Computational Evidence for Tunneling and a Hidden Intermediate in the Biosynthesis of Tetrahydrocannabinol.

Quantum tunneling is computed for a reaction sequence that models the conversion of the ortho-quinone methide of cannabigerolic acid 1 to the decarboxylated product (-)-trans-Δ9-tetrahydrocannabinol (THC, 3). This calculation is the first to evaluate multidimensional tunneling in this sequence. Computations were carried out with POLYRATE and GAUSSRATE using B3LYP/6-31G(d,p) to examine the mechanism of THC 3 formation. The pentyl chain on THC 3 and its precursors were replaced with a methyl group to compute tunneling contributions to the rates of four separate steps: (i) initial Diels-Alder reaction of the quinone methide with the trisubstituted alkene end-group of the geranyl 1Z-CH3 to give 2Z-CH3, (ii) acid-catalyzed keto-enol tautomerization, which converts 2rZ-CH3 to 4rZ-CH3, (iii) carboxyl rotamerization converting 4rZ-CH3 to 4E-CH3, and (iv) decarboxylation that converts 4E-CH3 to 3-CH3. Tunneling contributions to the rate constants of steps (i)-(iv) are between 19 and 76% at 293 K. In step (ii), nonuniform changes in the zero-point vibrational energy along the reaction path created a shallow minimum in the 0 K free energy. It is a hidden intermediate because it is not a minimum on the potential energy surface and is detectable only when zero-point energy is taken into account along the reaction path. Predicted kinetic isotope effects would be experimentally observable at temperatures that are convenient to use. This is particularly relevant in the decarboxylation stage of the reaction sequence and has important implications because of its role in THC 3 formation.

Influence of water and enzyme SpnF on the dynamics and energetics of the ambimodal [6+4]/[4+2] cycloaddition.

SpnF is the first monofunctional Diels-Alder/[6+4]-ase that catalyzes a reaction leading to both Diels-Alder and [6+4] adducts through a single transition state. The environment-perturbed transition-state sampling method has been developed to calculate free energies, kinetic isotope effects, and quasi-classical reaction trajectories of enzyme-catalyzed reactions and the uncatalyzed reaction in water. Energetics calculated in this way reproduce the experiment and show that the normal Diels-Alder transition state is stabilized by H bonds with water molecules, while the ambimodal transition state is favored in the enzyme SpnF by both intramolecular hydrogen bonding and hydrophobic binding. Molecular dynamics simulations show that trajectories passing through the ambimodal transition state bifurcate to the [6+4] adduct and the Diels-Alder adduct with a ratio of 1:1 in the gas phase, 1:1.6 in water, and 1:11 in the enzyme. This example shows how an enzyme acts on a vibrational time scale to steer post-transition state trajectories toward the Diels-Alder adduct.

Evidence for tunneling in base-catalyzed isomerization of glyceraldehyde to dihydroxyacetone by hydride shift under formose conditions.

Hydrogen atom transfer reactions between the aldose and ketose are key mechanistic features in formose chemistry by which formaldehyde is converted to higher sugars under credible prebiotic conditions. For one of these transformations, we have investigated whether hydrogen tunneling makes a significant contribution to the mechanism by examining the deuterium kinetic isotope effect associated with the hydrogen transfer during the isomerization of glyceraldehyde to the corresponding dihydroxyacetone. To do this, we developed a quantitative HPLC assay that allowed us to measure the apparent large intrinsic kinetic isotope effect. From the Arrhenius plot of the kinetic isotope effect, the ratio of the preexponential factors AH/AD was 0.28 and the difference in activation energies Ea(D) - Ea(H) was 9.1 kJ·mol(-1). All these results imply a significant quantum-mechanical tunneling component in the isomerization mechanism. This is supported by multidimensional tunneling calculations using POLYRATE with small curvature tunneling.

Heavy-Atom Tunneling Calculations in Thirteen Organic Reactions: Tunneling Contributions are Substantial, and Bell's Formula Closely Approximates Multidimensional Tunneling at ≥250†K.

Multidimensional tunneling calculations are carried out for 13 reactions, to test the scope of heavy-atom tunneling in organic chemistry, and to check the accuracy of one-dimensional tunneling models. The reactions include pericyclic, cycloaromatization, radical cyclization and ring opening, and SN 2. When compared at the temperatures that give the same effective rate constant of 3×10-5  s-1 , tunneling accounts for 25-95 % of the rate in 8 of the 13 reactions. Values of transmission coefficients predicted by Bell's formula, κBell , agree well with multidimensional tunneling (canonical variational transition state theory with small curvature tunneling), κSCT . Mean unsigned deviations of κBell vs. κSCT are 0.08, 0.04, 0.02 at 250, 300 and 400 K. This suggests that κBell is a useful first choice for predicting transmission coefficients in heavy-atom tunnelling.

Trajectory Calculations for Bergman Cyclization Predict H/D Kinetic Isotope Effects Due to Nonstatistical Dynamics in the Product.

An unusual H/D kinetic isotope effect (KIE) is described, in which isotopic selectivity arises primarily from nonstatistical dynamics in the product. In DFT-based quasiclassical trajectories of Bergman cyclization of (Z)-3-hexen-1,5-diyne (1) at 470 K, the new CC bond retains its energy, and 28% of nascent p-benzyne recrosses back to the enediyne on a vibrational time scale. The competing process of intramolecular vibrational redistribution (IVR) in p-benzyne is too slow to prevent this. Deuteration increases the rate of IVR, which decreases the fraction of recrossing and increases the yield of statistical (trapable) p-benzyne, 2. Trapable yields for three isotopomers of 2 range from 72% to 86%. The resulting KIEs for Bergman cyclization differ substantially from KIEs predicted by transition state theory, which suggests that IVR in this reaction can be studied by conventional KIEs. Leakage of vibrational zero point energy (ZPE) into the reaction coordinate was probed by trajectories in which initial ZPE in the CH/CD stretching modes was reduced by 25%. This did not change the predicted KIEs.

Molecular dynamics of the Diels-Alder reactions of tetrazines with alkenes and N2 extrusions from adducts.

The cycloadditions of tetrazines with cyclopropenes and other strained alkenes have become among the most valuable bioorthogonal reactions. These reactions lead to bicyclic Diels-Alder adducts that spontaneously lose N2. We report quantum mechanical (QM) and quasiclassical trajectory simulations on a number of these reactions, with special attention to stereoelectronic and dynamic effects on spontaneous N2 loss from these adducts. QM calculations show that the barrier to N2 loss is low, and molecular dynamics calculations show that the intermediate is frequently bypassed dynamically. There is a large preference for N2 loss anti to the cyclopropane moiety rather than syn from adducts formed from reactions with cyclopropenes. This is explained by the interactions of the Walsh orbitals of the cyclopropane group with the breaking C-N bonds in N2 loss. Dynamical effects opposing the QM preferences have also been discovered involving the coupling of vibrations associated with the formation of the new C-C bonds in the cycloaddition step, and those of the breaking C-N bonds during subsequent N2 loss. This dynamic matching leads to pronounced nonstatistical effects on the lifetimes of Diels-Alder intermediates. An unusual oscillatory behavior of the intermediate decay rate has been identified and attributed to specific vibrational coupling.

Dynamics, transition states, and timing of bond formation in Diels-Alder reactions.

The time-resolved mechanisms for eight Diels-Alder reactions have been studied by quasiclassical trajectories at 298 K, with energies and derivatives computed by UB3LYP/6-31G(d). Three of these reactions were also simulated at high temperature to compare with experimental results. The reaction trajectories require 50-150 fs on average to transverse the region near the saddle point where bonding changes occur. Even with symmetrical reactants, the trajectories invariably involve unequal bond formation in the transition state. Nevertheless, the time gap between formation of the two new bonds is shorter than a C ─ C vibrational period. At 298 K, most Diels-Alder reactions are concerted and stereospecific, but at high temperatures (approximately 1,000 K) a small fraction of trajectories lead to diradicals. The simulations illustrate and affirm the bottleneck property of the transition state and the close connection between dynamics and the conventional analysis based on saddle point structure.

Computational evidence for heavy-atom tunneling in the bergman cyclization of a 10-membered-ring enediyne.

DFT and CASSCF calculations for the cyclization of (3Z)-cyclodec-3-en-1,5-diyne were carried out to investigate heavy-atom tunneling. At 37 °C, tunneling was computed to enhance the rate by 38-40% over the transition-state theory rate. Intramolecular (12)C/(13)C kinetic isotope effects were predicted to be substantial, with a steep temperature dependence. These results are discussed in relation to recent experimental findings that show heavy-atom tunneling at moderate temperatures. The calculations point to the possibility of a simple computational test for the likelihood of heavy-atom tunneling using standard quantum-chemical information.

Theory of divalent main group H2 activation: electronics and quasiclassical trajectories.

Density functional theory (DFT), absolutely localized molecular orbital (ALMO) analysis, and quasiclassical trajectories (QCTs) were used to study the structure, barrier heights, thermodynamics, electronic properties, and dynamics of dihydrogen (H2) activation by singlet divalent main group compounds (ER2; E = C, Si, Ge). ALMO energy and charge decomposition calculations reveal that in the transition state CR2 acts as an ambiphile toward H2 because of equal forward-bonding and back-bonding orbital stabilization while SiR2 and GeR2 act as nucleophiles with dominant orbital energy stabilization arising from ER2 to H2 donation. Frontier molecular orbital (FMO) energy gaps do not provide a reasonable estimate of energy stabilization gained between the ER2 and H2 in the transition state or an accurate description of the nucleophilic versus electrophilic character because of electron repulsion and orbital overlap influences that are neglected. In CR2 transition states, forward-bonding and back-bonding are maximized in the nonleast motion geometry. In contrast, SiR2/GeR2 transition states have side-on geometries to avoid electron-electron repulsion. Electron repulsion, rather than orbital interactions, also determines the relative barrier heights of CR2 versus SiR2/GeR2 reactions. Examination of barrier heights and reaction energies shows a clear kinetic-thermodynamic relationship for ER2 activation of H2. A computational survey of R groups on ER2 divalent atom centers was performed to explore the possibility for H2 activation to occur with a low barrier and thermodynamically reversible. QCTs show that dihydrogen approach and reaction with CR2 may involve geometries significantly different than the static transition-state structure. In contrast, trajectories for dihydrogen addition to SiR2 involve geometries close to the side-on approach suggested by the static transition-state structure. QCTs also demonstrate that addition of H2 to CR2 and SiR2 is dynamically concerted with the average time gap of bond formation between E-H bonds of approximately 11 and 21 fs, respectively.

Dynamics of carbene cycloadditions.

Quasiclassical trajectory calculations using quantum mechanical energies and forces generated by the Venus and Gaussian programs provide for the first time a detailed dynamical picture of singlet carbene, CCl(2) and CF(2), cycloadditions to alkenes on the B3LYP/6-31G* surface. For CF(2), B3LYP/6-31G* with exact exchange reduced to 12% HF was also employed to better mimic the high accuracy surface. The range of geometries sampled in reactive trajectories and the timing of bond formation were explored. All trajectories follow the nonlinear approach proposed by Moore and Hoffmann. The reaction of CCl(2) with ethylene is a dynamically concerted reaction, with an average time gap between formation of the two bonds of 50 fs. The reaction of CF(2) with ethylene is dynamically complex with biexponential decay of the diradical species formed from the first bond formation. A general quantitative dynamical classification of cycloaddition mechanisms is proposed, based on the timing of bond formation.

Dynamics of 1,3-dipolar cycloadditions: energy partitioning of reactants and quantitation of synchronicity.

The dynamics of 1,3-dipolar cycloadditions of nine 1,3-dipoles with ethylene and acetylene have been explored by quasiclassical trajectory and single trajectory calculations in the retro-cycloaddition direction to compute energy partitioning of reactants among relative translation, vibration, and rotation. The results are interpreted with an expanded version of Polanyi's Rules for bimolecular reactions, and three trends are evident. (1) Relative translation of reactants is the main contributor to surmounting the barrier, since all transition states (TSs) are early with respect to sigma bond formation. (2) Vibrational excitation in the 1,3-dipole bending modes required for reaction is related to the lateness of the TS with respect to dipole bending: diazonium betaines (late TS, dipole bending required) > nitrilium betaines > azomethine betaines (early TS, dipole bending least important). This is also the order of the activation barriers (high --> low). (3) The previously reported linear correlation between activation barriers and the energy required to distort reactants to their TS geometries are understandable in terms of the requirements for vibrational excitation computed here. For the 1,3-dipolar cycloadditions, single trajectory calculations, which contain no zero point vibrational energy, give reasonable estimates of the mean energy partitioning of reactants derived from potential energy barrier release. The timing of bond formation and relative reactivities of different 1,3-dipoles are discussed.

Dynamics of 1,3-dipolar cycloaddition reactions of diazonium betaines to acetylene and ethylene: bending vibrations facilitate reaction.

Getting the bends: The dynamics of 1,3-dipolar cycloaddition reactions have been explored by decomposing transition vector, quasi-classical trajectories, and single trajectories. Dipole bending (see picture) makes the largest contribution to the TS distortion energy and constitutes the major part of transition-state distortion energy in the favored concerted pathway.

QM/MM Protocol for Direct Molecular Dynamics of Chemical Reactions in Solution: The Water-Accelerated Diels-Alder Reaction.

We describe a solvent-perturbed transition state (SPTS) sampling scheme for simulating chemical reaction dynamics in condensed phase. The method, adapted from Truhlar and Gao's ensemble-averaged variational transition state theory, includes the effect of instantaneous solvent configuration on the potential energy surface of the reacting system (RS) and allows initial conditions for the RS to be sampled quasiclassically by TS normal mode sampling. We use a QM/MM model with direct dynamics, in which QM forces of the RS are computed at each trajectory point. The SPTS scheme is applied to the acceleration of the Diels-Alder reaction of cyclopentadiene (CP) + methyl vinyl ketone (MVK) in water. We explored the effect of the number of SPTS and of solvent box size on the distribution of bond lengths in the TS. Statistical sampling of the sampling was achieved when distribution of forming bond lengths converged. We describe the region enclosing the partial bond lengths as the transition zone. Transition zones in the gas phase, SMD implicit solvent, QM/MM, and QM/MM+QM (3 water molecules treated by QM) vary according to the ability of the medium to stabilize zwitterionic structures. Mean time gaps between formation of C-C bonds vary from 11 fs for gas phase to 25 fs for QM/MM+QM. Mean H-bond lengths to O(carbonyl) in QM/MM+QM are 0.14 Å smaller at the TS than in MVK reactant, and the mean O(carbonyl)-H(water)-O(water) angle of H-bonds at the TS is 10° larger than in MVK reactant.

Dynamics of the degenerate rearrangement of bicyclo[3.1.0]hex-2-ene.

Quasiclassical direct dynamics simulations are applied to a 4-fold degenerate rearrangement which yields a nonstatistical product distribution. The simulated product ratio agrees with experiment and is found to be entirely dynamically determined. Trajectory lifetimes are on the order of a low-frequency vibrational period. The interaction of reaction momentum with the geometric features of the potential surface produces selectivity despite a common energy barrier. A geometric model is described for qualitatively estimating much of the dynamically determined product ratio independently of trajectory calculations. The characteristics of this reaction are expected also to apply to others involving modestly stabilized diradical intermediates.

Energetics, transition states, and intrinsic reaction coordinates for reactions associated with O(3P) processing of hydrocarbon materials.

Electronic structure calculations based on multiconfiguration wave functions are used to investigate a set of archetypal reactions relevant to O(3P) processing of hydrocarbon molecules and surfaces. These include O(3P) reactions with methane and ethane to give OH plus methyl or ethyl radicals, O(3P) + ethane to give CH3O + CH3, and secondary reactions of the OH product radical with ethane and the ethyl radical. Geometry optimization is carried out with CASSCF/cc-pVTZ for all reactions, and with CASPT2/cc-pVTZ for O(3P) + methane/ethane. Single-point energy corrections are applied with CASPT2, CASPT3, and MRCI + Q with the cc-pVTZ and cc-pVQZ basis sets, and the energies extrapolated to the complete basis set limit (CBL). Where comparison of computed barriers and energies of reaction with experiment is possible, the agreement is good to excellent. The best agreement (within experimental error) is found for MRCI + Q/CBL applied to O(3P) + methane. For the other reactions, CASPT2/CBL and MRCI + Q/CBL predictions differ from experiment by 1-5 kcal/mol for 0 K enthalpies of reaction, and are within 1 kcal/mol of the best-estimate experimental range of 0 K barriers for O(3P) + ethane and OH + ethane. The accuracy of MRCI + Q/CBL is limited mainly by the quality of the active space. CASPT2/CBL barriers are consistently lower than MRCI + Q/CBL barriers with identical reference spaces.