J. Phys. Chem. 1994,98, 1826-1829
1826
Heat of Formation of CH20H Charles W.Bauschlicher, Jr.,' and Harry Partridge' NASA Ames Research Center, Moffett Field, California 94035 Received: July 26, 1993"
The heat of formation of CHlOH at 298 K is determined to be -15.2 f 3.5 kJ/mol using high levels of theory. This is in good agreement with some recent experimental determinations. The assignment of the error bars is discussed in detail and compared with,that assigned in previous theoretical calculations. The largest uncertainty arises from the calculation of the zero-point energy.
Introduction
There is some uncertainty in the heat of formation of CH20H; several recent experimental determinationshave yielded somewhat different results. The following heats of formation (in kJ/mol) at 298 K have been reported: Seetula and Gutman' -8.9 f 1.8, Ruscic and Berkowitz2 -16.6 f 0.9, and Traeger and Homes3 -18.9 f 1.0. Traeger and Holmes suggested that the value of Seetula and Gutman was in error due to the assumption of free rotation about the C-O bond; using the experimental frequency for this rotation, Traeger and Holmes3 corrected the value of Seetula and Gutman to-14.7 f 1.4 kJ/mol, thereby bringing the recent values into better agreement. Ruscic and Berkowitz2also corrected thevalueofSeetulaandGutman,but treated therotation about the C-O bond as a hindered rotation rather than as a vibration; this lead to a value of -12.7 f 1.7 kJ/mol. The C-H bond energy in CHJOH has been computed to be 96.2 f 2 kcal/mol using two different ab initio appro ache^.^-^ This bond energy corresponds to a CH2OH heat of formation of -10.1 f 8.4 kJ/mol. Sana and Leroy6 computed the heat of formation using several different reactions. At their highest level of theory, they obtained values between -1 5.0 and -21.9 kJ/mol. Their best value (-19.7 kJ/mol) should be that determined using the isodesmic reaction, CH30H
+ CH,
-
CH20H
+ CH,
(1)
More recently, Espinosa-Garcia and Olivares del Valle7reported a heat of formation of -15.6 f 1.5 kJ/mol. However, it appears that they assigned the error based solely on the uncertainty in their computed heats of reactions (such as reaction I ) . Unfortunately, they overlooked theuncertainty in the zero-point energy, the heat of formation of CH3, and the correction from 0 to 298
K. In this work we report on the heat of formation of CH2OH using higher levels of theory than used in any of the previous work. We analyze the sources of error in the ab initio calculations and attempt to assign realistic error bars to the computed heat of formation.
Methods The use of an isodesmic reaction (Le., a reaction which has the same number and kind of bonds in both the reactants and products) is known to be an accurate method for computingheat of reactions, because many of the errors cancel. In order to determine the C-H bond energy in CHSOH, we use reaction 1. Using the computed heat of reaction and the known8-10C-H bond energy in CH4, the C-H bond energy in CH30H can be determined. Using this bond energy and the known11 heats of formation of Abstract published in Advance ACS Abstracts, February 1, 1994.
CH30H and H, the heat of formation of CHzOH is determined by CH,OH
-
CH20H
+H
(2)
It is then possible to convert the heat of formation to 298 K. The basis sets employed are the correlation-consistent polarized valence triple-zeta and quadruple zeta sets of Dunning12, denoted cc-pVTZ and cc-pVQZ, respectively. The cc-pVQZ carbon and oxygen basis sets can be denoted as (12s 6p 3d 2f lg)/[5s 4p 3d 2f lg] while the hydrogen basis set is (6s 3p 2d lf)/[4s 3p 2d If]. Only the pure spherical harmonic components of the basis set were used. The orbitals are optimized at the self-consistent-field (SCF) level using the spin-restricted approach. Correlation is added using either second-order Moller-Plesset perturbation theory13 (MP2) or the coupled cluster singles and doubles approach14 including a perturbational estimate of the triple excitation^^^ [denoted CCSD(T)]. In these calculations the C and 0 1s-like electrons are not correlated. The CCSD(T) calculations are performed using ACES 11'6 while the MP2 calculations are performed using DISC0.17 The geometry is taken from previous work', Le., optimized at the SCF level using a double-zeta plus polarization basis set. This approximation is tested by repeating the MP2 calculations in the cc-pVTZ basis using the MP2 geometry obtained using a 6-311G** basis set.18 These MP2 geometry optimizations, the calculation of the vibrational frequencies, and the calculation of the C-O rotational potential are performed using Gaussian 9019and are based on spin-unrestricted wave functions. In both thegeometry optimizationsand frequency evaluations all electrons are correlated. The calculation of the zero-point energy is computed in several ways including as half the sum of the experimental fundamentals,2&*4 the SCF harmonic frequencies, and the MP2 harmonic frequencies. The SCF and MP2 harmonic frequencies are computed using a 6-3 11G** basis set;18the frequencies at the MP2 level are also computed using a larger 6-311+G(3df,2p) basis set.18 The calculation of the zero-point energy is discussed in more detail below. The correction to the heat of formation from 0 to 298 K uses the assumptionsof a rigid rotor and harmonic oscillators, except for the rotation about the C-0 bond in CH2OH, where, following Pitzer and co-workers,2' this mode is treated as a hindered rotor. This rotational potential is studied at the MP2 level using the 6-31G** basis. The effect of basis set on the barrier height is studied by performing an MP2 calculations using the 6-3 1l+G(3df,2p) basis set, while the effect of improved correlation treatments is tested by using the quadratic configuration interaction approach26 with singles and doubles with a perturbational estimate of the triple excitations,ls denoted QCISD(T). For this system, the QCISD(T) approach should yield results very similar to the CCSD(T).
This article not subject to U S . Copyright. Published 1994 by the American Chemical Society
The Journal of Physical Chemistry, Vol. 98, No. 7, 1994 1827
Heat of Formation of CH20H
TABLE 1: Thermodynadc Quantities Used in This Work' molecule AHOO w 2 9 8 f l 2 9 8 - WO CH4 -66.818 -74.81 9.991 CHI 146.69' 10.366c H 216.003 211.965 6.197 CH3OH -189.765 -200.66 11.427 CH20Hd -8.37 f 3.3 -15.2 f 3.5 11.21 a All values are in kJ/mol and are taken from ref 11 unless otherwise noted. b Reference 9. Computed in this work using the frequencies (3004.8,606.45,3 160.82(2), and 1396.0(2) cm-I) from ref 22. Present work.
-
TABLE 2 Summary of the Com uted Heat of Reaction (Not Including Zero-Point Energy! for CH3OH + C H 3 CH2OH + C H 4 SCF MP2 CCSD(T) CC-PVTZ -5.85 -8.88" -9.00 CC-pVQZ -5.79 -8.68 Using the MP2 geometry obtained using the 6-31 1G** basis set yields -8.91 kcal/mol. Results and Discussion We first consider the C-H bond energy in CH4. Chupkas determined the C-H bond energy to be 103.24 f 0.12 kcal/mol from the photoionization spectrum of methane. Dobis and Benson9 determined the heat of formation of CH3 at 298 K from the reaction of methane with C1. From this value and known thermodynamic data, which we have summarized in Table 1, we deduce a C-H bond energy of 103.45 f 0.1 kcal/mol. The CH3 heat of formation by Russell et a1.10 yields a C-H bond energy of 103.2 f 0.3 kcal/mol. On the basis of these experiments, we adopt a C-H bond energy of 103.35 f 0.2 kcal/mol. The summary of our results for the heat of reaction,' without zero-point energy, is given in Table 2. The results are not strongly affected by the level of correlation treatment, the basis set, or the choice of geometry (provided a consistent set of geometries is used). This is not unexpected for an isodesmic reaction. Our best result in the cc-pVTZ basis set is that obtained using the CCSD(T) approach, which is our highest level of correlation treatment. From the small difference between the MP2 and CCSD(T) values, we believe that the CCSD(T) result is close to the n-particle limit. The small change in the MP2 result when the basis set is improved suggests that the heat of reaction does not have a strong basis set dependence. Using the MP2 results as a measure of basis set convergence,we estimate that the CCSD(T) result in the cc-pVQZ basis would be -8.80 kcal/mol. Assuming that the remaining basis set errors are not larger than the difference between the cc-pVTZ and cc-pVQZ basis set, we assign an error of f 0 . 2 kcal/mol to this heat of reaction. This error bar should also account for any small uncertainty due to the choice of geometry. It is common to compute the zero-point vibrational energies as half the sum of the experimental fundamentals. While the fundamentals are known from experiment for CH30H,20CHd,21 and CH3,ZZ only seven of the nine frequencies in CH20H have been measured.23 (We note that recent calculation^^^ have confirmed that the experimental band23 at 569 cm-1 should be assigned to CH20H.) If we take the scaled SCF frequencies of Saebo, Radom, and Schaeferz' for the remaining two modes, we find a zero-point correction of +0.20 kcal/mol to the heat of reaction 1. On the other hand, if we take our best estimatez4for the two unobserved modes, we obtain a correction of +0.37 kcal/ mol; see Table 3. Regardless of the accuracy of the fundamentals, this does not correspond to the true zero-point energy. As noted by Grev, Janssen, and Schaefer,zB if one averages half the sum of the fundamentals and half the sum of the harmonic frequencies one obtains a much better approximation to the zero-point energy.
TABLE 3 kcal/mol) molecule
Summary of the Zero-Point Energies (in exut"
MP2 6-311+G(3df,2u)
0.91 XSCF 6-311G**
MP2 6-31 1G**
~
CH,OH 31.15 32.80 31.33 32.90 19.09 17.49 18.93 CH3 18.19 23.91 CHzOH 22.62' 22.81 24.14 28.63 26.81 28.58 CHI 27.09 a The experimental fundamentalsare taken from refs 20-23. The two missing frequencies for CHzOH are those from ref 24. The value is 22.45 kcal/mol if the two missing frequencies are taken from Sacbo, Radom, and Schaefer?' For the harmonic frequencies,we use those computed at the MP2 level of theory in a 6-31 l+G(3df,2p) basis set, which yields a zero-point correction to the heat of reaction 1 of +0.65 kcal/mol. (The smaller 6-311G** basis set yields +0.88 kcal/mol at the MP2 level.) Combining this value with that deduced for the sum of the fundamentals leads to our best estimate for the effect of zero-point energy on the heat of reaction 1 of +0.42 f 0.4 kcal/ mol. The lower limit is smaller than the value computed using the scaled SCF frequencies2' for CHzOH to account for the possibility that even these C-H stretching frequencies are too large. Using the scaling factor of 0.91 recommended by Grev, Janssen, and Schaefer,Z8the scaled SCF zero-point correction to the heat of reaction is +0.80 kcal/mol. This is at the upper limit of our estimate for the zero-point correction. Using the heat of reaction 1, the zero-point energy, and the experimental C-H bond energy of CH4, we deduce a C-H bond energy in CH30H of 94.98 f 0.80 kcal/mol. The uncertainty is arrived at using h0.4 kcal/mol for the error in the zero point, f0.2 kcal/mol for the experimental uncertainty in the CH4 bond strength, and *0.2 kcal/mol for the uncertainty in the heat of reaction 1. The current value overlaps with the results of the previous calculation^^*^ within the combined error bars. Using this C-H bond energy and known thermodynamic quantities (tabulated in Table 1) leads to a heat of formation of -8.4 f 3.3 kJ/mol at 0 K. There has been some on how best to correct this quantity to 298 K. Seetula and Gutman1 assumed free rotation about the C-O bond; however, both Traeger and Holmes3 and Ruscic and Berkowitz2 have argued that this is not correct. Traeger and Holmes computed the correction to 298 K treating all modes as vibrations, this yields a value for H'298 - PO of 11.31 kJ/mol. Using a combination of theoryZ4 (3008 and 3150 cm-l) and experimentz3(420, 569, 1048, 1183, 1334, 1459, and 3650 cm-l) for the CH2OH vibrational frequencies, we compute the same value for H'298 - H'o as Traeger and Holmes. Using this approach for CH30H yields 1 1.32 M/ mol, which is only 0.11 M/mol smaller than that given in the NBS tables." However, Ruscic and Berkowitzz suggested that rotation about the C-O axis should be treated as a hindered rotation, and using this approximation they obtained a Ho298 Hoo value of 12.2 kJ/mol for CH20H. Espinosa-Garcia and Olivares del Valle7report the sum of zero-point energies and the corrections to 298 K that were taken from Sana and Leroy.6 Unfortunately, Sana and Leroy did not report these quantities separately. Because the value of Ruscic and Berkowitz is very different from that of Traeger and Holmes, we have considered treating this mode as a hindered rotation. As a first step we determine the rotational potential at the MP2 level using the 6-31G** basis set with all other parameters fixed at their equilibrium values; this potential is shown in Figure 1. The inequivalence of the two hydrogens bound to the carbon is seen by the difference in the well depths at approximately 30' and 180'. However, it is known27 that the inversion barrier is low. Therefore, if rotation about the C-0 bond is considered and all other parameters are optimized at each angle, one obtains the rotationalpotential shown in Figure 2.
1828 The Journal of Physical Chemistry, Vol. 98, No. 7, 1994
6
0
-2
0
80
120
180
240
300
380
Rotation angle, degrees Figure 1. Potential for rotation about the C-O bond in CH20H. All
other parameters are fixed at their value from equilibrium. The MP2 level of theory is used in the 6-31G** basis set.
5
1
-1
-180 -120
-80
0
80
120
180
Rotation angle, degrees Figure 2. Potential for rotation about the C-O bond in CH20H. All other parameters are optimized. The MP2 level of theory is used in the 6-31G**basis set. The small barriers between the large barriers correspond to the inversion of the CHI group.
Using the approach of Pitzer and co-workers25 the rotational potential is assumed to be of the form l/zVo( 1 - cos m$), where VOis the barrier height. From Figure 2, we conclude that n = 2. We determined the barrier by optimizing the geometry of the saddle point and equilibrium structures at the MP2 level using 6-31G** basis set. The barrier at this level is 4.43 kcal/mol. Using the QCISD(T) approach increases the barrier (4.5 1 kcal/ mol) as does improving the basis set to 6-31+G(3df,2p) at the MP2 level (4.58 kcal/mol). Adding the correction for level of correlation treatment and for basis set improvement leads to our best estimate of this quantity of 4.7 kcal/mol. The moment of inertia for the internal rotation is determined using our computed geometry and the formula given by Pitzer,25 namely, Z, = A (1 - c~,,[a~A/Zt]),where A is the moment of inertia of the spherical top, the Z,'s are the principal moments of inertia of the molecule, and the a,'s are the direction cosines between the axis
Bauschlicher and Partridge of rotation and the principal axes. This leads to a contribution to ff0298 - H O o of this mode of 0.206 kcal/mol. The remaining modes are treated as vibrations which leads to a w298 - HOO valueof 11.21 kJ/mol. Thisvalueisverysimilartothatcomputed treating all modes as vibrations. It is much smaller than that of Ruscic and Berkowitz because they used a barrier of 4.0 kcal/ mol and assumed n = 1 for the form of the rotational potential. Using our ff0298- PO value of 11.21 kJ/mol results in a heat of formation at 298 K of -15.3 f 3.5 kJ/mol, where we have increased the uncertainty by 0.2 kJ/mol because of uncertainties in the correction to 298 K. This value is consistent with the result of Ruscic and Berkowitz2 (-16.6 f 0.9 kJ/mol) and also suggests that the true heat of formation lies in the lower half of the Traeger and Holmes3 result (-18.9 f 1.0 kJ/mol). Our value is also consistent with the revised values for the experiment of Seetula and Gutman,I either by Traeger and Holmes3 (-14.7 f 1.4 kJ/ mol) or Ruscic and Berkowitz2 (-12.7 f 1.7 kJ/mol). Our theoretical value overlaps with that of Espinosa-Garcia and Olivares del Valle (-15.6 f 1.5 kJ/mol), but somewhat surprisingly, the value computed by Sana and Leroy using eq 1 is clearly too large (-19.7 kJ/mol). As one of our motivations was to develop realistic error bars, we compare our results with previous theory in some detail. Espinosa-Garcia and Olivares del Valle computea heat of reaction 1 of -8.17 and -8.38 kcal/mol at the MP4 level using their BS2 (6-3 l+G(2df,p)) and BS3 (TZ(2df,p)) basis sets, respectively. Given that they assign an uncertainty of f0.36 kcal/mol to their results, they are in reasonable agreement with our best estimate of this quantity (-8.8 f 0.2 kcal/mol). Sana and Leroy compute -9.4 kcal/mol for the same quantity; this is somewhat surprising because their calculation should be identical to the BS2 result of Espinosa-Garcia and Olivares del Valle. An inspection of the total energies shows that while the two sets of calculations are in agreement for the CH3, CH,, and CH20H total energies,they differ for CH30H. Sana and Leroy obtain-8.94 kcal/mol at the MP2 level using a smaller basis set. This is in good agreement with the other determinations. Thus we suspect that there is some error in the large basis set MP4 calculations of Sana and Leroy, which results in their heat of reaction being too large. Espinosa-Garcia and Olivares del Valle' take their values for the zero-point energies and correction to 298 K from Sana and Leroy.6 For CH30H, by substracting the NBS" correction to 298 K, it is clear that their zero-point energy is half the sum of the experimental fundamentals.2O Using their MP4/BS3 heat of reaction 1in conjunction with our data leads to a heat of formation of -13.4 kJ/mol. This value is outside their error bars. Since improving the calculation of the zero-point energy and correction to 298 K changes their value by more than their error bars, we conclude that their error bars were overly optimistic, especially in light of their choice of using experimental fundamentals for the zero-point energy. On the basis of their calculations thevalue of Traeger and Holmes can be ruled out, while based on our calculations such, a conclusion cannot be made. Conclusions
Our best value for the heat of formation of CHzOH is -15.2 f 3.5 kJ/mol. This is consistent with the experimental value of
Ruscic and Berkowitz (-16.6 f 0.9 kJ/mol) and theexperimental value of Seetula and Gutman as revised by either Traeger and Holmes (-14.7 f 1.4 kJ/mol) or Ruscic and Berkowitz (-12.2 f 1.7 kJ/mol). Our value is also consistent with that of Traeger and Holmes (-18.9 f 1.0 kJ/mol) within the combined error bars of both determinations. We showed that the largest uncertainty in the calculations arises from the calculation of the zero-point energy. Our heat of formation and assignment of error bars has been compared with previous theoretical work, and we conclude that some of the previous error bars were too optimistic.
Heat of Formation of CHzOH
Acknowledgment. These authors thank Dr. Berkowitz for helpful discussions.
The Journal of Physical Chemistry, Vol. 98, No. 7, 1994 1829
Stanton, J. Gauss, J. D. Watts, W. J. Lauderdale, and R. J. Bartlett. The two-electron integrals are taken from the vectorized MOLECULE code of J. AlmlBf and P. R. Taylor. ACES I1 includm a modified version of the ABACUS integralderivativcsprogram, written by T. Helgabr, H. J. JCMCII,P. J~rensm, References and Notes J. Olsen, and P.R. Taylor, and the geometry optimization and vibrational analysis package written by J. F. Stanton and D. E. Bernholdt. (1) Seetula, J. A.; Gutman, D. J. Phys. Chem. 1992, 96, 5401. (17) DISCO is a direct SCF and MP2 program written by J. Almldf, K. (2) Ruscic, B.; Berkowitz, J. J. Phys. Chem. 1993, 97, 11451. Faegri, M. Feyereisen, and K. Korsell. Also see: Almldf, J.; Faegri, K.; (3) Traeger, J. C.; Holmes, J. L. J. Phys. Chem. 1993, 97, 3453. Korsell, K. J. Compur. Chem. 1982, 3, 385. Saebo, S.;AlmlBf, J. Chem. (4) Curtiss, L. A.; Kock, D.; Pople, J. A. J . Chem. Phys. 1991,95,4040. Phys. Lett. 1987, 154, 521. (5) Bauschlicher, C. W.; Langhoff, S.R.; Walch, S.P. J. Chem. Phys. (18) Frixh, M. J.; Pople, J. A.; Binkley, J. S . J . Chem. Phys. 1984, 80, 1992, 96, 450. 3265 and references therein. (6) Sana, M.; Leroy, G. J. Mol. Struct. (THEOCHEM.)1991,226,307. (19) Gaussian 90, Rivision J. Frisch, M. J.; Head-Gordon, M.; Trucks, (7) Espinosa-Garcia, J.; Olivares del Valle, F. J. J . Phys. Chem. 1993, G. W .; Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M.; Binkley, 97, 3377. J. S.;Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Secger, R.; (8) Chupka, W. A. J . Chem. Phys. 1968,48, 2337. Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, (9) Dobis, 0.;Benson, S.W. Int. J. Chem. Kine?. 1987, 19, 691. S.;Pople, J. A. Gaussian, Inc., Pittsburgh, PA, 1990. (10) Russell, J. J.;Seetula, J.A.;Senkan,S. M.;Gutman,D.Inr.J. Chem. (20) Shimanouchi, T. Tables of Molecular Vibrational Frequencies; Kine?. 1988, 20, 759. National Bureau of Standards: Washington, DC, 1972. (11) Wagman,D.D.;Evans,W.H.;Parker,V.B.;Schumm,S.H.;Halow, (21) Jones, L. H.; McDowell, R. S.J. Mol. Specrrosc. 1959, 3, 632. I.; Bailey, S.M.; Churney, K. L.; Nutall, R. L. J . Phys. Chem. Re$ Dura (22) Jacox, M. E. J . Phys. Chem. ReJ Dara 1984, 13, 945. 1982, 11, Suppl. 1. (23) Jacox, M. E. Chem. Phys. 1981,59, 213. (12) Dunning, T. H.J . Chem. Phys. 1989, 90, 1007. (24) Bauschlicher, C. W.; Partridge,H. Chem.Phys. Lett. 1993,215,451. (13) Pople, J. A.; Binkley, J. S.;Seeger, R. Inr. J . Quantum Chem. Symp. (25) Pitzer, K. S.;Gwinn, W. D. J. Chem. Phys. 1942, 10,428. Pitzer, 1976. 10. 1. K. S . J. Chem. Phys. 1946,14,239. Kilpatrick, J. E.; Pitzer, K. S.J . Chem. (14) Bartlett, R. J. Annu. Rev. Phys. Chem. 1981, 32,359. Rittby, M.; Phys. 1949, 17, 1064. Bartlett, R. J. J . Phys. Chem. 1988, 92, 3033. (26) Pople, J. A,; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. (15) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. 1987, 87, 5968. Chem. Phyi. Letr. 1989,157,479. (27) Saebo, S.;Radom, L.; Schaefer, H. F. J. Chem. Phys. 1983,78,845. (16) ACES I1 is computationalchemistrypackage especially designed for (28) Grev, R. S.;Janssen, C. L.; Schaefer, H. F. J. Chem. Phys. 1991,95, coupled cluster and many body perturbation calculations. The SCF, 5128. transformation, correlation energy and gradient d e s were written by J. F.
