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The Sharpless reaction is an enantioselective epoxidation of prochiral allylic alcohols that employs a Ti(IV) catalyst formed from titanium tetra(isopropoxide), Ti(O-i-Pr)4, diethyl tartrate (DET), and the oxidizing agent tert-butyl hydroperoxide. The M06-2X DFT functional with the 6-311+G(d,p) basis set has been employed to model the structures and energetics of the Sharpless epoxidation reaction. The monomeric tetracoordinate titanium(IV) diethyltartrate is thermodynamically strongly favored to dimerize, producing a pentacoordinate catalyst, [Ti(DET)(O-i-Pr)2]2, that is a more reactive chiral epoxidation catalyst. The rapid ligand exchange reactions needed to generate the “loaded” catalyst and to repeat the overall catalytic cycle have been examined and are found to have activation energies that are much lower than the epoxidation barriers. The transition structures and activation energies for the enantioselective epoxidation of allyl alcohol, trans-methyl-allyl alcohol and trans-tert-butyl-allyl alcohol with the “loaded” Sharpless catalyst, [Ti2(DET)2(O-i-Pr)2-(OAllyl)-(OOt-Bu)], are presented. The effect of the C═O···Ti interactions on the activation energies and the significance of the O–C–C═C dihedral angle on the enantioselectivity of the epoxidation reaction are discussed.

The M06-2X DFT functional has been employed to examine monomeric titanium(IV) hydroperoxo catalysts that model the individual steps in the dimeric titanium(IV)-catalyzed Sharpless reaction. This is the first example of a transition structure for titanium(IV) tert-butyl hydroperoxide-catalyzed epoxidation that describes the molecular motion required for oxygen atom transfer. These epoxidation catalysts have been examined for both bimolecular reactions with E-2-butene and the intramolecular epoxidation of allyl alcohol. The transition structure for the bimolecular peroxyacetic acid epoxidation of E-2-butene has been shown to be spiro in nature, and likewise, the intramolecular epoxidation of allyl alcohol is also nearly spiro. The significance of the O–C–C═C dihedral angle of allyl alcohol is examined for the Ti(IV) tert-butyl hydroperoxide epoxidation mechanism. Evidence is presented that supports a hexacoordinate titanium peroxo environment that exists in the dimeric form of the Sharpless catalyst. The mechanism for a 1,3-rearrangement of the alkoxide ligand in a titanium hydroperoxide to the Ti center in concert with oxygen atom transfer of the proximal oxygen to the C═C bond of the substrate is presented. The dimerization of Ti(IV)-(R,R)-diethyl tartrate-diisopropoxide and its hydrolysis have been calculated. The mechanism for rapid ligand exchange with alkyl hydroperoxides involving the Ti(O-i-Pr)4precursor is examined to show how the active epoxidation catalyst is produced.

When dealing with organic peroxides in both laboratory and industrial applications, the relative strengths of the O–O bond are of vital importance, both from a safety and mechanistic perspective. Although it is well known that such oxidizing agents are highly reactive, reliable O–O bond dissociation energies (BDEs) have only recently been established. In an earlier report, we suggested a median O–O BDE value of ca. 45 kcal/mol for a variety of well-known peroxides based upon G2 ab initio calculations. In the present report, we have calculated the O–O BDE of twenty peroxides of varying structures at a more accurate CBS-APNO level. We have also compared these bond energies to the corresponding BDEs calculated with several DFT functionals and shown that the M06-2X functional produces O–O bond energies that compare very favorably with G4 and CBS-APNO values.

DFT calculations (B3LYP/6-311+G(d,p)) have been employed to reexamine the mechanism of the oxidation of saturated hydrocarbons and the epoxidation of alkenes with a series of hydroperoxides, α-hydroxy perhydrates, and peroxyacids. Hydrocarbon oxidation and alkene epoxidation with the hydroperoxide group involve a diradicaloid process initiated by a homolytic O–O bond cleavage involving a somersault rearrangement (1,2-hydrogen shift) induced abstraction of a hydrogen atom followed by a final product forming an “oxygen rebound” step. The epoxidation of alkenes and the oxidation of saturated hydrocarbons with peroxyacids is a concerted process involving a 1,4-hydrogen shift in the transition state. Accurate (G4) O–O bond dissociation energies (BDEs) for the series of peroxides are included. Although the O–O BDEs for the series of peroxides examined differ by only 3 kcal/mol, the activation energies reported differ by more than an order of magnitude. Both SCRF-PCM and natural bond order (NBO) analyses have been included.

The barriers for decarboxylation of various forms of the biotin analogue N-carboxy-2-imidazolidinone (1) and related systems have been discussed. None of the systems exhibits a significant reduction in classical barrier with respect to the gas phase process that might account for the enzymatic activity. The role of dynamical effects at the active site of the enzymes has been examined by stochastic dynamic simulation. The microscopic parameters for interparticle interactions have been obtained through ab initio and density functional theory calculations at the MP2 and B3LYP levels. The numerical analysis of a model system embedded in a harmonic bath shows how the vibrational density of states of the bath significantly affects its response factor. A statistical treatment of a system with more than one critical oscillator cooperating with the reaction coordinate exhibits a dramatic increase in rate with respect to the corresponding system with only one active critical oscillator. A quantitative interpretation of enzymatic activity in this hypothesis and its relationship with a classical Arrhenius analysis are offered.

Fully optimized STO‐3G SCF MO calculations were conducted on a series of methyl substituted ethylene radical cations. The stabilizing effect of a methyl group is found to be 14 kcal/mol using ethylene as a reference. Analysis of the orbital make‐up of the radical cations and their calculated geometry suggests that hyperconjugative 1‐, 2‐, and 3‐electron interactions between the alkyl groups and the π‐system is largely responsible for the stabilization. Analysis of hyperconjugation in propene suggests that 2‐electron stabilization outweighs 4‐electron destabilization energetically but that effects of the 2‐electron stabilization are manifested in a low‐lying MO (Φ1, Fig. 6).

The relative reactivity of a series of nucleophiles that includes ethylene, sulfides, sulfoxides, amines, and phosphines toward dioxirane, dimethyldioxirane, carbonyloxide and dimethylcarbonyloxide has been examined at the MP4/6‐31G*//MP2/6‐31G*, QCISD(T)/6‐31G*//MP2/6‐31G*, and B3‐LYP/6‐31G* levels of theory. The barriers for the oxidations with dimethyldioxirane are higher (up to 2.5 kcal/mol for the oxidation of H2S) than those for the oxidations with the parent dioxirane. The oxidation barriers for dioxirane are larger than those for the oxidations with peroxyformic acid, except the barriers for the oxidation of sulfoxides. The reactivity of dimethylsulfide toward dimethyldioxirane was found to be comparable to that of dimethylsulfoxide both in the gas phase and in solution (chloroform). The classical gas phase barrier for the oxidation of trimethylamine to trimethylamine oxide was higher (6.3 kcal/mol at the MP4//MP2/6‐31G* level) than that for oxygen atom transfer to trimethylphosphine. When the transition states were examined by self‐consistent reaction field (SCRF) methods, the predicted barriers for the oxidation of amines and phosphines were found to be in good agreement with experiment. The general trend in reactivity for oxidation by dioxirane was R2S≈R2SO, R3P>R3N in the gas phase, and R2S≈R2SO, R3N≈R3P (R=Me) in solution. The oxidation barriers calculated using the B3‐LYP functional were lower than those computed at the MP4 and QCISD(T) levels. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1353–1369, 1998

The interactions between paint/adhesive polymers and metal surfaces that are critical for adhesion have been studied theoretically. This study used zinc oxide as a model of a galvanized steel surface, and ammonia, water, and ethylene as models for amino, hydroxy, and unsaturated functionalities in paint/adhesive polymers. Ab initio molecular orbital calculations were carried out on zinc oxide and zinc oxide dimer. Geometries were optimized at the HF/3-21G level and relative energies were calculated by CASSCF/3-21G and by MP2 with the DZP basis set of Wachters and Hay. Ethylene forms a stable complex with zinc oxide dimer that has a stabilization energy of 24.9 kcal/mol. Insertion of ethylene into zinc oxide dimer to form a stable six-membered ring adduct occurs with a surprisingly low activation energy of 8.8 kcal/mol. The binding energy of ammonia with zinc oxide dimer is 38.5 kcal/mol and the activation energy for insertion of ammonia forming covalent Zn-NH2and O-H bonds is calculated to be 9.6 kcal/mol. Aminolysis of zinc oxide dimer with two ammonia molecules has a predicted barrier height of 6.7 kcal/mol. The transition structure for Zn-O bond rupture with one NH3and one H2O molecule is only 1.5 kcal/mol higher in energy than the reactant cluster. The calculations suggest that alkenes, amines, and alcohols could readily form covalent bonds with the ZnO surface, thereby facilitating adhesion of the polymer containing these functional groups to a galvanized surface.

The heats of formation and strain energies for saturated and unsaturated three- and four-membered nitrogen and phosphorus rings have been calculated using G2 theory. G2 heats of formation (ΔHf298) of triaziridine [(NH)3], triazirine (N3H), tetrazetidine [(NH)4], and tetrazetine (N4H2) are 405.0, 453.7, 522.5, and 514.1 kJ mol⁻¹, respectively. Tetrazetidine is unstable (121.5 kJ mol⁻¹ at 298 K) with respect to its dissociation into two trans-diazene (N2H2) molecules. The dissociation of tetrazetine into molecular nitrogen and trans-diazene is highly exothermic (ΔH298 = −308.3 kJ mol⁻¹ calculated using G2 theory). G2 heats of formation (ΔHf298) of cyclotriphosphane [(PH)3], cyclotriphosphene (P3H), cyclotetraphosphane [(PH)4], and cyclotetraphosphene (P4H2) are 80.7, 167.2, 102.7, and 170.7 kJ mol⁻¹, respectively. Cyclotetraphosphane and cyclotetraphosphene are stabilized by 145.8 and 101.2 kJ mol⁻¹ relative to their dissociations into two diphosphene molecules or into diphosphene (HP(DOUBLE BOND)PH) and diphosphorus (P2), respectively. The strain energies of triaziridine [(NH)3], triazirine (N3H), tetrazetidine [(NH)4], and tetrazetine (N4H2) were calculated to be 115.0, 198.3, 135.8, and 162.0 kJ mol⁻¹, respectively (at 298 K). While the strain energies of the nitrogen three-membered rings in triaziridine and triazirine are smaller than the strain energies of cyclopropane (117.4 kJ mol⁻¹) and cyclopropene (232.2 kJ mol⁻¹), the strain energies of the nitrogen four-membered rings in tetrazetidine and tetrazetine are larger than those of cyclobutane (110.2 kJ mol⁻¹) and cyclobutene (132.0 kJ mol⁻¹). In contrast to higher strain in cyclopropane as compared with cyclobutane, triaziridine is less strained than tetrazetidine. The strain energies of cyclotriphosphane [(PH)3, 21.8 kJ mol⁻¹], cyclotriphosphene (P3H, 34.6 kJ mol⁻¹), cyclotetraphosphane [(PH)4, 24.1 kJ mol⁻¹], and cyclotetraphosphene (P4H2, 18.5 kJ mol⁻¹), calculated at the G2 level are considerably smaller than those of their carbon and nitrogen analog. Cyclotetraphosphene containing the P(DOUBLE BOND)P double bond is less strained than cyclotetraphosphane, in sharp contrast to the ratio between the strain energies for the analogous unsaturated and saturated carbon and nitrogen rings. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 373–384, 1997

Bond dissociation energy (BDE) has been calculated for a series of compounds that contain N–O bonds. These structures encompass model N,N,O-trisubstituted hydroxylamines that include O-methoxy, O-acyl, and O-phenyl hydroxylamines. The calculations used three accurate composite methods, CBS-QB3, CBS-APNO, and G4 methods and the computationally more affordable M06-2X/6-311+G(3df,2p) density functional theory (DFT) functional. The calculated N–O single-bond BDEs are 5–15 kcal/mol higher than a generic N–O BDE of 48 kcal/mol quoted in the literature and in textbooks. The M06-2X DFT functional provides BDEs that are in excellent agreement with the higher-level composite methods. We also provided a comparison of the N–O BDE for pyridine-N-oxide to simple trialkylamine oxides. Based on an experimental BDE of 63.3 ± 0.5 kcal/mol for pyridine-N-oxide, our best estimate gives 56.7 ± 0.9 kcal/mol N–O BDE for trimethylamine-N-oxide and 59.0 ± 0.8 kcal/mol for triethylamine-N-oxide.

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