Activation energies of pericyclic reactions: performance of DFT, MP2, and CBS-QB3 methods for the prediction of activation barriers and reaction energetics of 1,3-dipolar cycloadditions, and revised activation enthalpies for a standard set of hydrocarbon pericyclic reactions

Activation barriers and reaction energetics for the three main classes of 1,3-dipolar cycloadditions, including nine different reactions, were evaluated with the MPW1K and B3LYP density functional methods, MP2, and the multicomponent CBS-QB3 method. The CBS-QB3 values were used as standards for 1,3-dipolar cycloaddition activation barriers and reaction energetics, and the density functional theory (DFT) and MP2 methods were benchmarked against these values. The MPW1K/6-31G* method and basis set performs best for activation barriers, with a mean absolute deviation (MAD) value of 1.1 kcal/mol. The B3LYP/6-31G* method and basis set performs best for reaction enthalpies, with a MAD value of 2.4 kcal/mol, while the MPW1K method shows large errors for reaction energetics. The MP2 method gives the expected systematic underestimation of barriers. Concerted and nearly synchronous transition structures are predicted by all DFT and MP2 methods. Also reported are revised estimated 0 K experimental activation enthalpies for a standard set of hydrocarbon pericyclic reactions and updated comparisons to experiment for DFT, ab initio, and multicomponent methods. B3LYP and MPW1K methods with MAD values of 1.5 and 2.1 kcal/mol, respectively, fortuitously outperform the multicomponent CBS-QB3 method, which has a MAD value of 2.3. The MAD value of the O3LYP functional improves to 2.4 kcal/mol from the previously reported 3.0 kcal/mol.     

Substituent effects on singlet-triplet gaps and mechanisms of 1,2-rearrangements of 1,3-oxazol-2-ylidenes to 1,3-oxazoles

Electronic structures, partial atomic charges, singlet-triplet gaps (Delta E ST), substituent effects, and mechanisms of 1,2-rearrangements of 1,3-oxazol-2-ylidene ( 5) and 4,5-dimethyl- ( 6), 4,5-difluoro- ( 7), 4,5-dichloro- ( 8), 4,5-dibromo- ( 9), and 3-methyl-1,3-oxazol-2-ylidene ( 10) to the corresponding 1,3-oxazoles have been studied using complete-basis-set methods (CBS-QB3, CBS-Q, CBS-4M), second-order M?ller-Plesset perturbation method (MP2), hybrid density functionals (B3LYP, B3PW91), coupled-cluster theory with single and double excitations (CCSD) and CCSD plus perturbative triple excitations [CCSD(T)], and the quadratic configuration interaction method including single and double excitations (QCISD) and QCISD plus perturbative triple excitations [QCISD(T)]. The 6-311G(d,p), 6-31+G(d,p), 6-311+G(d,p), and correlation-consistent polarized valence double-xi (cc-pVDZ) basis sets were employed. The carbenes have singlet ground states, and the CBS-QB3 and CBS-Q methods predict Delta E ST values for 5- 8 and 10 of 79.9, 79.8, 74.7, 77.0, and 82.0 kcal/mol, respectively. CCSD(T), QCISD(T), B3LYP, and B3PW91 predict smaller Delta E ST values than CBS-QB3 and CBS-Q, with the hybrid density functionals predicting the smallest values. The concerted unimolecular exothermic out-of-plane 1,2-rearrangements of singlet 1,3-oxazol-2-ylidenes to their respective 1,3-oxazoles proceed via cyclic three-center transition states. The CBS-predicted barriers to the 1,2-rearrangements of singlet carbenes 5- 9 to their respective 1,3-oxazoles are 41.4, 40.4, 37.8, 40.4, and 40.5 kcal/mol, respectively. During the 1,2-rearrangements of singlet 1,3-oxazol-2-ylidenes 5- 9, there is a decrease in electron density at oxygen, N3 (the migration origin), and C5 and an increase in electron density at C2 (the migration terminus), C4, and the partially positive migrating hydrogen.     

Transition states and energetics of nucleophilic additions of thiols to substituted α,β-unsaturated ketones: substituent effects involve enone stabilization, product branching, and solvation

CBS-QB3 enthalpies of reaction have been computed for the conjugate additions of MeSH to six α,β-unsaturated ketones. Compared with addition to methyl vinyl ketone, the reaction becomes 1-3 kcal mol(-1) less exothermic when an α-Me, β-Me, or β-Ph substituent is present on the C=C bond. The lower exothermicity for the substituted enones occurs because the substituted reactant is stabilized more by hyperconjugation or conjugation than the product is stabilized by branching. Substituent effects on the activation energies for the rate-determining step of the thiol addition (reaction of the enone with MeS(-)) were also computed. Loss of reactant stabilization, and not steric hindrance, is the main factor responsible for controlling the relative activation energies in the gas phase. The substituent effects are further magnified in solution; in water (simulated by CPCM calculations), the addition of MeS(-) to an enone is disfavored by 2-6 kcal mol(-1) when one or two methyl groups are present on the C=C bond (ΔΔG(?)). The use of CBS-QB3 gas-phase energies in conjunction with CPCM solvation corrections provides kinetic data in good agreement with experimental substituent effects. When the energetics of the thiol additions were calculated with several popular density functional theory and ab initio methods (B3LYP, MPW1PW91, B1B95, PBE0, B2PLYP, and MP2), some substantial inaccuracies were noted. However, M06-2X (with a large basis set), B2PLYP-D, and SCS-MP2 gave results within 1 kcal mol(-1) of the CBS-QB3 benchmark values.     

Transition states for the dimerization of 1,3-cyclohexadiene: a DFT, CASPT2, and CBS-QB3 quantum mechanical investigation

Quantum mechanical calculations using restricted and unrestricted B3LYP density functional theory, CASPT2, and CBS-QB3 methods for the dimerization of 1,3-cyclohexadiene (1) reveal several highly competitive concerted and stepwise reaction pathways leading to [4 + 2] and [2 + 2] cycloadducts, as well as a novel [6 + 4] ene product. The transition state for endo-[4 + 2] cycloaddition (endo-2TS, DeltaH(double dagger)(B3LYP(0K)) = 28.7 kcal/mol and DeltaH(double dagger)(CBS-QB3(0K)) = 19.0 kcal/mol) is not bis-pericyclic, leading to nondegenerate primary and secondary orbital interactions. However, the C(s) symmetric second-order saddle point on the B3LYP energy surface is only 0.3 kcal/mol above endo-2TS. The activation enthalpy for the concerted exo-[4 + 2] cycloaddition (exo-2TS, DeltaH(double dagger)(B3LYP(0K)) = 30.1 kcal/mol and DeltaH(double dagger)(CBS-QB3(0K)) = 21.1 kcal/mol) is 1.4 kcal/mol higher than that of the endo transition state. Stepwise pathways involving diallyl radicals are formed via two different C-C forming transition states (rac-5TS and meso-5TS) and are predicted to be competitive with the concerted cycloaddition. Transition states were located for cyclization from intermediate rac-5 leading to the endo-[4 + 2] (endo-2) and exo-[2 + 2] (anti-3) cycloadducts. Only the endo-[2 + 2] (syn-3) transition state was located for cyclization of intermediate meso-5. The novel [6 + 4] "concerted" ene transition state (threo-4TS, DeltaH(double dagger)(UB3LYP(0K)) = 28.3 kcal/mol) is found to be unstable with respect to an unrestricted calculation. This diradicaloid transition state closely resembles the cyclohexadiallyl radical rather than the linked cyclohexadienyl radical. Several [3,3] sigmatropic rearrangement transition states were also located and have activation enthalpies between 27 and 31 kcal/mol.     

Thinking out of the black box: accurate barrier heights of 1,3-dipolar cycloadditions of ozone with acetylene and ethylene

Accurate barriers for the 1,3-dipolar cycloadditions of ozone with acetylene and ethylene have been determined via the systematic extrapolation of ab initio energies within the focal point approach of Allen and co-workers. Electron correlation has been accounted for primarily via coupled cluster theory, including single, double, and triple excitations, as well as a perturbative treatment of connected quadruple excitations [CCSD, CCSD(T), CCSDT, and CCSDT(Q)]. For the concerted [4 + 2] cycloadditions, the final recommended barriers are DeltaH(0K) = 9.4 +/- 0.2 and 5.3 +/- 0.2 kcal mol(-1) for ozone adding to acetylene and ethylene, respectively. These agree with recent results of Cremer et al. and Anglada et al., respectively. The reaction energy for O3 + C2H2 exhibits a protracted convergence with respect to inclusion of electron correlation, with the CCSDT/cc-pVDZ and CCSDT(Q)/cc-pVDZ values differing by 2.3 kcal mol-1. Recommended enthalpies of formation (298 K) for cycloadducts 1,2,3-trioxole and 1,2,3-trioxolane are +32.8 and -1.6 kcal mol(-1), respectively. Popular composite ab initio approaches [CBS-QB3, CBS-APNO, G3, G3B3, G3(MP2)B3, G4, G4(MP3), and G4(MP2)] predict a range of barrier heights for these systems. The CBS-QB3 computed barrier for ozone and acetylene, DeltaH(0K) = 4.4 kcal mol(-1), deviates by 5 kcal mol(-1) from the focal point value. CBS-QB3 similarly underestimates the barrier for the reaction of ozone and ethylene, yielding a prediction of only 0.7 kcal mol(-1). The errors in the CBS-QB3 results are significantly larger than mean errors observed in application to the G2 test set. The problem is traced to the nontransferability of MP2 basis set effects in the case of these reaction barriers. The recently published G4 and G4(MP2) approaches perform substantially better for O3 + C2H2, predicting enthalpy barriers of 9.0 and 8.4 kcal mol(-1), respectively. For the prediction of these reaction barriers, the additive corrections applied in the majority of the composite approaches considered lead to worse agreement with the reference focal point values than would be obtained relying only on single point energies evaluated at the highest level of theory utilized within each composite method.     

Ab initio and density functional theory reinvestigation of gas-phase sulfuric acid monohydrate and ammonium hydrogen sulfate

We have calculated the thermochemical parameters for the reactions H(2)SO(4) + H(2)O <--> H(2)SO(4).H(2)O and H(2)SO(4) + NH(3) <--> H(2)SO(4).NH(3) using the B3LYP and PW91 functionals, MP2 perturbation theory and four different basis sets. Different methods and basis sets yield very different results with respect to, for example, the reaction free energies. A large part, but not all, of these differences are caused by basis set superposition error (BSSE), which is on the order of 1-3 kcal mol(-1) for most method/basis set combinations used in previous studies. Complete basis set extrapolation (CBS) calculations using the cc-pV(X+d)Z and aug-cc-pV(X+d)Z basis sets (with X = D, T, Q) at the B3LYP level indicate that if BSSE errors of less than 0.2 kcal mol(-1) are desired in uncorrected calculations, basis sets of at least aug-cc-pV(T+d)Z quality should be used. The use of additional augmented basis functions is also shown to be important, as the BSSE error is significant for the nonaugmented basis sets even at the quadruple-zeta level. The effect of anharmonic corrections to the zero-point energies and thermal contributions to the free energy are shown to be around 0.4 kcal mol(-1) for the H(2)SO(4).H(2)O cluster at 298 K. Single-point CCSD(T) calculations for the H(2)SO(4).H(2)O cluster also indicate that B3LYP and MP2 calculations reproduce the CCSD(T) energies well, whereas the PW91 results are significantly overbinding. However, basis-set limit extrapolations at the CCSD(T) level indicate that the B3LYP binding energies are too low by ca. 1-2 kcal/mol. This probably explains the difference of about 2 kcal mol(-1) for the free energy of the H(2)SO(4) + H(2)O <--> H(2)SO(4).H(2)O reaction between the counterpoise-corrected B3LYP calculations with large basis sets and the diffusion-based experimental values of S. M. Ball, D. R. Hanson, F. L Eisele and P. H. McMurry (J. Phys. Chem. A. 2000, 104, 1715). Topological analysis of the electronic charge density based on the quantum theory of atoms in molecules (QTAIM) shows that different method/basis set combinations lead to qualitatively different bonding patterns for the H(2)SO(4).NH(3) cluster. Using QTAIM analysis, we have also defined a proton transfer degree parameter which may be useful in further studies.     

Molecular orbital calculations of ring opening of the isoelectronic cyclopropylcarbinyl radical, cyclopropoxy radical, and cyclopropylaminium radical cation series of radical clocks

Detailed molecular orbital calculations were directed to the cyclopropylcarbinyl radical (1), the cyclopropoxy radical (2), and the cyclopropylaminium radical cation (3) as well as their ring-opened products. Since a considerable amount of data are published about cyclopropylcarbinyl radicals, calculations were made for this species and related ring-opened products as a reference for 2 and 3 and their reactions. Radicals 1-3 have practical utility as "radical clocks" that can be used to time other radical reactions. Radical 3 is of further interest in photoelectron-transfer processes where the back-electron-transfer process may be suppressed by rapid ring opening. Calculations have been carried out at the UHF/6-31G*, MP4//MP2/6-31G*, DFT B3LYP/6-31G*, and CCSD(T)/cc-pVTZ//QCISD/cc-pVDZ levels. Energies are corrected to 298 K, and the barriers between species are reported in terms of Arrhenius E(a) and log A values along with differences in enthalpies, free energies, and entropies. The CCSD(T)-calculated energy barrier for ring opening of 1 is E(a) = 9.70, DeltaG* = 8.49 kcal/mol, which compares favorably to the previously calculated value of E(a) = 9.53 kcal/mol by the G2 method, but is higher than an experimental value of 7.05 kcal/mol. Our CCSD(T)-calculated E(a) value is also higher by 1.8 kcal/mol than a previously reported CBS-RAD//B3LYP/6-31G* calculation. The cyclopropoxy radical has a very small barrier to ring opening (CCSD(T), E(a) = 0.64 kcal/mol) and should be a very sensitive time clock. Of the three series studied, the cyclopropylaminium radical cation is most complex. In agreement with experimental data, bisected cyclopropylaminium radical cation is not found, but instead a ring-opened species is found. A perpendicular cyclopropylaminium radical cation (4) was found as a transition-state structure. Rotation of the 2p orbital in 4 to the bisected array results in ring opening. The minimum onset energy of photoionization of cyclopropylamine was calculated to be 201.5 kcal/mol (CCSD(T)) compared to experimental values of between about 201 and 204 kcal/mol. Calculations were made on the closely related cyclopropylcarbinyl and bicyclobutonium cations. Stabilization of the bisected cyclopropylcarbinyl conformer relative to the perpendicular species is much greater for the cations (29.1 kcal/ mol, QCISD) compared to the radicals (3.10 kcal/mol, QCISD). A search was made for analogues to the bicyclobutonium cation in the radical series 1 and 2 and the radical cation series 3. No comparable species were found. A rationale was made for some conflicting calculations involving the cyclopropylcarbinyl and bicyclobutonium cations. The order of stability of the cyclopropyl-X radicals was calculated to be X = CH2 > X = O > X = NH2+, where the latter species has no barrier for ring opening. The relative rate of ring opening for cyclopropyl-X radicals X = CH2 to X = O was calculated to be 3.1 x 10(6) s(-1) at 298 K (QCISD).     

Thermodynamic and ab initio analysis of the controversial enthalpy of formation of formaldehyde.

There are two values, -26.0 and -27.7 kcal mol(-1), that are routinely reported in literature evaluations for the standard enthalpy of formation, Delta(f) H(o)(298), of formaldehyde (CH(2)=O), where error limits are less than the difference in values. In this study, we summarize the reported literature for formaldehyde enthalpy values based on evaluated measurements and on computational studies. Using experimental reaction enthalpies for a series of reactions involving formaldehyde, in conjunction with known enthalpies of formation, its enthalpy is determined to be -26.05+/-0.42 kcal mol(-1), which we believe is the most accurate enthalpy currently available. For the same reaction series, the reaction enthalpies are evaluated using six computational methods: CBS-Q, CBS-Q//B3, CBS-APNO, G2, G3, and G3B3 yield Delta(f) H(o)(298)=-25.90+/-1.17 kcal mol(-1), which is in good agreement to our experimentally derived result. Furthermore, the computational chemistry methods G3, G3MP2B3, CCSD/6-311+G(2df,p)//B3LYP/6-31G(d), CCSD(T)/6-311+G(2df,p)//B3LYP/6-31G(d), and CBS-APNO in conjunction with isodesmic and homodesmic reactions are used to determine Delta(f) H(o)(298). Results from a series of five work reactions at the higher levels of calculation are -26.30+/-0.39 kcal mol(-1) with G3, -26.45+/-0.38 kcal mol(-1) with G3MP2B3, -26.09+/-0.37 kcal mol(-1) with CBS-APNO, -26.19+/-0.48 kcal mol(-1) with CCSD, and -26.16+/-0.58 kcal mol(-1) with CCSD(T). Results from heat of atomization calculations using seven accurate ab initio methods yields an enthalpy value of -26.82+/-0.99 kcal mol(-1). The results using isodesmic reactions are found to give enthalpies more accurate than both other computational approaches and are of similar accuracy to atomization enthalpy calculations derived from computationally intensive W1 and CBS-APNO methods. Overall, our most accurate calculations provide an enthalpy of formation in the range of -26.2 to -26.7 kcal mol(-1), which is within computational error of the suggested experimental value. The relative merits of each of the three computational methods are discussed and depend upon the accuracy of experimental enthalpies of formation required in the calculations and the importance of systematic computational errors in the work reaction. Our results also calculate Delta(f) H(o)(298) for the formyl anion (HCO(-)) as 1.28+/-0.43 kcal mol(-1).     

Transition state structure and energetics of the N(2)O + X (X = Cl,Br) reactions

The structural and vibrational properties of the transition state of the N(2)O + X (X = Cl,Br) reactions have been characterized by ab initio methods using density functional theory. We have employed Becke's hybrid functional (B3LYP), and transition state optimizations were performed with 6-31G(d), 6-311G(2d,2p), 6-311+G(3d,2p), and 6-311+G(3df,2p) basis sets. For the chlorine atom reaction the coupled-cluster method (CCSD(T)) with 6-31G(d) basis set was also used. All calculations resulted in transition state structures with a planar cis arrangement of atoms for both reactions. The geometrical parameters of transition states at B3LYP are very similar, and the reaction coordinates involve mainly the breaking of the N-O bond. At CCSD(T)/6-31G(d) level a contribution of the O-Cl forming bond is also observed in the reaction coordinate. In addition, several highly accurate ab initio composite methods of Gaussian-n (G1, G2, G3), their variations (G2(MP2), G3//B3LYP), and complete basis set (CBS-Q, CBS-Q//B3LYP) series of models were applied to compute reaction energetics. All model chemistries predict exothermic reactions. The G3 and G2 methods result in the smallest deviations from experiment, 1.8 and 0 kcal mol(-1), for the enthalpies of reaction for N(2)O reaction with chlorine and bromine, respectively. The G3//B3LYP and G1 methods perform best among the composite methods in predicting energies of the transition state, with a deviation of 1.9 and 3.0 kcal mol(-1), respectively, in the activation energies for the above processes. However, the B3LYP/6-311+G(3df,2p) method gives smaller deviations of 0.4 and -1.0 kcal mol(-1), respectively. The performance of the methodologies applied in predicting transition state energies was analyzed.     

Mechanisms of [1,3]-Sigmatropic Migrations of the Nitroso Group in the ON-X-CH=X Systems (X = O,S, Se,NH, CH<Subscript>2</Subscript>)

[1,3]-Sigmatropic migrations of the nitroso group in the systems ON-X-CH=X (X = O, S, Se, NH, CH₂) were studied by MP2(fc)/6-311+G** and B3LYP/6-311+G** quantum-chemical calculations. The energy barrier in the process was estimated at 2.4 (2.5), 20.0 (25.0), and 22.3 (23.4) kcal/mol for X = O, NH, and CH₂, respectively. The energy minima for X = S and X = Se correspond to cyclic structures with two-coordinate NO group, which are more stable than acyclic structures by 9.3 (4.3) (X = S) or 13.1 (5.7) kcal/mol (X = Se).     

Accurate calculation of the heats of formation for large main group compounds with spin-component scaled MP2 methods

Three MP2-type electron correlation treatments and standard density functional theory (DFT) approaches are used to predict the heats of formation for a wide variety of different molecules. The SCF and MP2 calculations are performed efficiently using the resolution-of-the-identity (RI) approximation such that large basis set (i.e., polarized valence quadruple-zeta quality) treatments become routinely possible for systems with 50-100 atoms. An atom equivalent scheme that corrects the calculated atomic energies is applied to extract the "real" accuracy of the methods for chemically relevant problems. It is found that the spin-component-scaled MP2 method (SCS-MP2, J. Chem. Phys, 2003, 118, 9095) performs best and provides chemical accuracy (MAD of 1.18 kcal/mol) for a G2/97 test set of molecules. The computationally more economical SOS-MP2 variant, which retains only the opposite-spin part of the correlation energy, is slightly less accurate (MAD of 1.36 kcal/mol) than SCS-MP2. Both spin-component-scaled MP2 treatments perform significantly better than standard MP2 (MAD of 1.77 kcal/mol) and DFT-B3LYP (MAD of 2.12 kcal/mol). These conclusions are supported by results obtained for a second test set of complex systems containing 70 molecules, including charged, strained, polyhalogenated, hypervalent, and large unsaturated species (e.g. C60). For this set, DFT-B3LYP performs badly (MAD of 8.6 kcal/mol) with many errors >10-20 kcal/mol while the spin-component-scaled MP2 methods are still very accurate (MAD of 2.8 and 3.7 kcal/mol, respectively). DFT-B3LYP shows an obvious tendency to underestimate molecular stability as the system size increases. Out of six density functionals tested, the hybrid functional PBE0 performs best. All in all, the SCS-MP2 method, together with large AO basis sets, clearly outperforms current DFT approaches and seems to be the most accurate quantum chemical model that routinely can predict the thermodynamic properties of large main group compounds.     

Energetics of the O-H bond and of intramolecular hydrogen bonding in HOC6H4C(O)Y (Y = H, CH3, CH2CH=CH2, C[triple bond]CH, CH2F, NH2, NHCH3, NO2, OH, OCH3, OCN, CN, F, Cl, SH, and SCH3) compounds

The energetics of the phenolic O-H bond in a series of 2- and 4-HOC 6H 4C(O)Y (Y = H, CH3, CH 2CH=CH2, C[triple bond]CH, CH2F, NH2, NHCH 3, NO2, OH, OCH3, OCN, CN, F, Cl, SH, and SCH3) compounds and of the intramolecular O...H hydrogen bond in 2-HOC 6H 4C(O)Y, was investigated by using a combination of experimental and theoretical methods. The standard molar enthalpies of formation of 2-hydroxybenzaldehyde (2HBA), 4-hydroxybenzaldehyde (4HBA), 2'-hydroxyacetophenone (2HAP), 2-hydroxybenzamide (2HBM), and 4-hydroxybenzamide (4HBM), at 298.15 K, were determined by micro- or macrocombustion calorimetry. The corresponding enthalpies of vaporization or sublimation were also measured by Calvet drop-calorimetry and Knudsen effusion measurements. The combination of the obtained experimental data led to Delta f H m (o)(2HBA, g) = -238.3 +/- 2.5 kJ.mol (-1), DeltafHm(o)(4HBA, g) = -220.3 +/- 2.0 kJ.mol(-1), Delta f H m (o)(2HAP, g) = -291.8 +/- 2.1 kJ.mol(-1), DeltafHm(o)(2HBM, g) = -304.8 +/- 1.5 kJ.mol (-1), and DeltafHm(o) (4HBM, g) = -278.4 +/- 2.4 kJ.mol (-1). These values, were used to assess the predictions of the B3LYP/6-31G(d,p), B3LYP/6-311+G(d,p), B3LYP/aug-cc-pVDZ, B3P86/6-31G(d,p), B3P86/6-311+G(d,p), B3P86/aug-cc-pVDZ, and CBS-QB3 methods, for the enthalpies of a series of isodesmic gas phase reactions. In general, the CBS-QB3 method was able to reproduce the experimental enthalpies of reaction within their uncertainties. The B3LYP/6-311+G(d,p) method, with a slightly poorer accuracy than the CBS-QB3 approach, achieved the best performance of the tested DFT models. It was further used to analyze the trends of the intramolecular O...H hydrogen bond in 2-HOC 6H 4C(O)Y evaluated by the ortho-para method and to compare the energetics of the phenolic O-H bond in 2- and 4-HOC 6H 4C(O)Y compounds. It was concluded that the O-H bond "strength" is systematically larger for 2-hydroxybenzoyl than for the corresponding 4-hydroxybenzoyl isomers mainly due to the presence of the intramolecular O...H hydrogen bond in the 2-isomers. The observed differences are, however, significantly dependent on the nature of the substituent Y, in particular, when an intramolecular H-bond can be present in the radical obtained upon cleavage of the O-H bond.     

Coupled cluster,B2PLYP and M06-2X investigation of the thermochemistry of five-membered nitrogen containing heterocycles,furan, and thiophene

Herein, the thermochemical properties of five-membered rings heterocycles were studied employing the CCSD(T) methodology coupled with the correlation consistent basis sets and including corrections for relativistic and core-valence effects as well as anharmonicities of the potentials. For pyrrole, furan, imidazole, pyrazole, 1H-1,2,4-triazole, and 1H-tetrazole, the mean absolute deviation (MAD) of the \Updelta \textH_{\textf, 2 9 8}^\texto \Updelta {\text{H}}_{{{\text{f}}, 2 9 8}}^{\text{o}} , computed at the CCSD(T) level, is 0.5 kcal/mol with respect to the experimental values. In the case of 1H-1,2,3-triazole, 2H-1,2,3-triazole, 4H-1,2,3-triazole, 4H-1,2,4-triazole, 2H-tetrazole, and pentazole, we propose the following \Updelta \textH_{\textf, 2 9 8}^\texto \Updelta {\text{H}}_{{{\text{f}}, 2 9 8}}^{\text{o}} : 62.6, 59.2, 85.0, 54.2, 77.7, and 107.5 kcal/mol, respectively. For thiophene, we revisit our previous result and propose a value of 26.0 kcal/mol. The theoretical estimations were used to study the performance of the M06-2X and B2PLYP functionals. Also, the convergence toward the complete basis set limit (CBS) was analyzed. M06-2X did not show a smooth convergence toward the CBS limit. Particularly, for the cc-pVTZ and cc-pVQZ basis sets, some problems were detected. Yet, along the cc-pVQZ, cc-pV5Z, and cc-pV6Z basis sets, the TAE smoothly decreased. The diminution of the TAE upon increase in basis set was not expected because the opposite behavior is more frequently observed. The MAD of the total atomization energies determined at the M06-2X level was 0.42 kcal/mol, with respect to the CCSD(T) results. In the case of the double hybrid B2PLYP functional, a smooth convergence toward the CBS limit was detected, even though the performance seriously degradated when the basis set was increased. At the CBS limit, the MAD with respect to the CCSD(T) TAEs was 8.26 kcal/mol.     

Conformational energies for 2-substituted butanes

The conformational free energies for some 2-substituted butanes where X = F, Cl, CN, and CCH were calculated using G3-B3, CBS-QB3, and CCSD(T)/6-311++G(2d,p) as well as other theoretical levels. The above methods gave consistent results with free energies relative to the trans conformers as follows: X = CCH, g+ = 0.77 +/- 0.05 kcal/mol. g- = 0.88 +/- 0.05 kcal/mol; X = CN, g+ = 0.85 +/- 0.05 kcal/mol, g- = 0.75 +/- 0.05 kcal/mol; X = Cl, g+ = 0.70 +/- 0.05 kcal/ml, g- = 0.80 +/- 0.05 kcal/mol; and X = F, g+ = 0.53 +/- 0.05 kcal/mol, g- = 0.83 +/- 0.05 kcal/mol. The conformational free energies also were estimated using the observed liquid phase IR spectra and intensities calculated using B3LYP/6-311++G** and MP2/6-311++G**. The rotational free energy profiles for all of the compounds were estimated at the G3-B3 level.     

Thermochemistry of Lewis adducts of BH3 and nucleophilic substitution of triethylamine on NH3BH3 in tetrahydrofuran

The thermochemistry of the formation of Lewis base adducts of BH(3) in tetrahydrofuran (THF) solution and the gas phase and the kinetics of substitution on ammonia borane by triethylamine are reported. The dative bond energy of Lewis adducts were predicted using density functional theory at the B3LYP/DZVP2 and B3LYP/6-311+G** levels and correlated ab initio molecular orbital theories, including MP2, G3(MP2), and G3(MP2)B3LYP, and compared with available experimental data and accurate CCSD(T)/CBS theory results. The analysis showed that the G3 methods using either the MP2 or the B3LYP geometries reproduce the benchmark results usually to within ~1 kcal/mol. Energies calculated at the MP2/aug-cc-pVTZ level for geometries optimized at the B3LYP/DZVP2 or B3LYP/6-311+G** levels give dative bond energies 2-4 kcal/mol larger than benchmark values. The enthalpies for forming adducts in THF were determined by calorimetry and compared with the calculated energies for the gas phase reaction: THFBH(3) + L → LBH(3) + THF. The formation of NH(3)BH(3) in THF was observed to yield significantly more heat than gas phase dative bond energies predict, consistent with strong solvation of NH(3)BH(3). Substitution of NEt(3) on NH(3)BH(3) is an equilibrium process in THF solution (K ≈ 0.2 at 25 °C). The reaction obeys a reversible bimolecular kinetic rate law with the Arrhenius parameters: log A = 14.7 ± 1.1 and E(a) = 28.1 ± 1.5 kcal/mol. Simulation of the mechanism using the SM8 continuum solvation model shows the reaction most likely proceeds primarily by a classical S(N)2 mechanism.     

Parameterization of a B3LYP specific correction for non-covalent interactions and basis set superposition error on a gigantic dataset of CCSD(T) quality non-covalent interaction energies

A vast number of non-covalent interaction energies at the counterpoise corrected CCSD(T) level have been collected from the literature to build a diverse new dataset. The whole dataset, which consists of 2027 CCSD(T) energies, includes most of the published data at this level. A large subset of the data was then used to train a novel, B3LYP specific, empirical correction scheme for non-covalent interactions and basis set superposition error (abbreviated as B3LYP-MM). Results obtained with our new correction scheme were directly compared to benchmark results obtained with B3LYP-D3(1) and M06-2X(2) (two popular density functions designed specifically to accurately model non-covalent interactions). For non-covalent complexes dominated by dispersion or dipole-dipole interactions all three tested methods give accurate results with the medium size aug-cc-pVDZ(3-6) basis set with MUE's of 0.27 (B3LYP-MM), 0.32 (B3LYP-D3) and 0.47 kcal/mol (M06-2X) (with explicit counterpoise corrections). These results validate both B3LYP-D3 and M06-2X for interactions of this type using a much larger data set than was presented in prior work. However, our new dispersion correction scheme shows some clear advantages for dispersion and dipole-dipole dominated complexes with the small LACVP* basis set, which is very popular in use due to its low associated computational cost: The MUE for B3LYP-MM with the LACVP* basis set for this subset of complexes (without explicit counterpoise corrections) is only 0.28 kcal/mol, compared to 0.65 kcal/mol for M06-2X or 1.16 kcal/mol for B3LYP-D3. Additionally, our new correction scheme also shows major improvements in accuracy for hydrogen-bonded systems and for systems involving ionic interactions, for example cation-π interactions. Compared to B3LYP-D3 and M06-2X, we also find that our new B3LYP-MM correction scheme gives results of higher or equal accuracy for a large dataset of conformer energies of di- and tripeptides, sugars, and cysteine.     

Theory of 1,3-dipolar cycloadditions: distortion/interaction and frontier molecular orbital models

Quantum chemical calculations of activation barriers and reaction energies for 1,3-dipolar cycloadditions by the high-accuracy CBS-QB3 method reveal previously unrecognized quantitative trends in activation barriers. The distortion/interaction model of reactivity explains why (1) there is a monotonic decrease of approximately 6 kcal/mol in the activation energy along the series oxides, imine, and ylide for the diazonium, nitrilium, and azomethine betaine classes of 1,3-dipoles; (2) nitrilium and azomethine betaines with the same trio of atoms have almost identical cycloaddition barrier heights; (3) barrier heights for the cycloadditions of a given 1,3-dipole with ethylene and acetylene have the same activation energies (mean absolute deviation of 0.6 kcal/mol) in spite of very different reaction thermodynamics (Delta DeltaH(rxn) range = 14-43 kcal/mol) and frontier molecular orbital (FMO) energy gaps. The energy to distort the 1,3-dipole and dipolarophile to the transition state geometry, rather than FMO interactions or reaction thermodynamics, controls reactivity for cycloadditions of 1,3-dipoles with alkenes or alkynes. A distortion/interaction energy analysis was also carried out on the transition states for the cycloadditions of diazonium dipoles with a set of substituted alkenes (CH2CHX, X = OMe, Me, CO 2Me, Cl, CN) and reveals that FMO interaction energies between the 1,3-dipole and the dipolarophile differentiate reactivity when transition state distortion energies are nearly constant.     

Substituent effects on the bond dissociation enthalpies of aromatic amines

Bond dissociation enthalpy differences, Z-X DeltaBDE = BDE(4-YC(6)H(4)Z-X) - BDE(C(6)H(5)Z-X), for Z = CH(2) and O are largely independent of X and are determined mainly by the stabilization/destabilization effect of Y on the 4-YC(6)H(4)Z(*) radicals. The effects of Y are small (< or =2 kcal/mol for all Y) for Z = CH(2), but they are large for Z = O, where good correlations with sigma(p)(+)(Y) yield rho(+) = 6.5 kcal/mol. For Z = NH, two sets of electrochemically measured N-H DeltaBDEs correlate with sigma(p)(+)(Y), yielding rho(+) = 3.9 and 3.0 kcal/mol. However, in contrast to the situation with phenols, these data indicate that the strengthening effect on N-H BDEs of electron-withdrawing (EW) Y's is greater than the weakening effect of electron-donating (ED) Y's. Attempts to measure N-H DeltaBDEs in anilines using two nonelectrochemical techniques were unsuccessful; therefore, we turned to density functional theory. Calculations on 15 4-YC(6)H(4)NH(2) gave N-H DeltaBDEs correlating with sigma(p)(+) (rho(+) = 4.6 kcal/mol) and indicated that EW and ED Y's had comparable strengthening and weakening effects, respectively, on the N-H bonds. To validate theory by connecting it to experiment, the N-H DeltaBDEs of four 4,4'-disubstituted diphenylamines and five 3,7-disubstituted phenothiazines were both calculated and measured by the radical equilibration EPR technique. For all compounds, theory and experiment agreed to better than 1 kcal/mol. Dissection of N-H DeltaBDEs in 4-substituted anilines and O-H DeltaBDEs in 4-substituted phenols into interaction enthalpies between Y and NH(2)/OH (molecule stabilization/destabilization enthalpy, MSE) and NH*/O* (radical stabilization/destabilization enthalpy, RSE) reveals that for both groups of compounds, ED Y's destabilize the molecule and stabilize the radical, while the opposite holds true for EW Y's. However, in the phenols the effects of substituents on the radical are roughly 3 times as great as those in the molecule, whereas in the anilines the two effects are of comparable magnitudes. These differences arise from the stronger ED character of NH(2) vs OH and the weaker EW character of NH* vs O*. The relatively large contributions to N-H BDEs in anilines arising from interactions in the molecules suggested that N-X DeltaBDEs in 4-YC(6)H(4)NH-X would depend on X, in contrast to the lack of effect of X on O-X and CH(2)-X DeltaBDEs in 4-YC(6)H(4)O-X and 4-YC(6)H(4)CH(2)-X. This suggestion was confirmed for X = CH(3), H, OH, and F, for which the calculated NH-X DeltaBDEs yielded rho(+) = 5.0, 4.6, 4.0, and 3.0 kcal/mol, respectively.