Chinese Journal of Chemistry, 2005, 23, 194—199
Full Paper
Assessment of Performance of G3B3 and CBS-QB3 Methods in Calculation of Bond Dissociation Energies QI, Xiu-Juan(亓秀娟)
FENG, Yong(封勇)
LIU, Lei(刘磊)
GUO, Qing-Xiang*(郭庆祥)
Department of Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China The performance of the newly developed G3B3 and CBS-QB3 methods in calculating absolute bond dissociation energy (BDE) was assessed. It was found that these two methods could predict the BDE with an accuracy of about 8.4 kJ/mol and therefore, they exhibited similar performance as the standard G3 and CBS-Q methods. On the other hand, it was demonstrated that the B3LYP method significantly underestimated the absolute BDE by 16.7— 20.9 kJ/mol. This finding was valuable and timely because many researchers could use this relatively cheap method in studying radical reactions. Finally, 38 compounds were showed for which the theoretical BDE seriously deviated from the experimental data. Keywords
G3B3, CBS-QB3, composite ab initio method, bond dissociation energy, density functional theory
Introduction Bond dissociation energy (BDE) is defined as the enthalpy change at 298 K and 101.3 kPa for the gas-phase reaction A—B (g) → A• (g)＋B• (g). A sound knowledge of BDE is fundamental to understanding many chemical and biochemical processes.1 Therefore, considerable efforts have been devoted to the determination of BDEs of various molecules. Nonetheless, because of the experimental difficulties in dealing with highly reactive radical species, it remains notoriously difficult to accurately measure the BDEs of many important compounds.1 Much controversy has also taken place in the literature over the past 20 years concerning the BDEs of some simple molecules. In the latest edition of CRC Handbook of Chemistry and Physics, only about four hundred BDEs were considered to be reliable and therefore, listed.2 An alternative approach to get BDE is to use quantum chemistry theories. This approach has proven to be useful and important in many fields because it is relatively simple, fast and cheap. Nevertheless, because open-shell radical systems are involved in the computation, one should be very careful to choose theoretical methods for the BDE calculations. Generally speaking, unrestricted Hartree-Fock and perturbation methods were not recommended for BDE calculations due to their spin-contamination problems.3 More sophisticated ab initio methods such as QCISD and CCSD certainly performed better than HF and MP2 for the BDE calculations, but recent studies showed that these advanced methods might also seriously underestimate some BDEs.3 A more popular theoretical method for BDE calcula-
tions is the density functional theory (DFT).4 This method usually does not show serious spin-contamination and therefore, is believed to be desirable for open-shell systems. The relatively low CPU-cost of the DFT method is also advantageous. Nevertheless, Jursic’s and our own recent studies have shown that many DFT methods tend to systematically underestimate the BDE by 4.2—16.7 kJ/mol.5,6 Therefore, it is not safe to use the DFT methods to calculate the absolute BDE. However, as the underestimation by the DFT method is usually systematic, it could be reliable enough to use the DFT methods to calculate the relative BDE between different molecules. At present the most reliable way to calculate BDE is to use the composite ab initio methods such as G3 and CBS-Q.7 These composite ab initio methods basically involve a series of calculations that are designed to recover the errors that result from the truncation of both the one-electron basis set and the number of configurations used for treating correlation energies. Many groups have recently demonstrated the validity of the composite ab initio methods in the BDE calculations for various groups of compounds.8 Our own examination of a fairly large sample including over 200 compounds also showed that the standard deviation between the experimental BDEs and theoretical values from either G3 or CBS-Q method is only 8.6 kJ/mol.6 We also found from these calculations that about 40 experimental BDEs documented in CRC Handbook of Chemistry and Physics are questionable.6 It is worth noting that in our previous study the standard G3 and CBS-Q methods were utilized.6 In the standard G3 method geometry optimization was performed at (U)MP2(full)/6-31G(d) level, while in the
* E-mail:
[email protected]; Fax: 86-551-3606689 Received February 23, 2004; revised September 2, 2004; accepted October 11, 2004. Project supported by the Chinese Academy of Sciences (No. KJCXZ-SW-04) and the National Natural Science Foundation of China (No. 20332020). © 2005 SIOC, CAS, Shanghai, & WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Chin. J. Chem., 2005 Vol. 23 No. 2 195
Bond dissociation energy
standard CBS-Q method geometry optimization was done at (U)MP2(FC)/6-31G* level.7 Because of spin contamination, many researchers worry that UMP2 geometries are not accurate enough. Thus it remains to clarify whether or not the BDEs from composite ab initio calculations using UMP2 geometries are reliable. In order to provide a clear answer to the above important question, we recently performed a detailed and careful examination on the performance of the newly developed G3B3 and CBS-QB3 methods in the calculation of BDE.9 These two novel methods utilize B3LYP geometries instead of UMP2 ones, and the B3LYP geometries have been shown to be as accurate as those from QCISD calculations.3
Experimental All the experimental data were taken from CRC Handbook of Chemistry and Physics.2 Only the molecules with less than eight non-hydrogen atoms were considered in this study because of the limitation of CPU resources. Using this criterion a data base containing about 200 compounds was established. The calculations were done using the Gaussian 03 softwares.10 Initial geometry optimization was conducted using the UB3LYP/6-31G(d) method. Each optimized structure was confirmed by the frequency calculation at the UB3LYP/6-31G(d) level to be the real minimum without any imaginary vibration frequency. For those compounds that have more than one conformers, the energy of each conformer was calculated using the UB3LYP/6-31G(d) method. The optimized-conformer with the lowest energy was then used as the starting point for the G3B3 or CBS-QB3 calculation. BDE was calculated using the G3B3 and CBS-QB3 methods as the enthalpy change of the following reaction in the gas phase at 298 K and 101.3 kPa. A—B (g) → A• (g)＋B• (g)
(1)
The enthalpy of each species was calculated using the following equation: H298＝E＋ZPE＋Htrans＋Hrot＋Hvib＋RT
(2)
In this equation ZPE is the zero point energy; Htrans, Hrot and Hvib are the temperature-dependent contributions to enthalpy from translation, rotational motion and vibrational motion, respectively. They are the standard temperature correction terms calculated using the equilibrium statistical mechanics with harmonic oscillator and rigid rotor approximations. It is worth mentioning that the G3B3 (or G3//B3LYP) method is a variant of G3 theory in which structures and zero point vibrational energies were calculated at the B3LYP/6-31G(d) level of theory.9 For the single-point energy calculation G3B3 is very similar to the original G3 method, i.e., a base energy calculated at MP4/631G(d) level is corrected to QCISD(T)(full)/G3Large level using several additivity approximations at MP2
and MP4 levels. The CBS-QB3 method is a variant of the CBS-Q method in which structures and zero point vibration energies were calculated using a B3LYP/6-311G(2d,d,p) method.9 The single-point energy was then calculated at MP2/6-311＋G(3d2f, 2df, 2p) and MP4(SDQ)/6-31＋ G[d(f),p] levels. This energy was then extrapolated to the complete basis set limit. The ultimate electron correlation was determined using the CCSD(T) method in CBS-QB3.
Results and discussion Comparing theoretical data with reliable experimental BDE In the first stage of the study 167 compounds were examined for which the experimental BDEs were found to be consistent with the theoretical results (i.e. G3 and CBS-Q results) in our previous study.6 For each of the experimental data we obtained the theoretical BDE utilizing G3B3 and CBS-QB3 methods (data shown in the supporting information). In order to evaluate the agreement between the theoretical and experimental BDEs, we performed linear regression analyses using the following equation: BDE(exp.)＝kBDE(theor.)
(3)
The regression slope k, correlation coefficient r, standard deviation (sd), and mean deviation (md) were obtained using standard correlation methods (See Table 1 and Figure 1). No intercept was used in the above regressions, so that the analyses would reveal the ability of the composite ab initio methods in calculating absolute BDE but not relative BDE. Table 1 Statistical analyses for the agreement between the experimental and theoretical BDEs for 167 compounds Method
CBS-Q
G3
Correlation slope k
0.986
0.990
0.986
0.992
Correlation coefficient r Standard deviation (sd)/ ( kJ•mol－1) Mean deviation (md)/ ( kJ•mol－1)
0.995
0.995
0.996
0.994
8.8
9.4
8.4
9.7
＋5.1
＋3.2
＋5.1
＋2.8
CBS-QB3 G3B3
Comparing the experimental and theoretical BDEs, it can be seen that all of the four composite ab initio methods are very successful in predicting absolute BDE. The correlation slopes are about 0.99 without any intercept in the regression. The correlation coefficients are about 0.995. The standard deviations are around 9 kJ/mol. The mean deviations are 3—5 kJ/mol. It is worth noting that a large number of compounds (i.e. 167 compounds) were considered in the assessment. The types of chemical bonds undergoing homolysis are fairly versatile including C—H, N—H, O—H, Si—H,
© 2005 SIOC, CAS, Shanghai, & WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
196 Chin. J. Chem., 2005, Vol. 23, No. 2
Figure 1 Correlations of the CBS-QB3 (a) and G3B3 (b) BDEs with the experimental data.
P—H, S—H, C—C, C—Si, C—N, C—O, C—S, C—F, C—Cl, Si—Cl, N—N, N—O, O—O, O—Cl, O—Si, S— S and Si — Si. Therefore, our results definitely demonstrate the remarkable accuracy of the composite ab initio methods in calculating absolute BDE. From the above correlation results, it can also be seen that the G3B3 and CBS-QB3 results are very close to those from standard G3 and CBS-Q methods, despite the fact that the former two methods utilize the B3LYP geometries while the latter two use the UMP2 geometries. This conclusion is supported by the direct correlation between the CBS-QB3 and CBS-Q BDEs, and the direct correlation between the G3B3 and G3 BDEs (Figure 2). As seen from Figure 2, the direct correlations have slopes very close to unity. The correlation coefficients are about 1.000. The standard deviations are around 2—4 kJ/mol. The mean deviations are only 0.3—0.4 kJ/mol. Detailed analyses of the geometries (data not shown) reveal that the optimized geometries in the CBS-Q and G3 methods are noticeably different from those in the CBS-QB3 and G3B3 methods. The difference in bond lengths is usually 0.001 nm (or 1%) and the difference in bond angle is usually 1 degree (or 1%). Nonetheless, our calculation results for a large and diverse sample of compounds suggest that the CBS-Q and G3 methods provide nearly the same results as the CBS-QB3 and G3B3 methods. Therefore, for most radicals (at least those ones included in the present study) geometry optimization is actually not very sensitive to the theoretical method. In order to get accurate thermodynamics, it is
QI et al.
Figure 2 Correlation between the CBS-Q and CBS-QB3 BDEs (a), and correlation between the G3 and G3B3 BDEs (b).
necessary for us to pay more attention to the basis set and correlation effects on energy calculations. Significant underestimation of the absolute BDE by some DFT methods Using relatively small groups of compounds, many researchers have assessed the performance of various DFT methods in BDE calculations and some of them claimed that the DFT methods could provide accurate absolute BDE.11 In the previous study we have shown clearly that this optimism might not be justified by examining the BDE of a relatively large and more reliable group of compounds (i.e. 167 compounds from CRC handbook).9 In fact, we found that most DFT methods significantly underestimated the absolute BDE by 14— 25 kJ/mol except for the B3P86 method.12 Since only the G3 and CBS-Q methods were used in the previous study, it was not clear at that time whether the underestimation problems of the DFT methods stemmed from geometry optimization or from incomplete treatment of the basis set truncation errors and correlation effects. Herein, in order to have a better understanding about the underestimation problem, the BDEs calculated using the G3B3 methods were compared with those calculated using the B3LYP/6-31G(d), B3LYP/6-311＋＋G(d,p) and B3LYP/6-311＋＋G(3df, 2p) methods (Table 2). It is worth mentioning that in all these methods the geometries are optimized using the same method, i.e. B3LYP/6-31G(d).
© 2005 SIOC, CAS, Shanghai, & WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Chin. J. Chem., 2005 Vol. 23 No. 2 197
Bond dissociation energy Table 2 Statistical analyses for the correlation between the G3B3 BDEs and the BDEs from three DFT methods for 167 compounds Method Correlation slope k Correlation coefficient r Standard deviation (sd)/(kJ•mol－1) Mean deviation (md)/(kJ•mol－1)
B3LYP/ 6-31g(d)
B3LYP/ 6-311＋＋ g(d,p)
B3LYP/ 6-311＋＋ g(3df,2p)
1.050
1.051
1.050
0.991
0.991
0.994
14.5
17.1
14.6
－16.7
－20.4
－19.5
As seen from Table 2, regardless of the basis set the B3LYP method showed significant underestimation of absolute BDE by 16—20 kJ/mol compared to the G3B3 method (Figure 3). Even if one considers on the basis of Table 1 that the G3B3 method might overestimate the absolute BDE by 2.8 kJ/mol, we still can say that the B3LYP methods underestimate the absolute BDE by 14—18 kJ/mol. Such underestimation is not trivial in chemistry and could lead to overestimation of bond breaking reaction rates by 200—1500 times at room temperature. Since the B3LYP method is currently widely used in calculating BDEs of many important classes of compounds such as antioxidants, polyaromatic compounds and high-energy materials, one should be very careful about the calculated absolute BDE data.
Figure 3 Underestimation of the absolute BDEs evidenced by the correlation between the G3B3 and B3LYP/6-311 ＋ ＋ G(3df,2p) BDEs.
Nevertheless, it is also clear from Table 2 that the B3LYP BDE correlate with the G3B3 BDE fairly well. The correlation coefficients are over 0.99 which means that the underestimation is mainly systematic. Therefore, the B3LYP method should be used to calculate the relative BDE between different compounds. A scaling coefficient could also be used to solve the underestimation problem of the B3LYP BDE. For the 6-31G(d), 6-311＋ ＋g(d,p) and 6-311＋＋g(3df,2p) basis sets, the recommended scaling coefficients are 1.050, 1.051 and 1.050, respectively.
Some questionable experimental BDE In Table 3 are listed 38 experimental BDEs from CRC handbook of Chemistry and Physics.2 Although these experimental BDEs were considered to be reliable in the Handbook, our previous theoretical analyses indicated that they are questionable.6 It was proposed that our analyses were sensible because the same theoretical methods (i.e. G3 and CBS-Q) provided highly accurate BDE for many other compounds but seriously failed (deviation＞20 kJ/mol) for these 38 molecules. Since geometry optimization was done using the UMP2 method in G3 and CBS-Q, it was a worry that the disagreement between the experimental and theoretical BDEs was due to the use of wrong geometry in the calculation. Therefore, in the present study the G3B3 and CBS-QB3 methods were utilized to recalculate the BDEs of the 38 compounds. The results in Table 3 show that the BDEs calculated using the G3B3 and CBS-QB3 methods are very close to those calculated using the G3 and CBS-Q methods (standard deviation≈3 kJ/mol). Geometry optimization is not a problem for these 38 species. Thus the conclusions drawn in our previous study are correct.6 There are indeed a number of questionable experimental BDEs in the Handbook. Certainly we are not saying that our theoretical BDEs are “more” correct than the experimental data, but it would be necessary and interesting to perform more careful experimental as well as more sophisticated theoretical studies on these questionable BDEs. In the following are shown some “very” questionable experimental BDEs, from which the readers may visualize how serious the deviations between the experimental and theoretical data are (unit: kJ/mol). H—cycloprop-2-en-1-yl: exp. (379.1±17) vs. CBSQB3 (421.8) and G3B3 (420.2). H—CHCF2: exp. (448±8) vs. CBS-QB3 (493.2) and G3B3 (492.0). H— NH＋ 3 : exp. (385±21) vs. CBS-QB3 (523.6) and G3B3 (518.9). NC—CN: exp. (536±4) vs. CBS-QB3 (580.5) and G3B3 (577.7). NC—NO: exp. (120.5±10.5) vs. CBS-QB3 (211.4) and G3B3 (210.6). CH2C(CH3)—NO2: exp. (245.2) vs. CBS-QB3 (297.1) and G3B3 (294.0). F — CN: exp. (469.9) vs. CBS-QB3 (517.5) and G3B3 (510.2).
Conclusions In the present study the performance of the newly developed G3B3 and CBS-QB3 methods was examined in calculating absolute bond dissociation energies. It was found that these two methods could predict the BDE with an accuracy of about 8.4 kJ/mol and therefore, would be very useful theoretical tool for BDE studies. It was also found that the G3B3 and CBS-QB3 methods
© 2005 SIOC, CAS, Shanghai, & WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
198 Chin. J. Chem., 2005, Vol. 23, No. 2 Table 3
QI et al.
The compounds for which the difference between the theoretical and experimental BDEs is larger than 20 kJ/mol (unit: kJ/mol) Compound
Exp.
CBS-Q
G3
CBS-QB3
G3B3
H—Cycloprop-2-en-1-yl
379.1±1.7
420.8
419.6
421.8
420.2
H—CH(CH3)CCH
347.7±9.2
366.8
370.6
369.8
370.2
H—C(CH3)2CCH
338.9±9.6
360.6
363.8
360.1
361.4
H—C(CH3)2CHCH2
323.0±6.3
341.6
346.7
345.2
348.4
H—CH2C(CH3)C(CH3)2
326.4±4.6
356.7
359.8
356.7
358.5
H—C(CH3)2C(CH3)CH2
319.2±4.6
345.0
355.7
353.3
356.9
364±8
387.7
387.1
388.3
387.3
H—CH2NHCH3 H—CH2N(CH3)2
351±8
387.8
387.7
388.3
387.8
387.9±4
417.4
417.7
419.2
417.8
H—CHCF2
448±8
492.6
492.5
493.2
492.0
H—CFCHF
448±8
481.1
483.1
482.2
483.0
H—CFCF2
452±8
492.4
494.1
493.7
494.3
H—CFCFCl
444±8
485.5
487.7
486.6
487.8
H—CClCFCl
439±8
472.2
474.0
473.0
473.9
H—CClCHCl
435±8
462.4
465.2
464.1
465.0
H—CHClCHCH2
370.7±5.9
348.5
352.7
352.2
354.7
H—NO2
327.6±2.1
290.0
293.5
294.3
295.1
366.1
342.8
343.7
344.3
344.8
H—COOCH3
H—NHNH2 NH＋ 3
385±21
522.6
518.7
523.6
518.9
H—OOC(CH3)3
374.0±0.8
349.6
350.3
354.5
352.3
369.0
402.0
384.8
—
379.6
295.8±6.3
330.1
321.8
322.9
320.5
H—
H—SiH2C6H5 CH3—C(CH3)2CCH n-C3H7—CH2CCH
306.3±6.3
334.9
326.7
328.4
326.0
C2H5—CH2CN
321.7±7.1
350.4
345.9
347.3
345.6
CH3—C(CH3)2CN
312.5±6.7
339.0
333.4
336.5
334.5
536±4
584.5
585.9
580.5
577.7
CH3CO—COCH3
282.0±9.6
312.7
309.6
311.6
310.0
NC—NO
120.5±10.5
211.5
211.8
211.4
210.6
NC—CN
CH2C(CH3)—NO2
245.2
300.8
294.6
297.1
294.1
t-C4H9—NO2
244.8
269.4
268.3
267.8
268.2
t-C4H9—SH
286.2±6.3
319.1
309.1
312.7
307.8
F—CN
469.9±5.0
522.5
521.9
517.5
510.2
F—COF
535±12
512.4
509.7
513.9
509.4
F—CHFCl
465.3±9.6
500.0
496.1
500.6
495.1
F—CF2Cl
490±25
520.2
516.8
520.1
516.0
F—CFCl2
462.3±10.0
486.5
483.6
486.3
482.9
Cl—CSCl
265.3±2.1
330.2
325.4
324.9
319.0
207.9
261.7
254.6
261.6
254.8
HO—NCHCH3
provided nearly the same predictions for a large number of compounds as the G3 and CBS-Q methods. This indicated that the geometry optimization by the UMP2 method was not always a problem. Furthermore, we demonstrated that the B3LYP method could significantly underestimate the absolute BDE. This finding was believed to be very important because many researchers might use this relatively cheap method in their studies. Finally, it was showed that there were some seriously questionable experimental BDEs in an autho-
ritative Handbook. More detailed studies on these questionable compounds should be performed.
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Chin. J. Chem., 2005 Vol. 23 No. 2 199
Bond dissociation energy
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chari, K. J. Chem. Phys. 1999, 110, 7650. (c) Montgomery, J. A. Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. J. Chem. Phys. 1999, 110, 2822. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven, Jr. T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A.; Gaussian 03, Revision A. 1, Gaussian, Inc., Pittsburgh PA, 2003. Johnson, E. R.; Clarkin, O. J.; DiLabio, G. A. J. Phys. Chem. A 2003, 107, 9953 and references cited therein. It is worthy noting that although the B3P86 method can predict a lot of absolute BDEs fairly well, it also seriously underestimates some BDEs. For example, the experimental Cl—Si BDE in SiCl4 is 464 kJ/mol, but the B3P86/6-311＋ ＋G(d,p) prediction is 423.5 kJ/mol which is underestimated by over 40 kJ/mol. In comparison, the G3B3 prediction is 461.7 kJ/mol and the CBS-QB3 prediction is 469.1 kJ/mol. Thus one must always be careful about using the cheap DFT methods in BDE calculations. (E0402235 LI, L. T.)
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