3377
J . Phys. Chem. 1993,97, 3377-3378
New Theoretical Value of the Enthalpy of Formation of the CH20H Radical J. Espinosa-Garcia' and F. J. Otivares del Valle Departamento de QuImica FIsica, Universidad de Extremadura, 06071 Badajoz, Spain Received: October 12, 1992
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We have estimated theoretically the enthalpy of formation of the CH2OH radical by using as working chemical reactions CH2OH + H2 CH3 H2O and CHzOH CHI CH3OH CH3. We have found that accurate results can be reached when theoretical methods use large basis sets and elaborate correlated wave functions. The value obtained, A H f . 2 9 8 K = -15.6 i 1.5 kJ-mol-', is in excellent agreement with the recent experimental value found by Ruscic and B e r k ~ w i t z . ~
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Introduction Experimental determination of thermochemical energies is a very important challenge. An example is the determination of the CH20H enthalpy of formation. This radical presents a lack of coincidencebetween proposed experimental values (from -34' to -8.92 kEmol-I), even for the latest values reported: -1 5.53and -8.92 kJ-mol-'. This is a typical case in which theoretical thermochemistry can be of major assistance. The theoretical values obtained in prior investigations by Sana and Leroy4at the MP4 level also present a wide range (between -1 4.98 and -21.93 kJ.mol-I) depending on the reaction used in the evaluation. From a theoretical viewpoint, the accuracy of the enthalpies of formation is conditioned mainly by just a few factors: the goodness of the enthalpies of formation of reference compounds, the uncertainty in the thermal corrections, the level and accuracy of the electronic energy, the spin contamination (if radicals are involved),and most important, thechoiceof the working chemical reaction used in the evaluation. The first two are obvious factors affecting the quality of the results, so we shall not go into details. As we noted above, the suitable choice of the reaction where the unknown compound participates is of great importance. Recently, Sana et a1.,4.5for XYH, compounds and radicals, carried out an exhaustive study with extended basis sets of three types of reaction: isogyric,hydrogenation,and hydrogen exchangeprocess. They conclude that, on average, the latter two reactions give M r values closer to the experimentalvalues. We have reached similar conclusionsfor radicals centered on N6and for the OOH radical.' In this work,weestimate theoretically theenthalpy of formation of the CH2OH radical and we analyze the influence of the factors above mentioned.
Theoretical calculationswere performed with the GAUSSIAN 90 system of programs.8 The geometrical parameters were fully optimized at the second order of the Moller-Plesset perturbation theory9(MP2 level) with full electron correlation,using the6-3 1G(d,p) basis set. We then performed a simple calculation of the correlation energy at the fourth order of the Moller-Plesset theory (MP4SDTQ(FC) level) with the frozen core (FC) approximation and single, double, triple, and quadruple excitations, using three extended basis sets: BS1, 6-31 l+G(d,p); BS2, 6-31+G(2df,p); and BS3,TZ(2df,p).Io The energies were obtained taking into account simultaneouslythe effects of diffuse (+) and polarization (d,f) basis functions, thus avoiding the approximation of their additivity.!I The fourth-order Moller-Plesset perturbation theory (MP4 level) carries with it various problems. Thus, MP perturbation theory (especially the unrestricted version, UMP4) converges slowly, and the situation becomes more complicated in the case of radicals, unsaturated molecules, and unsaturated free radi0022-3654193 12091-337 I SO4.OO/O
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TABLE I: Total Energies (Hartrees), Thermal Corre~tion~ (kcal.mol-'), and Enthalpies of Formation (kcal-mol-') energies at the MP4 leveliJ TC( 298 K) A H i . w ~ BS 1 BS2 BS3 8.32h O.O* -1.16 769 -1.16456 -1.16681 20.67h -39.73 191 -39.73 859 -39.75 060 35.1&' (-39.73 300 -39.73 969 -39.75 171) 29.5~0~ -17.89h -40.40 5 14 -40.41 257 -40.42 531 CHr 15.24h -57.85h H2 0 -76.28 703 -76.29 484 -76.32 624 CHLOH 24.98, ? -1 14.81 705 -1 14.83 428 -1 14.87 592 (-114.81 810 -I 14.83 535 -114.87 701) -48.07' -I 15.47 727 -1 15.49 524 -I 15.53 727 CHiOH 33.86"
compd
H! CHj
Values in parentheses are those with spin projection (PMP4 level). Reference 17. Reference 18. Reference 19. e Reference 20. J Reference 2 1.
~ a l s . ~ Some J ~ J more14J5 ~ or less' I economical methods have been put forward with the aim of taking the post-MP4 energy into account. We estimated the post-MP4 total energies using the empirical PMP-SAC4 method of Truhlar14 and the theoretical fourth-order invariant quantity of Feenberg.15 As the UHF wave function is not necessarily an eigenfunction of the S2operator, we find spin contamination in the radicals. The small spin contamination of the radicals treated here has been corrected by use of projection operatorsl6 (PMP4 level: projected MP4).
Results and Discussion The total energies with (PMP4 level) and without (MP4 level) spin projection are listed in Table I, together with the thermal corrections, TC, and the enthalpies of formation of reference compounds. To avoid errors, we use experimental thermal corrections and enthalpies of formation whenever possible. The working chemical reactions we use (hydrogenation and hydrogen exchange process) and the enthalpies of formation of the CHzOH radical, Mf,are listed in Table 11, together with selected theoretical values reported in the literature. The difference between the Mr values obtained with (PMP4 level) and without (MP4 level) spin projection is negligible, due to the very small spin contamination of the radicals treated here. However, if unsaturated radicals are involved, the Mrdifference between MP4 and PMP4 levels becomes very important.6 Using the empirical method of TruhlarI4 and the upper bound energy of Feenberg,l5 we analyze the effect of the post-MP4 corrections. In general, the difference between the values obtained with and without these corrections is small, so that we may conclude that post-MP4 corrections are not critical if the reaction chosen is that of either hydrogenation or hydrogen exchange. We find differences less than 2 kEmol-1 between the two approximate methods. The PMP-SAC4 method seems to give results which are overestimated. 0 1993 American Chemical Society
3318 The Journal of Physical Chemistry, Vol. 97, No. 13, 1993
TABLE 11: Reactions and Enthalpies of Formation
References and Notes
(kcabmol-I) for the CHzOH Radical basis
MP4
CHJOH + H! C H I + H:O
reaction
BSI BS2
CH:OH + C H , + CHiOH + C H I
BSI BS2
-16.10 -15.05 -16.30 -14.17 -14.21
BS3
BS3
our AH, results PMP4 SAC4 Feenberg'
-15.02 -15.98 -16.32 -14.14 -16.24 -14.06 -15.94 -15.10 -15.06 -17.24
-15.84 -16.87 -16.70 -14.38 -14.25 -15.28
Espinosa-Garcia and Olivares del Valle
otherh -14.98
-19.67
and E2 E J ,and E d are the second-, third-, and fourth-order contributions to the electronic correlation, respectively.'5 Reference 4. MP4 calculations.
In conclusion, we can propose a value of -15.6 i 1.5 kEmol-' for the enthalpy of formation of the CH20H radical. The agreement between the predictions based on the various reactions and basis sets gives confidence in the A f i f , 2 9 8 K value that we have obtained. This value is in excellent agreement with the recent experimental value found by Ruscic and Berkowitz,3and we hope that this resolves the discrepancy in the enthalpy of formation of the CHzOH radical. Conclusions The accuracy of the theoretical enthalpy of formation of the CHzOH radical depends, mainly, on the amount of correlation energy taken into account and on the type of reaction chosen for its determination: we prefer hydrogenationor exchange reactions. Here, the spin projection and post-MP4 corrections are of minor importance.
( I ) Buckley, E.; Whittle. E. Trans. Faraday Soc. 1962, 58, 536. (2) Seetula, J. A.; Gutman, D. J . Phys. Chem. 1992, 96, 5401.
Ruscic. B.; Berkowitz, J. J. Chem. Phys. 1991, 95, 4033. Sana, M.; Leroy, G. J . Mol. Struct. (THEOCHEM) 1991,226,307. Sana, M.; Nguyen, M. T. Chem. Phys. Lett. 1992, 196, 390. Espinosa-Garcia, J.; Corchado, J. C.: Sana, M. To be published. ( 7 ) Espinosa-Garcia, J. To be published. (8) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foreman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M. A.; Binkley, J. S.; GonzBlez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.; Pople, J. A. GAUSSIAN 90; Gaussian, Inc.: Pittsburgh, PA, 1990. (9) Moller, C.; Plesset, M. S. Phys. Reu. 1934, 46, 618. (IO) Triple f basis of Dunning: Dunning, T. H., Jr. J . Chem. Phys. 1971, 55, 7 16. ( I I ) Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtis, L. A. J . Chem. Phys. 1989,90,5622(GI Theory). Curtis, L. A,; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J . Chem. Phys. 1991,94,7221 (G2 Theory). (12) Nobes,R. H.; Pople, J. A.; Radom, L.; Handy, N. C.; Knowles, P. L.Chem. Phys. Lett. 1987, 138, 481. ( I 3) Raghavachari, K. J. Chem. Phys. 1985.82,4607. (14) Gordon, M. S.; Truhlar, D. G. J . Am. Chem. SOC.1986,108, 5412. (IS) Feenberg, E. Ann. Phys. (N.Y.), 1958, 3, 292. Wilson, S. Int. J . Quantum Chem. 1980, XVIII, 905. (16) Lowdin, P. 0. Phys. Reu. 1955, 97, 1509. ( 1 7 ) Chase, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A.;Syverud, A. N. JANAFThermochemical Tables. J . Phys. Chem. ReJ Data, Suppl. 1985, 14. (18) Sana, M.; Leroy, G.; Peeters, D.; Younang, E. J . Mol. Struct. (THEOCHEM) 1987, 151, 325. (19) Sana, M.; Leroy, G.; Peeters, D.; Wilante, C. J . Mol. Struct. (THEOCHEM) 1988, 164, 249. (20) McMillen, D. F.; Golden, D. M. Annu. Rev. Phys. Chem. 1982, 33, 493. (21) Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organometallic Compounds; Academic Press: London and New York, 1970. (3) (4) (5) (6)
