Chloroacetone photodissociation at 193 nm and the subsequent dynamics of the CH3C(O)CH2 radical--an intermediate formed in the OH + allene reaction en route to CH3 + ketene

We use a combination of crossed laser-molecular beam experiments and velocity map imaging experiments to investigate the primary photofission channels of chloroacetone at 193 nm; we also probe the dissociation dynamics of the nascent CH(3)C(O)CH(2) radicals formed from C-Cl bond fission. In addition to the C-Cl bond fission primary photodissociation channel, the data evidence another photodissociation channel of the precursor, C-C bond fission to produce CH(3)CO and CH(2)Cl. The CH(3)C(O)CH(2) radical formed from C-Cl bond fission is one of the intermediates in the OH + allene reaction en route to CH(3) + ketene. The 193 nm photodissociation laser allows us to produce these CH(3)C(O)CH(2) radicals with enough internal energy to span the dissociation barrier leading to the CH(3) + ketene asymptote. Therefore, some of the vibrationally excited CH(3)C(O)CH(2) radicals undergo subsequent dissociation to CH(3) + ketene products; we are able to measure the velocities of these products using both the imaging and scattering apparatuses. The results rule out the presence of a significant contribution from a C-C bond photofission channel that produces CH(3) and COCH(2)Cl fragments. The CH(3)C(O)CH(2) radicals are formed with a considerable amount of energy partitioned into rotation; we use an impulsive model to explicitly characterize the internal energy distribution. The data are better fit by using the C-Cl bond fission transition state on the S(1) surface of chloroacetone as the geometry at which the impulsive force acts, not the Franck-Condon geometry. Our data suggest that, even under atmospheric conditions, the reaction of OH with allene could produce a small branching to CH(3) + ketene products, rather than solely producing inelastically stabilized adducts. This additional channel offers a different pathway for the OH-initiated oxidation of such unsaturated volatile organic compounds, those containing a C=C=C moiety, than is currently included in atmospheric models.     

Product branching from the CH2CH2OH radical intermediate of the OH + ethene reaction

Using a crossed laser-molecular beam scattering apparatus and tunable photoionization detection, these experiments determine the branching to the product channels accessible from the 2-hydroxyethyl radical, the first radical intermediate in the addition reaction of OH with ethene. Photodissociation of 2-bromoethanol at 193 nm forms 2-hydroxyethyl radicals with a range of vibrational energies, which was characterized in our first study of this system ( J. Phys. Chem. A 2010 , 114 , 4934 ). In this second study, we measure the relative signal intensities of ethene (at m/e = 28), vinyl (at m/e = 27), ethenol (at m/e = 44), formaldehyde (at m/e = 30), and acetaldehyde (at m/e = 44) products and correct for the photoionization cross sections and kinematic factors to determine a 0.765:0.145:0.026:0.063:<0.01 branching to the OH + C(2)H(4), H(2)O + C(2)H(3), CH(2)CHOH + H, H(2)CO + CH(3), and CH(3)CHO + H product asymptotes. The detection of the H(2)O + vinyl product channel is surprising when starting from the CH(2)CH(2)OH radical adduct; prior studies had assumed that the H(2)O + vinyl products were solely from the direct abstraction channel in the bimolecular collision of OH and ethene. We suggest that these products may result from a frustrated dissociation of the CH(2)CH(2)OH radical to OH + ethene in which the C-O bond begins to stretch, but the leaving OH moiety abstracts an H atom to form H(2)O + vinyl. We compare our experimental branching ratio to that predicted from statistical microcanonical rate constants averaged over the vibrational energy distribution of our CH(2)CH(2)OH radicals. The comparison suggests that a statistical prediction using 1-D Eckart tunneling underestimates the rate constants for the branching to the product channels of OH + ethene, and that the mechanism for the branching to the H(2)O + vinyl channel is not adequately treated in such theories.     

Crossing bifurcations and unstable dimension variability

A crisis is a global bifurcation in which a chaotic attractor has a discontinuous change in size or suddenly disappears as a scalar parameter of the system is varied. In this Letter, we describe a global bifurcation in three dimensions which can result in a crisis. This bifurcation does not involve a tangency and cannot occur in maps of dimension smaller than 3. We present evidence of unstable dimension variability as a result of the crisis. We then derive a new scaling law describing the density of the new portion of the attractor formed in the crisis. We illustrate this new type of bifurcation with a specific example of a three-dimensional chaotic attractor undergoing a crisis.     

Rotation numbers of periodic orbits in the Hénon map

For invertible, area-contracting maps of the plane, it is common for a basin of attraction to have a fractal basin boundary. Certain periodic orbits on the basin boundary are distinguished by being accessible (by a path) from the interior of the basin. A numerical study is made of the accessible periodic orbits for the Hénon family of maps. Theoretical results on rotary homoclinic tangencies are given, which describe the appearance of the accessible saddles, and organize them in a natural way according to the continued fractions expansions of their rotation numbers.Partially supported by the National Science FoundationPartially supported by a contract from the Applied and Computational Mathematics Program of DARPA     

The dissociation of vibrationally excited CH3OSO radicals and their photolytic precursor, methoxysulfinyl chloride

The dissociation dynamics of methoxysulfinyl radicals generated from the photodissociation of CH(3)OS(O)Cl at 248 nm is investigated using both a crossed laser-molecular beam scattering apparatus and a velocity map imaging apparatus. There is evidence of only a single photodissociation channel of the precursor: S-Cl fission to produce Cl atoms and CH(3)OSO radicals. Some of the vibrationally excited CH(3)OSO radicals undergo subsequent dissociation to CH(3) + SO(2). The velocities of the detected CH(3) and SO(2) products show that the dissociation occurs via a transition state having a substantial barrier beyond the endoergicity; appropriately, the distribution of velocities imparted to these momentum-matched products is fit by a broad recoil kinetic energy distribution extending out to 24 kcal/mol in translational energy. Using 200 eV electron bombardment detection, we also detect the CH(3)OSO radicals that have too little internal energy to dissociate. These radicals are observed both at the parent CH(3)OSO(+) ion as well as at the CH(3)(+) and SO(2)(+) daughter ions; they are distinguished by virtue of the velocity imparted in the original photolytic step. The detected velocities of the stable radicals are roughly consistent with the calculated barriers (both at the CCSD(T) and G3B3 levels of theory) for the dissociation of CH(3)OSO to CH(3) + SO(2) when we account for the partitioning of internal energy between rotation and vibration as the CH(3)OSOCl precursor dissociates.     

Analyzing velocity map images to distinguish the primary methyl photofragments from those produced upon C-Cl bond photofission in chloroacetone at 193 nm

We use a combination of crossed laser-molecular beam scattering experiments and velocity map imaging experiments to investigate the three primary photodissociation channels of chloroacetone at 193 nm: C-Cl bond photofission yielding CH(3)C(O)CH(2) radicals, C-C bond photofission yielding CH(3)CO and CH(2)Cl products, and C-CH(3) bond photofission resulting in CH(3) and C(O)CH(2)Cl products. Improved analysis of data previously reported by our group quantitatively identifies the contribution of this latter photodissociation channel. We introduce a forward convolution procedure to identify the portion of the signal, derived from the methyl image, which results from a two-step process in which C-Cl bond photofission is followed by the dissociation of the vibrationally excited CH(3)C(O)CH(2) radicals to CH(3) + COCH(2). Subtracting this from the total methyl signal identifies the methyl photofragments that result from the CH(3) + C(O)CH(2)Cl photofission channel. We find that about 89% of the chloroacetone molecules undergo C-Cl bond photofission to yield CH(3)C(O)CH(2) and Cl products; approximately 8% result in C-C bond photofission to yield CH(3)CO and CH(2)Cl products, and the remaining 2.6% undergo C-CH(3) bond photofission to yield CH(3) and C(O)CH(2)Cl products.     

Families of periodic orbits: Virtual periods and global continuability

For a differential equation depending on a parameter, there have been numerous investigations of the continuation of periodic orbits as the parameter is varied. Mallet-Paret and Yorke investigated in generic situations how connected components of orbits must terminate. Here we extend the theory to the general case, dropping genericity assumptions.