Stefan Schmatz

Theoretical study of the rovibrational energy spectrum and the numbers and densities of bound vibrational states for the system HCO+/HOC+

Large-scale calculations of accurate energy levels for the system HCO+/HOC+ in its electronic ground state are reported. The rovibrational levels are calculated for total angular momentum J=0, 1, and 2 by means of the discrete variable representation of the angular coordinate in conjunction with a distributed Gaussian basis for the radial degrees of freedom. A new analytical potential energy surface is used which is based on high level ab initio calculations [CCSD(T)/cc-pVQZ]. The rovibrational energy spectra of HCO+ and HOC+, as well as of the isotopomers DCO+ and DOC+, are analyzed in detail up to the ground state adiabatic isomerization barrier at 28u2009798u2009cm−1. Spectroscopic parameters calculated for low lying vibrational states show distinct differences between HCO+ and HOC+. A total number of 6042 bound states up to the first classical dissociation limit (H++CO) at 51u2009621u2009cm−1 and a density at the threshold of 0.52/cm−1 are estimated for J=0. Semiclassical phase space integration yields nearly identic...

Quantum scattering on SN2 reactions: Influence of azimuthal rotations

Time independent quantum scattering calculations have been carried out on the SN2 Walden inversion reaction Cl−+CH3Cl(v,k)→ClCH3(v′,k′)+Cl−. The two C–Cl stretching degrees of freedom (quantum numbers v and v′) and the azimuthal angle describing the rotation of the CH3 group (quantum numbers k and k′) are treated explicitly. An infinite order sudden approximation has been introduced using Radau coordinates for the stretching modes. The potential energy surface of Vande Linde and Hase is used. The scattering problem is formulated in hyperspherical coordinates. For the reaction (k=0→k′=0) substitution is observed for initial vibrational excitation with v⩾2. If the system departs from the collinear reaction pathway (initial rotational excitation) the substitution cross sections are strongly decreased. The state-to-state cross sections σvk→v′k′ are large only for transitions with Δk=0. The total reaction cross sections σvk for given v vary only slightly at low values of the azimuthal quantum number k and rise...

Symmetry specificity in the unimolecular decay of the Cl−⋯CH3Cl complex: Two-mode quantum calculations on a coupled-cluster [CCSD(T)] potential energy surface

The decay of resonance states in the complex-forming nucleophilic substitution reaction Cl−+CH3Cl is investigated by means of two-dimensional quantum mechanical calculations on a coupled-cluster [CCSD(T)] potential energy surface. The dynamics calculations employ Radau coordinates to describe the two C–Cl stretching degrees of freedom, filter diagonalization, and an absorbing (optical) potential. The resonance widths and the corresponding decay rates vary by several orders-of-magnitude, reflecting the large degree of separability of the intramolecular and the intermolecular mode. The decay is found to be strongly symmetry specific: For energies above the reaction barrier, the smallest rates of the ungerade states are about two orders-of-magnitude smaller than the smallest rates of the gerade states. An explanation is given in terms of an adiabatic model formulated in hyperspherical coordinates. The nonadiabatic coupling elements, which control the energy transfer between the two modes and therefore determ...

Quantum scattering calculations on the SN2 reaction Cl−+CH3Br→ClCH3+Br−

The gas-phase SN2 reaction Cl−+CH3Br(v,k)→ClCH3(v′k′)+Br− has been studied using reduced dimensionality time independent quantum scattering theory. The C–Br and C–Cl stretching degrees of freedom (quantum numbers v and v′) and the azimuthal angle (rotation of the CH3 group; quantum numbers k and k′) are treated explicitly. An infinite order sudden approximation and Radau coordinates for the stretching modes are used. The scattering problem is formulated in hyperspherical coordinates. A potential energy surface of Wang, Zhu, and Hase is used. It is found that this surface can reproduce the experimentally observed independence of the rate constant on the internal temperature of CH3Br only if it is scaled to enable the transition state geometry to agree with high level ab initio data. The reaction cross sections show the propensity rule Δk=0 for the azimuthal rotation.

Decomposition of Tertiary Alkoxy Radicals

Abstract Rate coefficients of β-scission reactions in tertiary alkoxy radicals, R(CH3)2CO (R = methyl, ethyl, tert-butyl and neo-pentyl) have been estimated via density functional theory (DFT) calculations in conjunction with statistical unimolecular rate theory. For tert-butoxy, results obtained by employing different basis sets are compared with experimental values, indicating that UB3LYP/6-31G(d,p) excellently predicts kinetic data. Rate coefficients for inter- and intramolecular hydrogen abstraction are also reported. Depending on R, the β-scission rate may vary by orders of magnitude. The predicted temperature dependence of the alcohol-to-ketone product ratios for alkoxy radical decomposition in a hydrocarbon environment is in remarkably close agreement with the corresponding ratios measured on the product mixtures from decomposition of tert-butyl and tert-amyl peroxyacetates in solution of n-heptane.

State-selected dynamics of the complex-forming bimolecular reaction Cl−+CH3Cl′→ClCH3+Cl′−: A four-dimensional quantum scattering study

Time-independent quantum scattering calculations have been carried out on the Walden inversion S(N)2 reaction Cl(-)+CH(3)Cl()(v(1),v(2),v(3))-->ClCH(3)(v(1) (),v(2) (),v(3) ())+Cl(-). The two C-Cl stretching modes (quantum numbers v(3) and v(3) ()) and the totally symmetric internal modes of the methyl group (C-H stretching vibration, v(1) and v(1) (), and inversion bending vibration, v(2) and v(2) ()) are treated explicitly. A four-dimensional coupled cluster potential energy surface is employed. The scattering problem is formulated in hyperspherical coordinates using the exact Hamiltonian and exploiting the full symmetry of the problem. Converged state-selected reaction probabilities and product distributions have been calculated up to 6100 cm(-1) above the vibrational ground state of CH(3)Cl, i.e., up to initial vibrational excitation (2,0,0). In order to extract all scattering resonances, the energetic grid was chosen to be very fine, partly down to a resolution of 10(-12) cm(-1). Up to 2500 cm(-1) translational energy, initial excitation of the umbrella bending vibration, (0,1,0), is more efficient for reaction than exciting the C-Cl stretching mode, (0,0,1). The combined excitation of both vibrations results in a synergic effect, i.e., a considerably higher reaction probability than expected from the sum of both independent excitations, even higher than (0,0,2) up to 1500 cm(-1) translational energy. Product distributions show that the umbrella mode is strongly coupled to the C-Cl stretching mode and cannot be treated as a spectator mode. The reaction probability rises almost linearly with increasing initial excitation of the umbrella bending mode. The effect with respect to the C-Cl stretch is five times larger for more than two quanta in this mode, and in agreement with previous work saturation is found. Exciting the high-frequency C-H stretching mode, (1,0,0), yields a large increase for small energies [more than two orders of magnitude larger than (0,0,0)], while for translational energies higher than 2000 cm(-1), it becomes a pure spectator mode. For combined initial excitations including the symmetric C-H stretch, the spectator character of the latter is even more pronounced. However, up to more than 1500 cm(-1) translational energy, the C-H vibration does not behave adiabatically during the course of reaction, because only 20% of the initial energy is found in the same mode of the product molecule. The distribution of resonance widths and peak heights is discussed, and it is found that individual resonances pertinent to intermediate complexes Cl(-)...CH(3)Cl show product distributions independent of the initial vibrational state of the reactant molecule. The relatively high reactivity, of resonance states with respect to excitation of any mode, found in previous work is confirmed in the present calculations. However, reactivity of intermediate states and reactivity with respect to initial vibrational excitation have to be distinguished. There is a strong mixing between the vibrational states reflected in numerous avoided crossings of the hyperspherical adiabatic curves.

Quantum-mechanical study of the resonances of the SN2 reaction Cl-+CH3Cl→ClCH3+Cl-

The nucleophilic substitution reaction Cl-+CH3Cl→ClCH3+Cl- has been studied quantum mechanically by means of stabilisation and scattering calculations. A reduced dimensionality Hamiltonian model has been employed in which the bonds that are broken and formed during reaction, Cl–C and C–Cl, are explicitly treated. The reaction is driven by many narrow scattering resonances, which are analysed by means of the stabilisation method. It is found that part of the quasibound states are assignable by quantum numbers v and n, describing excitations in the intramolecular, C–Cl, and intermolecular, Cl-···C, stretching modes of the Cl-···CH3Cl complex, respectively. The connection between reactivity and the splitting of resonance states of different symmetry at the reaction barrier region is discussed. Interestingly, it is found that the density of states in the transition state region directly correlates with the resonance structure of the cumulative reaction probability.

Four-mode calculation of resonance states of intermediate complexes in the SN2 reaction Cl−+CH3Cl′→ClCH3+Cl′−

A four-dimensional coupled-cluster [CCSD(T)] potential energy surface has been constructed for the collinear symmetric SN2 reaction Cl−+CH3Cl′→ClCH3+Cl′−. Making use of the filter diagonalization method and optical potentials, bound states as well as resonance states up to energies far above the dissociation threshold have been calculated. Most of the bound and resonance states up to the first overtone of the symmetric C–H stretching vibration could be assigned four quantum numbers (symmetric C–H stretching mode, umbrella bending mode, intra- and intermolecular C–Cl stretching modes). The effect of different average lifetimes of resonance states with gerade and ungerade symmetry that was found in previous two-mode calculations [J. Chem. Phys. 114, 5233 (2001)] is preserved in the four-dimensional calculations. The range of the resonance widths has become appreciably more widespread because many resonance states with excitation in the high-frequency C–H stretching mode and the umbrella bending mode are par...

Resonances in SN2 reactions: Two-mode quantum calculations for Cl-+CH3Br on a coupled-cluster potential energy surface

An effective two-dimensional potential energy surface has been constructed for the SN2 reaction Cl−+CH3Br→ClCH3+Br− from coupled-cluster calculations with a large basis set. In the quantum dynamics calculations Radau coordinates were employed to describe the Cl–C and C–Br stretching modes. Making use of the filter diagonalization method and an optical potential, bound states as well as resonance states up to energies far above the dissociation threshold have been calculated. The resonance widths fluctuate over several orders of magnitude. In addition to a majority of Feshbach-type resonances there are also exceedingly long-lived shape resonances, which can only decay by tunneling. Owing to a smaller width of the potential barrier and a larger density of states, tunneling through the barrier is more important for Cl−+CH3Br than for Cl−+CH3Cl despite the larger total mass of this system. Excitation of the C–Br stretching vibration enhances the tunneling probability of the entrance channel complex.

Rotational effects in complex-forming bimolecular substitution reactions: A quantum-mechanical approach.

The quantum dynamics of the complex-forming S(N)2 reaction Cl(-)+CH(3)Br-->ClCH(3)+Br(-) is studied with emphasis on rotational effects. The pseudotriatomic system Cl-Me-Br is treated with a corresponding three-dimensional (3D) potential energy surface as a function of the two scattering coordinates and the enclosed angle where the geometry of the methyl group Me is optimized at each point. The 3D space is divided into three different parts, the interaction region, an intermediate region, and the asymptotic region. In line with simple classical-mechanical arguments and previous classical trajectory calculations, initial rotational motion of CH(3)Br seemingly decreases the reaction probability. However, the dynamical inclusion of the rotational degree of freedom and the presence of the many rovibrational product states overall lead to a large increase in reactivity compared to our previous collinear study on this reaction. If the reactant is rotationally excited, the higher vibrational product states are depleted in favor of lower-lying levels. Starting the reaction with rotationless reactants may end up in significant rotational excitation in the product molecules (translation-to-rotation energy transfer). On the other hand, initial rotational energy in rotationally highly excited reactants is to a large amount converted into translational and vibrational energy. The average amount of rotational energy in the products shows a twofold vibrational excitation-independent saturation (i.e., memorylessness), with respect to both initial rotational excitation and translational energy. Since only about one-half of all reactant states end in rotationless products, the reaction probability should be increased by a factor of 2; the actually larger reactivity points to other dynamical effects that play an important role in the reaction.