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A QM/QM Multilayer Composite Methodology: The ONIOM Correlation Consistent Composite Approach (ONIOM-ccCA) Somak R. Das, T. Gavin Williams, Michael L. Drummond, and Angela K. Wilson* Department of Chemistry and Center for AdVanced Scientific Computing and Modeling (CASCaM), UniVersity of North Texas, 1155 Union Circle No. 305070, Denton, Texas 76203-5070 ReceiVed: June 30, 2010
A QM/QM approach incorporating the correlation consistent composite approach (ccCA) into the ONIOM multilayer methodology has been implemented. This new multilayer composite scheme, ONIOM-ccCA, enables the accurate prediction of thermochemical properties for systems containing dozenssand potentially hundredssof atoms. ONIOM-ccCA is used to predict the C-H bond dissociation energies of 18 anthracene and fluorene analogues, containing up to 43 atoms, to within 1.2 kcal mol-1 of experimental values. Several density functional and basis set combinations are evaluated for use as the low level QM layer. The mean absolute deviation (1.2 kcal mol-1) using the most accurate ONIOM-ccCA method, ccCA:B3LYP/cc-pVTZ, is significantly lower than that of an earlier reported multilayer composite scheme [2.4 kcal mol-1, Li, M.-J.; Liu, L.; Fu, Y.; Guo, Q.-X. J. Phys. Chem. B, 2005, 109, 13818]. Thus, through use of ONIOM-ccCA, accurate thermochemical calculations are now feasible for sizable molecular systems of chemical or biological interest. Through the use of ab initio composite methods, it is possible to predict energetic properties, such as enthalpies of formation and ionization energies, of varied molecular systems to within “chemical accuracy” (e1 kcal mol-1 from experiment). Some of the more widely used composite methods include the Gaussian [G(n)] methods,1-5 the Weizmann [W(n)] methods,6-9 the complete basis set [CBS(n)] methods,10 and HEAT.11,12 Recently, the correlation consistent composite approach (ccCA), developed in our laboratory, has been shown to predict energetic properties such as enthalpies of formation, ionization energies, and electron affinities of main group and s-block molecules, with a mean absolute deviation (MAD) of 1.0 kcal mol-1 from reliable experimental data.13-18 ccCA has also been used to predict the enthalpies of formation of transition metal complexes to within “transition metal chemistry accuracy,” that is, with a MAD of 3 kcal mol-1 with respect to experimental results.17,19 Computational cost is reduced with these composite methods by taking advantage of the additive effects of a series of computationally expedient ab initio calculations. Thus, in effect, composite methods can provide accurate results for systems that are otherwise too prohibitively expensive to be studied computationally with a single ab initio electron correlation method [e.g., CCSD(T)] and a large basis set. However, despite the performance increases afforded via these approaches, they are still generally limited to systems containing no more than roughly ten non-hydrogen atoms.20 This limitation can prohibit the use of composite methods in large systems, such as those of biological importance (e.g., a base pair of DNA or the active site of an enzyme); as a result, a faster, more approximate level of theory must be used and chemical accuracy cannot routinely be achieved. To expand the applicability of ccCA to larger molecular species, a multilayer composite methodology combining ccCA with a lower level of theory, such as density functional theory * To whom correspondence should be addressed. E-mail: akwilson@ unt.edu.
(DFT), is in order. Herein, we develop a two-layered version of Morokuma and co-workers’ ONIOM21 approach utilizing ccCA. This approach divides the molecular system into layers and describes each layer with a different level of theory. The smallest but most important layer for determining the properties of the molecular system is treated with the highest level of theory, whereas the remaining bulk of the molecule is treated with a less rigorous but more computationally efficient level of theory. Through extrapolation, the ONIOM approach effectively approximates the results of the entire system at the highest level of theory. Morokuma and co-workers also developed the first multilayer composite method, IMOMO-G2MS.22,23 The innermost layer was treated with G2MS, a simplified version of the G2-type composite method, and ROMP2/6-31G(d) was used as the lower level of theory. More recently, Li and co-workers developed the ONIOM-G3B3 method, with G3B324 as the high-level method and the B3LYP/6-31G(d) as the low-level method.25-27 Their calculated bond dissociation energies (BDEs) of 63 molecules were generally within 2 kcal mol-1 of experimental values. However, the G2 and G3 methods used in these two multilayer composite approaches each contain optimized parameters, the “high-level correction”, which raises questions about the validity of using these methods on molecular systems that differ greatly from those used in the parametrization process. By contrast, ccCA contains no such empirical parameters, thus it is ideal as a basis for developing a sophisticated multilayer composite method without resorting to empirical parameters. Ionization potentials, enthalpies of formation, electron affinities, and proton affinities are some of the properties that ccCA has accurately predicted for various molecular systems.13-18,28 In the present study, we focus on computing C-H BDEs with a two-layer ccCA method, which we name ONIOM-ccCA. Computational studies are of use in evaluating BDEs due to complexities that arise experimentally from short-lived, often difficult to characterize radicals. Accurate evaluation of BDEs is important to judge the formation of free radicals, which play
10.1021/jp1060396 2010 American Chemical Society Published on Web 08/11/2010
QM/QM Multilayer Composite Methodology
Figure 1. Diagrams of anthracene and fluorene analogues. The high levels of the 18 molecules in this study are marked in red. Substituents are also given in Table 1.
significant roles in oxidative damage of biomolecules, such as DNA, proteins, and membrane lipids.29,30 In addition, C-H BDEs are essential for studying hydrogen transfer and abstraction reactions, which occur in such diverse environments as enzymatic reactions, DNA strand breaking, and catalysis.31 The polycyclic aromatic hydrocarbons (PAHs) comprising our test set are shown in Figure 1 and were chosen because they all contain either an anthracene or a fluorene backbone. Systems such as these are similar to antioxidants32 and form the basis for known chemotherapeutic drugs. For example, anthracenediones, a specific class of anthracene analogues, are DNA intercalating agents currently favored to replace anthracycline antibiotics, which are cytotoxic but are also cardiotoxic.33 Moreover, as these molecules have been studied with a previous multilayer composite method,26 they provide a useful benchmark set for the current approach. The ability to accurately calculate the C-H BDEs of these compounds would be of great use in developing in silico quantitative structure/property screening of such species, but many of them are too large for extant composite methods. In contrast, as will be shown, the ONIOMccCA method can readily provide C-H BDEs for these molecules, on average, to nearly within chemical accuracy. Computational Methods For a two-layered ONIOM approach, the total energy is defined as
E(ONIOM) ) E(low, real) + E(high, model) E(low, model) (1) In ONIOM-ccCA, the composite method ccCA is used as the high level of theory. Specifically, a restricted open-shell Hartree-Fock (HF)-based ccCA (RO-ccCA) protocol is used,28 in which the unrestricted wave function of the latest published HF-based ccCA formulation14 is replaced by a restricted openshell HF wave function to remove spin contamination from open-shell systems. Separate extrapolation of the HF and correlation energy to the complete basis set (CBS) limit is done, as the HF energy converges more rapidly to the CBS limit than does the correlation energy. The ROHF/CBS energy and ROMP2/CBS correlation are then combined to form the “reference energy.” A series of corrections are then added to the reference energy to account for scalar relativistic effects, core-valence effects, and correlation energy beyond the MP2
J. Phys. Chem. A, Vol. 114, No. 34, 2010 9395 level of theory, as estimated by the CCSD(T) level of theory. (For a more comprehensive description, see elsewhere.14) For the low level of theory in the multilayer ONIOM-ccCA calculations, we evaluated the performance of the DFT methods B3LYP25,27 and BMK34 paired with both the Pople-style basis setstraditionallyusedintheGnmethods[6-31G(d),6-311+G(2df,p), 6-311+G(3df,2p)], as well as a Dunning-style correlation consistent polarized valence basis set, cc-pVTZ.35 B3LYP and BMK were identified by Izgorodina and co-workers as the most accurate density functionals when used for calculations on radical reactions in conjunction with a Gn-type composite method in a two-layered ONIOM approach.36 Geometry optimizations and zero-point energies (scaled by 0.96) at the B3LYP/6-31G(d) level, as well as the low-level and standalone DFT calculations, were computed using the Gaussian 03 software package.37 The high-level ccCA calculations were performed with the MOLPRO 2006.1 software package.38 Using the ONIOM-ccCA method, the C-H bond dissociation energies in the gas phase (298 K, 1 atm) were calculated for 18 molecules and compared to experimental data, as well as to results calculated with ONIOM-G3B3,26 B3LYP/6-31G(d), and B3LYP/6-311+G(3df,2p). The fluorene and anthracene analogues in Figure 1 were selected from Li and co-workers’ test set, using their guidelines for partitioning the system into highand low-level regions.26 A core layer of five or six heavy atoms is sufficient, because bond dissociation is a local phenomenon, and the high levels of electron correlation accounted for by ccCA are only required for the local region of the bond to be broken. Moreover, limiting the core layer to this size provides a suitable balance between accuracy and computational efficiency; test calculations with larger core layers only affected the accuracy by at most a few tenths of a kcal mol-1. Results and Discussion Overall, the ONIOM-ccCA C-H BDEs are in good agreement with experimental values (see Table 1). Indeed, these predictions, when compared with experiment, are the most accurate in this study, with an MAD of 1.2 kcal mol-1 for ccCA: B3LYP/6-31G(d), ccCA:B3LYP/6-311+G(2df,p), and ccCA: B3LYP/cc-pVTZ. The agreement between these three sets of results, despite a widely varying low-level basis set size, suggests that ONIOM-ccCA is not very sensitive to the choice of basis set at the low-level. The results with these three varieties of ONIOM-ccCA, on average, are nearly within chemical accuracy and are comparable to typical experimental error bars (1-2 kcal mol-1).26 By contrast, the ONIOM-G3B3 BDEs for these species are, on average, outside of chemical accuracy. Additionally, the maximum error yielded by ONIOM-G3B3 (4.2 kcal mol-1) is roughly 1 kcal mol-1 greater than the typical maximum error resulting from ONIOM-ccCA. With respect to the choice of density functional used in the lower level, Li and co-workers concluded that B3LYP on its own is generally insufficient for C-H BDE calculations.26 However, in the current study, standalone B3LYP/6-31G(d) calculations yield an MAD of 2.8 kcal mol-1, only slightly less accurate than the MAD (2.4 kcal mol-1) of the more involved multilayer composite ONIOM-G3B3 method; neither, however, are within chemical accuracy. Indeed, B3LYP with a larger basis set, 6-311+G(3df,2p), yields a smaller MAD (1.8 kcal mol-1) than ONIOM-G3B3, albeit with the largest root-mean-square deviation (RMSD, 4.0 kcal mol-1) and maximum error (-10.1 kcal mol-1) of all approaches considered. This finding suggests that the poor performance of B3LYP noted by Li et al.26 may
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TABLE 1: Experimental, ONIOM-ccCA (With Different Low Levels of Theory), ONIOM-G3B3, and Standalone B3LYP C-H BDEs (kcal mol-1) ONIOM-ccCA B3LYP molecule
BMK
6-311+ 6-311+ 6-31G(d) G(2df,p) cc-pVTZ G(3df,2p) cc-pVTZ
ONIOM-G3B326
Standalone
B3LYP
B3LYP
6-31G(d)
6-311+ 6-31G(d) G(3df,2p) experiment26
80.5 82.1 82.2 82.7 82.6 83.2 83.0
81.0 82.5 82.5 83.3 82.7 83.4 83.8
Anthracene 81.1 81.0 82.5 82.5 82.6 82.5 83.3 83.3 82.8 82.8 83.5 83.5 83.8 83.8
81.3 82.9 83.0 83.8 83.4 84.0 84.1
82.7 84.2 85.0 84.9 85.6 85.1 80.3
79.1 80.3 81.0 81.1 80.7 81.4 81.1
78.4 79.7 79.5 80.5 79.7 80.4 80.9
80.4 80.0 81.8 82.6 81.4 81.8 82.3
8a 9 R2 ) N(CH3)2, R3 ) H 10 R2 ) OCH3, R3 ) H 11 R2 ) H, R3 ) CH2, R4 ) C(CH3)2Ph 12 R2 ) H, R3 ) CH2, R4 ) Ph 13 R2 ) H, R3 ) N, R4 ) (CH3)2 14 R2 ) H, R3 ) O, R4 ) CH2CH3 15 R2 ) H, R3 ) O, R4 ) Ph 16 R2 ) H, R3 ) N, R4 ) (CH2CH3)2 17 R2 ) H, R3 ) N, R4 ) (CH(CH3)2)2 18a
79.3 80.8 80.9 74.8 76.8 70.2 75.5 77.0 69.9 73.2 77.0
79.0 80.6 80.7 74.5 76.7 70.2 74.6 76.0 70.1 72.3 77.3
Fluorene 78.9 79.0 80.5 80.6 80.6 80.7 74.5 74.5 76.6 76.8 70.2 70.2 75.0 74.7 76.5 75.9 70.1 70.1 72.5 72.2 77.2 77.3
80.3 81.8 81.9 74.4 78.1 69.9 75.6 77.4 69.9 72.8 76.8
80.3 81.7 81.8 76.5 77.5 72.0 75.9 77.6 71.4 74.6 77.4
77.0 78.6 78.7 69.2 73.5 63.6 69.2 70.8 63.2 66.3 70.9
76.1 78.2 78.2 69.2 72.9 62.7 69.2 70.6 71.5 62.9 65.6
78.8 80.0 80.0 73.8 75.9 71.5 72.9 74.3 70.5 73.0 74.0
MAD RMSD MAX ERROR
1.2 1.4 +3.0
1.2 1.4 +3.3
1.2 1.5 +3.2
1.7 1.9 +3.1
2.4 2.6 +4.2
2.8 3.6 -7.9
1.8 4.0 -10.1
1 2 3 4 5 6 7
R1 R1 R1 R1 R1 R1 R1
a
) ) ) ) ) ) )
CHO CN CH3 NO2 OCH3 Ph COPh
1.2 1.4 +3.3
See Figure 1 for identity.
not be attributable to the density functional, but is rather likely an artifact of basis set incompleteness, as they utilized the 6-31G(d) basis set. Additionally, B3LYP yields more accurate results when used as the lower level in an ONIOM-ccCA scheme (ccCA:B3LYP/cc-pVTZ, MAD ) 1.2 kcal mol-1) for the current test set than does a similar BMK approach (ccCA: BMK/cc-pVTZ, MAD ) 1.7 kcal mol-1), despite previous results to the contrary.36 One unexpected result in Table 1 is that the ONIOM-ccCA predictions are unusually insensitive to the size of the low-level basis set: the ccCA:B3LYP calculations all yield MAD values of 1.2 kcal mol-1 and RMSD values of 1.4 - 1.5 kcal mol-1. This lack of variation may be a reflection of the ease in calculating C-H BDEs, relative to C-C, C-O, or other bond types, a conjecture that can only be verified as ONIOM-ccCA is utilized in calculations on other species and properties. Absent further results, B3LYP/cc-pVTZ is recommended as an appropriate low level of theory for ONIOM-ccCA, as the Dunningtype basis sets are already present in ccCA, thus allowing for consistency between the high and low levels of theory; however, future work may confirm that a low-level 6-31G(d) basis set provides an acceptable balance between accuracy and computational efficiency. The analogues of anthracene (1-7) all have identical high layers, shown in red in Figure 1, which are treated with ccCA. In contrast, the high layers of the analogues of fluorene (8-18) vary. However, for both molecular backbones, irrespective of the specific high layer chosen, the calculated BDE is almost always within 2.5 kcal mol-1 of experiment, the sole exception being 18 (3.2 kcal mol-1 from experiment). Given this insensitivity to model system selection, it is reasonable to expect generally accurate C-H bond dissociation energies from ONIOM-ccCA for PAHs.
Conclusions There has been considerable interest in expanding the limit in which accurate computational thermochemistry is possible, particularly to allow calculations on systems of biological importance. Although composite methods have been shown to predict energetic properties to within (1 kcal mol-1 of experiment, they are generally limited to systems containing only 10 non-hydrogen atoms. However, the multilayer composite ONIOM-ccCA method proposed has been shown to predict the C-H BDEs of 18 molecules with up to 23 heavy atoms. The ccCA:B3LYP/ccpVTZ variant of ONIOM-ccCA yielded an MAD with respect to experiment of 1.2 kcal mol-1, which is comparable to the experimental error bar of 1-2 kcal mol-1, without any empirical parameters. The molecules studied herein are analogues of anthracene and fluorene, which hold close similarities to both antioxidants and chemotherapeutic drugs, and thus the goal of obtaining accurate thermochemical properties for sizable systems of biological interest has been achieved. Acknowledgment. The authors gratefully acknowledge support from the National Science Foundation (Grant No. CHE0809762). Local computer resources were, in part, provided via NSF (CHE-0342824 and CHE-0741936), and by Academic Computing Services at the University of North Texas on the UNT Research Cluster. Additional resources were provided by the TeraGrid under Grant No. TG-CHE010021 and utilized the NCSA SGI Altix. Grateful acknowledgements also go to the United States Department of Education for support of the Center for Advanced Scientific Computing and Modeling (CASCaM). S. R. D. was supported by a summer research fellowship from the Texas Academy of Mathematics and Science. We thank Trevor Riegelman for graphical design assistance.
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