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Hybrid density functional theory study of proton transfer between methane and methyl radical
6 October 1995
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 244 (1995) 263-268
Hybrid density functional theory study of proton transfer between methane and methyl radical Branko S. Jursic Department of Chemistry, University of New Orleans, New Orleans, LA 70148, USA
Received 18 May 1995; in final form 7 August 1995
Abstract The hybrid density functional theory (DFT) has been applied to model the proton transfer reaction between methane and methyl radicals. The obtained results were compared with the ROHF and MP2 ab initio calculations and the experimental results. Several basis sets from 6-31G(d) to 6-311 + + G(3df, 3pd) are applied. The suitability of the hybrid DFI" methods for modeling proton transfer reactions are discussed.
1. Introduction One of the most important features of computational chemistry is the reliability in predicting the geometries and energies of chemicals of interest by the experimental chemist [1-3]. Although, the ab initio methods with correlation and large basis set produce results that are close to the experimental results, that are computationally expensive and applicable only to very small molecules. Recently, we have been involved in the practical application of the DFT methods for solving some ab initio hard to handle problems [4-8]. Usually, the local DFI" methods, such as SVWN, produce reasonably well the geometries but drastically underestimate the activation energies. On the other hand, the non-local DFT methods, such as the BLYP and BP86, produce longer bonds and overestimate the activation energies [9]. For these systems, the hybrid DFT methods produce much better results than the RHF or MP2 ab initio, and the local and non-local DFT methods. The proton transfer between neutral and radical molecules is an important organic reaction [10-12].
The mechanism of the proton transfer has been the subject of both theoretical and experimental studies. For the theoretical study, the ab initio [13-15], semiempiricai [16], the local density approximation (LDA) and non-local (NL) [17] DFT methods were used. The energy barrier calculated by the various ab initio methods are significantly higher than the corresponding experimental activation energy (14.1 kcal/mol) [18]. On the other hand, both the LDA and NL DFI" methods predict significantly lower barriers (1.9 and 11.7 kcal/mol, respectively) [17]. We will considerably improve the results obtained by the hybrid DFT study. The objective of the present study is to apply the hybrid DFT methods to calculate the transition-state structures, reaction barriers and to compare the results with the those obtained by the RHF and MP2 ab initio methods and by the experiment.
2. Computational methodology All of the calculations were performed with the GAUSSIAN 92 [19] implementation of the density
0009-2614/95/$09.50 © 1995 Elsevier Science B.V, All rights reserved SSDI [1009-2614(95)00930-2
264
B.S. Jursic / Chemical Physics Letters 244 (1995) 263-268
functional theory. The optimizations were performed without any g e o m e t r i c restrictions using the F l e t c h e r - P o w e l l [20] method and the default Gaussian convergence criteria. Four different D F T hybrid methods were used: (1) BHandH, the method that includes 50% H F exchange and 50% Slater exchange [21] with no correlation functional; (2) BHandHLYP, Becke 5 0 - 5 0 method with LYP [22] correlation added; (3) Becke3LYP, B e c k e ' s 3 [23] functional parameter with the non-local correlation provided by the LYP [22] expression; and (4) Becke3P86, B e c k e ' s 3 [23] functional parameters with the non-local correlation provided by the Perdew 86 expression [24-27]. For comparison of the computational results, two ab
initio methods, a spin-restricted open-shell H a r t r e e Fock (ROHF) self-consistent field [28,29] and second-order M011er-Plesset (MP2) perturbation theory [30,31], were used.
3. Results and discussion The geometries of the reactants, the transition-state structure, and the m e t h a n e - m e t h y l radical complex have been optimized fully without using any symmetry elements and structural constrains. The data are compiled in Tables 1 and 2. The BHandH, BHandHLYP, Becke3LYP, and Becke3P86 DFT
Table 1 Optimized geometries of the species involved in the proton transfer from methane to methyl radical H
al/H/rl ,,: H--C Theory model
ROHF/6-31G(d) ROHF/6-311 + G(2d, 2p) ROHF/6-311 + G(2df, 2pd) ROHF/6-311 + + G(3df, 3pd) BHandH/6-31G(d) BHandH/6-311 + G(d, p) BHandH/6-311 + G(2d, 2p) BHandHLYP/6-31G(d) BHandHLYP/6-311 + G(d, p) BHandHLYP/6-311 + G(2d, 2p) BHandHLYP/6-311 + G(2df, 2pd) BHandHLYP/6-311 + + G(3df, 3pd) Becke3LYP/6-31G(d) Becke3LYP/6-311 + G(d, p) Becke3LYP/6-311 + G(2d, 2p) Becke3LYP/6-311 + G(2df, 2pd) Becke3LYP/6-311 + + G(3df, 3pd) Becke3P86/6-31G(d) Becke3P86/6-311 + G(d, p) Becke3P86/6-311 + G(2d, 2p) MP2-FC/6-a1G(d) MP2-FC/6-311 + G(d, p) MP2-FC/6-311 + G(2d, 2p) MP2-FC/6-311 + G(2df, 2pd) LDA [17] NL [17]
H
CH 3
CH 4
TS
r (.~)
r (,~)
r 1 (,~)
r2 (A)
al (deg)
a2 (deg)
1.072 1.070 1.070 1.070 1.079 1.078 1.075 1.074 1.073 1.070 1.071 1.071 1.082 1.081 1.078 1.078 1.078 1.082 1.081 1.078 1.079 1.079 1.073 1.074 1.092 1.092
1.084 1.084 1.082 1.082 1.088 1.087 1.085 1.085 1.084 1.081 1.081 1.081 1.093 1.091 1.088 1.088 1.088 1.092 1.090 1.088 1.090 1.090 1.084 1.085 1.101 1.092
1.080 1.078 1.078 1.078 1.086 1.085 1.082 1.082 1.081 1.078 1.078 1.078 1.090 1.088 1.085 1.085 1.085 1.090 1.088 1.085 1.088 1.088 1.082 1.083 1.100 1.100
1.336 1.336 1.336 1.336 1.329 1.328 1.327 1.340 1.339 1.337 1.337 1.337 1.346 1.346 1.345 1.345 1.346 1.342 1.340 1.339 1.332 1.326 1.327 1.323 1.334 1.359
112.8 113.0 113.0 113.0 113.2 112.5 113.6 113.1 113.3 113.4 113.4 113.4 113.2 113.5 113.5 113.5 113.5 113.3 113.5 113.6 112.9 113.2 113.3 113.4
105.9 105.7 105.7 105.7 105.4 105.1 105.0 105.5 105.2 105.2 105.2 105.2 105.4 105.1 105.0 105.1 105.0 105.3 105.0 105.0 105.7 105.4 105.3 105.2 104.7 104.7
B.S. Jursic / Chemical Physics Letters 244 (1995) 263-268
265
suits of these calculations are presented in Table 3. The Hartree-Fock calculations predict the activation barrier to be high. Presently, there is no sensitivity that is found to be considerable to the basis set. The predicted activation barrier is around 35 kcal/mol. Other ab initio methods using these calculations also predict the activation energy to be higher than the experimental value. Although, in the case of the MP2 calculations, the energy is determined to be only 5 - 6 kcal/mol higher. All of the applied hybrid DFT methods predict much better activation energies than the ROHF calculations and even the MP2 calculations. Only the BHandH 50-50 hybrid method is found to considerably underestimate the activation energy. Nevertheless, the quality of the obtained results are at least comparable to the Ziegler NL calculations. The best results are obtained with the Becke3LYP method. When the 6-31G(d) method was used, the predicted activation energy was only 0.28 kcal/mol different than the experimental value. A similar occurrence was obtained with the second and the hybrid DFT methods that included the P86 functional method. With the Becke3P86 6-311 + G(2d, 2p), the predicted energy is 0.32 kcal/mol below the experimental value. The Hartee-Fock calculations and LDA predict the double-well potential surface with the methanemethyl radical as the minimum on the surface. Thus, the reaction barrier should be the energy difference
methods are compared with ROHF, MP2 ab initio, LDA and NL DFF calculations that were previously carried out [17]. The structures were optimized by different ab initio, while the hybrid DFT methods were found to be quite similar. The C - H bond of the methyl radical varies from 1.07 to 1.08 ,~ and for methane from 1.08 to 1.09 A, making the difference to be around 1%. One exception, the C - H - C bond distance in the transition-state structure varies from 1.323 ,~ predicted by the MP2-FC/6-311 + G(2df, 2pd) to 1.346 A by the Becke3LYP, thereby, making the bond differences to be below 2%. Maximal disagreement was obtained for the methane-methyl radical complex (Table 2). The C - H - C bond distance varies by almost 1 ,~, from 2.467 A calculated by the BHandH/6-31G(d) to 3.400 .~ calculated by ROHF/6-31G(d). A similar, but higher level of agreement was also obtained when the bond angles of the transition-state structures were predicted. The maximal difference is less than 1°, making the geometries to be almost superimposed. The total and relative energies for the proton transfer reactions are presented in Tables 3 and 4. The activation energy for the reaction has been determined experimentally to be 14.1 kcal/mol [18]. If we do not assume the formation of the Coulomb complex between the reactants, then the reaction barrier should be the energy difference between the transition-state structure and the reactants. The reo
Table 2 Optimized geometries of methane-methyl radical complex
a4 ._../HH
ai• Theory model
r l (A)
r2 (.~)
r3 (,~)
r4 (,~)
al (deg)
a2 (deg)
a3 (deg)
a4 (deg)
a5 (deg)
ROHF/6-31G(d) BHandH/6-31G(d) BHandHLYP/6-31G(d) Becke3LYP/6-31G(d) Becke3P86/6-31G(d) Becke3P86\6-311 + G(d, p) Becke3P86/6-311 + G(2d, 2p) MP2-FC/6-31G(d) LDA [17]
1.084 1.088 1.085 1.093 1.092 1.090 1.088 1.090
1.083 1.091 1.085 1.094 1.093 1.091 1.088 1.090
3.400 2.467 3.000 3.002 2.930 3.209 3.359 3.102 2.979
1.072 1.079 1.075 1.083 1.082 1.081 1.078 1.079
109.4 109.4 109.4 109.4 109.4 109.4 109.4 109.4
109.5 109.6 109.5 109.5 109.5 109.5 109.6 109.6
176.9 177.0 176.9 176.9 176.7 176.0 174.8 177.5
95.3 91.4 91.7 91.7 90.2 89.9 91.3 91.2
119.3 120.0 120.0 120.0 120.0 120.0 120.0 120.0
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B.S. Jursic / Chemical Physics Letters 244 (1995) 263-268
Table 3 Total energies (hartrees) for methyl radical, methane and transition-state structure, and relative energy of transition-state structure in regard to separated reactants Theory model
CH 3
CH 4
TS
TS - reactans
ROHF/6-31G(d) ROHF/6-3 l I + G(2d, 2p) ROHF/6-3I 1 + G(2df, 2pd) ROHF/6-311 + + G(3df, 3pd) BHandH/6-31G(d) BHandH/6-311 + G(d, p) BHandH\6-311 + G(2d, 2p) BHandHLYP \ 6-31G(d) BHandHLYP\6-311 + G(d, p) BHandHLYP \ 6-311 + G(2d, 2p) BHandHLYP \ 6-311 + G(2df, 2pd) BHandHLYP\6-311 + + G(3df, 3pd) Becke3LYP \ 6-31G(d) Becke3LYP\6-311 + G(d, p) Becke3LYP \ 6-311 + G(2d, 2p) Becke3LYP\6-311 + G(2df, 2pd) Becke3LYP\6-311 + + G(3df, 3pd) Becke3P86 \ 6-31G(d) Becke3P86 6-311 + G(d, p) Becke3P86 6-311 + G(2d, 2p) MP2-FC \ 6-31G(d) MP2-FC\ 6-311 + G(d, p) MP2-FC\6-311 + G(2d, 2p) MP2-FC\ 6-311 + G(2df, 2pd) LDA [17] NL [17] exp. [18]
- 39.55477 -39.57260 -39.57200 -39.57248 -39.47953 -39.49507 - 39.49731 -39.80947 -39.82513 -39.82760 -39.82834 -39.82829 - 39.83829 -39.85517 - 39.85749 -39.85833 -39.85836 -39.99947 -40.01474 -40.01690 -39.66875 -39.70853 -39.72029 -39.73506
-40.19517 -40.21216 -40.21283 -40.21262 -40.14224 -40.15621 -40.15889 -40.48300 -40.49741 -40.50035 -40.50110 -40.50090 -40.51838 -40.53393 -40.53669 -40.53756 -40.53739 -40.69998 -40.71412 - 40.71668 -40.33255 -40.37953 -40.39369 -40.41079
- 79.69400 -79.72725 - 79.72876 -79.72862 - 79.60439 -79.63266 - 79.63709 -80.26298 - 80.29181 -80.29659 -80.29831 -80.29816 - 80,33376 -80.36465 - 80.36914 -80.37104 - 80.37095 -80.67890 -80.70733 -80.71156 - 79.96603 - 80.05663 -80.08234 -80.11526
35.10 36.09 35.19 35.45 10,91 11,68 12.00 18.51 19.28 19.68 19.53 19.48 14.38 15.34 15.71 15.59 15.56 12.90 13.51 13.82 22.13 19.72 19.87 19.19 2.8 12.6 14.1
between the transition-state structure and this complex. We have calculated the activation energies in this way (Table 4). With the 6-31G(d) basis set used for all methods, the energy of the complex is 0.3-0.7
kcal/mol below the reactant energies, making the prediction of the activation barrier of the ab initio method to be even worse. The activation energies predicted by the ROHF and MP2 are now 35.33 and
Table 4 Total energies (hartrees) for methane-methyl radical complex and transition-state structure, and relative energy (kcal/mol) of transition-state structure in regard to the complex Theory model
Complex
Transition state
Relative energy
ROHF/6-31G(d) BHandH/6-31G(d) BHandHLYP/6-31G(d) Becke3LYP/6-31G(d) Becke3P86/6-31G(d) Becke3P86/6-311 + G(d, p) Becke3P86/6311 + G(2d, 2p) MP2-FC/6-31G(O) LDA [17] exp. [18]
-
-
35.33 12.5 18.94 14.85 13.28 13.51 13.81 22.63 1.9 14.1
79.75031 79.62432 80.29316 80.35742 80.70007 80.72887 80.73357 80.00209
79.69400 79.60439 80.26298 80.33376 80.67890 80.70733 80.71156 79.96603
B.S. Jursic / Chemical Physics Letters 244 (1995) 263-268
22.63 kcal/mol, respectively. The BHandH energy is somewhat better, while the BHandHLYP predicts energies that are of the same quality as the one obtained by MP2. The best results are again obtained with Becke3LYP method. In the optimization of the methane-methyl radical complex, there was a considerable problem with the convergency, especially the hybrid methods. In all cases, the energy of the complex and the separate reactants were almost identical when large basis sets were used. This is demonstrated perfectly in the case of the Becke3P86 calculations. The energy differences calculated between the transition-state structures and the reactants (Table 3), and between the transition state and the complex (Table 4) with 6-311 + G(d, p) and 6-311 + G(2d, 2p) basis set are identical. These results are quite similar to the one obtained by NL DFF calculations [17]. In these calculations, the double-well profile predicted by lower level of calculations is disappearing. It can be explained by the fact that the lower level of calculation favors bonding among atoms that are similar to the LDA [32,33]. So, the higher level of hybrid DFT calculations predicts that the reaction is occurring without the formation of the methane-methyl radical complex. We can only demonstrate that at a high level of DFT calculations, which eliminates the double-well theory of proton abstraction reaction in the gas phase. We do not want to state, that experimentally it does not exist, but that this might also be an artifact of the hybrid DFT calculations. The basis set sensitivity for modeling proton transfer is extremely low. We have noticed this behavior in many of our previous computational studies with DFT methods [4-8]. This is an unusual behavior for the ab initio methods. Presently, we do not have a suitable explanation for the occurrence of this behavior.
4. Conclusion From the results presented here, we can draw a couple of very interesting remarks. The ab initio methods overestimate the activation barrier for the proton abstraction reaction. These results are in agreement with the previously published study. The ROHF predicts activation energies that are even twice as high as the experimental values, while the
267
MP2 method has an overestimated value of 5.0 kcal/mol. Almost all of the hybrid DFF methods produce better results than both ab initio methods. Two of the hybrid methods, Becke3LYP and Becke3P86, produce energies that are less than 1 k c a l / m o l away from the experimental results. The double-well potential energy surface of the proton transfer is favored by the ab initio method and the low level of hybrid DFT method. When the extended basis set, like 6-31 + G(d, p) or higher was used, the energy of the complex and the reactants was indistinguishable. Thus, the bond dissociation energies calculated by the applied ab initio methods were much higher than the experimental estimates. Therefore, one has reason to suspect that the shallow minimum predicted by ab initio methods might be an artifact. A similar conclusion was obtained by the NL DFT method. It has been demonstrated that the hybrid Becke methods with LYP and P86 functional are practical tools for the study of organic reactions that include proton transfers between neutral molecules and organic radicals.
References [1] J.B. Foresman and ,'E. Frisch, Exploring chemistry with electronic structure methods: a guide to using Gaussian (Gaussian, Pittsburgh, 1993). [2] W.J. Hehre, L.D. Burke, A.J. Shusterman and W.J. Pietro, Experiments in computational organic chemistry (Wavefunction, Irvine, 1993). [3] W.L Hehre, L. Radom, P. yon R. Schleyer and J.A. Pople, Ab initio molecular orbital theory (Wiley, New York, 1986). [4] B.S. Jursic and Z. Zdravkovski, Intern. J. Quantum Chem. 54 (1995) 161. [5] B.S. Jursic, Chem. Phys. Letters 236 (1995) 206. [6] B.S. Jursic, J. Comput. Chem., in press. [7] B.S. Jursic, Intern. J. Quantum. Chem., in press. [8] B.S. Jursic, J. Mol. Struct. (THEOCHEM), in press. [9] B.S. Jursic and Z. Zdravkovski, J. Chem. Soc. Perkin Trans. II (1995) 1225. [10] J.L. Ducan and L.M. Mills, Spectrochim. Acta 20 (1964) 523. [11] J. Pacansky and J. Bargon, J. Am. Chem. Soc. 97 (1975) 6896. [12] B.A. Hess and R. Zahradnik Jr., J. Am. Chem. Soc. 112 (1990) 5731. [13] T.A. Wildman, Chem. Phys. Letters 126 (1986) 325. [14] M. Sana, G. Leroy and J.L. Villaveces, Theoret. Chem. Acta 65 (1984) 109.
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[15] M.T. Rayez-Meaume, J.J. Dannenberg and J.L Whitten, J. Am. Chem. Soc. 100 (1978) 747. [16] M.J.S. Dewar and E. Haselbach, J. Am. Chem. Soc. 92 (1970) 590. [17] L. Fan and T. Zigler, J. Am. Chem. Soc. 114 (1992) 10890. [18] J.A. Kerr and S.J. Moss, CRC Handbook of bimolecular and thermolecular gas reactions, Vol. 1 (CRC Press, Boca Raton, 1981). [19] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.W. Wong, J.B. Foresman, M.A. Robb, M. Head-Gordon, E.S. Replogle, R. Gomperts, J.L. Andres, K. Raghavachari, J.S. Binkley, C. Gonzalez, R.L. Martin, D.J. Fox, D.J. DeFrees, J. Baker, J.J.P. Stewart and J.A. Pople, GAUSSIAN 92/DFT, Revision G.2 (Gaussian, Pittsburgh, 1993). [20] R. Fletcher and M.J.D. Powell, Comput. J. 6 (1963) 163. [21] J.C. Slater, Advan. Quantum Chem. 6 (1972) 1.
[22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33]
C. Lee, W. Yang and R.G. Parr, Phys. Rev. B 37 (1988) 785. A.D. Becke, J Chem. Phys, 97 (1992) 9173 J.P. Perdew, Phys. Rev. B 33 (1986) 8822. J.P. Perdew, Phys. Rev. 34 (1986) 7406 (E). J.P. Perdew and Y. Wang, Phys. Rev. B 33 (1986) 8800. J.P. Perdew, in: Electronic structure of solids, eds. P. Ziesche and H Eschrig (Akademie Verlag, Berlin, 1991). R. McWeeny and G. Dierksen, J. Chem. Phys. 49 (1968) 4852. C.C.J. Roothaan, Rev. Mod. Phys. 23 (1951) 69. C. Moiler and M.S. Plesset, Phys. Rev. 90 (1934) 618. P. Carsky, B.A. Hess Jr. and L.J. Schaad, J. Comput. Chem. 5 (1984) 280. T. Ziegler, Chem. Rev. 91 (1991) 651. J.K. Labonowsky and J. Andzelm, Density functional methods in chemistry (Springer, Berlin, 1991).
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 244 (1995) 263-268
Hybrid density functional theory study of proton transfer between methane and methyl radical Branko S. Jursic Department of Chemistry, University of New Orleans, New Orleans, LA 70148, USA
Received 18 May 1995; in final form 7 August 1995
Abstract The hybrid density functional theory (DFT) has been applied to model the proton transfer reaction between methane and methyl radicals. The obtained results were compared with the ROHF and MP2 ab initio calculations and the experimental results. Several basis sets from 6-31G(d) to 6-311 + + G(3df, 3pd) are applied. The suitability of the hybrid DFI" methods for modeling proton transfer reactions are discussed.
1. Introduction One of the most important features of computational chemistry is the reliability in predicting the geometries and energies of chemicals of interest by the experimental chemist [1-3]. Although, the ab initio methods with correlation and large basis set produce results that are close to the experimental results, that are computationally expensive and applicable only to very small molecules. Recently, we have been involved in the practical application of the DFT methods for solving some ab initio hard to handle problems [4-8]. Usually, the local DFI" methods, such as SVWN, produce reasonably well the geometries but drastically underestimate the activation energies. On the other hand, the non-local DFT methods, such as the BLYP and BP86, produce longer bonds and overestimate the activation energies [9]. For these systems, the hybrid DFT methods produce much better results than the RHF or MP2 ab initio, and the local and non-local DFT methods. The proton transfer between neutral and radical molecules is an important organic reaction [10-12].
The mechanism of the proton transfer has been the subject of both theoretical and experimental studies. For the theoretical study, the ab initio [13-15], semiempiricai [16], the local density approximation (LDA) and non-local (NL) [17] DFT methods were used. The energy barrier calculated by the various ab initio methods are significantly higher than the corresponding experimental activation energy (14.1 kcal/mol) [18]. On the other hand, both the LDA and NL DFI" methods predict significantly lower barriers (1.9 and 11.7 kcal/mol, respectively) [17]. We will considerably improve the results obtained by the hybrid DFT study. The objective of the present study is to apply the hybrid DFT methods to calculate the transition-state structures, reaction barriers and to compare the results with the those obtained by the RHF and MP2 ab initio methods and by the experiment.
2. Computational methodology All of the calculations were performed with the GAUSSIAN 92 [19] implementation of the density
0009-2614/95/$09.50 © 1995 Elsevier Science B.V, All rights reserved SSDI [1009-2614(95)00930-2
264
B.S. Jursic / Chemical Physics Letters 244 (1995) 263-268
functional theory. The optimizations were performed without any g e o m e t r i c restrictions using the F l e t c h e r - P o w e l l [20] method and the default Gaussian convergence criteria. Four different D F T hybrid methods were used: (1) BHandH, the method that includes 50% H F exchange and 50% Slater exchange [21] with no correlation functional; (2) BHandHLYP, Becke 5 0 - 5 0 method with LYP [22] correlation added; (3) Becke3LYP, B e c k e ' s 3 [23] functional parameter with the non-local correlation provided by the LYP [22] expression; and (4) Becke3P86, B e c k e ' s 3 [23] functional parameters with the non-local correlation provided by the Perdew 86 expression [24-27]. For comparison of the computational results, two ab
initio methods, a spin-restricted open-shell H a r t r e e Fock (ROHF) self-consistent field [28,29] and second-order M011er-Plesset (MP2) perturbation theory [30,31], were used.
3. Results and discussion The geometries of the reactants, the transition-state structure, and the m e t h a n e - m e t h y l radical complex have been optimized fully without using any symmetry elements and structural constrains. The data are compiled in Tables 1 and 2. The BHandH, BHandHLYP, Becke3LYP, and Becke3P86 DFT
Table 1 Optimized geometries of the species involved in the proton transfer from methane to methyl radical H
al/H/rl ,,: H--C Theory model
ROHF/6-31G(d) ROHF/6-311 + G(2d, 2p) ROHF/6-311 + G(2df, 2pd) ROHF/6-311 + + G(3df, 3pd) BHandH/6-31G(d) BHandH/6-311 + G(d, p) BHandH/6-311 + G(2d, 2p) BHandHLYP/6-31G(d) BHandHLYP/6-311 + G(d, p) BHandHLYP/6-311 + G(2d, 2p) BHandHLYP/6-311 + G(2df, 2pd) BHandHLYP/6-311 + + G(3df, 3pd) Becke3LYP/6-31G(d) Becke3LYP/6-311 + G(d, p) Becke3LYP/6-311 + G(2d, 2p) Becke3LYP/6-311 + G(2df, 2pd) Becke3LYP/6-311 + + G(3df, 3pd) Becke3P86/6-31G(d) Becke3P86/6-311 + G(d, p) Becke3P86/6-311 + G(2d, 2p) MP2-FC/6-a1G(d) MP2-FC/6-311 + G(d, p) MP2-FC/6-311 + G(2d, 2p) MP2-FC/6-311 + G(2df, 2pd) LDA [17] NL [17]
H
CH 3
CH 4
TS
r (.~)
r (,~)
r 1 (,~)
r2 (A)
al (deg)
a2 (deg)
1.072 1.070 1.070 1.070 1.079 1.078 1.075 1.074 1.073 1.070 1.071 1.071 1.082 1.081 1.078 1.078 1.078 1.082 1.081 1.078 1.079 1.079 1.073 1.074 1.092 1.092
1.084 1.084 1.082 1.082 1.088 1.087 1.085 1.085 1.084 1.081 1.081 1.081 1.093 1.091 1.088 1.088 1.088 1.092 1.090 1.088 1.090 1.090 1.084 1.085 1.101 1.092
1.080 1.078 1.078 1.078 1.086 1.085 1.082 1.082 1.081 1.078 1.078 1.078 1.090 1.088 1.085 1.085 1.085 1.090 1.088 1.085 1.088 1.088 1.082 1.083 1.100 1.100
1.336 1.336 1.336 1.336 1.329 1.328 1.327 1.340 1.339 1.337 1.337 1.337 1.346 1.346 1.345 1.345 1.346 1.342 1.340 1.339 1.332 1.326 1.327 1.323 1.334 1.359
112.8 113.0 113.0 113.0 113.2 112.5 113.6 113.1 113.3 113.4 113.4 113.4 113.2 113.5 113.5 113.5 113.5 113.3 113.5 113.6 112.9 113.2 113.3 113.4
105.9 105.7 105.7 105.7 105.4 105.1 105.0 105.5 105.2 105.2 105.2 105.2 105.4 105.1 105.0 105.1 105.0 105.3 105.0 105.0 105.7 105.4 105.3 105.2 104.7 104.7
B.S. Jursic / Chemical Physics Letters 244 (1995) 263-268
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suits of these calculations are presented in Table 3. The Hartree-Fock calculations predict the activation barrier to be high. Presently, there is no sensitivity that is found to be considerable to the basis set. The predicted activation barrier is around 35 kcal/mol. Other ab initio methods using these calculations also predict the activation energy to be higher than the experimental value. Although, in the case of the MP2 calculations, the energy is determined to be only 5 - 6 kcal/mol higher. All of the applied hybrid DFT methods predict much better activation energies than the ROHF calculations and even the MP2 calculations. Only the BHandH 50-50 hybrid method is found to considerably underestimate the activation energy. Nevertheless, the quality of the obtained results are at least comparable to the Ziegler NL calculations. The best results are obtained with the Becke3LYP method. When the 6-31G(d) method was used, the predicted activation energy was only 0.28 kcal/mol different than the experimental value. A similar occurrence was obtained with the second and the hybrid DFT methods that included the P86 functional method. With the Becke3P86 6-311 + G(2d, 2p), the predicted energy is 0.32 kcal/mol below the experimental value. The Hartee-Fock calculations and LDA predict the double-well potential surface with the methanemethyl radical as the minimum on the surface. Thus, the reaction barrier should be the energy difference
methods are compared with ROHF, MP2 ab initio, LDA and NL DFF calculations that were previously carried out [17]. The structures were optimized by different ab initio, while the hybrid DFT methods were found to be quite similar. The C - H bond of the methyl radical varies from 1.07 to 1.08 ,~ and for methane from 1.08 to 1.09 A, making the difference to be around 1%. One exception, the C - H - C bond distance in the transition-state structure varies from 1.323 ,~ predicted by the MP2-FC/6-311 + G(2df, 2pd) to 1.346 A by the Becke3LYP, thereby, making the bond differences to be below 2%. Maximal disagreement was obtained for the methane-methyl radical complex (Table 2). The C - H - C bond distance varies by almost 1 ,~, from 2.467 A calculated by the BHandH/6-31G(d) to 3.400 .~ calculated by ROHF/6-31G(d). A similar, but higher level of agreement was also obtained when the bond angles of the transition-state structures were predicted. The maximal difference is less than 1°, making the geometries to be almost superimposed. The total and relative energies for the proton transfer reactions are presented in Tables 3 and 4. The activation energy for the reaction has been determined experimentally to be 14.1 kcal/mol [18]. If we do not assume the formation of the Coulomb complex between the reactants, then the reaction barrier should be the energy difference between the transition-state structure and the reactants. The reo
Table 2 Optimized geometries of methane-methyl radical complex
a4 ._../HH
ai• Theory model
r l (A)
r2 (.~)
r3 (,~)
r4 (,~)
al (deg)
a2 (deg)
a3 (deg)
a4 (deg)
a5 (deg)
ROHF/6-31G(d) BHandH/6-31G(d) BHandHLYP/6-31G(d) Becke3LYP/6-31G(d) Becke3P86/6-31G(d) Becke3P86\6-311 + G(d, p) Becke3P86/6-311 + G(2d, 2p) MP2-FC/6-31G(d) LDA [17]
1.084 1.088 1.085 1.093 1.092 1.090 1.088 1.090
1.083 1.091 1.085 1.094 1.093 1.091 1.088 1.090
3.400 2.467 3.000 3.002 2.930 3.209 3.359 3.102 2.979
1.072 1.079 1.075 1.083 1.082 1.081 1.078 1.079
109.4 109.4 109.4 109.4 109.4 109.4 109.4 109.4
109.5 109.6 109.5 109.5 109.5 109.5 109.6 109.6
176.9 177.0 176.9 176.9 176.7 176.0 174.8 177.5
95.3 91.4 91.7 91.7 90.2 89.9 91.3 91.2
119.3 120.0 120.0 120.0 120.0 120.0 120.0 120.0
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B.S. Jursic / Chemical Physics Letters 244 (1995) 263-268
Table 3 Total energies (hartrees) for methyl radical, methane and transition-state structure, and relative energy of transition-state structure in regard to separated reactants Theory model
CH 3
CH 4
TS
TS - reactans
ROHF/6-31G(d) ROHF/6-3 l I + G(2d, 2p) ROHF/6-3I 1 + G(2df, 2pd) ROHF/6-311 + + G(3df, 3pd) BHandH/6-31G(d) BHandH/6-311 + G(d, p) BHandH\6-311 + G(2d, 2p) BHandHLYP \ 6-31G(d) BHandHLYP\6-311 + G(d, p) BHandHLYP \ 6-311 + G(2d, 2p) BHandHLYP \ 6-311 + G(2df, 2pd) BHandHLYP\6-311 + + G(3df, 3pd) Becke3LYP \ 6-31G(d) Becke3LYP\6-311 + G(d, p) Becke3LYP \ 6-311 + G(2d, 2p) Becke3LYP\6-311 + G(2df, 2pd) Becke3LYP\6-311 + + G(3df, 3pd) Becke3P86 \ 6-31G(d) Becke3P86 6-311 + G(d, p) Becke3P86 6-311 + G(2d, 2p) MP2-FC \ 6-31G(d) MP2-FC\ 6-311 + G(d, p) MP2-FC\6-311 + G(2d, 2p) MP2-FC\ 6-311 + G(2df, 2pd) LDA [17] NL [17] exp. [18]
- 39.55477 -39.57260 -39.57200 -39.57248 -39.47953 -39.49507 - 39.49731 -39.80947 -39.82513 -39.82760 -39.82834 -39.82829 - 39.83829 -39.85517 - 39.85749 -39.85833 -39.85836 -39.99947 -40.01474 -40.01690 -39.66875 -39.70853 -39.72029 -39.73506
-40.19517 -40.21216 -40.21283 -40.21262 -40.14224 -40.15621 -40.15889 -40.48300 -40.49741 -40.50035 -40.50110 -40.50090 -40.51838 -40.53393 -40.53669 -40.53756 -40.53739 -40.69998 -40.71412 - 40.71668 -40.33255 -40.37953 -40.39369 -40.41079
- 79.69400 -79.72725 - 79.72876 -79.72862 - 79.60439 -79.63266 - 79.63709 -80.26298 - 80.29181 -80.29659 -80.29831 -80.29816 - 80,33376 -80.36465 - 80.36914 -80.37104 - 80.37095 -80.67890 -80.70733 -80.71156 - 79.96603 - 80.05663 -80.08234 -80.11526
35.10 36.09 35.19 35.45 10,91 11,68 12.00 18.51 19.28 19.68 19.53 19.48 14.38 15.34 15.71 15.59 15.56 12.90 13.51 13.82 22.13 19.72 19.87 19.19 2.8 12.6 14.1
between the transition-state structure and this complex. We have calculated the activation energies in this way (Table 4). With the 6-31G(d) basis set used for all methods, the energy of the complex is 0.3-0.7
kcal/mol below the reactant energies, making the prediction of the activation barrier of the ab initio method to be even worse. The activation energies predicted by the ROHF and MP2 are now 35.33 and
Table 4 Total energies (hartrees) for methane-methyl radical complex and transition-state structure, and relative energy (kcal/mol) of transition-state structure in regard to the complex Theory model
Complex
Transition state
Relative energy
ROHF/6-31G(d) BHandH/6-31G(d) BHandHLYP/6-31G(d) Becke3LYP/6-31G(d) Becke3P86/6-31G(d) Becke3P86/6-311 + G(d, p) Becke3P86/6311 + G(2d, 2p) MP2-FC/6-31G(O) LDA [17] exp. [18]
-
-
35.33 12.5 18.94 14.85 13.28 13.51 13.81 22.63 1.9 14.1
79.75031 79.62432 80.29316 80.35742 80.70007 80.72887 80.73357 80.00209
79.69400 79.60439 80.26298 80.33376 80.67890 80.70733 80.71156 79.96603
B.S. Jursic / Chemical Physics Letters 244 (1995) 263-268
22.63 kcal/mol, respectively. The BHandH energy is somewhat better, while the BHandHLYP predicts energies that are of the same quality as the one obtained by MP2. The best results are again obtained with Becke3LYP method. In the optimization of the methane-methyl radical complex, there was a considerable problem with the convergency, especially the hybrid methods. In all cases, the energy of the complex and the separate reactants were almost identical when large basis sets were used. This is demonstrated perfectly in the case of the Becke3P86 calculations. The energy differences calculated between the transition-state structures and the reactants (Table 3), and between the transition state and the complex (Table 4) with 6-311 + G(d, p) and 6-311 + G(2d, 2p) basis set are identical. These results are quite similar to the one obtained by NL DFF calculations [17]. In these calculations, the double-well profile predicted by lower level of calculations is disappearing. It can be explained by the fact that the lower level of calculation favors bonding among atoms that are similar to the LDA [32,33]. So, the higher level of hybrid DFT calculations predicts that the reaction is occurring without the formation of the methane-methyl radical complex. We can only demonstrate that at a high level of DFT calculations, which eliminates the double-well theory of proton abstraction reaction in the gas phase. We do not want to state, that experimentally it does not exist, but that this might also be an artifact of the hybrid DFT calculations. The basis set sensitivity for modeling proton transfer is extremely low. We have noticed this behavior in many of our previous computational studies with DFT methods [4-8]. This is an unusual behavior for the ab initio methods. Presently, we do not have a suitable explanation for the occurrence of this behavior.
4. Conclusion From the results presented here, we can draw a couple of very interesting remarks. The ab initio methods overestimate the activation barrier for the proton abstraction reaction. These results are in agreement with the previously published study. The ROHF predicts activation energies that are even twice as high as the experimental values, while the
267
MP2 method has an overestimated value of 5.0 kcal/mol. Almost all of the hybrid DFF methods produce better results than both ab initio methods. Two of the hybrid methods, Becke3LYP and Becke3P86, produce energies that are less than 1 k c a l / m o l away from the experimental results. The double-well potential energy surface of the proton transfer is favored by the ab initio method and the low level of hybrid DFT method. When the extended basis set, like 6-31 + G(d, p) or higher was used, the energy of the complex and the reactants was indistinguishable. Thus, the bond dissociation energies calculated by the applied ab initio methods were much higher than the experimental estimates. Therefore, one has reason to suspect that the shallow minimum predicted by ab initio methods might be an artifact. A similar conclusion was obtained by the NL DFT method. It has been demonstrated that the hybrid Becke methods with LYP and P86 functional are practical tools for the study of organic reactions that include proton transfers between neutral molecules and organic radicals.
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