3092
J. Phys. Chem. 1994,98, 3092-3093
A Simple Failing of 6 2 Theory: Heats of Combustion Athanassios Nicolaides and Leo Radom' Research School of Chemistry, Australian National University, Canberra, ACT 0200, Australia Received: December 21, 1993'
G2 theory, which is normally very reliable for the prediction of reaction thermochemistry, is shown to be quite unsuitable for the prediction of heats of combustion. This arises because of significant errors in G2 energies for 0 2 and COz that reinforce rather than cancel one another in combustion equations. The errors increase with size of system. For example, errors of 3 1 and 163 kJ mol-' are found for the heats of combustion of methane and benzene, respectively.
TABLE 1: Calculated 6 2 Energies (hartrees) and Heats of Formation (AH, 2 ~ kJ , mol-')
Introduction The G2 theoretical procedure, introduced by Pople and coworkers,' for the purpose of reliable theoretical thermochemical predictions,has been found to be of widespread utility, consistently reproducing atomization energies, ionization energies, electron affinities, gas-phase acidities, and proton affinities to within 10 kJ mol-1.14 In cases where the G2 theoretical predictions and experimenthavediffered by more than 10 kJ mol-', this has often been taken as a sign that the experimental data should be reexamined. Indeed, in several such instances, new experimental data or analyses have confirmed the theoretical predictions.5One reaction whose thermochemistry is of great fundamental and practical importance is combustion. In this Letter, we show that this is unfortunately one instance where G2 theory fares very poorly: the discrepancy between theoretical (G2) and experimental heats of combustion is consistently considerably greater than 10 kJ mol-' due to errors in G2 energies for 0 2 and C02.
Theoretical Procedures and Results Standard ab initio molecular orbital calculations6 were performed with the GAUSSIAN92' and MOLPRO* series of programs. Energies were obtained at the G2 level of theory.' This corresponds effectively to calculations at the QCISD(T)/631 l+G(3df,2p) level on MP2(FULL)/6-31G(d) optimized geometries,incorporatingscaled HF/6-3 1G(d) zero-point energies and a so-called higher level correction. Enthalpy temperature corrections were derived using the calculated vibrational frequencies and standard statistical thermodynamics formulas. Calculated total energies at 0 and 298 K for the species relevant to this paper are presented in Table 1. Theoretical values of heats of formation at 0 K were obtained from calculated G2 atomization energies in conjunction with standard experimental AHf 0 values for the atomseg The AHf 298 values were then obtained using the theoretical enthalpy temperature corrections for the species under consideration in combination with literature values1° of enthalpy temperature correctionsfor elementsin their standard states. The theoretical AHf 298 values are compared with experimental values, taken from the compendium of Lias et a1.,9 also in Table 1.
Discussion Whereas the G2 heats of formation for the hydrocarbons, alcohols, and amines in Table 1 are generally in good agreement with experimentalvalues (benzene being the only poor case with a discrepancy of 16.2 kJ mol-'), significant errors are found for 0 2 (10.1 kJ mol-' too high) and C02 (1 1.3 kJ mol-' too low), as Abstract published in Aduance ACS Abstracts, March IS, 1994.
0022-3654/94/2098-3092S04.50/0
total energy G2(0K) G2(298K) Nz
-109.392 62 -150.148 22 -188.361 32 -76.332 05 -40.410 89 -79.630 88 -118.855 82' -78.415 93 -1 17.645 09" -77.185 73 -115.534 90 -154.764 46 -95.666 91 -231.780 53
0 2
co2 Hz0 CH4 CHnCHj CHsCH2CH3 CH2=CH2 CH3CH4H2 CHWH CH3OH CH~CHZOH CH3NH2 C6H6 a
G2
-109.389 31 -150.144 91 -188.357 75 -76.328 27 -40.407 07 -79.626 40 -1 18.850 24" -78.411 93 -1 17.639 98" -77.182 04 -115.53061 -154.759 15 -95.662 52 -231.775 08
5.2 10.1 -404.8 -243.0 -77.7 -86.0 -106.3 53.4 22.2 233.4 -206.7 -239.3 -22.9 99.1
%a expt
0.0 0.0 -393.5 -241.8 -74.5 -84.0 -104.5 52.2 20.2 228.0 -201.6 -234.8 -23.0 82.9
From: Wong, M.W.; Radom, L., to be published.
Calculated and Experimental Heats of Combustion (AH= kJ mol-')
TABLE 2
MBa
-
reaction
+
expt"
CH, 202 -802.7 COz + 2H20 CH3CH3 7/202 -1428.5 2c02 4-3Hz0 CHaCH2CH3 + 502-2043.4 3co2 4Hz0 CHF.CH2 + 302 -1322.9 2C02 + 2H20 CH3CH=CH2 9/202 -1926.2 3co2 + 3H20 C H 4 H +5/202 -1256.9 2C02 H i 0 CH3OH + 3 / 2 0 2 -675.6 CO2 + 2H20 CHsCHzOH+ 302-1277.7 2c02 + 3Hz0 CH3NH2 + 9 / 4 0 2 -L -975.1 COz 5/2H20+ I/2N2 C6H6 + " / 2 0 2 -3169.5 6CO2 + 3H20
-
+
+
+
+
-
+
-
-
G2b -833.3
diffC G2/exptd difP -799.5
3.2
-1487.9
59.4 -1426.5
2.0
-2130.7
87.3 -2041.6
1.8
-1379.4
56.5 -1324.1
1.2
-201 1.1
84.9 -1928.2
2.0
-1311.3
54.4 -1262.3
5.4
23.6
-670.4
5.2
-1329.6
51.9 -1273.2
4.5
-1006.9
31.8
-975.2
0.1
163.3 -3185.7
16.2
-699.2
-3332.8
30.6
'
a Experimental values obtained using data from ref 9. Standard G2 theory. C Absolute difference between G2 and experimental values. Obtained using G2 heats of formation for the hydrocarbon, alcohol, or amine from Table 1 and experimental values for 0 2 , C02, N2, and H20. e Absolute difference between GZ/experiment and experimental values.
noted previously.' This is a warning sign of potential problems in the calculation of heats of combustion. Calculatedand experimental heats of combustion are compared in Table 2. We can see that the G2 values are indeed very poor, 0 1994 American Chemical Society
Letters with errors ranging from 23.6 kJ mol-' for the combustion of CH30H to 163.3 kJ mol-' for the combustion of C6H6. The mean absolute difference between theory and experiment is a massive 64 kJ mol-'. If it is necessary to calculate the heat of combustion for a molecule for which the experimental value is not available, the standard G2 procedure of simply taking differences in G2 total energies is clearly completely unsuitable. An alternative procedure would be to use the G2 heat of formation for the molecule of interest, together with experimental values for the heats of formation of 02,C02, N2, and H20. This process eliminates, in particular, the G2 errors for 0 2 and C02. The results obtained in this way are also included in Table 2 as the column "GZ/expt". The errors in the heats of combustion are now much more reasonable, being in fact the same as the errors in the heats of formation in Table 1. The mean absolute difference between theory and experiment is a very respectable 4.2 kJ mol-', with a maximum deviation of 16.2 kJ mol-'.
Concluding Remarks The standard G2 theoretical procedure is unsuitable for calculating heats of combustion because of significant noncand i n g errors for 0 2 and C02. A combination of using the G2 heat of formation for the molecule of interest, together with experimental heats of formation for 02, C02, N2, and H20, is therefore recommended when the heat of combustion of a new molecule needs to be determined.
Acknowledgment. We gratefully acknowledge a generous allocation of time on the Fujitsu VP-2200 supercomputer of the Australian National University Supercomputing Facility.
The Journal of Physical Chemistry, Vol. 98, No. 12, 1994 3093 References and Notes (1) Curtiss, L. A.; Raghavachari, K.; Truck, G.W.; Pople, J. A. 1. Chem. Phys. 1991,94,7221. (2) See,for example: (a) Curtiss, L. A.; Koch, D.; Pople, J. A. J. Chem. Phys. 1991,95,4040. (b) Curtiss, L. A,; Raghavachari, K.; Dcutsch, P. W.; Pople, J. A. J. Chem. Phys. 1991.95, 2433. (c) Pople, J. A.; Curtiss, L.A. J . Chem. Phys. 1991,95,4385. (d) Curtiss, L. A.; N o h , R. H.; Pople, J. A.;Radom,L.J. Chem.Phys. 1992,97,6766. (e)Curtiss,L. A.;Raghavachari, K.; Pople, J. A. Chem. Phys. Lett. 1993, 214, 183. (3) See, for example: (a) Smith, B. J.; Radom, L. J. Phys. Chem. 1991, 95,10549. (b) Ma, L. N.; Smith, B. J.; Pople, J. A,; Radom, L. J. Am. Chem. SOC.1991, 113, 7903. (c) Smith, B. J.; Curtiss, L. A,; Pople, J. A.; Radom, L. Aust. J. Chem. 1992,45,285. (d) N o h , R. H.; Radom, L. Chem. Phys. Lett. 1992,189,554. (e) Wong, M. W.; Radom, L. J. Am. Chem. Soc. 1993, 115,1507. (f) Smith, B. J.; Radom, L. J. Am. Chem. Soc. 1993,115,4885. (4) See,for example: (a) Chiu, S. W.; Li, W. K.; Tzeng, W. B.; Ng,C. Y .J. Chem. Phys. 1992,97,6557. (b) Schlegel,H. B.; Skancke, A. J. Am. Chem. Soc. 1993, 115,7465. (5) See, for example: (a) Ruscic, B.; Berkowitz, J. J . Chem. Phys. 1992, 97,1818. (b) Naulin, C.; Costes, M.; Moudden, Z.; Ghanem, N.; Dorthe, G. Chem. Phys. Lorr. 1993,202,452. (c) Szulejko, J. E.; McMahon, T. B. J . Am. Chem. Soc. 1993, 115, 7839. (d) Keister, J. W.; Riley, J. S.;Baer, T. J. Am. Chem. Soc. 1993, 115, 12613. (e) Traeger, J. Unpublished data. (6) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (7) Friwh, M. J.; Trucks, G.W.; Had-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.;Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; DeFrecs, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN 92; Gaussian Inc.: Pittsburgh, PA, 1992. (8) MOLPRO is written by H. J. Wemer and P. J. Knowles with contributions of J. Almlof, R. Amos, S. Elbert, K. Hampel, W. Meyer, K.
Peterson, R. Pitzer, and A. Stone. The M~ller-Plesset and coupled-cluster treatments are discussed in: Hampel, C.; Peterson, K.;Wemer, H. J. Chem. Phys. Lett. 1992, 190, 1. The program to compute perturbative triples corrections has been developed by M. Deegan and P. J. Knowles (1992). (9) Lias, S.G.;Bart", J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data, Suppl. 1988, 17. (10) Wagman,D.D.;Evans,W.H.;Parker,V. B.;Schumm,R. H.;Halow, I.; Bailey, S.M.; Chumey, K. L.; Nuttall, R. L. J. Phys. Chem. Ref. Dura, Suppl2 1982, I I .
