Article pubs.acs.org/JPCA
High-Accuracy Estimates for the Vinylidene-Acetylene Isomerization Energy and the Ground State Rotational Constants of :CCH2 Hyunwoo Lee,† Joshua H. Baraban,‡ Robert W. Field,*,‡ and John F. Stanton*,† †
Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, Texas 78712, United States Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
‡
ABSTRACT: Highly accurate calculations are reported for properties of vinylidene (H2CC:), specifically the position of its zero-point vibrational level relative to that of acetylene and its equilibrium structure and ground state rotational constants. The isomerization energy of vinylidene calculated at the HEAT-456QP level of theory is 43.53 ± 0.15 kcal mol−1, in agreement with the previous best estimate, but associated with a much smaller uncertainty. In addition, the thermochemical calculations presented here also allow a determination of the H2CC−H bond energy of the vinyl radical at the HEAT345(Q) level of theory, which is 77.7 ± 0.3 kcal mol−1. The equilibrium structure of vinylidene, estimated with an additivity scheme that includes treatment of correlation effects beyond CCSD(T) as well as relativistic and adiabatic (diagonal Born−Oppenheimer correction) contributions, is rCC = 1.2982 ± 0.0003 Å, rCH = 1.0844 ± 0.0003 Å, and θCCH = 120.05 ± 0.05°, with zero-point rotational constants (including vibrational contributions and electronic contributions to the moment of inertia) estimated to be A0 = 9.4925 ± 0.0150 cm−1, B0 = 1.3217 ± 0.0017 cm−1, and C0 = 1.1602 ± 0.0016 cm−1.
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INTRODUCTION Vinylidene, depicted in Figure 1, is the simplest example of an unsaturated carbene1 and, as such, has attracted a considerable
analysis of the ground (singlet) electronic state of vinylidene is complicated significantly by its transient existence: it lies well above the more stable acetylene isomer, and there is a rather small barrier to the rearrangement.4,5 In fact, the barrier is so small that it was once believed that vinylidene is not a minimum on the potential energy surface of C2H2 at all; rather, it was thought to serve as an intermediate for end-to-end hydrogen transfer reaction in the more stable isomer.6 However, the X̃ 1A1 electronic state of vinylidene was first observed spectroscopically by Ervin, Ho, and Lineberger in 1989 using negative ion photoelectron spectroscopy (NIPES).7 As the ground state of the C2H2 anion has the same qualitative molecular structure as vinylidene, the vertical (Franck− Condon) region of the spectrum corresponds to the vinylidene transient and the NIPES techniquecombined with more sophisticated ab initio calculations8,9has succeeded to establish the existence of X̃ 1A1 vinylidene as a bona f ide minimum on the potential energy surface. Despite continued efforts to observe vinylidene in the laboratory, both directly and via search for the telltale signs left by vinylidene on the rovibrational energy level structure of acetylene,10−13 little progress has been made in recent years in determining more about the properties of this important prototype intermediate. In this paper, we employ current stateof-the-art theoretical tools to calculate thermodynamic and spectroscopic properties of :CCH2. The purpose is twofold:
Figure 1. Geometry of vinylidene, with representations of its highest occupied and lowest unoccupied molecular orbitals. Also shown is the principal axis system.
amount of interest from both theoreticians and experimentalists. Of course, the global minimum energy structure on the C2H2 potential energy surface is acetylene, but evidence suggesting the involvement of the parent and substituted vinylidenes in chemical reactions dates back at least a half century.2 Hence, a significant amount of work has been devoted to studying the mechanistic chemistry involving vinylidene and related (substituted) alkylidene carbenes (RR′CC:). Despite its importance, it was not until 1980 that a report appeared regarding the direct spectroscopic detection of :C CH2, that being the assignment of a transient observed in flash photolysis to a triplet electronic state.3 Direct spectroscopic © 2013 American Chemical Society
Special Issue: Curt Wittig Festschrift Received: January 2, 2013 Revised: March 15, 2013 Published: April 26, 2013 11679
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Table 1. Contributions to the HEAT-456QP Energies of Acetylene and Vinylidene (Atomic Units) and Corresponding Contributions to the Isomerization Energy (cm−1)a running total contribution
acetylene (a.u.)
vinylidene (a.u)
difference (cm−1)
(cm−1)
(kJ mol−1)
(kcal mol−1)
E∞ SCF ΔE∞ CCSD(T)
−76.8555849 −0.4796080 0.0002233 −0.0010347 −0.0321422 0.0037777 0.0262111
−76.8001751 −0.4620007 −0.0005703 −0.0006649 −0.0322685 0.0038525 0.0231134
+12161 +3864 −174 +81 −28 +16 −697
12161 16025 15851 15932 15905 15921 15224
145.48 191.70 189.62 190.59 190.27 190.46 182.12
34.77 45.82 45.32 45.55 45.48 45.52 43.53
ΔECCSDT ΔEHLC ΔErel ΔEDBOC ΔEZPE a
Precise definitions of all the energy contributions below can be found in ref 17.
Figure 2. Various estimates of the bond energy of vinylidene, together with uncertainty estimates: (a) RRKM analysis of ref 14; (b) negative ion thermochemical cycle, ref 7; (c) calculation of ref 15; (d) present results.
are documented in Table 1, and again fall slightly below the most recent estimates quoted above. At the full HEAT-456QP level, as the method is defined in ref 18, the isomerization energy is calculated to be 43.53 kcal mol−1, in essentially perfect agreement with the ancient calculation mentioned above that included relativistic and non-Born−Oppenheimer (adiabatic) corrections.15 The present set of calculations includes only slightly different relativistic and adiabatic corrections,17 but its treatment of the total electronic energy is substantially better. It is of interest to analyze these results, in the context of both other high-level calculations and experimental determinations. First, the works of Joseph and Varandas,4 as well as Zou and Bowman,5 did not include relativistic effects, adiabatic corrections, or treatment of electron correlation beyond the coupled-cluster singles, double and perturbative triples [CCSD(T)] level.19 When these terms are removed from the HEAT456QP composite energies, an isomerization energy of 43.83 kcal mol−1 is obtained; the higher-level corrections (quadruples and pentuples) account for about 75% of this small difference, indicating that the electronic structure calculations done by Zou and Bowman were very close to the basis-set limit CCSD(T) results. Also significant here is that the anharmonic contribution to the vibrational zero-point energies (−0.26 kcal mol−1 for vinylidene and −0.11 kcal mol−1 for acetylene), also not commonly used in computational thermochemistry, accounts for an additional 0.15 kcal mol−1. Taken together, the relativistic, adiabatic, high-level correlation and anharmonic ZPE effects stabilize vinylidene by nearly 0.5 kcal mol−1 (2 kJ mol−1) relative to acetylene, serving as an additional reminder that such effects have to be considered in such high accuracy analyses. Certainly this is true when 1 kJ mol−1 accuracy is desired, which has been amply documented in the literature,16−18,20,21 but also appears necessary for the present example to obtain even half this level of accuracy. A statistical analysis of HEAT-456QP accuracy for the atomization energy of small molecules, as compared to the
to update previous results with better calculations, and to provide improved predictions that might help to guide future experiments.
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THERMOCHEMISTRY The isomerization energy between acetylene and vinylidene was first estimated to be 44 ± 2 kcal mol−1 by a Rees− Ramsperger−Kassel−Marcus (RRKM) analysis of a shock tube study.14 Ervin et al. used information about the H2CC-H bond energy of vinyl radical and the C−H bond energy of ethylene to construct a negative ion thermodynamic cycle, which yielded an isomerization energy of 46.4 ± 5.5 kcal mol−1,7 which corresponds to an enthalpy of formation [Δf H(:CCH2, 0 K)] of 101.5 ± 5.5 kcal mol−1. Gratifyingly similar values have been obtained by theory over a number of years; virtually all early estimates were between 40 and 50 kcal mol−1, and more recent calculations seem to be converging near the middle of this range. The highest-level quantum chemical calculations reported in recent years have given zero-point-corrected isomerization energies of 45.134 and 44.055 kcal mol−1, while an old study from the previous century that included relativistic effects and corrections to the Born−Oppenheimer approximation gave a slightly lower value of 43.47 ± 0.59 kcal mol−1.15 Within stated (or reasonable, when unstated) error bars, all of these numbers are consistent with the experimental estimates discussed above. The present calculations use the HEAT (High Accuracy Extrapolated Ab Initio Thermochemistry) protocol for computational thermochemistry,16−18 an approach that has a demonstrated ability to calculate bond energies and heats of formation to within 1 kJ mol−1 (about 0.25 kcal mol−1) for molecules of this size. The small size of acetylene and vinylidene allows the highest-level HEAT approach yet benchmarkedthe HEAT-456QP variant that includes electron correlation effects involving both quadruple and pentuple excitations18to be used here. The results of the calculations 11680
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Active Thermochemical Tables (ATcT) of Ruscic,22 gave an root-mean-square (RMS) error of 0.42 kJ mol−1 and a 95% confidence interval of 0.84 kJ mol−1. As atomization energies are harder to calculate than relative energies of isomers, a somewhat smaller uncertainty is appropriate in the present context. Hence, we suggest a revised best estimate of the isomerization energy of acetylene to vinylidene as 43.53 ± 0.15 kcal mol−1 (182.12 ± 0.6 kJ mol−1; 15224 ± 52 cm−1), with the error bars indicating a (conservative) 2σ uncertainty in the calculation. This narrows the range of isomerization energies to about 100 cm−1, about a 4-fold improvement over previous work (see Figure 2). Another thermochemical parameter that can be analyzed at this point is the H2CC−H bond energy in the vinyl radical. Vinyl was the subject of a quite recent HEAT study,23 using the somewhat simpler HEAT-345(Q) thermochemical model. That study found an enthalpy of formation of 301.5 ± 1.3 kJ mol−1, in essentially perfect agreement with an experimental result of 301.7 ± 2.5 kJ mol−1 by Ervin and DeTuri.24 The HEAT345(Q) acetylene−vinylidene isomerization energy is 182.16 kJ mol−1 (essentially identical to the higher level HEAT-456QP number), which carries an uncertainty of about 1 kJ mol−1. Combining this value with an ATcT Δf H(0 K) for acetylene (228.82 ± 0.30 kJ mol−1) gives a HEAT-345(Q) heat of formation (0 K) of vinylidene as 411.0 ± 1.1 kJ mol−1. Using Δf H(0 K) for the hydrogen atom (216.03 kJ mol−1), this yields a bond energy (D0) of 325.3 ± 1.3 kJ mol−1 (77.7 ± 0.3 kcal mol−1) for the H2CC−H bond in the vinyl radical at the HEAT-345(Q) level. This is in agreement with the value of 80.0 ± 5.0 kcal mol−1 determined from the electron affinity of the vinylidene anion and a gas-phase acidity bracketing experiment on vinyl.25
inertia along the inertial axes (inversely proportional to the corresponding ) e values), derivatives of the moments of inertia with respect to the normal coordinates Qk (ak), and the Coriolis zeta matrices ζ) . In addition, there is an additional contribution due to the contribution of the electron mass to the moments of inertia29,30 m )0 ⇐ Y ) ≡ e g ) )e mp (3) where g) is a (diagonal) element of the rotational g-tensor. To obtain the rotational constants, the equilibrium structure was first estimated by an additivity approach similar in spirit to those discussed in refs 31 and 32. Specifically, the basis-set limit structure was estimated at the all-electron CCSD(T) level of theory, using large basis sets that appropriately handle corecorrelation effects33 (cc-pCVQZ, cc-pCV5Z, and cc-pCV6Z) and assuming an exponential convergence of the geometrical parameters with respect to the cardinal number of the basis set. Then, using the cc-pVTZ basis set,34 the equilibrium structure of :CCH2 was calculated at the CCSDT(Q) level of theory; the difference between this structure and the CCSD(T)/ccpVTZ structure was then taken as the “higher-level correlation” contribution. A similar approach was used with the cc-pVTZ for the relativistic contribution, using the same relativistic treatment (one- and two-electron Darwin and mass-velocity terms) used in HEAT-345(Q) and HEAT-456QP methods. Finally, the contribution of the diagonal Born−Oppenheimer correction was estimated, but found to be completely negligible (less than 0.0001 Å for the bond distances). The resulting structure and uncertainties assigned to it were used to compute the equilibrium rotational constants. Vibrational corrections were also calculated with the cc-pCVQZ and cc-pCV5Z basis sets at the CCSD(T) level, using second and third derivatives of the energy calculated with analytic derivative procedures,35,36 and the electronic term was computed from the rotational g tensor computed at the CCSD(T) level37 with the cc-pCVQZ basis. These calculations, as well as those using the HEAT protocol for thermochemistry, were carried out with the CFOUR package,38 while quadruple and pentuple excitations were evaluated with MRCC.39 The results of the calculations are listed in Table 2. It is perhaps notable that the electronic contribution to the A0 rotational constant is actually larger than the overall uncertainty in the calculation, the latter being dominated by that associated with the equilibrium structure. Generally this term is ignored in analyses of rotational spectra, but one other case is known where it makes a substantial contribution: the SiC3 molecule studied by Thaddeus and co-workers.40,41 In any event, the estimates made here (the more important B0 and C0 constants have been determined to roughly 0.1%) should be helpful for verifying the identification of vinylidene as a transient by microwave spectroscopy. In addition, Table 3 documents the rotation-vibration interaction constants αi) for :CCH2, which allow for predictions of the rotational constants of (practically speaking, only low-lying) vibrationally excited states via the VPT2 relation
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EQUILIBRIUM STRUCTURE AND ROTATIONAL CONSTANTS One promising, and new, experimental technique for the detection of transient polar species is chirped-pulse (broadband) microwave spectroscopy, developed recently by Pate and co-workers.26 Hence, the rotational constants of vinylidene, which have not previously been targeted by high-level ab initio calculations, would serve useful to those attempting to detect vinylidene by chirped-pulse millimeter-wave (CPmmW) spectroscopy.27 Accordingly, such an effort has been undertaken here, in addition to the thermochemical calculations reported in the previous subsection. According to second-order vibrational perturbation theory, ground state rotational constants (A0, B0, and C0) are given by the equation28 )0 = )e + Ω)
(1)
where ) can be A, B, or C, and ⎧ ⎪ 3(ak)) ′)2 Ω) ≡ (Be) )2 ⎨ ∑ + e ⎪ ⎩ k , ) ′ ωkI) ′
∑ k
