Index of content:
Volume 103, Issue 8, 22 August 1995

The lattice dynamics of β‐hydroquinone clathrate
View Description Hide DescriptionDynamic properties of β‐hydroquinone (Q _{β}) clathrate with various guest molecules have been calculated by the method of lattice dynamics within the atom–atom potential approximation; van der Waals interactions, H‐bond interactions, and electrostatic interactions for charges localized on the atoms are included. External vibration spectra have been calculated for the empty framework of Q _{β} and with different guest molecules (HCN, CO_{2}, SO_{2}, C_{2}N_{2}, C_{2}H_{6}, CH_{3}OH, O_{2}CO). Vibrational frequencies of the guest molecules in cavities are determined. The phonondensity of states for these compounds has been calculated. The influence of the encaged guest molecules on the vibrational spectrum of the host lattice has been investigated. The most visible changes are observed upon the insertion of guest molecules with large dipole moment or those positioned asymmetrically inside the Q _{β}clathrate cages. Peculiarities of different interactions have been revealed. Analysis of the calculated and experimental results have been carried out.

Experimental and theoretical study of the B–Ne nonbonding interaction: The free‐bound B ^{2}Σ^{+}–X ^{2}Π electronic transition
View Description Hide DescriptionWe report a new investigation of the interaction between atomic boron, in both the ground 2p ^{2} P and excited 3s ^{2} S electronic states, with Ne. BNe complexes are formed in a pulsed free jet expansion and detected by laser fluorescence excitation. A broad, asymmetric feature is seen, with maximum intensity ∼270 cm^{−1} to the blue of the 3s ^{2} S–2p ^{2} P _{ J } atomic transition. This feature corresponds to electronic excitation from the ground vibrational level of the BNe(X ^{2}Π_{1/2}) state into the BNe(B ^{2}Σ^{+}) state, which is unbound. High level ab initio configuration–interaction calculations, involving large atomic orbital bases, were carried out to describe the relevant potentials. The potential curve for the B state reveals a broad shoulder, but no well. The calculated potential curves are corrected, very slightly, by an additional scaling of the correlation energy. Spectral simulations based on these corrected curves reproduce, nearly quantitatively, the experimental spectrum.

Quantum and classical dynamics of a methyl group with tunneling frequency 3.4 MHz studied by low field NMR
View Description Hide DescriptionNuclear magnetic resonance(NMR) investigations of methyl tunneling in 2,5‐dimethyl‐1,3,4‐thiadiazole are reported. The tunneling frequency (ν_{ t } = 3.39 MHz) was obtained using low field NMR spectroscopy. By means of rapid field cycling irradiation and relaxation measurements the probabilities of the absorption transitions, responsible for the spectral lines in the low field NMRspectra, can be quantified. The results obtained agree well with the calculated probabilities of rf induced transitions between the eigenstates of a methyl rotor with ν_{ t } = 3.39 MHz. Measurements of the temperature dependence of ν_{ t }, the spin conversion time τ_{con} and an analysis of the proton spin lattice relaxation timeT _{1}, the latter two revealing the correlation time τ_{ c }, enabled the study of the methyl group dynamics over a temperature range encompassing both the quantum mechanical and the classical regimes. The dynamical data can be explained well with a threefold hindering barrier of height V _{3}/k _{ B } = 1175 K and are compared with existing theoretical models.

Coupling of electrons to intermolecular phonons in molecular charge transfer dimers: A resonance Raman study
View Description Hide DescriptionWe report resonanceRaman scattering (RRS) spectra and Raman excitation profiles (REP) of a system containing π dimers of identical molecular radical ions measured with laser excitation in resonance with the charge transfer(CT) transition. A Peierls–Hubbard (PH) Hamiltonian has been used to model the investigated system and to calculate its optical and RRS properties. Results are reported for two polyoxometallate salts of tetrathiafulvalene (TTF), namely (TTF)_{2}(W_{6}O_{19}) and (TTF)_{2}(Mo_{6}O_{19}) whose structures contain almost isolated (TTF^{+})_{2} dimers. The RRS spectra of (TTF)_{2}(W_{6}O_{19}), measured in resonance with the CT absorption band centered at 832 nm, show three phonon modes located at 55, 90, and 116 cm^{−1} which are strongly resonance enhanced. These modes have been associated to the out‐of‐phase combinations of the translational motions of the two molecules composing the dimer. Such modes are effective in modulating the intradimer transfer integral, thus providing an efficient mechanism for coupling with the electronic system and for enhancement of the scattering intensity at resonance with the CT transition. The REP for the three strongly coupled modes of (TTF)_{2}(W_{6}O_{19}) have been measured with laser excitation wavelengths ranging from 740 to 930 nm. Quantitative analysis of the REP data has been performed based on a perturbative solution of the PH model to second order in the electron‐molecular‐vibration (EMV) and electron‐intermolecular‐phonon (EIP) interactions. The CT absorption profile and the REP’s have been calculated using a time correlator technique and the model parameters have been optimized in order to fit the experimental REP data. Infrared vibronic absorptions of (TTF)_{2}(W_{6}O_{19}), originated by the EMV coupling, have been measured and independent information on the electronic parameters of the PH model have been derived. This has made the choice of the fitting parameters used for the REP calculations rather unambiguous and has allowed us to obtain, for the first time, reliable experimental estimates of the EIP coupling constants.

Homogeneous vibrational dynamics and inhomogeneous broadening in glass‐forming liquids: Infrared photon echo experiments from room temperature to 10 K
View Description Hide DescriptionA study of the temperature dependence of the homogeneous linewidth and inhomogeneous broadening of a high‐frequency vibrational transition of a polyatomic molecule in three molecular glass‐forming liquids is presented. Picosecond infrared photon echo and pump–probe experiments were used to examine the dynamics that give rise to the vibrational line shape. The homogeneous vibrational linewidth of the asymmetric CO stretch of tungsten hexacarbonyl (∼1980 cm^{−1}) was measured in 2‐methylpentane, 2‐methyltetrahydrofuran, and dibutylphthalate from 300 K, through the supercooled liquids and glass transitions, to 10 K. The temperature dependences of the homogeneous linewidths in the three glasses are all well described by a T ^{2} power law. The absorption linewidths for all glasses are seen to be massively inhomogeneously broadened at low temperature. In the room temperature liquids, while the vibrational line in 2‐methylpentane is homogeneously broadened, the line in dibutylphthalate is still extensively inhomogeneously broadened. The contributions of vibrational pure dephasing, orientational diffusion, and population lifetime to the homogeneous line shape are examined in detail in the 2‐methylpentane solvent. The complete temperature dependence of each of the contributions is determined. For this system, the vibrational line varies from inhomogeneously broadened in the glass and low temperature liquid to homogeneously broadened in the room temperature liquid. The homogeneous linewidth is dominated by the vibrational lifetime at low temperatures and by pure dephasing in the liquid. The orientational relaxation contribution to the line is significant at some temperatures but never dominant. Restricted orientational relaxation at temperatures below ∼120 K causes the homogeneous line shape to deviate from Lorentzian, while at higher temperatures the line shape is Lorentzian.

Rotational spectra of the mixed rare gas dimers Ne–Kr and Ar–Kr
View Description Hide DescriptionPure rotational spectra of several isotopomeric species of the rare gas dimers Ne–Kr and Ar–Kr have been measured using a pulsed jet cavity microwaveFourier transformspectrometer. Equilibrium internuclear distances have been evaluated by taking advantage of the isotopic data, for both these dimers and three Xe‐containing dimers, whose spectra were reported earlier [Jäger et al., J. Chem. Phys. 99, 919 (1993)]. The dipole moments have been estimated using the ‘‘π/2‐pulse’’ excitation condition. ^{83}Kr nuclear quadrupolehyperfine structure has been observed in some rotational transitions of ^{20}Ne–^{83}Kr and of Ar–^{83}Kr, and the corresponding quadrupole coupling constants have been derived.

Theoretical study of Fermi resonance in the vibrational spectrum of HO_{2}
View Description Hide DescriptionFermi resonance complicates the vibrational spectrum of the hydroperoxyl radical, HO_{2}. Using a recent three‐dimensional potential energy surface, we calculate vibrational wave functions for H–^{16}O–^{16}O and H–^{18}O–^{18}O. We identify low‐lying Fermi resonant pairs and determine the degree of coupling by constructing linear combinations of these Fermi resonantwave functions. The coefficients are systematically varied to find the linear combination which, through visual inspection, replicates the nodal patterns of ‘‘pure’’ vibrational wave functions. The energies of the pure vibrational levels and the Fermi resonance shifts are also calculated.

The structure, spectroscopy, and excited state predissociation dynamics of GeH_{2}
View Description Hide DescriptionThe spectroscopy and excited state dynamics of Ã ^{1} B _{1} germylene (GeH_{2}) have been investigated experimentally and theoretically. Jet‐cooled laser‐induced fluorescence spectra of GeH_{2} were obtained by subjecting germane (GeH_{4}) to an electric discharge at the exit of a pulsed nozzle. The band origins of ten vibronic transitions were determined, giving values for the upper state fundamentals of ν_{1}=783.0 cm^{−1} and ν_{2}=1798.4 cm^{−1}. Sufficient numbers of 0^{0} _{0} band rovibronic transitions were observed to give the ground and excited state structures as r″=1.591(7) Å, θ″=91.2(8)° and r′=1.553(12) Å, θ′=123.4(19)°. Fluorescence lifetime measurements show that the 0_{0,0} rotational levels decay radiatively; higher J rotational states in the 0^{0} vibronic level decay much faster, due to a heterogeneous predissociation in the excited state. High quality ab initio studies are consistent with a model in which the lower vibronic levels of the Ã state predissociate through the ã ^{3} B _{1} state to produce Ge(^{3} P)+H_{2}(^{1}Σ^{+} _{ g }). The transition state for this process has been located and the barrier to dissociation is 15.2 kcal/mol above the Ã ^{1} B _{1} state, so that tunneling through the barrier must occur. Above 4000 cm^{−1} of vibrational energy in the Ã state, a breaking off of fluorescence is observed as a second predissociation channel involving GeH_{2}(Ã ^{1} B _{1})→Ge(^{1} D)+H_{2}(^{1}Σ^{+} _{ g }) becomes accessible. This process is also found to have a barrier, in contrast to previous theoretical studies of SiH_{2}, where the analogous dissociation was predicted to be barrierless.

Isomeric structures of the electronically excited acetylene⋅Ar complex: Spectroscopy and potential calculations
View Description Hide DescriptionAcetylene⋅Ar complex in the S _{1} state has been characterized through laser fluorescence excitation spectra in the acetylene Ã←X̃, 3^{ n } _{0} (n=0–4) bands region. Two isomeric structures have been determined for the acetylene(Ã)⋅Ar complex from rotational band analysis, even though only one structure was known to exist for the ground state acetylene(X̃)⋅Ar. The in‐plane isomer has the Ar atom situated in the molecular plane of the trans‐bent acetylene, 3.77 Å from the acetylene center of mass and tilted from the H atoms. The out‐of‐plane isomeric structure, directly inverted from the rotational constants, has argon 3.76 Å away from the acetylene center of mass and 18° tilted from the C _{2} rotational axis. This structure is most likely due to large amplitude bending motions away from the equilibrium position which is along the C _{2} axis. Axis switching effect in the rotational band analysis for both isomers has been examined and found to be negligible. (Formulas for calculating the three‐dimensional axis switching angles are detailed in the Appendix.) Three van der Waals vibrational mode frequencies have been determined from the vibrational progressions in the spectra; the stretching fundamental of the out‐of‐plane isomer is 28 cm^{−1}; the in‐plane bending fundamental, and the out‐of‐plane bending first overtone of the in‐plane isomer are 11 and 17 cm^{−1}, respectively.
The isomeric structures have been compared with the results from a pairwise‐atom potential calculation with parameters transferred from the ones previously derived for C_{2}H_{4}⋅Ar potential calculations. It was found that when the set of parameters that most closely reflects the electronic density distribution in C_{2}H_{2}(Ã) orbitals was used, two potential minima mimicking the two isomeric structures were generated. This potential calculation can even qualitatively reproduce the complex spectral shift induced by the ν_{3} mode excitation in acetylene. Combining the observed spectral shifts and previous experimental and theoretical studies of acetylene(X̃)⋅Ar, we have estimated the binding energy of the out‐of‐plane C_{2}H_{2}(Ã)⋅Ar isomer to be 179 cm^{−1}, and that of the in‐plane isomer to be 170 cm^{−1}.

Direct measurement of the transition dipole moment of the v _{3} asymmetric C–H stretching vibration of the CH_{3} radical
View Description Hide DescriptionA direct measurement of the transitiondipole moment, μ_{3}, of the degenerate v _{3} in‐plane asymmetric C–H stretching vibration of the methyl radical has been made. The measurements were carried out in a flow reactor using laser‐photolysis transient infrared absorption spectroscopy. Cyano (CN) radicals (and Cl atoms) were produced by laser photolysis of BrCN (or ClCN) at 193 nm and reacted with methane to give both CH_{3} and HCN (and HCl). The intensities of 18 rotational lines of the v _{3} fundamental band were measured relative to the R(8) line of the C–H stretching vibration (v _{3}) of HCN(001←0). The best estimate of the transitiondipole moment of the CH_{3} (001^{1}0←0) transition was provided by the measured line intensity for the CH_{3} (001^{1}0←0)^{ rR }(3,3) transition and was determined to be μ_{3}=0.0327±0.0021 D.

Electron spin resonance line shapes for one‐ and two‐dimensional random walk processes
View Description Hide DescriptionOne‐ and two‐dimensional random walk processes and their effects on EPR (electron spin paramagneticresonance) line shapes are examined. Discrepancies between the coarse continuum model and the discrete hopping model are discussed. Closed‐form formulas are prescribed for the distribution function,correlation (memory) function and the EPR line shapes, covering the entire range between the slow and the fast hopping limits. Deviation from Gaussian or Lorentzian line shape is shown for intermediate hopping rates. Differences between the cases of a closed loop and an open chain are illustrated. Time‐domain analysis of line shape measurements can provide information about the hopping rate constants, site numbers in an open or closed chain, and the activation energy.

Ion‐pair formation in the photodissociation of HF and DF
View Description Hide DescriptionThe excitation functions for ion‐pair formation in supersonically cooled HF and DF have been measured using synchrotron radiation with photon resolutions of 0.12 and 0.06 nm. The excitation functions for both molecules are characterized by an intense, sharp peak, essentially coincident with the thermodynamic onset for ion‐pair formation, followed by weaker, broader structure to higher energy. All of the structure is interpreted as arising from the photoexcitation of Rydberg states of the neutral molecules that are predissociated by the V ^{1}Σ^{+} ion‐pair state potential. Ab initio calculations using multichannel quantum defect theory to include both predissociation and autoionization enabled assignments of the observed structure to be made and the construction of simulated ion‐pair excitation function spectra in an energy region encompassing ∼0.25 eV of the lowest energy part of the experimental excitation functions. The intense first peak in the ion‐pair excitation function of both molecules is assigned to a high vibrational level of the 3sσ Rydberg state converging to the A ^{2}Σ^{+} ion state, while most of the structure immediately following the first peak is assigned to dRydberg complexes converging to the v ^{+}=1 level of both X ^{2}Π ion substates.

A semiclassical self‐consistent‐field approach to dissipative dynamics. II. Internal conversion processes
View Description Hide DescriptionA semiclassical time‐dependent self‐consistent‐field (TDSCF) formulation is developed for the description of internal conversion (IC) processes in polyatomic molecules. The total density operator is approximated by a semiclassical ansatz, which couples the electronic degrees of freedom to the nuclear degrees of freedom in a self‐consistent manner, whereby the vibrational density operator is described in terms of Gaussian wave packets. The resulting TDSCF formulation represents a generalization of familiar classical‐path theories, and is particularly useful to make contact to quantum‐mechanical formulations. To avoid problems associated with spurious phase factors, we assume rapid randomization of the nuclear phases and a single vibrational density operator for all electronic states. Classically, the latter approximation corresponds to a single trajectory propagating along a ‘‘mean path’’ instead of several state‐specific trajectories, which may become a critical assumption for the description of IC processes. The validity and the limitations of the mean‐path approximation are discussed in detail, including both theoretical as well as numerical studies. It is shown that for constant diabatic coupling elements V _{ kk }′ the mean‐path approximation should be appropriate in many cases, whereas in the case of coordinate‐dependent coupling V _{ kk }′(x) the approximation is found to lead to an underestimation of the overall relaxation rate.
As a remedy for this inadequacy of the mean‐path approximation, we employ dynamical corrections to the off‐diagonal elements of the electronic density operator, as has been suggested by Meyer and Miller [J. Chem. Phys. 70, 3214 (1979)]. We present detailed numerical studies, adopting (i) a two‐state three‐mode model of the S _{1}−S _{2} conical intersection in pyrazine, and (ii) a three‐state five‐mode and a five‐state sixteen‐mode model of the C̃→B̃→X̃ IC process in the benzene cation. The comparison with exact basis‐set calculations for the two smaller model systems and the possible predictions for larger systems demonstrate the capability of the semiclassical model for the description of ultrafast IC processes.

A simple recursion polynomial expansion of the Green’s function with absorbing boundary conditions. Application to the reactive scattering
View Description Hide DescriptionThe new recently introduced [J. Chem. Phys 102, 7390 (1995)] empirical recursion formula for the scattering solution is here proved to yield an exact polynomial expansion of the operator [E−(Ĥ+Γ̂)]^{−1}, Γ̂ being a simple complex optical potential. The expansion is energy separable and converges uniformly in the real energy domain. The scaling of the Hamiltonian is trivial and does not involve complex analysis. Formal use of the energy‐to‐time Fourier transform of the ABC (absorbing boundary conditions)Green’s function leads to a recursion polynomial expansion of the ABC time evolution operator that is global in time. Results at any energy and any time can be accumulated simultaneously from a single iterative procedure; no actual Fourier transform is needed since the expansion coefficients are known analytically. The approach can be also used to obtain a perturbation series for the Green’s function. The new iterative methods should be of a great use in the area of the reactive scattering calculations and other related fields.

Manipulating reactant–product distributions in electron transfer reactions with a laser field
View Description Hide DescriptionThe effect of a strong cw laser field on the process of nonadiabaticelectron transfer in polar solvents is considered. First‐order kinetic equations are derived in which the forward and backward rate constants depend on the electric field parameters. The forward rate constant, which governs the early time dynamics, exhibits dramatic variation with field intensity in the barrierless and activationless regimes. The sum of forward and backward rate constants, which determines the long time kinetics and hence may be termed the full rate constant, is less sensitive to the field intensity in the same regime of molecular parameter space. It is shown that the asymptotic populations of the reactant and product states are in general non‐Boltzmann; their ratio can be varied by many orders of magnitude as the frequency and intensity of the applied electric field are varied.

Canonical flexible transition state theory revisited
View Description Hide DescriptionA simple formula for the canonical flexible transition state theory expression for the thermal reaction rate constant is derived that is exact in the limit of the reaction path being well approximated by the distance between the centers of mass of the reactants. This formula evaluates classically the contribution to the rate constant from transitional degrees of freedom (those that evolve from free rotations in the limit of infinite separation of the reactants). As a result of this treatment, the formula contains the product of two factors: one that exclusively depends on the collision kinematics and one that exclusively depends on the potential energy surface that controls the transitional degrees of freedom. This second factor smoothly varies, in the classical limit, from harmonic oscillator to hindered rotor to free rotor partition functions as the potential energy surface varies from quadratic to sinusoidal to a constant in its dependence on the relative orientation angles of the fragments. An application to the recombination of CH_{3}+H essentially demonstrates exact agreement with a previous flexible transition state theory study in which all integrals are carried out numerically. The simple formulas presented in this paper allow the classical inclusion of large amplitude motion of arbitrary complexity in the determination of the canonical rate constant for reactions whose reaction path is dominated by the distance between the centers of mass of the reactants.

The classical statistical theory of three‐atom reactions governed by short‐range forces: Energy transfers and recoil energy distribution
View Description Hide DescriptionWhen the nascent products of a three‐atom reaction governed by chemical forces separate, energy transfers may occur between vibrational, rotational, and translational motions. In the first part of the paper, we show from quasiclassical trajectory calculations on a modelpotential energy surface that (a) the vibrational energy is adiabatic on average as usually assumed in statistical theories, (b) rotational‐translational energy transfer mainly favors translational motion (as was initially suggested by Marcus), but that (c) this transfer is inefficient when the product atom is sufficiently light with respect to the other two. A qualitative analysis of these findings is proposed based on arguments differing from those of Marcus, and Quack and Troe. In the second part of the paper, we extend the classical statistical formalism proposed recently by ourselves, initially limited to reactions governed by long‐range forces, to the present more general case of reactions involving tight transition states and for which energy transfers are inefficient. In such a case, energy distributions at the exit transition state and in the products are the same. We focus our developments on the recoil energy distribution. Agreement between our theoretical result and the quasiclassical trajectory approach is shown to be very satisfactory.

Selective efficiency of vibrational excitations in ion–molecule collisions: A comparison of behavior for H^{+}–H_{2} and H^{−}–H_{2}
View Description Hide DescriptionThe vibrational excitation processes which occur in molecular beam experiments on H_{2} molecules, and using H^{+} or H^{−} as projectiles, are discussed from the theoretical viewpoint of the microscopic quantum dynamics and in relation to the various features of the two potential energy surfaces. The present study employs the vibrational close‐coupling–rotational infinite‐order sudden (VCC–RIOS) decoupling scheme and analyzes in detail the differences of behavior of the various inelastic differential cross sections in the small‐angle region. It is clearly found that two separate mechanisms can be invoked in the two systems to explain the differences in efficiency between the two excitation processes. Such mechanisms can be related in turn to specific features of the two potential energy surfaces and to their bearing on the final dynamical observables. Rather good agreement between calculated and observed cross sections is found for both systems.

High pressure range of the addition of HO to HO, NO, NO_{2}, and CO. I. Saturated laser induced fluorescence measurements at 298 K
View Description Hide DescriptionSaturated laser induced fluorescence is used for the sensitive detection of radicals in high pressure gases. The method and its application to a series of addition reactions of HO radicals in the high pressure regime are described. Experiments between 1 and 150 bar of the bath gas He allow for falloff extrapolations to the high pressure limit of the recombination reactions. Limiting rate constants (in cm^{3} molecule^{−1} s^{−1}) of 2.2×10^{−11} for HO+HO→H_{2}O_{2}, of 3.3×10^{−11} for HO+NO→HONO, of 7.5×10^{−11} for HO+NO_{2}→HONO_{2}, and of 9.7×10^{−13} for HO+CO→HOCO (and H+CO_{2}) are derived at 298 K.

High pressure studies of the acridine/fluorene photoreaction: Vibration assisted tunneling
View Description Hide DescriptionWe report a multifaceted investigation of the hydrogen transfer photoreaction in acridine‐doped fluorene crystals at higher temperature. The purpose is to elucidate the role of vibrationally assisted tunneling in this reaction system. Raman experiments were conducted at various pressures and 77 K to document the change of vibrational frequency for the promoting mode(s). Upon compression, a line with a large pressure coefficient emerges from under the strong phonon mode at 96.5 cm^{−1}. Through polarization studies under pressure, we have identified it as a molecular butterfly mode of B _{1} symmetry. We have measured the reaction rate at 150 K in order to examine the effect of a suggested promoting mode at ∼440 cm^{−1}. The reaction rate again increases exponentially with pressure, but with a significantly higher pressure coefficient than that at 1.4 and 77 K. Mode patterns based on a recently published [J. Phys. Chem. 98, 12 223 (1994)] normal coordinate analysis of fluorene are used to help establish the promoting modes for this reaction. This consideration suggests that the 95 and 238 cm^{−1} modes are likely promoting modes in addition to the 125 cm^{−1} libration. A computation of the Franck–Condon factor for the H‐transfer process indicates that a small population of a high overtone of a promoting mode may make a disproportionally large contribution to the reaction rate. This calculation fails to account for the greater pressure coefficient of the reaction rate at higher temperature. Instead, such an increase may come partly from a greater compressibility at higher temperature.