Structural Distortion of Cycloalkynes Influences Cycloaddition Rates both by Strain and Interaction Energies

The reactivities of 2-butyne, cycloheptyne, cyclooctyne, and cyclononyne in the 1,3-dipolar cycloaddition reaction with methyl azide were evaluated through DFT calculations at the M06-2X/6-311++G(d)//M06-2X/6-31+G(d) level of theory. Computed activation free energies for the cycloadditions of cycloalkynes are 16.5–22.0 kcal mol⁻¹ lower in energy than that of the acyclic 2-butyne. The strained or predistorted nature of cycloalkynes is often solely used to rationalize this significant rate enhancement. Our distortion/interaction–activation strain analysis has been revealed that the degree of geometrical predistortion of the cycloalkyne ground-state geometries acts to enhance reactivity compared with that of acyclic alkynes through three distinct mechanisms, not only due to (i) a reduced strain or distortion energy, but also to (ii) a smaller HOMO–LUMO gap, and (iii) an enhanced orbital overlap, which both contribute to more stabilizing orbital interactions.     

Diels-Alder reaction mechanisms of substituted chiral anthracene: A theoretical study based on the reaction force and reaction electronic flux

Quantum chemical calculations were used to study the mechanism of Diels-Alder reactions involving chiral anthracenes as dienes and a series of dienophiles. The reaction force analysis was employed to obtain a detailed scrutiny of the reaction mechanisms, it has been found that thermodynamics and kinetics of the reactions are quite consistent: the lower the activation energy, the lower the reaction energy, thus following the Bell-Evans-Polanyi principle. It has been found that activation energies are mostly due to structural rearrangements that in most cases represented more than 70% of the activation energy. Electronic activity mostly due to changes in σ and π bonding were revealed by the reaction electronic flux (REF), this property helps identify whether changes on σ or π bonding drive the reaction. Additionally, new global indexes describing the behavior of the electronic activity were introduced and then used to classify the reactions in terms of the spontaneity of their electronic activity. Local natural bond order electronic population analysis was used to check consistency with global REF through the characterization of specific changes in the electronic density that might be responsible for the activity already detected by the REF. Results show that reactions involving acetoxy lactones are driven by spontaneous electronic activity coming from bond forming/strengthening processes; in the case of maleic anhydrides and maleimides it appears that both spontaneous and non-spontaneous electronic activity are quite active in driving the reactions.     

Concerted cycloaddition reactions: a study using the parabolic model and quantum chemical modeling

Concerted cycloaddition reactions were studied by the method of intersecting parabolas (M3IP) and quantum chemical calculations. Experimental data were processed within the framework of the M3IP method and an algorithm for calculating the activation energies (E) and rate constants (k) for reactions from the enthalpies of reactions was developed. The parameters E and k for twelve cycloaddition reactions not studied previously were calculated. Factors affecting the activation energies were established and evaluated; these include the enthalpy of reaction, substituents, and the molecular structure of reactants. Quantum chemical modeling and topological analysis of transition states (TS) of six concerted cycloaddition reactions were performed. Depending on structure of the starting olefins, the TS of reactions can have either a symmetric or asymmetric geometry. This influences their electronic structures, the energies of chemical bonds, and the activation energies of reactions. A comparison of the activation energy values obtained from the M3IP and DFT(B3lyp/6-311++G** ) calculations revealed good agreement between them.     

Roles of Lewis Acid Catalysts in Diels-Alder Reactions between Cyclopentadiene and Methyl Acrylate

The Diels-Alder reaction of cyclopentadiene with methyl acrylate catalyzed by AlCl₃ has been theoretically investigated. M06-2X level DFT calculations have shown that the formation of two C−C bonds is asynchronous in the cycloaddition both in the endo path and in the exo path, thus making a good contrast to the well-known concept of [4+2] reactions based on the orbital symmetry arguments. It was found that the catalyst facilitates the cycloaddition and brings a higher endo selectivity in the highly asynchronous process, as compared with the reaction of the diene and the dienophile without the catalyst.     

A DFT study of hydride transfers to the carbonyl oxygen of DDQ

Hydride‐transfer reactions between benzylic substrates and 2,3‐dichloro‐5,6‐dicyano‐1,4‐benzoquinone (DDQ) were investigated by DFT (density functional theory) calculations. The lowest unoccupied molecular orbital of DDQ has the largest extension on two carbonyl oxygens, which comes from two‐step mixing of antisymmetric orbitals of fragment π MOs. Transition‐state (TS) geometries and activation energies of reactions of four benzylic substrates R²? CH₂‐para‐C₆H₄? R¹ (R¹, R² = H and/or OCH₃) with DDQ were calculated. M06‐2X/6‐311(+*)G* was found to be a practical computational method, giving energies and geometries similar to those of M06‐2X/6‐311++G(3df,2pd) and wB97xD/6‐311++G(3df,2pd). For toluene (R¹ = R² = H), an initiation‐propagation model was suggested, and the calculated kinetic isotope effect k(H)/k(D) = 5.0 with the tunnel correction at the propagating step is in good agreement with the experimental value 5.2. A reaction of para‐MeO? C₆H₄? CH₂(OMe) + DDQ + (H₂O)₁₄ → para‐MeO? C₆H₄? C(?O)H + HOMe + DDQH₂ + (H₂O)₁₃ was investigated by M06‐2X/6‐311(+*)G*. Four elementary processes were found and the hydride transfer (TS1) is the rate‐determining step. The hydride transfer was promoted by association with the water cluster. The size of the water cluster, (H₂O)_n, at TS1 was examined. Three models of n = 14, 20, and 26 were found to give similar activation energies. Metal‐free neutral hydride transfers from activated benzylic substrates to DDQ were proposed to be ready processes both kinetically and thermodynamically. © 2015 Wiley Periodicals, Inc.     

Theoretical Studies on the Aminolysis of Ester: Effects of the Catalysis and Substituent to the Reaction of Methyl Indole-3-acetate with Ammonia

A comprehensive exploration of the aminolysis mechanism for methyl indole-3-acetate with ammonia is carried out by employing the B3 LYP/6-311++G(d,p), M06-2 X/6-311++G(d,p) and MP2/6-311++G(d,p)//M06-2 X/6-311++G(d,p) levels. Two alterative reaction channels of the concerted and addition/elimination stepwise processes including the uncatalyzed, base-catalyzed reactions are taken into consideration. Subsequently, the substituent effects and solvent effects in methanol are also evaluated at the M06-2 X/6-311++G(d,p) level. The calculated results indicate that the calculated values of M06-2 X level are quite close to those of MP2, the stepwise pathway has more advantages to the concerted one for all of the reaction processes and the catalyst facilitates the proton migration and decreases the energy barriers as well. It is shown that the most preferred mechanism is the based-catalyzed stepwise process, the substituent of NH2 group slightly accelerates all the aminolysis reaction processes, and the solvent effect does not remarkably change the mechanism of the reaction.     

The preparation of 7-substituted norbornadiene-2,3-dicarboxylic anhydrides and an experimental and theoretical study of their reactivity

Four new substituted methano-bridged or heteroatom-bridged norbornadienomaleic anhydrides have been prepared and converted to sesquinorbornadiene anhydrides by reaction with cyclic 1,3-dienes. The versatility of parity reversal, in conjunction with N-substituent steric effects, has been used to produce all three possible stereoisomers of the N,O-sesquinorbornadiene anhydrides in separate, stereoselective cycloadditions. The anhydrides have been synthesized by cyclization of their diacids (in situ production) or by flash vacuum pyrolysis of their furan adducts (yielding crystalline products); further fragmentation occurs at these or higher temperatures to produce five-membered carbocyclic or heterocyclic anhydrides. Activation energies have been evaluated for the fragmentation and cycloaddition processes using DFT calculations (B3LYP/6-31G∗) and these calculations correctly predict, which reaction can be intercepted at the norbornadienomaleic anhydride stage and preferred stereochemistry of cycloadducts.     

A comparison of the behavior of functional/basis set combinations for hydrogen-bonding in the water dimer with emphasis on basis set superposition error

We evaluate the performance of ten functionals (B3LYP, M05, M05-2X, M06, M06-2X, B2PLYP, B2PLYPD, X3LYP, B97D, and MPWB1K) in combination with 16 basis sets ranging in complexity from 6-31G(d) to aug-cc-pV5Z for the calculation of the H-bonded water dimer with the goal of defining which combinations of functionals and basis sets provide a combination of economy and accuracy for H-bonded systems. We have compared the results to the best non-density functional theory (non-DFT) molecular orbital (MO) calculations and to experimental results. Several of the smaller basis sets lead to qualitatively incorrect geometries when optimized on a normal potential energy surface (PES). This problem disappears when the optimization is performed on a counterpoise (CP) corrected PES. The calculated interaction energies (ΔEs) with the largest basis sets vary from -4.42 (B97D) to -5.19 (B2PLYPD) kcal/mol for the different functionals. Small basis sets generally predict stronger interactions than the large ones. We found that, because of error compensation, the smaller basis sets gave the best results (in comparison to experimental and high-level non-DFT MO calculations) when combined with a functional that predicts a weak interaction with the largest basis set. As many applications are complex systems and require economical calculations, we suggest the following functional/basis set combinations in order of increasing complexity and cost: (1) D95(d,p) with B3LYP, B97D, M06, or MPWB1k; (2) 6-311G(d,p) with B3LYP; (3) D95++(d,p) with B3LYP, B97D, or MPWB1K; (4) 6-311++G(d,p) with B3LYP or B97D; and (5) aug-cc-pVDZ with M05-2X, M06-2X, or X3LYP.     

Quantum-chemical DFT calculations of the energies of the O—H bond of phenols

The energies of homolytic cleavage of the O—H bonds in 36 phenols with various structures were calculated within the scope of density functional theory using a series of exchange-correlation functionals and basis sets. The best agreement between the calculated and experimental data is given by the M06-2X/6-311++G(2d,2p)//B3LYP/6-31G(d) method.     

Assessment of density functionals and force field methods on anion–π interaction in heterocyclic calix complexes

The performance of ten density functionals and four force field methods in describing non-covalent interactions have been assessed by studying the interaction energies and structures of the four anion–π complexes involving tetraoxacalix[2]arene[2]triazine and various anions. Their structures are optimized at MP2/6-311++G(d,p) level, and interaction energies are obtained at DF-MP2-F12/aug-cc-pVDZ level. The result shows that the functional M06-2X predicts the most reliable interaction energy, followed by wB97XD and BHandH. B97D slightly overestimates the interaction energy. Other functionals and force field methods seriously overestimate the interaction energy. For the structures, three functionals M06-2X, wB97XD and BH and H predict the most reliable results, followed by B97D. The force field methods predict the largest deviations. The present work suggests that the functional M06-2X is a reliable method to describe energies and structural properties of the large molecules involving the anion–π interactions.     

A density functional theory study on the reaction mechanism of hydrazones with α-oxo-ketenes: Comparison between stepwise 1,3-dipolar cycloaddition and Diels–Alder pathways

Density functional theory calculations have been performed at the B3LYP/6-311+G(d,p) and M06-2X/6-31G(d,p) levels to obtain an insight into the nature of the stepwise cycloaddition reactions of hydrazones with α-oxo-ketenes. Three reaction pathways are possible, two Diels–Alder reactions and a 1,3-dipolar cycloaddition (1,3-DC) reaction. Despite the high energy required for 1,2-hydrogen shift in hydrazone to form an azomethine imine, 1,3-DC reaction among the possible pathways is the most favorable. The mechanism has been explained on the basis of transition state stabilities, global and local reactivity indices of the reactants, intrinsic reaction coordinate calculation, and the electron localization function topological analysis of the bonding changes along the 1,3-DC reaction. The computed free energies and enthalpies agree with the experimental outcome.     

Coordination of methanol clusters to benzene: a computational study

Benzene-methanol cluster structures were investigated with theoretical chemistry methods to describe the microsolvation of benzene and the benzene-methanol azeotrope. Benzene-methanol (MeOH) clusters containing up to six methanol molecules have been calculated by ab initio [MP2/6-311++G(d,p)//MP2/6-31+G(d,p) + BSSE correction] method. The BSSE was found quite large with this basis set, hence, different extrapolation schemes in combination with the aug-cc-pVxZ basis sets have been used to estimate the complete basis set limit of the MP2 interaction energy [ΔE(MP2/CBS)]. For smaller clusters, n ≤ 3, DFT procedures (DFTB+, MPWB1K, M06-2X) have also been applied. Geometries obtained for these clusters by M06-2X and MP2 calculations are quite similar. Based on the MP2/CBS results, the most stable C(6)H(6)(MeOH)(3) cluster is characterized by a hydrogen bonded MeOH trimer chain interacting with benzene via π···H-O and O···H-C(benzene) hydrogen bonds. Larger benzene-MeOH clusters with n ≥ 4 consist of cyclic (MeOH)(n) subclusters interacting with benzene by dispersive forces, to be denoted by C(6)H(6) + (MeOH)(n). Interaction energies and cooperativity effects are discussed in comparison with methanol clusters. Besides MP2/CBS calculations, for selected larger clusters the M06-2X/6-311++G(d,p)//M06-2X/6-31+G(d,p) procedure including the BSSE correction was also used. Interaction energies obtained thereby are usually close to the MP2/CBS limit. To model the benzene-MeOH azeotrope, several structures for (C(6)H(6))(2)(MeOH)(3) clusters have been calculated. The most stable structures contain a tilted T-shaped benzene dimer interacting by π···H-O and O···H-C (benzene) hydrogen bonds with a (MeOH)(3) chain. A slightly less negative interaction energy results for a parallel displaced benzene sandwich dimer with a (MeOH)(3) chain atop of one of the benzene molecules.     

Modern valence-bond description of chemical reaction mechanisms: the 1,3-dipolar addition of diazomethane to ethene

The electronic mechanism for the gas-phase concerted 1,3-dipolar cycloaddition of diazomethane (CH2N2) to ethene (C2H4) is described through spin-coupled (SC) calculations at a sequence of geometries along the intrinsic reaction coordinate obtained at the MP2/6-31G(d) level of theory. It is shown that the bonding rearrangements occurring during the course of this reaction follow a heterolytic pattern, characterized by the movement of three well-identifiable orbital pairs, which are initially responsible for the pi bond in ethene and the C-N pi bond and one of the N-N pi bonds in diazomethane and are retained throughout the entire reaction path from reactants to product. Taken together with our previous SC study of the electronic mechanism of the 1,3-dipolar cycloaddition of fulminic acid (HCNO) to ethyne (C2H2) (Theor. Chim. Acc. 1998, 100, 222), the results of the present work suggest strongly that most gas-phase concerted 1,3-dipolar cycloaddition reactions can be expected to follow a heterolytic mechanism of this type, which does not involve an aromatic transition state. The more conventional aspects of the gas-phase concerted 1,3-dipolar cycloaddition of diazomethane to ethene, including optimized transition structure geometry, electronic activation energy, activation barrier corrected for zero-point energies, standard enthalpy, entropy and Gibbs free energy of activation, have been calculated at the HF/6-31G(d), B3LYP/6-31G(d), MP2/6-31G(d), MP2/6-31G(d,p), QCISD/6-31G(d) and CCD/6-31G(d) levels of theory. We also report the CCD/6-311++G(2d, 2p)//CCD/6-31G(d), MP4(SDTQ)/6-311++G(2d,2p)//CCD/6-31G(d) and CCSD(T)/6-311++G(2d, 2p)//CCD/6-31G(d) electronic activation energies.     

New non-symmetric azido-diacetylenic s-triazine monomer for polycycloaddition

An original synthesis of a new non-symmetric energetic ABB' type monomer, 2-azido-4-propargylamino-6- propargyloxy-s-triazine, with a total yield of 40% involves the sequential introduction of propargylamino, propargyloxy and azido groups into s-triazine. DFT investigation of azide- Cl alkyne cycloaddition mechanism at M06-2X/6-311++G(d,p) level of theory for this monomer predicts that the regioselectivity of polycycloaddition reaction should increase with the number of propargylamino groups in the monomer structure due to the stabilization of the transition state, leading to 1,5-triazole regioisomer.     

The Structure of 2-Methylphenylcyanamide in the Solid State

The structure of 2-methylphenylcyanamide NCNH(C₆H₄Me-2) is established in the solid state using single crystal X-ray diffraction data. The contribution of various intermolecular contacts to the crystal packing is studied using the Hirshfeld surface analysis and quantum chemical calculations within the density functional (DFT) M06-2X/6-311++G(d,p) level of theory.     

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.     

Assessment of density functionals with long‐range and/or empirical dispersion corrections for conformational energy calculations of peptides

Density functionals with long‐range and/or empirical dispersion corrections, including LC‐ωPBE, B97‐D, ωB97X‐D, M06‐2X, B2PLYP‐D, and mPW2PLYP‐D functionals, are assessed for their ability to describe the conformational preferences of Ac‐Ala‐NHMe (the alanine dipeptide) and Ac‐Pro‐NHMe (the proline dipeptide) in the gas phase and in water, which have been used as prototypes for amino acid residues of peptides. For both dipeptides, the mean absolute deviation (MAD) is estimated to be 0.22–0.40 kcal/mol in conformational energy and 2.0–3.2° in torsion angles ? and ψ using these functionals with the 6‐311++G(d,p) basis set against the reference values calculated at the MP2/aug‐cc‐pVTZ//MP2/aug‐cc‐pVDZ level of theory in the gas phase. The overall performance is obtained in the order B2PLYP‐D ≈ mPW2PLYP‐D > ωB97X‐D ≈ M06‐2X > MP2 > LC‐ωPBE > B3LYP with the 6–311++G(d,p) basis set. The SMD model at the M06‐2X/6‐31+G(d) level of theory well reproduced experimental hydration free energies of the model compounds for backbone and side chains of peptides with MADs of 0.47 and 4.3 kcal/mol for 20 neutral and 5 charged molecules, respectively. The B2PLYP‐D/6‐311++G(d,p)//SMD M06‐2X/6‐31+G(d) level of theory provides the populations of backbone and/or prolyl peptide bond for the alanine and proline dipeptides in water that are consistent with the observed values. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Theoretical study on reaction mechanism of sulfuric acid and ammonia and hydration of (NH4)2SO4

In order to understand the mechanism of nucleation of (NH₄)₂SO₄ aerosol, the reaction between sulfuric acid and ammonia in the absence of water molecule is performed at M06/6-311++G(d,p) level. The results show that the (NH₄)₂SO₄ and NH₄HSO₄ units may exist instantaneously in gas phase without water molecule, which is a theoretical prediction that needs detection by further experiment. To further study the growth of the primary nuclei, the geometries, energies, and harmonic frequencies of (NH₄)₂SO₄ · (H₂O) _n (n = 0–9) are calculated both at M06/6-311++G(d,p) and B3LYP/6-311++G(d,p) levels. The tendency of the theoretical vibration frequencies is in accordance with the experimental results. The influence of the water molecule on the properties of (NH₄)₂SO₄ is also analyzed. Our results indicate that M06 is more accurate than B3LYP for this kind of system. Moreover, the first principle molecular dynamics method is used to simulate the structural transformation for two representative isomers whose energies are close, to understand the relationship between solvent-shared ion pairs and contact ion pairs.     

A theoretical study of the interaction between [HB≡CH]<Superscript>−</Superscript>, [H<Subscript>2</Subscript>B=CH<Subscript>2</Subscript>]<Superscript>−</Superscript>, and boratabenzene anions with alkali and alkaline earth metals: properties and structures

The nature of [HB≡CH]⁻, [H₂B=CH₂]⁻, and boratabenzene interactions with alkaline and alkaline earth metals are studied by ab initio calculations. The interaction energies are calculated at the B3LYP/6-311++G(d,p) level. The calculations suggest that the cation size and charge are two influential factors that affect the nature of the interaction. AIM and NBO analyses of the complexes indicate that the variation of densities and the extent of charge transfers upon complexation correlate well with the obtained interaction energies.