Phase Space Theory Calculations Research Articles

Photodissociation dynamics of weakly bound ion–neutral clusters: SO2 ⋅ O+2

A photodissociation study of SO2 ⋅ O+2 is presented. The experiments were carried out on mass selected ion beams that were crossed with a polarized laser beam and then photoproducts were mass and energy analyzed. The SO2 ⋅ O+2 ions were formed by three body association reactions in a pressure and temperature dependent ion source. Studies were carried out at wavelengths of 582, 514, 488, 458, and 357±7 nm using an argon ion laser/dye laser system. Both O+2/SO2 and SO+2/O2 photoproducts were observed and the branching ratio measured as a function of λ. In addition, product kinetic energy distributions and angular distributions (asymmetry parameters) were measured and statistical phase space theory calculations were carried out. The results indicate the O+2/SO2 products are formed from photon absorption to a bound excited state at all wavelengths followed by internal conversion to the ground state and statistical vibrational predissociation. The SO+2/O2 products are formed by two mechanisms. At long wavelengths (582 nm) the products are formed exclusively by photon absorption to a bound state followed by internal conversion and statistical predissociation from the ground state. At short wavelengths (357 nm) direct dissociation from a repulsive upper state dominates. Both mechanisms are involved at intermediate wavelengths. Arguments are made that both the bound and repulsive upper states correlate to SO+2(X̃ 1A1)/O2(b 1∑+g) products and that the bound upper state corresponds to the low energy band in the photodissociation cross section measurements of Hodges and Vanderhoff and the repulsive state to the high energy band.

Reactive scattering from double-minimum potentials

We present a crossed-beam study of the elimination reactions of Li+ with t-butyl alcohol (TBA), isopropyl chloride (IPC), n-propyl chloride (NPC), and isopropyl bromide (IPB) over the collision energy range 0.6–2.5 eV. Full differential cross-sections at collision energies up to 1.2 eV show increasing asymmetry in the angular distributions as a function of initial collision energy and suggest that the reactions take place on a timescale of 0.2–0.5 ps. The observation of Li+ being non-reactively ejected from the initial encounter complex formed by approaching reactants is consistent with a double-minimum reaction coordinate and a comparison of the non-reactive flux with the flux for elimination products allows an estimate of the heights of intermediate isomerization barriers separating the wells on the potential surface. The kinetic energy distributions for Li+(HX) and Li+(olefin) products and non-reactively scattered Li+ are in reasonable agreement with phase-space theory calculations which include all product vibrational modes. The energy dependence of the Li+(HX)/Li+(olefin) branching ratio can be accounted for with statistical calculations which include product dissociation. The discrepancy between the statistical recoil energy distributions and apparent complex lifetimes several orders of magnitude shorter than the predictions of RRKM theory can be understood in terms of the specific dynamics of passage from the crest of the isomerization barrier to the second well of the potential surface and the apparent failure of the system to re-establish microcanonical equilibrium in that well.

Photodissociation dynamics of negative ion clusters: (SO2)−2

The photodissociation dynamics of (SO2)−2 to form SO2/SO−2 products is investigated over the wavelength range 656 (1.89 eV) to 458 nm (2.71 eV). Product angular distributions are obtained. An asymmetry parameter analysis indicates the lifetime of the (SO2)−2 photoexcited state is much less than a rotational period. Product kinetic energy distributions are obtained at all wavelengths. Both the overall shape of these distributions and comparison with statistical phase space theory calculations indicate the excited state assessed by the photon is repulsive consistent with the asymmetry parameter analysis. An impulsive model analysis suggests the bond between the two SO2 moeities in (SO2)−2 is probably between one oxygen atom on each moeity and the structure is quasilinear. Structure is also observed in the kinetic energy distributions. It is suggested this is due to selective photoexcitation of vibrational states of either the SO2 or SO−2 moeity in (SO2)−2. Hodges and Vanderhoff have reported a bimodel photodestruction cross section for (SO2)−2, with major peaks near 600 and 400 nm. We argue these peaks are due to photodissociation of (SO2)−2 not photodetachment, with the first excited doublet state (repulsive) leading to the 600 nm peak and the second excited doublet state (bound) leading to the second maxima. The repulsive state must correlate to ground state SO2/SO−2 products and the bound state to electronically excited SO2/SO−2 products. Predictions regarding the dissociation dynamics of the bound state are made.

The orbiting transition state for systems containing linear molecules: application to (H2O)OH- + CO2 .fwdarw. HCO3- + H2O

Two approximations to the orbiting transition state sum of states (i.e., phase space theory) for systems containing linear molecules are examined. The first is a low angular momentum approximation which was originally introduced by Klots and shown by him to be exact in the zero angular momentum limit. The second is an integral approximation in that it is designed to work well when the sum of states is integrated over large ranges of angular momentum, a situation in which the Klots approximation usually fails. The approximations are used in phase space theory calculations on the translational energy dependence of the cross section for the title reaction. Excellent agreement with the experimental data of Hierl and Paulson is obtained if the HCO/sub 3//sup -/ product ions are allowed to dissociate via the reaction HCO/sub 3//sup -/ ..-->.. OH/sup -/ + CO/sub 2/ provided that the enthalpy of dissociation is taken to be 1.8 eV as determined by Keesee and Castleman.

Photodissociation of cyanogen: Angle and velocity distributions of state resolved fragments

The disposal of excess energy above the dissociation threshold into internal excitation and translation in a photochemical decomposition of C2N2 has been determined by utilizing a technique by which measurements of the recoil velocity distribution for particular rotational states are possible. Simple phase space theory calculations appear to give a fairly good interpretation of the rotational energy distributions in a particular vibrational state, while the vibrational energy disposal is definitely nonstatistical with only about 63% of the total population predicted by statistical calculation in the first vibrational state and no excitation observed in the v=2 state. Our experimental results support the previous predictions of high translational energy disposal ( fT=75%) compared to a low or moderate product internal state excitations ( fR=18.6%, fv=6.4%). We also measure the dissociation energy of C2N2 to be 133±1 kcal/mol rather than the previously reported 128±1 kcal/mol.

The 540–900 nm photodissociation of 300 K NCNO: One- and two-photon processes

The laser photodissociation of 300 K NCNO throughout the region 540–900 nm is reported, and both 1- and 2-photon processes are discussed. By monitoring CN fragments produced via the 1-photon process, we show that with photolysis wavelengths >592 nm, dissociation occurs predominantly by exciting NCNO ‘‘hot bands.’’ At shorter photolysis wavelengths, dissociation from the ground vibrational state of NCNO is observed as well, but the contributions from hot bands are still manifest in high CN rotational levels which are energetically inaccessible from the ground state (D0=48.8 kcal mol−1). Energy distributions in the CN fragments were determined for excess energies up to 1800 cm−1, and are in agreement with phase space theory calculations and a vibrational predissociation mechanism. In addition, throughout the region 620–900 nm, stepwise two-photon photodissociation proceeds using the à 1A″ state as a gateway, and results in rotationally and vibrationally ‘‘hot’’ CN fragments. The hot CN fragment yield vs photolysis wavelength shows peaks which correspond exactly to peaks in the NCNO absorption spectrum, allowing us to obtain high resolution spectra of the à 1A″← X̃ 1A′ absorption system. The one- and two-photon processes are in competition, and the latter disappears at wavelengths where one-photon photodissociation of NCNO via its ground vibrational level sets in. The nature of the electronic states involved in the one- and two-photon processes is also discussed.

Ion–molecule association reactions: A study of the temperature dependence of the reaction N+⋅2+N2+M → N+⋅4+M for M=N2, Ne, and He: Experiment and theory

The temperature dependence of the N+⋅2+N2 → N+⋅4 association has been investigated using a mass spectrometer source with coaxial electron entrance and ion exit apertures. The source resembles a miniature drift tube in that a small electric field is used to move the ions through the source. The effect of the field on the ion energy is discussed. Thermal reaction rate coefficients are obtained over the temperature range of 80 to 450 K, using He, Ne, and N2 as buffer gases. The experimental data reported here are compared with literature data as well as with the predictions of phase space theory calculations. Good agreement was found for the pure N2 system between the present results, previous experiments and theoretical calculations. Less good agreement was found between previous and present experiments when He was used as the buffer gas. In this case, the calculations tended to support the present results. The theoretical calculations also indicate a significant pressure dependence in the third-order rate coefficient which may account at least in part for the discrepancy between results.

Internal energy of CH+ produced by the C+(H2,H)CH+ reaction

The energy spectrum of CH+ from the reaction C+(H2,H)CH+ was measured with a tandem mass spectrometer with improved energy resolution as a function of projectile kinetic energy. These spectra indicate the presence of the three lowest electronic states of CH+ and product vibrational excitation was observed in favorable cases. The internal energy distribution in the CH+ product was in satisfactory agreement with published results of phase space theory calculations for this reaction.

Statistical phase space theory of polyatomic systems: Rigorous energy and angular momentum conservation in reactions involving symmetric polyatomic species

Classical formulas for the sum and density of rotational and rotational–orbital states pairs of polyatomic molecules are derived using a geometrical approach that rigorously conserves energy and angular momentum. The pair combinations considered include a spherical top in combination with either a linear, spherical, or symmetric top molecule. With the formulas presented here it is possible to perform exact classical statistical phase space theory calculations for bimolecular reactions involving polyatomic molecules. In suitable limits our results reduce to well-known classical expressions for rotational state densities and sums or to equations previously derived by Klots using an aprroximate phase space approach. Calculations are given that demonstrate the distortions produced in the system phase space by molecular oblateness and prolateness are usually small.