,(CI=CZ) = 1.338 A r,(HIICI) = 1.093 A rE(HlZCI) = 1.097 A rE(Hz1C2) = 1.087 A LHllClC2 122.3' LHzlCzCl = 133.7' LHlzCIC2 = 120.6' r,(C=C) = 1.336 A r,(HC)= 1.095 A LHCH= 120.0' r,(C==C) = 1.340 A r,(HC)= 1.095 A LHCH = 118.4' re(-) = 1.219A r,(HC)= 1.075 A r,(C=C) = 1.353 A r,(HC)= 1.094A LHCC = 128.7' re(=) = 1.217A r,(HC) = 1.075 A re(=) = 1.312A r,(HC) = 1.073 A re(=) = 1.243 A re(=) = 1.209 A r,(HC) = 1.127 A LHCH = 129.1' r,(CH) = 1.136 A r,(CH) = 1.084 A re(-)
gcometries(expt1)
r,(C=C) = 1.339 A" r,(HC)= 1.085 A LHCH = 117.8'
geometries(other theory) re = 1.335 AI4
r,(HC) = 1.085A LHCH = 119.15' rc(Cl
