Zeb C. Kramer

Will water act as a photocatalyst for cluster phase chemical reactions? Vibrational overtone-induced dehydration reaction of methanediol

The possibility of water catalysis in the vibrational overtone-induced dehydration reaction of methanediol is investigated using ab initio dynamical simulations of small methanediol-water clusters. Quantum chemistry calculations employing clusters with one or two water molecules reveal that the barrier to dehydration is lowered by over 20 kcal/mol because of hydrogen-bonding at the transition state. Nevertheless, the simulations of the reaction dynamics following OH-stretch excitation show little catalytic effect of water and, in some cases, even show an anticatalytic effect. The quantum yield for the dehydration reaction exhibits a delayed threshold effect where reaction does not occur until the photon energy is far above the barrier energy. Unlike thermally induced reactions, it is argued that competition between reaction and the irreversible dissipation of photon energy may be expected to raise the dynamical threshold for the reaction above the transition state energy. It is concluded that quantum chemistry calculations showing barrier lowering are not sufficient to infer water catalysis in photochemical reactions, which instead require dynamical modeling.

Water Catalysis and Anticatalysis in Photochemical Reactions: Observation of a Delayed Threshold Effect in the Reaction Quantum Yield

The possible catalysis of photochemical reactions by water molecules is considered. Using theoretical simulations, we investigate the HF-elimination reaction of fluoromethanol in small water clusters initiated by the overtone excitation of the hydroxyl group. The reaction occurs in competition with the process of water evaporation that dissipates the excitation and quenches the reaction. Although the transition state barrier is stabilized by over 20 kcal/mol through hydrogen bonding with water, the quantum yield versus energy shows a pronounced delayed threshold that effectively eliminates the catalytic effect. It is concluded that the quantum chemistry calculations of barrier lowering are not sufficient to infer water catalysis in some photochemical reactions, which instead require dynamical modeling.

Reaction Path Bifurcation in an Electrocyclic Reaction: Ring-Opening of the Cyclopropyl Radical

Following previous work [J. Chem. Phys. 2013, 139, 154108] on a simple model of a reaction with a post-transition state valley ridge inflection point, we study the chemically important example of the electrocyclic cyclopropyl radical ring-opening reaction using direct dynamics and a reduced dimensional potential energy surface. The overall reaction requires con- or disrotation of the methylenes, but the initial stage of the ring-opening involves substantial internal rotation of only one methylene. The reaction path bifurcation is then associated with the relative sense of rotation of the second methylene. Clear deviations of reactive trajectories from the disrotatory intrinsic reaction coordinate (IRC) for the ring-opening are observed and the dynamical mechanism is discussed. Several features observed in the model system are found to be preserved in the more complex and higher dimensional ring-opening reaction. Most notable is the sensitivity of the reaction mechanism to the shape of the potential manifested as a Newtonian kinetic isotope effect upon deuterium substitution of one of the methylene hydrogens. Dependence of the product yield on frictional dissipation representing external environmental effects is also presented. The dynamics of the post-transition state cyclopropyl radical ring-opening are discussed in detail, and the use of low dimensional models as tools to analyze complicated organic reaction mechanisms is assessed in the context of this reaction.

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori, it is possible to define phase space dividing surfaces that are analogous to the dividing surfaces governing transition from reactants to products near a critical point of the potential energy surface. We investigate the problem of capture of an atom by a diatomic molecule and show that a normally hyperbolic invariant manifold exists at large atom-diatom distances, away from any critical points on the potential. This normally hyperbolic invariant manifold is the anchor for the construction of a dividing surface in phase space, which defines the outer or loose transition state governing capture dynamics. We present an algorithm for sampling an approximate capture dividing surface, and apply our methods to the recombination of the ozone molecule. We treat both 2 and 3 degrees of freedom models with zero total angular momentum. We have located the normally hyperbolic invariant manifold from which the orbiting (outer) transition state is constructed. This forms the basis for our analysis of trajectories for ozone in general, but with particular emphasis on the roaming trajectories.

Roaming: A Phase Space Perspective

In this review we discuss the recently described roaming mechanism for chemical reactions from the point of view of nonlinear dynamical systems in phase space. The recognition of the roaming phenomenon shows the need for further developments in our fundamental understanding of basic reaction dynamics, as is made clear by considering some questions that cut across most studies of roaming: Is the dynamics statistical? Can transition state theory be applied to estimate roaming reaction rates? What role do saddle points on the potential energy surface play in explaining the behavior of roaming trajectories? How do we construct a dividing surface that is appropriate for describing the transformation from reactants to products for roaming trajectories? How should we define the roaming region? We show that the phase space perspective on reaction dynamics provides the setting in which these questions can be properly framed and answered. We illustrate these ideas by considering photodissociation of formaldehyde. The phase-space formulation allows an unambiguous description of all possible reactive events, which also allows us to uncover the phase space mechanism that explains which trajectories roam, as opposed to evolving toward a different reactive event.

Dynamics on the Double Morse Potential: A Paradigm for Roaming Reactions with no Saddle Points

In this paper we analyze a two-degree-of-freedom Hamiltonian system constructed from two planar Morse potentials. The resulting potential energy surface has two potential wells surrounded by an unbounded flat region containing no critical points. In addition, the model has an index one saddle between the potential wells. We study the dynamical mechanisms underlying transport between the two potential wells, with emphasis on the role of the flat region surrounding the wells. The model allows us to probe many of the features of the “roaming mechanism” whose reaction dynamics are of current interest in the chemistry community.

A semiclassical adiabatic calculation of state densities for molecules exhibiting torsion: application to hydrogen peroxide and its isotopomers

A practical computational method is discussed for obtaining the rotational–vibrational molecular state densities of molecules with large amplitude torsional degrees of freedom (DoFs). This method goes beyond the traditional harmonic oscillator/rigid rotor or separable hindered rotor approximations in that it includes coupling between the torsion, the remaining vibrational modes, and the overall rotation. The method is based on the vibrationally adiabatic approximation whereby the torsional motion is assumed to be slow compared to the remaining vibrational DoFs although the nonseparability may be large. The torsional coordinate therefore parameterizes the rotational constants and the effective vibrational potential. A semiclassical method is then introduced to calculate the total state density in which the torsion is treated classically while the remaining coordinates are treated quantum mechanically. The method is also formulated for reactive problems in which the density of states is parameterized by a second large amplitude degree of freedom, the reaction coordinate. The performance of the method is assessed using the dissociation reaction of the hydrogen peroxide molecule and its isotopomers. It is found that the method performs well based on numerical tests. The torsional nonseparability is found to yield errors of factors of 2–3 in the statistical rate coefficient when compared with results of traditional separable models.

CHAPTER 6:Adiabatic Treatment of Torsional Anharmonicity and Mode Coupling in Molecular Partition Functions and Statistical Rate Coefficients: Application to Hydrogen Peroxide

A semi-classical method is proposed for accurately incorporating torsional degrees of freedom into molecular state sums and partition functions in a computationally economic way. This method applies an adiabatic separation of the ‘slow’ torsional mode from the other ‘fast’ internal degrees of freedom. The state sum is carried out quantum mechanically over the fast vibrations and the molecular rotations as a local function of the slow torsion coordinate. The torsional states are then included as a classical phase space integral over the local state sum with a zero point energy correction. The method is formulated for both bound and reactive systems. This method was applied to two test cases: (a) a simple coupled-harmonic oscillators model problem; and (b) the HOOH molecule, its isotopomer DOOH, and with the explicit calculation of the unimolecular rate coefficient for the dissociation reaction. The results are compared with those obtained from the usual separable treatments, including the harmonic oscillator–rigid rotor (HO-RR) and Pitzer–Gwinn separable hinder rotor methods. The coupled oscillator model shows the tendency of the HO-RR model to significantly miscount states at high energy. It is generally observed that the separable models tend to underestimate the state count of the HOOH molecule at lower energies relative to the more rigorous semi-classical method. The Rice–Ramsberger–Kassel–Marcus; (RRKM) rate constants predicted for the O–O bond breaking of HOOH are higher for the semi-classical model than those of the separable models. These differences highlight the necessity of accounting for the coupling between torsional motion and other degrees of freedom in any sophisticated model and we recommend the semi-classical adiabatic torsion method in future applications.