Relative Kinetic Energy Distributions Research Articles

A statistical, ab initio, quantum mechanical study of the photolysis and final state distributions of singlet ketene

A new quantum mechanical, statistical, total angular momentum conserving theory designed to describe relative kinetic energy and fragment quantum state distributions in unimolecular dissociation processes is described. The theory is called the statistical adiabatic product distribution method and is based on a variational Rice–Ramsperger–Kassel–Marcus (RRKM) treatment of the break-up process. It requires the definition of a break-up pathway or intrinsic reaction coordinate and the normal mode vibrational frequencies in the coordinate space orthogonal to this coordinate. In the present application to the break up of highly excited singlet ketene, the reaction coordinate and vibrational frequencies are evaluated using ab initio molecular electronic structure codes. The variational aspect of the theory involves locating, independently for every total angular momentum and total energy, the reaction coordinate value which leads to the lowest sum-of-states. In order to make predictions of the product quantum state and relative kinetic energy distributions the variational RRKM treatment is augmented by a J conserving quantum phase space treatment of the dissociation process. This treatment also takes into account the variation of the electronic energy along the reaction coordinate during the final stage of the break-up process. The conserved modes of the molecule are treated adiabatically during the break-up process as the fragment separation increases beyond the position of the critical geometry. The quantum phase space theory treatment enables us to identify the energy associated with rotation and translation at the critical geometry. The rotational motion of the fragments is also treated adiabatically during the break-up process, while the relative translational energy is used to surmount the potential and centrifugal barrier which may still have to be overcome to permit the fragments to separate. The phase space theory used takes proper account of the limitations placed on the dynamics by the necessity for the system to surmount these barriers. Extensive investigations are carried out as to whether the transition state or critical geometry arising in the variational RRKM treatment is best computed by treating the system as a bound molecule or as two separated fragments. For the dissociation of ketene at the high levels of excitation treated in the present work, we conclude that the variational calculation of the critical geometry is best performed by treating the system as a bound molecule and using the ab initio computed normal mode vibrational frequencies in the coordinate space perpendicular to the reaction path.

Experimental determination of fragment excitation energies in multifragmentation events

For 50 MeV/nucleon 129Xe+natSn multifragmentation events, we deduced, by means of correlation techniques, the multiplicities of the hydrogen and helium isotopes which were emitted by the hot primary excited fragments produced at the stage of the disassembly of an equilibrated hot source. We also derived the relative kinetic energy distributions between the primary clusters and the light charged particles that they evaporate. From the comparison between the secondary multiplicities observed experimentally and the multiplicities predicted by the GEMINI model, we concluded that the source breaks into primary fragments which are characterized by the same N/Z ratio as the combined system. Knowing the secondary light charged particle multiplicities and kinetic energies, we reconstructed the average charges of the hot fragments and we estimated their mean excitation energies. The fragment excitation energies are equal to 3.0 MeV/nucleon for the full range of intermediate mass fragment atomic number. This global constancy indicates that, on the average, thermodynamical equilibrium was achieved at the disassembly stage of the source.Received 13 March 1998DOI:https://doi.org/10.1103/PhysRevC.58.256©1998 American Physical Society

Internal Excitation in the Products of Nucleophilic Substitution from the Dissociation of Metastable Ion Complexes

The relative kinetic energy distributions for the products of the dissociation of four metastable gas-phase ion clusters have been analyzed by means of ion kinetic energy spectroscopy, and the results modeled using statistical phase space theory. The systems studied represent reaction intermediates in bimolecular nucleophilic substitutions (SN2). These studies build on previous investigations that demonstrated vibrational excitation in the products of the substitution reactions of halide ions with methyl halides.1 The present studies explore the effects of molecular structure, reaction exothermicity, and nucleophile and leaving group variation. The experimental kinetic energy distributions are compared with theoretical distributions calculated for statistical partitioning of energy among internal modes and relative kinetic energy of the products. In each reaction, the calculated distributions agree with the experimental distributions only if a significant fraction of the energy released in the exothermic ...

Low-Frequency Raman Scattering from Water at High Pressures and High Temperatures

Low-frequency isobaric Raman spectra were obtained from water at 0.5, 1.0, 1.5, and 2.0 kbar and temperatures from −18 to 342 °C. Peaks near ≈60 and ≈175 cm-1 were observed at −18 °C and 2.0 kbar, but only a single, asymmetric 50−60 cm-1 feature, skewed to ≈300 cm-1, remained near ≈170 °C and above. The low-temperature ≈60 and 175 cm-1 peaks arise respectively from transverse acoustic (TA) and longitudinal acoustic (LA) standing waves, whereas the skewed, high-temperature Raman feature is well-fitted by a relative kinetic energy distribution (RKED). The TA phonon and RKED peaks are coincident near 60 cm-1. Spectra taken at intermediate temperatures, e.g., 77 and 124 °C, were fitted by a combination of the appropriate RKED and the (−18 °C, 2.0 kbar) TA + LA phonon spectrum. Temperature rise breaks hydrogen bonds and the solidlike patches which support the TA and LA phonons. This continues until only the gaslike RKED remains at high temperatures. Librational spectra were also obtained isochorically. They in...

On colloidal suspension Brownian stability ratios: Theoretical approaches

Various theories on colloidal suspension Brownian stability ratios at primary and secondary minima are discussed. A serious problem is found in an earlier theory's basic assumption. It is claimed that only the relative kinetic energy of the two colliding particles can be spent to overcome the particle interaction potential energy barrier or the potential energy well. Stricter theoretical approaches based on the relative kinetic energy distribution of Brownian particles are presented. Very simple formulas have been obtained for the stability ratios. Comparison with the previous theories is presented too. Good agreement with the experimental data has been found.

Interpretation of energy spectra of neutral particles in scattering of positive molecular ions from surfaces

Abstract The energy distributions of secondary neutral particles produced by grazing scattering of O+2 ions from a silver and a silicon surface have been studied at energies between 400 eV and 3 keV. Experimental results of the dissociation probability are compared with results of a classical trajectory calculation. In the simulation of energy spectra of the molecular fragments a simple conversion of the energy distributions from the center of mass system into the laboratory system yields the same result as the classical trajectory calculation. From the energy spectra of the neutral O atoms the relative kinetic energy distributions of the fragments are obtained. These give information on the processes leading to dissociation. Charge capture into an antibonding O2 state is the dominant origin for the dissociation of molecules.

Interpretation of energy spectra of neutral particles in scattering of positive molecular ions from surfaces

The energy distributions of secondary neutral particles produced by grazing scattering of O + 2 ions from a silver and a silicon surface have been studied at energies between 400 eV and 3 keV. Experimental results of the dissociation probability are compared with results of a classical trajectory calculation. In the simulation of energy spectra of the molecular fragments a simple conversion of the energy distributions from the center of mass system into the laboratory system yields the same result as the classical trajectory calculation. From the energy spectra of the neutral O atoms the relative kinetic energy distributions of the fragments are obtained. These give information on the processes leading to dissociation. Charge capture into an antibonding O 2 state is the dominant origin for the dissociation of molecules.

The relative kinetic energy distribution of the hydrogen atoms formed by the dissociation of the electronically excited H2 molecule

We develop a model describing the relative kinetic energy distribution of the hydrogen atom pair formed by spontaneous photon emission in a transition from the bound state g 3Σ+g of H2 to the repulsive state b 3Σ+u. The results are compared to the experiments of Koot, van der Zande, and Los. The calculations are based on a time dependent theory of the dissociation process.

Photodissociation of weakly bound ion-molecule clusters: krypton-sulfur dioxide (Kr.SO2+)

A photodissociation study of Kr.SO/sub 2//sup +/ is presented. Kr.SO/sub 2//sup +/ was formed by three-body recombination of SO/sub 2//sup +/ with Kr in a high-pressure ion source. Two ionic products, Kr/sup +/ and SO/sub 2//sup +/, were observed when the ion beam was crossed with a focused laser beam. Wavelengths of 458, 488, 514 and 585 nm were used. Product relative kinetic energy distributions, product angular distributions (asymmetry parameters), and product branching ratios were obtained. A statistical phase space calculation was carried out for the SO/sub 2//sup +//Kr product channel. These results suggest either the SO/sub 2//sup +/ product is both vibrationally and electronically excited or a new electronic state of SO/sub 2//sup +/ at approx.1.5 eV is formed. Product relative kinetic energy distributions and angular distributions suggest the Kr/sup +/ ionic product is produced nonstatistically, probably via direct transition to a repulsive state(s) that correlate to Kr/sup +/(/sup 2/P/sub 3/2/)/SO/sub 2/ products. The Kr/sup +//SO/sub 2/ and SO/sub 2//sup +//Kr products come from two noninterconverting sets of photoexcited states. The lifetime of the state(s) leading to Kr/sup +//SO/sub 2/ products is substantially less than a rotational period of the Kr.SO/sub 2//sup +/ cluster while the lifetime of themore » states leading to SO/sub 2//sup +//Kr products is equal to or somewhat larger than a rotational period. The branching ratio varies form 53% Kr/sup +//SO/sub 2/ at 458 nm to 21% Kr/sup +//SO/sub 2/ at 585 nm and reflects changes in the absorption cross sections to the two sets of noninterconverting excited states from the Kr.SO/sub 2//sup +/ ground state. The data provide an upper bound of 0.30 eV for the bond dissociation energy of Kr-SO/sub 2//sup +/ and indicate the cluster has the structure Kr.OSO/sup +/ not Kr.S(O/sub 2/)/sup +/.« less

The interaction of fast N 2+ ions with a Ni(111) surface

The reflection of nitrogen molecular ions from a nickel surface has been studied at energies between 200 eV and 4400 eV. In the scattered beam neutral atoms and molecules and atomic and molecular ions are detected. From the energy spectra of the atoms the relative kinetic energy distributions of the fragments are obtained. These give information on the processes leading to dissociation. The main mechanism for dissociation at low primary energies is charge capture. At higher energies vibrational and rotational excitation dominates.

Photodissociation of weakly bound ion-molecule clusters: the krypton.carbon dioxide (Kr.CO2+) cluster

The results of a laser-ion beam study of the photodissociation of the Kr.CO/sub 2//sup +/ cluster are presented. The photodissociation spectrum, product branching ratios, product angular distributions, and product relative kinetic energy distributions are reported. The photodissociation spectrum has a broad maximum of 2.4 x 10/sup -17/ cm/sup 2/ at around 500 nm. Two ionic products were observed: Kr/sup +/ (around 60%) and CO/sub 2//sup +/. The product angular distributions could be adequately fit by the expression P(theta) = 1 + ..beta..P/sub 2/(cos theta) with a value of 1.55 for ..beta.. for the Kr/sup +/ product and 1.35 for the CO/sub 2/ product, indicating parallel type transitions and lifetimes shorter than a rotational period. The product relative kinetic energy distributions peak at large values of relative kinetic energy indicating nonstatistical energy disposal. The kinetic energy distributions for the Kr/sup +/ product are bimodal at 650 nm. The two components probably arise from production of both spin-orbit states of Kr/sup +/: /sup 2/P/sub 1/2/ and /sup 2/P/sub 3/2/. 28 references, 8 figures, 1 table.

Photodissociation of the SO2⋅SO+2 dimer in the visible region of the spectrum: Product relative kinetic energy distributions and product angular distributions

The results of an investigation of the photodissociation of the SO2⋅SO+2 cluster ion in the visible wavelength range (458–590 nm) are presented. The studies were performed using a crossed fast ion beam/laser beam experiment. Product relative kinetic energy distributions and product center of mass angular distributions are reported. Methods used to extract the angular distributions from the experimental measurements are described. The only ionic product observed from the photodissociation of SO2⋅SO+2 was SO+2. The product relative kinetic energy distributions are characteristic of statistical energy disposal. However, statistical phase space theory substantially overestimates the fraction of available energy partitioned into relative kinetic energy. The product angular distributions are discussed in terms of the asymmetry parameter β. β increases with the products relative velocity. A simple phase space theory model for β is developed for statistical dissociation with complete rotational averaging. The model accounts for the variation of β with the products relative velocity. β also varies with wavelength. The variation of β with wavelength is ascribed to changes in the lifetime of the cluster. At 458 nm the values of β indicate that complete rotational averaging has not occurred. At 590 nm the data are consistent with complete rotational averaging, implying a lifetime>5 average rotational periods. The results are interpreted in terms of a transition to a low lying bound excited state of the SO2⋅SO+2 cluster which arises from one of the low lying excited states of SO+2 and the ground state of SO2.

Charge transfer half-collisions: Photodissociation of the Kr⋅O+2 cluster ion with resolution of the O2 product vibrational states

The photodissociation of the Kr⋅O+2 cluster ion has been studied in the visible and UV regions of the spectrum (350–580 nm) using a crossed high energy ion beam/laser beam experiment. Photodissociation of Kr⋅O+2 occurs by a charge transfer transition to Kr+⋅O2 state(s). The only ionic product observed was Kr+. A value for the dissociation energy of the Kr⋅O+2 cluster of D00(Kr–O+2) ∼0.33 eV was estimated from the results. A compilation of ion–molecule cluster dissociation energies is given. The product angular distributions indicate that the lifetime of the excited state(s) is less than a rotational period. In the visible region of the spectrum the products are Kr+(2P3/2)+O2(2Σ−). For the UV it is argued that one of the products is probably electronically excited [i.e., either Kr+(2P1/2) or O2(1Δg)]. The product relative kinetic energy distributions show resolved features that can be assigned to production of the product O2 in specific vibrational states. Information on the product rotational excitation was also derived from these results. The potential surfaces of the [Kr⋅O2]+ system are discussed along with literature data on the charge transfer reaction between Kr+ and O2.

The dynamics of photodissociation of cluster ions. II. Photodissociation of the (NO)+3 cluster in the visible wavelength range

The photodissociation of the (NO)+3 cluster ion has been studied in the visible region of the spectrum (460–660 nm) using a crossed high energy ion beam/laser beam experiment. Total photodissociation cross sections, product branching ratios, product relative kinetic energy distributions, and information about the product angular distributions have been measured. The total photodissociation cross section peaks to the blue end of the visible spectrum with a maximum in excess of 5×10−17 cm2. The only ionic products observed were NO+ and (NO)+.2. The fraction of (NO)+⋅2 formed is 26±4% and is essentially independent of wavelength in the range studied. For (NO)+⋅2 the product kinetic energy distributions are narrow and characteristic of dissociation occurring on a repulsive surface. At 610 nm, 24% of the available energy appears as product relative kinetic energy, this fraction increases to 32% at 488 nm. The (NO)+⋅2 angular distributions are well described by an angular distribution of the form 1+βP2(θ) with β=1.5 indicating that dissociation occurs rapidly with respect to a rotational period. Product stability restrictions play a major role in the dynamics of stable (NO)+⋅2 formation and the mechanism of dissociation effectively channels energy into internal excitation of the neutral NO⋅ product. The NO+ kinetic energy distributions are bimodal for large photon energies suggesting that NO+ is generated by two mechanisms. The higher energy component was assigned to direct formation of NO+ on a time scale short compared to a rotational period and the lower energy component was assigned to unimolecular dissociation of excited (NO)+⋅2 photoproducts. The energy released in the unimolecular dissociation of (NO)+⋅2 forming the lower energy NO+ product is on the order of 0.1 eV which is consistent with statistical dissociation.

Translational spectroscopy of N + and O + fragments from 5 keV collision-induced dissociation of NO + ions by helium

Laboratory kinetic energy distributions of N + and O + fragments arising from 5 keV collision-induced dissociation of parent NO + ions with helium, are reported. These observations allow us to determine both the amount of translational energy converted into internal energy of NO +* and the relative translational energy of the (pre)dissociating fragments. The O − - N relative kinetic energy distribution extends from 0 to 18 eV, and a collision-induced transition to level of a predissociating state is shown to have lifetimes ranging from 40 to 140 ns. The N − + O distribution lies between 0 and 11 eV and involves transition to five (pre)dissociating states, three of which have the energies of 29±0.2 eV, 34±0.3 eV, 34.5±0.3 eV with respect to the ground state of NO.