How Well Can New-Generation Density Functionals Describe Protonated Epoxides Where Older Functionals Fail?

Mechanism of the Oxidation of Heptafulvenes to Tropones Studied by Online Mass Spectrometry and Density Functional Theory Calculations

We have identified the most likely reaction mechanism for oxidizing heptafulvenes to the corresponding tropones by experimental and theoretical investigations. The experimental studies were done by coupling a three-dimensional printed miniaturized reactor with an integrated electrospray ionization needle to a mass spectrometer. Using the experimentally observed ions as a basis, nine alternative reaction pathways were investigated with density functional theory calculations. The lowest energy reaction pathway starts with the formation of an epoxide that is opened upon the addition of a second equivalent of the oxidizing species meta-chloroperoxybenzoic acid. The adduct formed then undergoes a Criegee-like rearrangement to yield a positively charged hemiketal, which on deprotonation dissociates into acetone and tropone. Overall, the reaction mechanism resembles a Hock-like rearrangement.

Experimental and DFT Studies on the Identity Exchange Reactions between Phenyl Chalcogen Iranium Ions and Alkenes

The gas-phase ion-molecule identity exchange reactions of phenyl chalcogen iranium ions with alkenes have been examined experimentally in a linear ion trap mass spectrometer by isotope labeling experiments. The nature of both the alkene and the chalcogen play crucial roles, with the bimolecular rates for π-ligand exchange following the order: [PhTe(c-C₆H₁₀)]⁺ + c-C₆D₁₀ > [PhTe(C₂D₄)]⁺ + C₂H₄ > [PhSe(c-C₆H₁₀)]⁺ + c-C₆D₁₀, with no reaction being observed for [PhSe(C₂D₄)]⁺ + C₂H₄, [PhS(C₂D₄)]⁺ + C₂H₄, and [PhS(c-C₆H₁₀)]⁺ + c-C₆D₁₀. The experimental results correlate with RRKM modeling and density functional theory (DFT) calculations, which also demonstrates that these reactions proceed via associative mechanisms. Natural bond orbital (NBO) analysis reveals a shift in the association complexes from a σ-hole interaction to ones mirroring the π-p⁺ and n-π* at the transition state in accordance with the rates of reaction.

Reactions of Thiiranium and Sulfonium Ions with Alkenes in the Gas Phase

Ion-molecule reactions between thiiranium ion 11 (m/z 213) and cyclohexene and cis-cyclooctene resulted in the formation of addition products 17a and 17b (m/z 295 and m/z 323, respectively) via an electrophilic addition pathway. Associative π-ligand exchange involving direct transfer of the PhS⁺ moiety, which has been observed for analogous seleniranium ions in the gas phase, did not occur despite previous solution experiments suggesting it as a valid pathway. DFT calculations at the M06-2X/def2-TZVP level of theory showed high barriers for the exchange reaction, while the addition pathway was more plausible. Further support for this pathway was provided with Hammett plots showing the rate of reaction to increase as the benzylic position of thiiranium ion derivatives became more electrophilic (ρ = +1.69; R² = 0.974). The more reactive isomeric sulfonium ion 22 was discounted as being responsible for the observed reactivity with infrared spectroscopy and DFT calculations suggesting little possibility for isomerization. To further explore the differences in reactivity, thiiranium ion 25 and sulfonium ion 27 were formed independently, with the latter ion reacting over 260 times faster toward cis-cyclooctene than the thiiranium ion rationalized by calculations suggesting a barrierless pathway for sulfonium ion 27 to react with the cycloalkene.

Theoretical investigation of [Ru(tpy)2]2+, [Ru(tpy)(bpy)(H2O)]2+ and [Ru(tpy)(bpy)(Cl)]+ complexes in acetone revisited: Inclusion of strong spin–orbit couplings to quantum chemistry calculations

In the present paper, we theoretically reinvestigate structural properties, and photo-physical and chemical characteristics and electronic absorption spectra of three kinds of ruthenium polypyridyl complexes [Ru(tpy)[Formula: see text], [Ru(tpy)(bpy)(H2O)][Formula: see text], and [Ru(tpy)(bpy)(Cl)][Formula: see text] complexes in acetone (tpy[Formula: see text]2,2[Formula: see text],2[Formula: see text]-terpyridine and bpy[Formula: see text]2,2[Formula: see text]-bipyridine). In particular, the experimental absorption spectra of these complexes are revisited theoretically in detail and are simulated using the first-order perturbation theory based on time-dependent density functional theory (TD-DFT) where the first-order perturbation term is the spin–orbit (SO) coupling Hamiltonian, and quantum chemistry calculations based on various functionals and basis sets. It was found that in general the theory including SO coupling can reproduce experimental data better than the simple quantum chemistry calculation neglecting SO coupling, which indicates that SO coupling is very important to understand the optical features of these complexes and that therefore the mixing between singlet and triplet states is strong due to the large SO coupling constant of Ru atom involved in these complexes. This suggests the fact that the disagreement between the experimental and calculated absorption spectra was found in TDB3LYP/(SDD with triple-[Formula: see text] for Ru and 6-31G* for others) [Jakubikova EJ et al., Inorg Chem 48:10720, 2009] can be tracked down to the neglect of SO couplings. It was also found that the choice of the DFT functionals and basis sets is crucial for a good theoretical reproduction of experimental data.

Exploring the Limit of Accuracy of the Global Hybrid Meta Density Functional for Main-Group Thermochemistry, Kinetics, and Noncovalent Interactions

The hybrid meta density functionals M05-2X and M06-2X have been shown to provide broad accuracy for main group chemistry. In the present article we make the functional form more flexible and improve the self-interaction term in the correlation functional to improve its self-consistent-field convergence. We also explore the constraint of enforcing the exact forms of the exchange and correlation functionals through second order (SO) in the reduced density gradient. This yields two new functionals called M08-HX and M08-SO, with different exact constraints. The new functionals are optimized against 267 diverse main-group energetic data consisting of atomization energies, ionization potentials, electron affinities, proton affinities, dissociation energies, isomerization energies, barrier heights, noncovalent complexation energies, and atomic energies. Then the M08-HX, M08-SO, M05-2X, and M06-2X functionals and the popular B3LYP functional are tested against 250 data that were not part of the original training data for any of the functionals, in particular 164 main-group energetic data in 7 databases, 39 bond lengths, 38 vibrational frequencies, and 9 multiplicity-changing electronic transition energies. These tests include a variety of new challenges for complex systems, including large-molecule atomization energies, organic isomerization energies, interaction energies in uracil trimers, and bond distances in crowded molecules (in particular, cyclophanes). The M08-HX functional performs slightly better than M08-SO and M06-2X on average, significantly better than M05-2X, and much better than B3LYP for a combination of main-group thermochemistry, kinetics, noncovalent interactions, and electronic spectroscopy. More important than the slight improvement in accuracy afforded by M08-HX is the conformation that the optimization procedure works well for data outside the training set. Problems for which the accuracy is especially improved by the new M08-HX functional include large-molecule atomization energies, noncovalent interaction energies, conformational energies in aromatic peptides, barrier heights, multiplicity-changing excitation energies, and bond lengths in crowded molecules.

A concise review of computational studies of the carbon dioxide–epoxide copolymerization reactions

The production of polycarbonates from carbon dioxide and epoxides is an important route by which waste CO₂ is converted into useful products. This review surveys the use of computational chemistry toward understanding this reaction.

Can the hybrid meta GGA and DFT-D methods describe the stacking interactions in conjugated polymers?

Newly developed hybrid meta density functionals and density functionals augmented by a classical London dispersion term have been systematically applied for the description of stacking energy and intermolecular distance of thiophene dimer and substituted thiophene dimer. The performance of the various approaches is compared with the benchmark ab-initio calculations done with CCSD(T) (Tsuzuki et al., JACS 2002, 124, 12200). Our results indicate that, contrary to the previous DFT methods which are not reliable, the new generation of DFT performs better the stacking interactions. These functionals, and especially those with an empirical correction, are suitable for general application in conducting polymers and, in particular, the modeling of solid state in which the overlap of Pi-Pi interactions between the conjugated chains is important.

Biogenesis of sesquiterpene lactones pseudoguaianolides from germacranolides: theoretical study on the reaction mechanism of terminal biogenesis of 8-epiconfertin

The fundamental study of the biogenetic origin of natural products has always been limited from the experimental point of view because proposed reaction mechanisms have only been supported on the molecular structures of reagents and the reaction products. In a seminal contribution, Ortega and Maldonado (Ortega, A.; Maldonado, E. Heterocycles, 1989, 29, 635-638.) described an experiment relevant for the development of the biogenetic theory of sesquiterpene lactones. They were able to obtain the one-pot transformation of a pseudoguaianolide sesquiterpenic lactone from a germacranolide using bentonitic earth as the catalyst. This transformation involved two steps in the biogenesis of these compounds (germacranolide --> guaianolide --> pseudoguaianolide) and is significant because when Brönsted or Lewis acids are used, it is only possible to isolate the product of the next step of the biogenesis. The results presented here support the biogenetic theories by Hendrickson and Fischer and question the concerted nature of the Herz proposal. Some questions about the mechanisms still remain unanswered; mainly because it was only possible to isolate a few stable byproducts. Using the third generation functional mPWB95 developed by Truhlar, it was possible to study the mechanisms associated with the biogenesis of pseudoguaiananolides. Its application can explain the origin of all the byproducts obtained in the original experiment and establish the validity of the original biogenetic hypothesis. The performance of the above-mentioned functional was compared to B3LYP, B97-2, and B1B95 functionals and the MP2 method, finding that mPWB95 competes successfully with all the latter in both, the determination of the magnitude of the activation energies and the ability to map the potential energy surface. Therefore, the mPWB95 method can be considered good to deal with this type of study.

Density functionals with broad applicability in chemistry

Although density functional theory is widely used in the computational chemistry community, the most popular density functional, B3LYP, has some serious shortcomings: (i) it is better for main-group chemistry than for transition metals; (ii) it systematically underestimates reaction barrier heights; (iii) it is inaccurate for interactions dominated by medium-range correlation energy, such as van der Waals attraction, aromatic-aromatic stacking, and alkane isomerization energies. We have developed a variety of databases for testing and designing new density functionals. We used these data to design new density functionals, called M06-class (and, earlier, M05-class) functionals, for which we enforced some fundamental exact constraints such as the uniform-electron-gas limit and the absence of self-correlation energy. Our M06-class functionals depend on spin-up and spin-down electron densities (i.e., spin densities), spin density gradients, spin kinetic energy densities, and, for nonlocal (also called hybrid) functionals, Hartree-Fock exchange. We have developed four new functionals that overcome the above-mentioned difficulties: (a) M06, a hybrid meta functional, is a functional with good accuracy "across-the-board" for transition metals, main group thermochemistry, medium-range correlation energy, and barrier heights; (b) M06-2X, another hybrid meta functional, is not good for transition metals but has excellent performance for main group chemistry, predicts accurate valence and Rydberg electronic excitation energies, and is an excellent functional for aromatic-aromatic stacking interactions; (c) M06-L is not as accurate as M06 for barrier heights but is the most accurate functional for transition metals and is the only local functional (no Hartree-Fock exchange) with better across-the-board average performance than B3LYP; this is very important because only local functionals are affordable for many demanding applications on very large systems; (d) M06-HF has good performance for valence, Rydberg, and charge transfer excited states with minimal sacrifice of ground-state accuracy. In this Account, we compared the performance of the M06-class functionals and one M05-class functional (M05-2X) to that of some popular functionals for diverse databases and their performance on several difficult cases. The tests include barrier heights, conformational energy, and the trend in bond dissociation energies of Grubbs' ruthenium catalysts for olefin metathesis. Based on these tests, we recommend (1) the M06-2X, BMK, and M05-2X functionals for main-group thermochemistry and kinetics, (2) M06-2X and M06 for systems where main-group thermochemistry, kinetics, and noncovalent interactions are all important, (3) M06-L and M06 for transition metal thermochemistry, (4) M06 for problems involving multireference rearrangements or reactions where both organic and transition-metal bonds are formed or broken, (5) M06-2X, M05-2X, M06-HF, M06, and M06-L for the study of noncovalent interactions, (6) M06-HF when the use of full Hartree-Fock exchange is important, for example, to avoid the error of self-interaction at long-range, (7) M06-L when a local functional is required, because a local functional has much lower cost for large systems.

The Concept of Protobranching and Its Many Paradigm Shifting Implications for Energy Evaluations

Branched alkanes like isobutane and neopentane are more stable than their straight chain isomers, n-butane and n-pentane (by 2 and 5 kcal mol(-1), respectively). Electron correlation is largely responsible. Branched alkanes have a greater number of net attractive 1,3-alkyl-alkyl group interactions, there are three such stabilizing 1,3 "protobranching" dispositions in isobutane, but only two in n-butane. Neopentane has six protobranches but n-pentane only three. Propane has one protobranch and is stabilized appreciably, by 2.8 kcal mol(-1), relative to methane and ethane. This value per protobranch also applies to the n-alkanes and cyclohexane. Consequently, energy evaluations employing alkane reference standards, for example, of small ring strain and stabilizations due to conjugation, hyperconjugation, and aromaticity, should be corrected for protobranching, for example, by employing Pople's isodesmic bond separation reaction method. This reduces the ring strain of cyclopropane to 19.2 from the conventional 27.7 kcal mol(-1), while the stabilization energies of alkenes and alkynes due to hyperconjugation (5.5 and 7.7 kcal mol(-1) for propene and propyne) and conjugation (14.8 and 27.1 kcal mol(-1) for butadiene and butadiyne) are considerably larger than the traditional estimates. Widely diverging literature evaluations of benzene resonance energy all give approximately 65 kcal mol(-1) after adjusting for conjugation, hyperconjugation, and protobranching "contaminations." The BLW (block localized wavefunction) method, which localizes pi bonds and precludes their interactions, largely confirms these stabilization estimates for hyperconjugation, conjugation, and aromaticity. Protobranching is seriously underestimated by theoretical computations at the HF and most DFT levels, which do not account for electron correlation satisfactorily. Such levels give bond separation energies, which can differ greatly from experimental values.

Computing reliable energetics for conjugate addition reactions

The performance of various density functionals along with second-order perturbation treatments has been tested for a set of conjugate addition reactions relevant to stereoselective organocatalysis. It is shown that B3LYP predictions seriously underestimate the reaction energies, whereas two newly designed functionals (M05-2X and M06-2X) and the SCS-MP2 method provide very accurate data. These new methods represent promising alternative approaches in future mechanistic studies.

An experimental and computational approach to defining structure/reactivity relationships for intramolecular addition reactions to bicyclic epoxonium ions

In this manuscript we report that oxidative cleavage reactions can be used to form oxocarbenium ions that react with pendent epoxides to form bicyclic epoxonium ions as an entry to the formation of cyclic oligoether compounds. Bicyclic epoxonium ion structure was shown to have a dramatic impact on the ratio of exo- to endo-cyclization reactions, with bicyclo[4.1.0] intermediates showing a strong preference for endo-closures and bicyclo[3.1.0] intermediates showing a preference for exo-closures. Computational studies on the structures and energetics of the transition states using the B3LYP/6-31G(d) method provide substantial insight into the origins of this selectivity.

How Accurate Are DFT Treatments of Organic Energies?

Increasing awareness that popular functionals fail to describe many energies accurately has ended expectations of black-box DFT usage. The performance of nine density functionals, compared by computing the bond separation energies of 72 illustrative hydrocarbons with available experimental data, reveals that only Zhao and Truhlar's recently proposed M05-2X functional, with a 2.13 kcal/mol average deviation from experiment, performs satisfactorily. B3LYP and other functionals show larger deviations.

Carbene Stabilization by Aryl Substituents. Is Bigger Better?

The geometries and relative stabilities of the singlet and triplet states of phenyl- (Cs), diphenyl- (C2), 1-naphthyl- (Cs), di(1-naphthyl)- (C2), and 9-anthryl-substituted (Cs) carbenes were investigated at the B3LYP/6-311+G(d,p) + ZPVE level of density functional theory. The singlet-triplet energy separations (DeltaEST), 2.7, 2.9, 3.4, 3.7, and 5.7 kcal/mol, respectively, after including an empirical correction (2.8 kcal/mol) based on the error in the computed singlet-triplet gap for methylene versus experiment, are in good agreement with available experimental values. Consistent with literature reports, triplet di(9-anthryl)carbene has a linear, D2d symmetrical, allene structure with 1.336 A C=C bond lengths and considerable biradical character. B3LYP favors such cumulene biradical structures and triplet spin states and predicts a large (>15 kcal/mol) "di(9-anthryl)carbene" singlet-triplet (biradical) energy gap. The resonance stabilization of both singlet and triplet carbenes increases modestly with the size of the arene substituent and overall, (di)arylcarbenes, both singlet and triplet, are better stabilized by bigger substituents. For example, methylene is stabilized more by a naphthyl than a phenyl group (singlets, 26.6 versus 24.4; and triplets, 20.9 versus 18.1 kcal/mol, respectively). The carbene geometries are affected by both steric effects and arene-carbene orbital interactions (sigma-p and p-pi). For instance, the central angles at the carbene are widened by a second arene group, which leads to increased s-character and shorter carbene bond lengths (i.e., C-C, C-H). In general, the aromaticity of the substituted rings in triplet carbenes is most affected by the presence of the unpaired electrons.