Volume 93, Issue 5, 01 September 1990
Index of content:

Picosecond measurements of relaxation of internal modes in crystalline benzene as a function of temperature
View Description Hide DescriptionThe relaxation rates of four internal vibrational levels of benzene crystal have been measured by time‐resolved coherent anti‐Stokes Raman scattering(CARS) at different temperatures. The important information on the dephasing mechanisms provided by the experiment has been supported by anharmonic calculations, which include the full contribution of the density of phonon states, by utilizing average coupling coefficients. Different behaviors have been observed for the different modes considered. Three of the four vibrations (v _{1},v _{6}, and v _{1} _{0}) show linewidths that increase linearly in the classical regime with temperature; the experimental evidence for the important role played by three‐phonon processes (driven by cubic anharmonicity) is confirmed by the calculations, which give a quantitative agreement with the observed linewidths. For the above‐mentioned vibrations the role of pure dephasing results in a minor contribution, while the effect of isotopic impurities is important in determining the low temperature relaxation rate. On the other hand, the linewidth of v _{9} increases quadratically with T: Both decay processes of high order and pure dephasing may be responsible for such a behavior. This ambiguity cannot be overcome by our calculations, since these do not include the effect of high order (mainly quartic) anharmonic terms. Finally, the analysis of the decay mechanisms as predicted by the calculation shows that the anharmonic coefficients may differ from mode to mode: the relaxation mechanism is highly mode selective, and its efficiency depends greatly on the nature of the molecular normal coordinates involved in the process.

Inelastic neutron scattering analysis of low‐frequency motions in proteins: Harmonic and damped harmonic models of bovine pancreatic tryspin inhibitor
View Description Hide DescriptionInelastic neutron scattering spectra are calculated from harmonic and damped harmonic models of the internal dynamics of a small protein, the bovine pancreatic trypsin inhibitor (BPTI). Numerical Fourier transformation of the intermediate scattering function F ^{vib} _{inc} (q, t) is used to calculate the inelastic scattering. This permits the inclusion of multiphonon scattering and frictional damping effects. Although for a typical experimental configuration, the multiphonon contribution does not significantly alter the form of the scattering at frequencies below about 30 cm^{−1}, it does have a significant effect on the scattering intensity at higher frequencies. Frictional damping is introduced into the harmonic model by assuming that each mode acts as an independent damped Langevin oscillator. With this model and the assumption that the lowest frequency modes are overdamped while the higher frequency modes are underdamped, improved agreement with the experimental BPTI powder results is obtained. The measuredscattering from BPTI in solution shows increased intensity at frequencies below 50 cm^{−1} relative to the powder results. The solution scattering profile can be reproduced approximately by the addition of overdamped Langevin oscillatornormal modes to the dynamic model in best agreement with the powder data. Several other aspects of neutron scattering from proteins are examined. Anisotropy in the harmonic resolution broadened scattering is demonstrated. Spectra calculated assuming classical equations of motion are shown to agree with those calculated with the full quantum‐mechanical dynamical model. Translational diffusion broadening is found to be small compared to the instrumental resolution broadening for the range of scattering wave vectors of interest. The contribution of the coherent scattering to the measured intensity is calculated for the case of a partially hydrated protein. Under typical experimental conditions, the measured cross sections are dominated by the incoherent scattering and the self part of the coherent scattering, a result that justifies the comparison of experimental data with calculated incoherent scattering spectra.

P‐type doubling in the infrared spectrum of NO–HF
View Description Hide DescriptionThe HF stretching band of the NO–HF open‐shell complex has been recorded using a molecular‐beam optothermal spectrometer. The spectrum exhibits P‐type doubling indicative of an unpaired electron spin coupled to the rotational angular momentum of a bent complex with substantially quenched electron orbital angular momentum. From B̄‘=0.111 320(17) cm^{−1}, and an off‐axis angle for the NO of 30°, the zero‐point center‐of‐mass separation is estimated to be 3.4396(3) Å. The HF frequency shift of 84 cm^{−1} indicates that the complex is hydrogen bonded, and the spectral intensities imply that the HF axis is aligned closely to the center‐of‐mass axis and the NO is off axis by 30±15°. The Renner–Teller‐like orbital quenching parameter is somewhat larger than the spin–orbit constant in the free NO molecule and increases substantially upon vibrational excitation. The transitions in this band exhibit vibrational predissociation broadening of 200±40 MHz (FWHM), similar to that observed for a number of closed‐shell hydrogen‐bonded HF complexes.

High resolution Raman spectroscopy in the α and β crystalline phases of N_{2}
View Description Hide DescriptionThe line shape of the E _{ g } libron at 32 cm^{−1} and of the two components (A _{ g } and T _{ g }) of the vibron at 2330 cm^{−1} of solid α‐N_{2} at normal pressure were measured as a function of temperature between 5 and 35.6 K by means of high‐resolution Raman spectroscopy with a limiting spectral resolution of 0.006 cm^{−1}. A suitable deconvolution procedure provides the respective weights of Lorentzian and Gaussian contributions to the true phononline shapes. The measured residual bandwidth of the E _{ g } libron at low temperature is noticeably narrower than that previously quoted in the literature (0.16 cm^{−1} instead of 0.8 cm^{−1}). At high temperature it is shown that the libron relaxation mechanisms are mainly governed by four‐phonon processes. The temperature dependence of the vibron dephasing mechanisms are discussed in terms of contributions arising from depopulation, elastic and inelastic quartic processes as well as from disorder. The influence of the low energy optical phonons (ω≂32 cm^{−1}) in the vibron relaxation mechanisms is emphasized. It is shown that between 25 K and the α–β transition temperature at T _{ c }=35.6 K, the temperature dependent vibron linewidths are driven by inelastic processes. Finally some results on the frequency and the bandwidth of the ν_{1} mode in the β phase are reported.

Band structure of stationary emission spectra from a three‐level molecule pumped by strong radiation fields
View Description Hide DescriptionA theory of the emission spectrum from a multilevel molecular system pumped by strong resonant radiation fields based on the double space theory of the density matrix is developed. We are especially concerned with a three‐level, one‐laser system, and a three‐level, two‐laser system. It is shown that the band structure cannot always be estimated by the energy level structure of the dressed states. In fact, in both model systems, triplet structures of the emission spectra can be observed in the case where the magnitude of the molecule‐field interaction is larger than that of the detuning. The characteristic features of the band structure are interpreted in terms of the dressed state picture based on analytically solvable models. Several numerical calculations are performed to show how the multiplet band structure in the emission spectrum is influenced by the detuning and the power of the pump field(s).

Selection rules for the photoionization of diatomic molecules
View Description Hide DescriptionIn the photoionization of the diatomic molecule AB to yield AB^{+}+e^{−} the photoelectron may be charatcterized by a partial wave expansion in terms of its orbital angular momentum quantum number l. For a given value of l, conservation of angular momentum implies that transitions can only occur for ΔJ=l+ (3)/(2) , l+ (1)/(2) , ... ,−l− (1)/(2) , −l− (3)/(2) , where ΔJ=J ^{+}−J is the change (half‐integer) in the total angular momentum (excluding nuclear spin) of the AB^{+} ion rovibronic level and the AB neutral rovibronic level. Other selection rules are ΔΩ=−λ+ (3)/(2) , −λ+ (1)/(2) , ... , −λ− (3)/(2) , and ΔM=−m _{ l }+ (3)/(2) , −m _{ l }+ (1)/(2) , ... , −m _{ l }− (3)/(2) . In addition, for Hund’s case (a) and case (b) coupling, ΔS=S ^{+}−S=± (1)/(2) , ΔΣ=± (1)/(2) , and ΔΛ=−λ, −λ±1. Parity selection rules have been derived for transitions connecting levels described by one of the four coupling schemes, Hund’s case (a), case (b), case (c), and case (d). In particular, for a case (a)–case (a) transition, ΔJ−ΔS+Δp+Δs+l=odd, where the symbols have their traditional spectroscopic meanings. The parity label p=0,1 has been associated with the e, f label, from which it may be shown that (e/f )↔(e/f ) for ΔJ− (1)/(2) +l=odd and (e/f )↔( f/e) for ΔJ− (1)/(2) +l=even. It also follows that ±↔± for l odd and ±↔∓for l even. Moreover, Σ^{±} is connected to Σ^{±} in general, but Σ^{±} is only connected to Σ^{∓} for l≥2 and λ=±1 (π wave). For homonuclear diatomics, the additional selection rules are (g/u)↔(g/u) for l=odd, (g/u)↔(u/g) for l=even, and (s/a)↔(s/a) but (s/a)↔/(a/s).

Highly excited vibration–rotation states of floppy triatomic molecules by a localized representation method: The HCN/HNC molecule
View Description Hide DescriptionAll rovibrational levels of HCN/HNC up to ∼16 000 cm^{−1}, relative to the HCN minimum, for J=0, 1, 2, have been calculated accurately. All internal degrees of freedom are included in these calculations, performed on the realistic, empirical potential surface by Murrel e t a l. [J. Mol. Spectrosc. 9 3, 307 (1982)]. Body‐fixed mass‐scaled Jacobi coordinates are employed, together with the discrete variable representation of the large amplitude motion (LAM) angular coordinate, and a 2‐D distributed Gaussian basis for the radial degrees of freedom. The successive diagonalization–truncation procedure results in a compact matrix representation of the full rovibrational Hamiltonian, allowing accurate and efficient determination of a large number (>350 for J=2, p=0 case) of highly excited LAM rovibrational states of HCN/HNC. This approach is suitable for a broad class of floppy, isomerizing triatomic molecules and van der Waals complexes. In addition to energy levels and wave functions, expectation values of Jacobi coordinates, 〈R〉, 〈r〉, and 〈θ〉, are calculated for most states. The majority of calculated J=1,2 levels lie above the top of the isomerization barrier, and are delocalized to a varying degree over both local minima. Rotation appears to lower the energy threshold for extensive delocalization; for the states with J=1, or 2, it is ∼460–480 cm^{−1} below that for J=0 states. Moreover, increasing rotational excitation affects significantly the degree of localization of a given state.

Rotational spectrum, structure, and chlorine nuclear quadrupole tensor of the vinyl fluoride–HCl dimer
View Description Hide DescriptionThe ground‐state rotational spectrum of the dimer formed between vinyl fluoride and hydrogen chloride has been detected by using a pulsed‐nozzle Fourier‐transform microwave spectrometer. The rotational constantsA _{0}, B _{0}, and C _{0}; the centrifugal distortion constants Δ_{ J }, Δ_{ J K }, δ_{J} and δ_{ J K }; and the components χ_{ a a }, χ_{ b b }−χ_{ c c }, and χ_{ a b } of the Cl nuclear quadrupole coupling tensor have been determined for each of the three isotopomers CH_{2}CHF⋅⋅⋅H ^{35}Cl, CH_{2}CHF⋅⋅⋅H ^{37}Cl, and CH_{2}CHF⋅⋅⋅D ^{35}Cl. An accidental near degeneracy of the 2_{11} and 3_{03} levels allows an accurate evaluation of the off‐diagonal component χ_{ a b }. Interpretation of the rotational constants establishes a near‐planar geometry for CH_{2}CHF⋅⋅⋅HCl, with HCl forming a hydrogen bond to F and R _{F⋅⋅⋅Cl}=3.382(3) Å. The angle CF⋅⋅⋅H is 116.1(1)° and there is some evidence that the HCl subunit lies slightly out of the plane (φ=8.0±1.5°). Diagonalization of the Cl nuclear quadrupole coupling tensor to give the principal components χ_{ x x }, χ_{ y y }, and χ_{ z z } leads to an angle of 30.8° between the a axis of the dimer and the H–Cl(z) axis. Comparison with the corresponding angle available from the geometry suggests that the z axis may be bent away by ≊10° from the F⋅⋅⋅H line in the F⋅⋅⋅HCl system. The preference for hydrogen‐bond formation to F rather than to the π bond in vinyl fluoride is consistent with the Legon–Millen rules for angular geometries and can also be rationalized by the numerical Buckingham–Fowler model.

A classical theory of pump–probe photodissociation for arbitrary pulse durations
View Description Hide DescriptionThe classical Condon picture for linear absorption spectroscopy is a time‐honored approximation known to give accurate results for broad spectral lines. The generalization of the classical Condon picture to nonlinear spectroscopies, however, is a problem under current investigation. Bersohn and Zewail have proposed a phenomenological formula applicable to the pump–probe photodissociation of iodine cyanide (ICN). We undertake an investigation of classical approximations in pump–probe spectroscopy from first principles. We present a new classical formula for the probe absorption that is derived using the density matrix in phase space and is valid for arbitrary pulse durations. Conditions whereby the signal depends only on field spectral or temporal intensities are specified. The classical formula presented here is compared with exact quantum mechanical calculations of the probe absorption for a simple model of ICN. Our formula shows very good agreement with the quantum calculations. We recover the formula of Bersohn and Zewail in the case of pulses that are very short compared to the time scale of nuclear dynamics.

Two‐photon spectroscopy of Rydberg states of molecular oxygen
View Description Hide DescriptionTwo‐photon resonant, three‐photon ionizationspectrum of O_{2} X ^{3}Σ^{−} _{ g }, v‘=0 is presented in the energy region between the 5s–4d complex and the O^{+} _{2} X ^{2}Π_{1/2g }, v ^{+}=0 ionization threshold. The spectrum exhibits a number of new transitions to n s and n dRydberg states with n=5‐9 and v’=0 and 1 as well as transitions to the previously unobserved 5s–4d, v’=3 levels. For a given value of n and v’, the observed bands split into two groups separated by approximately the O^{+} _{2} X ^{2}Π_{1/2g }−^{2}Π_{3/2g } spin–orbit splitting. All of the bands show at least some sharp rotational structure, although in most cases this structure is limited to a few lines. In addition, the direct two‐photon ionizationspectrum of O_{2} X ^{3}Σ^{−} _{ g }, v‘=0 is presented in the energy region between the O^{+} _{2} X ^{2}Π_{1/2g }, v ^{+}=0 and 1 thresholds; the spectrum shows transitions to Rydberg states with n=8‐12 and v’=1. These states are analogous to the v’=0 states observed below the ionization threshold, and they decay by vibrational autoionization into the v ^{+}=0 continuum. Taken together, the v’=0 and 1 Rydberg states observed here provide a significant addition to the knowledge of Rydberg series converging to the ground electronic state of O^{+} _{2}.

Calculations of vibrational state mixing leading to intramolecular vibrational energy redistribution in S _{1} anthracene: Comparison with quantum beat experiments
View Description Hide DescriptionA simple model for the anharmonic coupling constants has been used to calculate vibrational state mixing in S _{1}anthracene. The aim of the calculations is to provide insight into the vibrational state mixing responsible for intramolecular vibrational energy redistribution (IVR). The calculations include all vibrations of the appropriate symmetry within a 100 cm^{−} ^{1} interval centered about the state of interest. The calculations are compared with experimental measurements of quantum beats in S _{1}anthracene [P. M. Felker and A. H. Zewail, J. Chem. Phys. 8 2, 2975 (1985)]. These experiments involved an investigation of rotational effects that established the coupling to be anharmonic in origin. We show that in order for the experimental data to be explained by anharmonic coupling alone, the high‐order anharmonic terms must be reasonably large. This implies that the anharmonic expansion converges quite slowly for E _{VIB}≲2000 cm^{−} ^{1} in anthracene, in contrast with spectroscopic data for small molecules. Anthracene does not appear to be unique with regard to its IVR behavior, and consequently we suggest that slow convergence of the anharmonic expansion will prove to be the norm for large molecules. As a consequence of the slow convergence, direct coupling through high‐order anharmonic terms is an important coupling mechanism. The model used to determine the anharmonic coupling constants is not specific to anthracene, and it is anticipated that it will be possible to predict vibrational state mixing in other molecules using the parameters deduced for anthracene.

Environmental dependence of preresonance Raman cross‐section dispersions: Benzene vapor‐phase excitation profiles
View Description Hide DescriptionThe vapor‐phase Raman cross‐section excitation profiles of the two totally symmetric modes of benzene have been measured between 514 and 220 nm. At wavelengths longer than 280 nm, the 992 cm^{−1} ν_{1} ring breathing‐mode cross‐section dispersion is not indicative of preresonance enhancement by the dipole‐allowed E _{1u } electronic transition near 185 nm. With excitation wavelengths shorter than 240 nm, however, the ν_{1} mode dispersion is dominated by enhancement from the B _{1u }/E _{1u } state. The ν_{2} 3060 cm^{−1} carbon–hydrogen stretching vibration shows no enhancement by the E _{1u } state in the 514–220 nm spectral region. The cross‐section dispersion is indicative of enhancement by states centered near 100 000 cm^{−1}. We compare the gas‐ and condensed‐phase Raman cross‐section dispersions of benzene, cyclohexane, and acetonitrile. Surprisingly, we do not observe the ‘‘extra’’ dispersion predicted to occur in the condensed phase which derives from the dispersion in the local electromagnetic field strength.

The metastable triplet state of CrO^{2−} _{4} in a calcium sulphate host: Electron‐spin‐echo experiments
View Description Hide DescriptionAn electron paramagnetic resonance(EPR) study with laser flash excitation and electron‐spin‐echo detection is reported on the very weakly luminescent state of the CrO^{2−} _{4} ion in an anhydrite (CaSO_{4}) host. On excitation a lowering of symmetry of the chromate ion occurs, and four sets of congruent excited species are observed, interrelated by the orthorhombic symmetry of the crystal. The results can be fitted to a spin Hamiltonian for an orbitally nondegenerate triplet state with parameters D=−20.337 GHz, E=−0.211 GHz, g _{11}=1.961, g _{22}= 1.989, and g _{33}=1.9817. The relaxation behavior of the triplet state has been studied by varying (1) the delay between the laser flash and the first microwave pulse and (2) the interval τ between the microwave pulses. The lifetimes of the zero‐field spin states are τ_{ x }=2.2, τ_{ y }=0.73, and τ_{ z }=0.023 μs. Because of the very fast decay of the T _{ z } level and attendant very short relaxation timeT _{2} for most orientations of the magnetic field, the four ‘‘allowed’’ stationary EPR transitions in our X‐band experiment could only be observed by using a stripline cavity and reducing τ to less than 100 ns.

Absolute infrared vibrational band intensities of molecular ions determined by direct laser absorption spectroscopy in fast ion beams
View Description Hide DescriptionThe technique of direct laser absorption spectroscopy in fast ion beams has been employed for the determination of absolute integrated band intensities (S ^{0} _{ v }) for the ν_{3} fundamental bands of H_{3}O^{+} and NH^{+} _{4}. In addition, the absolute band intensities for the ν_{1} fundamental bands of HN^{+} _{2} and HCO^{+} have been remeasured. The values obtained in units of cm^{−2} atm^{−1} at STP are 1880(290) and 580(90) for the ν_{1} fundamentals of HN^{+} _{2} and HCO^{+}, respectively; and 4000(800) and 1220(190) for the ν_{3} fundamentals of H_{3}O^{+} and NH^{+} _{4}, respectively. Comparisons with a b i n i t i o results are presented.

Electron mobilities in low density helium and nitrogen gases: Momentum transfer cross sections at very low energies
View Description Hide DescriptionElectron mobilities have been measured in low density helium and nitrogen gases as reference standards in the ongoing study of effects of molecular shape and density on electron transport in fluids. Wider temperature ranges were used than heretofore. Electron mobilities in helium gas at temperatures T=11–466 K and densities n=4.9–7.3 (10^{25} molec/m^{3}) are consistent with previously reported scattering cross sections. The value of σ_{ m } at 10^{−23} J (10^{−4} eV) is 4.9×10^{−20} m^{2}, corresponding to a scattering length of 6.2×10^{−11} m. Density normalized mobilitiesnμ in nitrogen gas at T=66–460 K and n=0.9–6.7 (10^{25} molec/m^{3}) decrease with increasing density. Values of nμ extrapolated to low field strengths and zero density gave values which were used to estimate momentum transfer cross sections. Further study of electron scattering by nitrogen at energies <3×10^{−21} J (20 meV) is desired.

Influence of radiative transport on energy transfer
View Description Hide DescriptionA model describing the radiative processes occurring in concentrated solutions of a donor able to transfer its electronic energy to an acceptor is presented. It was found that both radiative transport over donors and transfer to the acceptor modify the decay curves of the donor, the effect being more pronounced at low acceptor concentrations owing to a small absorption of the donor emission by the acceptor and an inefficient donor–acceptor nonradiative energy transfer process. Fitting or decay curves influenced by radiative transport can lead to incorrect evaluation of nonradiative energy transfer parameters if the radiative processes are not accounted for. The true nonradiative parameters can be evaluated using the theoretical decay law predicted by the model.

Dissociative excitation of GeH_{4} by collisions with Ar and He active species
View Description Hide DescriptionThe product channels in reactions of metastable Ar(^{3} P _{2}) and He(2^{3} S) atoms and Ar^{+}, (Ar^{+})*, He^{+}, and He^{+} _{2}ions with GeH_{4} have been studied by observing emission spectra in the flowing afterglow and beam apparatus. H*, Ge*, GeH(A ^{2}Δ–X ^{2}Π), and GeH^{+}(a ^{3}Π_{0+,1}–X ^{1}Σ^{+}) emissions were observed in the 190–600 nm region. The effect of SF_{6} addition into the discharge flow indicated that secondary electron‐ion recombination processes participate in the formation of Ge* and GeH(A) in the Ar and He afterglows. The formation of Ge* through the Ar^{+}/GeH_{4}reaction followed by electron‐ion recombination processes was confirmed by simultaneous formation of Ar^{+} and low‐energy electrons through the He(2 ^{3} S)/Ar Penning ionization. The total emission rate constants were determined to be 8.6 and 0.15×10^{−12} cm^{3} s^{−1} for Ge* and GeH(A) in the Ar(^{3} P _{2})/GeH_{4}reaction, and 0.068 and 5.8×10^{−12} cm^{3} s^{−1} and for H* and Ge* in the He(2 ^{3} S)/GeH_{4}reaction, respectively.

Relaxation of conformers and isomers in seeded supersonic jets of inert gases
View Description Hide DescriptionWe have studied the relaxation of conformers and the formation/relaxation of isomeric, weakly bonded dimers in pulsed supersonic expansions of seeded inert gases (He, Ne, Ar, Kr). The relaxation was determined from the intensity of a rotational transition for the higher energy species as a function of carrier gas composition, using the Balle/Flygare Fourier transformmicrowave spectrometer. Of thirteen molecules with rotational conformers which we examined, those with barriers to internal rotation greater than 400 cm^{−1} did not relax significantly in any of the carriers. The higher energy forms of ethyl formate, ethanol, and isopropanol, with smaller barriers, were not relaxed by He; those of ethanol and isopropanol were somewhat relaxed by Ne; and all were completely relaxed by as little as 5 to 20 mole percent of Ar or Kr in He or Ne. The relaxation in He or Ne is first order in the concentration of added Ne, Ar, or Kr as well as in the concentration of the high energy conformer. The pseudo first‐order rate constants (larger in Ne than in He) increase sharply with Z of the rare gas, roughly in a 0:1:2:4 progression for He, Ne, Ar, and Kr, suggesting that the relaxation involves relatively long‐range polarization effects. Similar behavior was found in the formation/relaxation of the weakly bonded dimer pairs: linear OCO–HCN, T‐shaped HCN–CO_{2}; linear FH–NNO and bent NNO–HF; and bent HF–DF and DF–HF. The case of the HCN/CO_{2} dimers is particularly striking. The T‐shaped dimer was found first, using Ar as the carrier gas. Five years later the linear form was found with first run neon as carrier, but it could not be detected at all with Ar as the carrier. These results show that in favorable cases high energy species can be studied in supersonic expansions by freezing out a ‘‘high‐temperature’’ concentration with a nonrelaxing carrier gas.

Temperature dependence of vibrational relaxation in the very‐low‐energy collision regime: The ground electronic state of p‐difluorobenzene prepared by stimulated emission pumping
View Description Hide DescriptionStimulated emission pumping is used to selectively populate the υ^{‘} _{3}=1 vibrational level (ε_{vib}=1258 cm^{−1}) in the S _{0} state of p‐difluorobenzene cooled in a supersonic free‐jet expansion of argon. The time‐dependent population of the υ^{‘} _{3}=1 level, as it is depleted by collisions with the argon carrier gas, is probed using single vibronic level fluorescence. By varying the point along the expansion axis (X/D) at which state preparation and population probing are carried out, the rate coefficient for vibrational relaxation of the 3_{1} state is measured as a function of temperature in the range 1–12 K. The temperature dependence of the rate coefficient is compared with the temperature dependence of hard‐sphere (HS) and Lennard‐Jones (LJ) elastic encounter rates. Comparison with data for the same collision system (p‐difluorobenzene–Ar) at room temperature in both the S _{1} and S _{0} electronic states suggests that the temperature dependence of the Lennard‐Jones elastic rate provides a useful means of scaling the temperature dependence of polyatomic vibrational relaxation over a wide range of temperatures, i.e., from 300 K down to near absolute zero.

Energy transfer and reaction dynamics of matrix‐isolated 1,2‐difluoroethane‐d _{4}
View Description Hide DescriptionThe molecular dynamics of vibrationally excited 1,2‐difluoroethane‐d _{4} isolated in Ar, Kr, and Xe matrices at 12 K are investigated using trajectory methods. The matrix model is an fcc crystal containing 125 unit cells with 666 atoms in a cubic (5×5×5) arrangement. It is assumed that 1,2‐difluoroethane‐d _{4} is held interstitially within the volume bounded by the innermost unit cell of the crystal. The transport effects of the bulk are simulated using the velocity reset method introduced by Riley, Coltrin, and Diestler [J. Chem. Phys. 8 8, 5934 (1988)]. The system potential is written as the separable sum of a lattice potential, a lattice–molecule interaction and a gas‐phase potential for 1,2‐difluoroethane. The first two of these are assumed to have pairwise form while the molecular potential is a modified form of the global potential previously developed for 1,2‐difluoroethane [J. Phys. Chem. 9 1, 3266 (1987)]. Calculated sublimationenergies for the pure crystals are in good accord with the experimental data.
The distribution of metastable‐state energies for matrix‐isolated 1,2‐difluoroethane‐d _{4} is Gaussian in form. In krypton, the full width at half maximum for the distribution is 0.37 eV. For a total excitation energy of 6.314 eV, the observed dynamic processes are vibrational relaxation, orientational exchange, and four‐center DF elimination reactions. The first of these processes is characterized by a near linear, first‐order decay curve with rate coefficients in the range 1.30–1.48×10^{11} s^{−1}. The average rates in krypton and xenon are nearly equal. The process is slightly slower in argon. The decay curves exhibit characteristic high‐frequency oscillations that are generally seen in energy transfer studies. It is demonstrated that these oscillations are associated with the frequencies for intramolecular energy transfer so that the entire frequency spectrum for such transfer processes can be obtained from the Fourier transform of the decay curve. Orientational exchange is shown to occur with much greater frequency as the unit cell spacing decreases. The occurrence of orientational exchange generally results in a very rapid dissipation of molecular rotational energy to the lattice which causes a characteristic break to occur in the decay curve. It is shown that 16% of the total energy transfer to the lattice in argon is a result of such rotational energy transfer. The propensity for four‐center DF elimination is found to be greater in argon than in either krypton or xenon. The relaxation data show that this effect is not the result of different energy transfer rates but is probably associated with steric effects resulting from the smaller lattice dimensions in argon. Isotope effects upon the energy partitioning in unimolecular reactions of 1,2‐difluoroethane and upon the energy transfer dynamics under matrix‐isolation conditions are also reported.