Charles Doubleday

Following steepest descent reaction paths. The use of higher energy derivatives with ab initio electronic structure methods

New methods of determining the steepest descent reaction path in dynamical calculations based on the reaction path Hamiltonian are investigated. These methods use first and second energy derivatives and are correct to third order in the Taylor series expansion of the path in the arc length. The reaction H+H2O→H2+OH using small basis set three electron‐three active orbital CASSCF wave functions with first and second analytically calculated energy derivatives is used as a test platform. Reaction paths using a number of different step sizes are computed and their accuracy determined by evaluating the deviations of the computed path curvature from the exact curvature and the RMS deviation of the computed transverse frequencies from the exact values, criteria more sensitive and more relevant to dynamical studies than are geometrical parameters. The new methods are compared to one another in computational efficiency and accuracy. For this example reaction and level of theory it is found that, in addition to bei...

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 Polanyis 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, 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.

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.

Time-resolved flash spectroscopic investigations of the reactions of singlet arylhalocarbenes

Abstract The results of time-resolved laser flash spectrometric studies of singlet arylhalocarbenes are reviewed. In particular, the absolute rate constants for reactions of phenylchlorocarbene and related carbenes with alkenes are summarized and systematized. The experiments described provide the basis for a detailed examination of carbenic reactivity-selectivity principles. The results of studies on the influence of temperature on the absolute rate constants for carbene reactions are consistent with the existence of transient carbene/alkene intermediates.

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.

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.

Photochemistry of large ring 2-phenylcyclanones. Formation of cyclophanes and encapsulation by a ship in bottle and by a reptation strategy

The photochemistry of five- and six-membered cyclanones has played an important role in the development of mechanistic organic chemistry and in our knowledge of biradicals. The dominant primary photochemical process of these alkanones is homolytic ..cap alpha..-cleavage (type I process) of a T/sub 1/ (n,..pi..*) state which produces a triplet biradical. The latter is stabilized after intersystem crossing to a singlet biradical by disproportionation reactions (to generate ketenes and/or enals) and by combination reactions (to regenerate the starting structure or an isomer). For example, the photolysis of 2-phenylcyclopentanone and 2-phenylcyclohexanone yields alkenals in good yields. We report that the photolysis of larger ring cyclanones (10, 11, 12, and 15 membered) produce paracyclopanes via a previously unanticipated and unprecedented combination process of biradical stabilization. We also report that the size/shape change that occurs in the photochemical cyclanone to cyclophane conversion can be exploited as the basis of a ship in bottle and of a reptation strategy to irreversibly encapsulate organic molecules in the super cage voids of zeolites.

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 Gaos 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 biradical mediating vinylcyclopropane–cyclopentene rearrangement

A previous direct dynamics trajectory study of the thermal vinylcyclopropane–cyclopentene rearrangement [C. Doubleday, J. Phys. Chem. A, 2001, 105, 6333], based on an AM1-SRP potential energy surface (PES), is extended to study details of the intramolecular and unimolecular dynamics in the biradical region of the PES. The branching ratio of the 4 diastereomeric products and the time dependence of their formation depend on the transition state at which the trajectories are initialized and its vibrational temperature or mode specific excitation. For the small amount of reaction occurring after ∼600 fs, there is considerable stereorandomness in the product yield, which contrasts with the short-time nonstatistical and mode specific reaction. Varying the initial amount of energy in reaction coordinate translation has only a minor effect on the biradical lifetime, but may have an appreciable effect on the relative product yield. Changing the rotational temperature has a negligible effect on the reaction dynamics. This study illustrates the utility of the quasiclassical trajectory method for studying short-time unimolecular dynamics and the importance of including zero-point energy motion in the trajectory initial conditions.