Performance of ab initio and DFT methods in modeling Diels-Alder reactions

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1 Indian Journal of Chemistry Vol. 50A, November 2011, pp Notes Performance of ab initio and DFT methods in modeling Diels-Alder reactions Gaddamanugu Gayatri Molecular Modeling Group, Organic Chemical Sciences, Indian Institute of Chemical Technology, Hyderabad , India Received 1 May 2011; revised and accepted 18 August 2011 The performance of a range of computational methods in modeling Diels-Alder reactions of acyclic, cyclic and annelated dienes with ethylene has been assessed. The average asynchronicity values, mean, mean absolute deviation and standard deviation values with respect to activation and reaction energies are calculated and the preference for one method over the other is validated. While generates less asynchronous transition states, more asynchronous transition states are obtained at M05 level amongst the methods considered. M05/6-311+G(d,p) is found to be adequate in modeling the Diels-Alder reactions involving acyclic systems. method in combination with G(d,p) basis set is found to be reliable to model the potential energy surface of cyclic systems. For modeling the reactions involving annelated dienes, the MPW1K method along with G(d,p) basis set is found to be adequate. Keywords: Theoretical chemistry, Diels-Alder reactions, Cycloadditions, Ab initio calculations, DFT calculations, Asynchronicity, Activation energy, Reaction energy The mechanism of pericyclic reactions, in general, and Diels-Alder reactions in particular, is controversial, leading to effective, and at times aggressive, interplay between the proponents of different schools of thought 1-6. The controversy regarding the concerted versus stepwise mechanisms has been settled with the elegant femto-second laser experiments 7. Thus, while both concerted and stepwise paths are feasible, the former is energetically favourable in majority of cases A number of articles have appeared benchmarking a range of quantum mechanical methods employed to assess the Diels-Alder reactivity 6, Modeling such reactions demand extensive treatment of electron correlation 13,14. Ab initio methods, in contrast to the semiempirical alternative, provide accurate qualitative descriptors for the transition structure. However, the quantitative agreement is far from desirable with HF overestimating and MP2 underestimating the barrier 15,16. Highly electron correlated methods appeared to be the only viable option to accurately model activation energies. Interestingly, B3LYP functional appears to provide excellent agreement with experimental activation energies. In contrast, the conventional ab initio alternatives (HF and MP2) are better than B3LYP with respect to reaction energies 21. Considering the necessity of having an accurate descriptor for modeling transition structures, the B3LYP functional has been chosen as a practical choice, albeit its poor predictive ability of reaction energies 15,17,18,22. Thus, all parts of the potential energy surface of Diels-Alder reactions could not be effectively modeled by HF, MP2 or B3LYP methodologies. Though MP3 gives reliable activation and reaction energies, it fails due to lack of analytical gradients 16. The results obtained by employing spin-component-scaled MP2 method corroborate with the experimental results and are found to perform well compared to B3LYP and MP2 methods 20. The multiconfigurational SCF method, CASSCF, is found to be inappropriate for modeling such reactions 19. The new DFT functional (MPW1K), developed by Truhlar 23, was also found unreliable in most cases to predict various parts of the potential energy surface (i. e., the transition states and the product) 19. Thus, using highly correlated methods, such as CCSD(T), appears to be the only option 15,17. Considering the high importance of Diels-Alder reactions in organic chemistry, it is extremely important to have an effective and affordable computational model which simultaneously yields reliable activation and reaction energies. Thus, it is necessary to assess the performance of theoretical methods on diverse types of Diels-Alder reactions. In the present study, three different sets of reactions, substituted butadienes (Type I), vinyl cyclopentadienes (Type II) and annelated cyclopentadienes (Type III), which have been reported previously 21,25-27, have been considered (Scheme 1). The optimized structures are shown in Fig. 1. Type I systems are reported to show a very complex behavior 24. Prediction of regioselectivity for this set of compounds is intricate and is noted to depend on several factors that work in concordance and discordance, which eventually decide the preferred orientation. In Type II and Type III systems, the product formation is determined by the aromatic stabilization In transition state (TS) and the loss of

2 1580 INDIAN J CHEM, SEC A, NOVEMBER 2011 aromaticity in the reactants during formation of the transition state 21, The regioselectivity resulting in intra- and extra-annular adducts (Type II), and in turn the relative reactivity, is shown to be interesting in its own respect. The reactivity of masked dienes (Type III) is governed by the loss of aromaticity and antiaromaticity during the course of reaction. For the past few years our group has been working on various aspects of Diels-Alder reactivity and have employed B3LYP method in modeling such a) Y E = CH 2, Y= CH 2 =1 =NH(cis), Y=CH 2 = 1N-a =NH(trans), Y=CH 2 = 1N-b Y = CH 2, Y= N =2N =PH(cis), Y=CH 2 = 1P-a =PH(trans), Y=CH 2 = 1P-b Y = CH 2, Y= P =2P = O, Y= CH 2 =1O = S, Y= CH 2 =1S b) Extraannular addition 3-vinyl systems E 2-vinyl systems Extraannular addition =CH 2 = 2 = NH =2N = O = 2O = S = 2S =CH 2 = 1 = NH =1N = O = 1O = S = 1S Intraannular addition Intraannular addition c) 1b E 1a 2b 2a 3b 3a Reaction path for the Diels-Alder reactions of (a) substituted butadienes (Type I), (b) vinyl cyclopentadienes (Type II) and (c) annelated cyclopentadienes (Type III), with ethylene Scheme 1

3 NOTES 1581 Fig. 1 Optimized structures of the products for Type I, Type II and Type III systems. Diels-Alder reactions 15,17,22, Reports have shown that B3LYP does not predict the correct structures when aromatic systems are considered Thus modeling such reactions becomes difficult and warrants a thorough benchmark study. The discussion here is based on the mean, mean absolute deviation (MAD) and standard deviation (SD) values calculated with reference to CCSD(T)/6-311+G(d,p)//M05/ G(d,p) method. Such an approach gives better understanding about the method dependency 34. CCSD(T) method is chosen as the reference as it is more reliable and corroborates well with the experimental results 15,17. Computational methodology Geometry optimizations and frequency calculations were carried out on the reactants, transition states (TSs) and products by employing HF, B3LYP, M05, M06, and MPW1K methods using both 6-31G(d) and G(d,p) basis sets. Further single point calculations were carried out at MP2, MP3, MP4D, MP4DQ, MP4SDQ, CCSD, CCSD(T) levels on optimized geometries of both B3LYP/ G(d,p) and M05/6-311+G(d,p). The 6-31G(d) and G(d,p) basis sets were employed for this purpose. Asynchronicity values were calculated by taking the difference between bond lengths of the two forming bonds in TS. The equations employed for obtaining mean, MAD and SD values are calculated as follows, ( Ex Ey ) Mean = i (1) n where E x is the activation/reaction energy at CCSD(T)/6-311+G(d,p)//M05/6-311+G(d,p) and E y is the activation/reaction energy at various methods. n 1 MAD = (2) ( Ex E ) y n i i= 1 where is the mean value calculated using the Eq. 1. SD = n ( ) 2 x y i i 1 ( E E ) = n 1 (3) Mean, MAD and SD values were calculated at various levels of theory with respect to values obtained at CCSD(T)/6-311+G(d,p)//M05/6-311+G(d,p) method as well as CCSD(T)/6-311+G(d,p)//B3LYP/ G(d,p) level. However the values calculated at CCSD(T)/6-311+G(d,p) level obtained using both the methods (B3LYP/6-311+G(d,p) and

4 1582 INDIAN J CHEM, SEC A, NOVEMBER 2011 M05/6-311+G(d,p)) showed similar trends. For convenience the results generated using CCSD(T)/ G(d,p) //M05/6-311+G(d,p) are given. All the calculations were carried out using G09 programme package 35. Results and discussion The discussion has been carried out in the following way. Initially asynchronous nature of TSs at various levels of theory has been assessed, followed by the comparative analysis of the results obtained using B3LYP functional with those obtained using the new DFT functionals. The performance of DFT methods over ab initio methods has also been looked at. Finally a reliable and affordable method has been suggested for predicting the Diels-Alder reactivity for a given set of reactions. The average asynchronicity values plotted against activation energies at various levels of theory are depicted in Fig. 2. The results show a high method and basis set dependency for Type II and Type III reactions. The basis set dependency for Type I systems is found to be very low. In general, M05 method predicts more asynchronous TSs while predicts less asynchronous TSs. On observing the individual sets of reactions, it is found that Type I systems showed less asynchronous TSs at level, and more asynchronous TSs at M05 and M06 levels as compared to B3LYP method. The asynchronous nature of the TSs generated at MPW1K Asynchronicity M052-1 M052-2 Type I Type II Type III Fig. 2 Plot showing the average asynchronicities for the transition states against various DFT methods for (a) Type I, (b) Type II and (c) Type III reaction series. [6-31G(d) basis set is represented as 1 and G(d,p) basis set is represented as 2]. and HF methods is almost similar to those obtained at B3LYP level. Further, the results attained at 6-31G(d) are comparable to G(d,p) when B3LYP, M05, and HF methods are considered. However considering M06 and MPW1K methods, 6-31G(d) generated more asynchronous TS compared to G(d,p). Similar to Type I systems, Type II systems generated more asynchronous TSs at M05 and M06 methods, and less asynchronous TSs at compared to B3LYP method. The difference is found in the case of MPW1K and HF methods wherein the TSs attained in the former are more asynchronous while the latter generated less asynchronous TSs compared to the B3LYP method. Irrespective of the method employed, 6-31G(d) basis set gave less asynchronous TSs compared to G(d,p) basis set, except for in which case either of the basis sets resulted in the TSs with comparable asynchronous nature. Similar to Type II systems, Type III systems generated more asynchronous TSs at M05 and M06 methods and less asynchronous TSs at and HF methods. The asynchronous nature of the TS at MPW1K is almost similar to that obtained at B3LYP method. Thus the performance of various methods employed with reference to the asynchronous nature of TSs for Type I, Type II and Type III systems can be summarized as follows: M052 < MPW1K ~ HF ~ B3LYP < M06 < M05 - Type I M052 < HF < B3LYP < M06 < MPW1K < M05 - Type II M052 < HF < B3LYP ~ MPW1K < M06 < M05 - Type III The performance of the new DFT functionals and ab initio methods has been compared with that of B3LYP method for odelling the potential energy surface of Diels-Alder reactions. The performance of the 6-31G(d) and G(d,p) basis sets is also looked at. The mean, MAD and SD values of activation and reaction energies plotted against various methods for different sets of reactions are depicted in Fig. 3(a-c). The absolute activation and reaction energy values are illustrated in Table 1. Figure 3(a-c) suggests that Type I systems show a huge method and basis set dependency. With the change in the DFT method employed a large variation in the activation and reaction energies is observed when compared to ab initio methods. DFT functionals in combination with G(d,p) basis set is found

5 NOTES 1583 (a) 10 Activation energies 10 Reaction energies (b) M052-1 M M052-1 M052-2 (c) M052-1 M M052-1 M M052-1 M M052-1 M052-2 Fig. 3 Plots showing (a) mean, (b) MAD and (c) SD values for activation and reaction energies with various methods considered in the present study. [ Type I Type II Type III ].

6 1584 INDIAN J CHEM, SEC A, NOVEMBER 2011 Table 1 Activation energies ( E ) and reaction energies ( E r ) obtained at B3LYP, M05, M06, M052, MPW1K and CCSD(T) levels of theory using G(d,p) basis set. [All the values are given in kcal/mol.] a Type I Type II Type III B3LYP M05 M06 M052 MPW1K CCSD(T) E E r E E r E E r E E r E E r E E r 1-E N-a-E N-b-E N-E P-a-E P-b-E P-E O-E S-E E E N-E N-E O-E O-E S-E S-E E E N-E N-E O-E O-E S-E S-E a-E b-E a-E b-E a-E b-E a Nomeuclature fot the systems is as shown in Fig. 1. to be better as compared to 6-31G(d) basis set except for B3LYP in which case 6-31G(d) is found to be better. The results obtained at M05/6-311+G(d,p) method are closer to the values obtained at CCSD(T)/6-311+G(d,p) level. However, the other DFT methods, B3LYP, M06, and MPW1K, shows variation from the CCSD(T) values. Compared to B3LYP method, while M06, and MPW1K perform poorly, the M05 method is found to be reliable in explaining both activation and reaction energies. Further, comparing the Moller-Plesset methods, almost all the methods are found to be inadequate in getting the activation energies analogous to B3LYP/6-31G(d), the only exception being MP4D/6-311+G(d,p). Though similar situation arises considering the reaction energies the deviation in the range is comparatively less. MP4D/6-311+G(d,p) is the only Moller-Plesset method which explains both activation and reaction energies. However, this method fails in getting the TS geometries due to the lack of analytical gradients. CCSD method irrespective of the systems considered predicts the reaction energies well. However, it is inadequate in predicting the activation energies. Thus, from the above results it can be suggested that M05/6-311+G(d,p) works better for activation and reaction energies for Type I systems. Considering Type II systems, Fig. 3(a-c) suggests that the new DFT functionals work well when compared to the conventional B3LYP/6-31G(d) method. Though Fig. 2(b-c) shows that the B3LYP/ G(d,p) method is better for modelling the reaction energies in comparison to the B3LYP/ 6-31G(d) method, it shows poor performance when

7 NOTES 1585 Fig. 3a is considered. Further, Fig. 3a suggests that while considering activation energies, the M05/ G(d,p) method is found to show poor performance as compared to B3LYP, although this method works well when reaction energies are considered. Fig. 3(b-c) show better performance of M05 and M06 methods when compared to B3LYP method. The results obtained at method are closer to the values obtained at CCSD(T)/ G(d,p) level. Thus in combination with either of the basis sets is found to be more reliable in predicting various parts of potential energy surface for these set of molecules compared to all other methods. Similar results are observed on considering Fig. 3(b-c). Analogous to the results obtained for Type I systems, the G(d,p) basis set in general is found to be more reliable in comparison to 6-31G(d). Though there is a slight preference for 6-31G(d) over G(d,p) considering activation energies, in certain cases G(d,p) remains the only choice in odelling the reaction energies for these set of reactions. Figure 3(a-c) suggests that though the MPW1K method predicts the activation energies, it does not work well in explaining the reaction energies irrespective of the basis set used. Similar to Type I systems, MP4D/6-311+G(d,p) is the only Moller-Plesset method which explains both activation and reaction energies for Type II systems. It should be noted that this method fails due to the lack of analytical gradients. 35 Thus, /6-311+G(d,p) seems to be the only choice for odelling the potential energy surface of Type II reactions. Similar to previous sets of reactions, B3LYP/ G(d,p) method does not work in odelling the potential energy surface in comparison to B3LYP/ 6-31G(d) method. Figure 3(a-c) suggests that M05/ 6-31G(d) method predicts activation and reaction energies better than the B3LYP method. Though M05/6-311+G(d,p) method predicts the activation energies, it does not give the reaction energies. Figure 3a shows that in combination with either of the basis sets is found to be more reliable in predicting various parts of potential energy surface. Nevertheless, this method is found to be unreliable in predicting various parts of potential energy surface compared to both B3LYP and M05 methods, when Fig. 3(b-c) are considered. Figure 3a illustrates that among all the DFT methods while MPW1K method works fairly well in predicting the activation energies, its performance is almost similar to the B3LYP/6-31G(d) method when reaction energies are considered. M06 method works well for obtaining activation energies as compared to the B3LYP method and almost comparable results when MPW1K method is considered. However, it shows poor performance when reaction energies are considered. Similar to Type I and Type II systems, MP4D/ G(d,p) is found to be the only Moller-Plesset method which explains both activation and reaction energies. However, it cannot be employed due to the lack of analytical gradients. Thus, MPW1K in combination with G(d,p) basis set seems to be better in predicting both activation as well as reaction energies for Type III systems. Figure 3(a-c) clearly demonstrates that when acyclic reactants (Type I) are considered the M05 method in combination with G(d,p) basis set is reliable in odelling the potential energy surface. However, the method with G(d,p) should be adequate for odelling the reactions involving monocyclic moieties (Type II). Considering the annelated dienes (Type III), MPW1K in combination with G(d,p) basis set will be a better option. The present computational study benchmarks various affordable methods to model both activation and reaction energies. Twelve different methods in combination with 6-31G(d) and G(d,p) basis sets are considered in odelling three sets of reactions, Type I, Type II and Type III, which include acyclic, monocyclic and annelated moieties respectively. While M05 method models more asynchronous TSs in comparison to all other methods, generates least asynchronous TSs. Mean, mean absolute deviation and standard deviation values are calculated with reference to CCSD(T)/ G(d,p)//M05/6-311+G(d,p) method. While the M05 method with G(d,p) basis set is found to be a better choice in odelling Diels-Alder reactions of acyclic systems, and MPW1K methods in combination with G(d,p) method is found to be better in odelling activation and reaction energies for monocyclic and annelated systems respectively. Though MP4D/6-311+G(d,p) is found to be better amongst the various Moller-Plesset methods, it fails due to the lack of analytical gradients. The new DFT functionals M05, MPW1K and seem to be well suited to model Diels-Alder potential energy surfaces depending on the system under study.

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