Theoretical determination of the heat of formation of methylene

Theoretical determination of the heat of formation of methylene Nikos L. Doltsinis and Peter J. Knowles School of Chemistry, University of Birmingham, Edgbaston, Birmingham B5 2TT, United Kingdom The heat of formation of CH 2 was calculated using high accuracy ab initio results for its dissociation energy. MRCI calculations were carried out with correlation consistent polarized valence basis sets (cc-pvxz, X=2 6). Core-valence correlation energies were computed using CCSD(T) with correlation consistent polarized core-valence basis sets (cc-pcvxz, X=2 5). For the ground state CH 2 ( X 3 B ) our best estimate of the heat of formation at 0 K is f,0 H 388 7 0 6 kjmol. This is in agreement with experimental results, in the range 384 5 395 8 kjmol. The result implies that for the first excited state CH 2 (ã A ), f,0 H 426 4 0 6 kjmol. Introduction Although methylene is one of the simplest organic molecules, there have been numerous controversies concerning its electronic and molecular structure. The energy separation T 0 between the ground state X 3 B and the lowest excited state ã A, in particular, has been the subject of a large number of experimental and theoretical studies. The issue was finally resolved in 988 by Jensen and Bunker [], who found a satisfactory solution of T 0 37 65 0 06kJmol. The reaction CH 3 OH CH 2 ( A ) H 2 O () is of fundamental importance in combustion chemistry, and a key quantity whose knowledge is important is the enthalpy change associated with (). Using standard thermodynamic tables [2] and the experimentally determined singlet-triplet splitting T 0 of Jensen and Bunker [] one obtains a value of H 2 8 4 5kJmol for the enthalpy change at 0 K. It is therefore inconclusive whether or not the reaction is exothermic. The most uncertain quantity used in obtaining this value is the Preprint submitted to J. Chem. Soc. Faraday Trans. 24 March 997

heat of formation of CH 2 ( A ), f,0 H 423 6 4 2kJmol. It is the purpose of this paper to report an attempt to arrive at a more precise estimate of this quantity by means of ab initio electronic structure computations. The heat of formation of CH 2 has been determined experimentally from photodissociation of ketene and other precursors. The results are summarized in Table. The majority of the data were obtained from photodissociation of ketene [3 6]. Similar experiments were carried out with methane [6,8,9] and CH 3 [7]. The value of Dibeler et al. [9] has to be corrected for rotational energy effects at threshold [8]. Grotheer et al. [0] have derived the enthalpy change at 300K for reaction () from rate constants and branching ratios to be H 8 2kJmol. This cannot be reconciled with the literature data [2], and therefore a methylene heat of formation of f 300K H CH 2 A 434 7kJmol was attributed. Using the temperature correction quoted in Ref. [2], this corresponds to a heat of formation at zero temperature of f,0 H CH 2 A 434 2kJmol. We note that the spread in these high-quality experimental data is significantly greater than the published error bars of 2 3kJmol. In order to obtain a prediction of H for reaction () to within, say, kjmol, a more accurate determination of the heat of formation of CH 2 is required. 2 Computational Details In order to calculate the heat of formation of CH 2, the two paths CH 2 ( X 3 B ) CH( X 2 Π) H C 3 P H H (2) CH 2 ( X 3 B ) C 3 P H 2 ( X Σ g ) (3) were used; the two schemes differ in whether the calculated or experimental values for the dissociation energy of H 2 are used. (2) yields additionally a value for the heat of formation of CH. In either case, the heat of formation of CH 2 (ã A ) can then be obtained using the experimental singlet-triplet splitting T 0 result of Jensen and Bunker []. Valence internally contracted multireference configuration interaction (MRCI) [] calculations were used to compute the equilibrium energy differences for both the above schemes; the valence shell correlation energy is probably the single most difficult contributor to the heats of formation to compute accurately, and the errors and convergence of our MRCI calculations are discussed in some detail below. The remaining contributions, which were considered separately, are (i) Zero-point energy differences. These were obtained from spectroscopic studies [,2,3]. 2

(ii) Scalar relativistic effects. Corrections to the ab initio energies were estimated using standard Cowan-Griffin perturbation theory [4]. (iii) Spin-orbit coupling. The effects of spin-orbit coupling on the equilibrium energies of CH 2 and H 2 can safely be assumed to be negligible. For CH( X 2 Π) and C( 3 P), the difference between the experimental ground state and the spinorbit barycentre [2] was added to the ab initio energies. (iv) Non-adiabatic effects. The largest non-adiabatic effects should be seen in H 2, and these are less than 0 0 kjmol in magnitude [3]; accordingly, nonadiabatic effects were neglected. (v) Core-core and core-valence electron correlation. Size-extensive CCSD(T) [5] computations on C, CH and CH 2 were carried out, with and without excitations from the carbon s orbital included, using the cc-pcv5z correlationconsistent polarized core-valence basis set [6]. The difference in correlation energy was used as an estimate of the core-core and core-valence correlation energy not included in the valence MRCI calculations. MRCI calculations for the carbon abstraction energies of CH 2 and CH were carried out using the supermolecule approach for the dissociation products, in order to minimize size-consistency errors. In order to reliably assess the degree of convergence in the valence-shell correlation energies, a series of orbital basis sets and a series of reference wavefunctions were used. The orbital basis functions were taken from the standard correlation-consistent polarized valence sets [7 9]. The reference wavefunctions were a series of complete active space (CAS) [20] expansions denoted n n where n n are the numbers of a a orbitals (C s point group was used) defining the active space. For each orbital basis set, the calculations were carried out at equilibrium geometries obtained from the smallest MRCI calculations ( 83 for CH 2 and 84 for CH) using the same basis. Table 2 gives the resulting values for the zero-temperature heats of formation, after correction for additional effects as described above. Table 3 explicitly lists the values which have been used for the various corrections arising from effects not described by the valence CI calculations. The two routes (2), (3) for computing f,0 H differ only in whether our ab initio values or exact results are used for the dissociation energy of H 2 ; we have adopted the results from (3) in the discussion which follows. Our most accurate computed value of 388 93kJmol will certainly be an overestimate of the fully converged result, with an error bar of approximately 0 4kJmol arising from residual incompleteness of the correlation treatment. The convergence pattern with respect to active reference space and orbital basis set is given in Table 2. The results are fully converged with respect to the active space defining the reference wavefunction. Convergence with respect to orbital basis set is smooth, and capable of extrapolation to the complete basis set limit. Figure shows the values of f,0 H obtained with successive basis sets cc-pvdz... cc-pv6z in the correlation consistent sequence [7 9] together with an exponential extrapolating function [2] fitted 3

to the three most accurate results. The fit is seen to be excellent, and gives confidence in the reliability of the extrapolated complete basis limit, 388 7kJmol, with a reasonable estimate of the remaining error being 0 2kJmol. The data for the dissociation of the CH molecule cannot be reasonably fitted using the procedure described above. We estimate that our best calculated result, f,0 H 592 kjmol, lies approximately 0kJmol above the fully converged complete basis set limit. Finally, we note that for path (2) our best atomization energy, D e 793 29kJmol, is 0 7kJmol greater than the theoretical value of [22]. Other major sources of error are (i) core-valence correlation estimates: our correction of 3 65kJmol agrees reasonably with the calculations of Partridge and Bauschlicher [22] (3 5 3 62 3 64kJmol ), but could still be in error by as much as 0 2kJmol due to the remaining basis set incompleteness and errors associated with the CCSD(T) ansatz. (ii) zero-point energies: the errors are estimated [,23] to be approximately 0 06kJmol ( A ) and 0 2kJmol ( 3 B ). (iii) other heats of formation: the value for f,0 H of atomic carbon which we have used is uncertain to 0 46kJmol [2]. In order to arrive at a total error estimate for f,0 H, these errors are to be combined in quadrature with the uncertainty ( 0 2kJmol ) in the extrapolated valence correlation treatment. Use of the cc-pv6z results instead implies an additional 0 2 kjmol systematic error. 3 Discussion Based on the above error estimates, our best computed values for the zero-temperature f,0 H are 388 9 0 8kJmol ( 3 B ) or 426 6 0 8kJmol ( A ) with bestestimate values of 388 7 0 6kJmol ( 3 B ) or 426 4 0 6kJmol ( A ). The latter in turn implies a predicted enthalpy change for reaction () of H 0 0 6kJmol, i.e., the reaction is essentially thermoneutral, in contradiction to the findings of Ref. [0]. The relatively large uncertainty arises from quoted errors in the heats of formation of C, CH 3, and OH [2]. In principle, this difficulty could be eliminated through application of the methods described in this paper to the reaction CH 3 CH 2 H. However, it might be more difficult to achieve good accuracy in the electronic structure problem using this alternative route. Our result for the heat of formation of CH 2 is in agreement with most of the experimental data, but has been successful in significantly reducing the uncertainty in knowledge of this quantity. The heat of formation of CH cannot be stated with the same accuracy. From the above considerations we obtain f,0 H 592 5kJmol. Nevertheless, al- 4

though this has not been the aim of this paper, we have been able to reduce the error quoted in Ref.[2] by a factor of 0. Acknowledgements The authors are grateful to Profs. P. Jensen and M. J. Pilling for valuable discussions. References [] P. Jensen and P. R. Bunker, J. Chem. Phys. 89 (988) 327. [2] M. W. Chase, Jr., C. A. Davies, J. R. Downey, Jr., D.. J. Frurip, R. A. McDonald, and A. N. Syverud, J. Phys. Chem. Ref. Data 4 (985), Suppl.. [3] C. C. Hayden, D. M. Neumark, K. Shobatake, R. K. Sparks, and Y. T. Lee, J. Chem. Phys. 76 (982) 3607. [4] D. Feldmann, K. Meier, H. Zacharias, and K. H. Welge, Chem. Phys. Letters 59 (978) 7. [5] R. K. Lengel and R. N. Zare, J. Amer. Chem. Soc. 00 (978) 7495. [6] K. E. M. Culloh and V. H. Dibeler, J. Chem. Phys. 64 (976) 4445. [7] W. A. Chupka and C. Lifshitz, J. Chem. Phys. 48 (968) 09. [8] W. A. Chupka, J. Chem. Phys. 48 (968) 2337. [9] V. H. Dibeler, M. Krauss, R. M. Reese, and F. Harllee, J. Chem. Phys. 42 (965) 379. [0] H. Grotheer, S. Kelm, H. S. T. Driver, R. J. Hutcheon, R. D. Lockett, and G. N. Robertson, Ber. Bunsenges. Phys. Chem. 96 (992) 360. [] H.-J. Werner and P. J. Knowles, J. Chem. Phys. 89 (988) 5803. [2] K. P. Huber and G. Herzberg, Constants of Diatomic Molecules (Van Nostrand Reinhold, 979). [3] W. Kolos and J. Rychlewski, J. Chem. Phys. 98 (993) 3960. [4] R. D. Cowan and D. C. Griffin, J. Opt. Soc. Am. 66 (976) 00. [5] K. Raghavachari, G. W. Trucks, J. A. Pople, and M. Head-Gordon, Chem. Phys. Letters 57 (989) 479. [6] D. E. Woon and T. H. Dunning, Jr., J. Chem. Phys. 03 (995) 4572. [7] T. H. Dunning, J. Chem. Phys. 90 (989) 007. [8] R. A. Kendall, T. H. Dunning, Jr., and R. J. Harrison, J. Chem. Phys. 96 (992) 6796. 5

[9] A. D. Pradhan, H. Partridge, and C. W. Bauschlicher, Jr., J. Chem. Phys. 0 (994) 3857. [20] B. Roos, P. Taylor, and P. E. M. Siegbahn, Chem. Phys. 48 (980) 57. [2] D. Feller, J. Chem. Phys. 98 (993) 7059. [22] H. Partridge and C. W. Bauschlicher, J. Chem. Phys. 03 (995) 0589. [23] P. Jensen, private communication. 6

Table Summary of experimentally obtained enthalpies of formation f,0 H. experiment f,0 H CH 2 3 B kjmol f,0 H CH 2 A kj mol Hayden et al. [3] 393 7 2 5 429 3 2 5 Feldmann et al. [4] 426 3 2 Lengel and Zare [5] 425 5 2 392 5 2 a 390 8 7 b McCulloh and Dibeler [6] Chupka and Lifshitz [7] 384 5 4 2 Chupka [8] 395 8 Dibeler et al. [9] 395 8 2 9 c Grotheer et al. [0] 434 2 a from methane b from ketene c corrected for rotational effects [2] 7

Table 2 Enthalpies of formation f,0 H of CH 2 and CH and Dissociation energy D e of H 2. basis set active space vdz vtz vqz v5z v6z f,0 H CH 2 kj mol (CH 2 CH H) 8 3 405.63 392.59 390.40 390.9 389.8 0 4 405.48 392.8 389.85 389.44 389.22 5 405.47 392. 389.74 389.27 389.3 fci 405.6 D e H 2 kj mol 433.5 453.38 456.66 457.34 457.63 f,0 H CH kjmol 8 4 626.57 60.52 594.95 593.29 592.53 0 4 626.50 60.33 594.72 593.6 592. f,0 H CH 2 kj mol (CH 2 C H 2 ) 8 3 44.92 397.5 39.8 389.62 0 3 45.07 397.0 39.3 389.43 388.93 2 4 45.4 396.95 39.3 389.43 Table 3 Corrections to valence MRCI results used to obtain the heats of formation in Table 2. correction energy kj mol CH 2 CH H CH C H CH 2 C H 2 core-valence correlation -2.72-0.93-3.65 scalar relativistic effects -.28-0.40 -.72 spin-orbit coupling d 0.35 0.24 0.35 nonadiabatic effects e 0 0 0 0 0 0 vibrational zero point effects 27 2 0 2 f 6.92 g 8 06 0 2 g d derived from Ref.[2] e estimated from Ref. [3] f from Ref. [] g from Ref. [2] 8

45.0 H f /kj mol 405.0 395.0 385.0 2 3 4 5 6 7 8 9 Basis set 9

Fig.. Convergence of the calculated f,0 H values ( ) to the extrapolated complete basis set limit (- - -), and fitted exponential function ( ). 0