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Volume 103, Issue 23, 15 December 1995

Line coupling effects in anisotropic Raman Q branches of the ν_{1}/2ν_{2} Fermi dyad in CO_{2}
View Description Hide DescriptionThe generalized energy corrected sudden model is used to calculate the Q branch of the anisotropic coherent anti‐Stokes Raman scatteringspectra corresponding to the ν_{1} and 2ν_{2} transitions of the Fermi dyad of CO_{2}. The corresponding experimental spectra have been recorded for pressures leading to a consistent overlapping between the rotational components. This leads to a new experimental evaluation of the relaxation time of the second‐order tensor associated with the rotational angular momentum. The value is in excellent agreement with that already obtained from the study of the infrared absorption Q branch, the Rayleigh scattering, and the viscomagnetic effect.

The complex mechanical modulus as a structural probe: The case of alkali borate liquids and glasses
View Description Hide DescriptionBrillouinlight scattering has been used to determine the high‐frequency complex mechanical modulus of alkali borate liquids and glasses, as a function of the temperature. The temperature dependence of the complex modulus can be described by an enhanced Maxwellmodel for linear viscoelastic systems. Accordingly, the module comprises relaxational components and a temperature dependent staticmodulus, which is determined by the equilibrium volume fraction of kinetically arrested domains. Application of this model to the Brillouin data indicates that the structural relaxations in undercooled glass forming liquids occur via relatively distinct mechanisms, each one becoming thermally activated within a different temperature range. The rate of degradation of the network structure increases with increasing alkali content, and is commensurate of the fragility of the liquid. The structural features which are subject to a change in the context of a particular degradation mechanism are released sequentially, i.e., relaxation, facilitated by the rupture of a given network link, is required before other links of the same type become affected by thermal motion. Mechanisms that are activated at high temperatures involve the diffusional displacements of various atomic species. Immediately above T _{ g }, however, structural relaxations are characterized by the dominance of the bulk viscosity over the shear viscosity, and by positive values of the imaginary part of the complex Poisson ratio. This indicates that, to a significant degree, compressive deformations and head‐on collisions between structural moieties are involved in the structural relaxations at these low temperatures. It is surmised that the deformation of boroxol rings, where a boron moves out of the BO_{3} plane to exchange one of its oxygen neighbors, is underlying to this relaxation mechanism, which results in an increase of the average network ring size.

Intermolecular vibrations of the phenol dimer revealed by spectral hole burning and dispersed fluorescence spectroscopy
View Description Hide DescriptionInter‐ and intramolecular vibrations of the Phenol dimer have been examined using spectralhole burning and dispersed fluorescence spectroscopy. The dispersed fluorescence spectra have been recorded via excitation of the electronic donor origin and all intermolecular vibrational transitions. The Franck–Condon intensity pattern allowed a straightforward assignment of the ground state vibrational frequencies to the excited state frequencies, which were examined by hole‐burning spectroscopy. The existence of another conformer that possibly absorbs in the region of interest was ruled out by hole‐burning spectroscopy. For obtaining the hole‐burning spectra, the electronic origin of the donor chromophore was analyzed, while the hole‐burning laser was scanned over the region of interest. As both acceptor and donor part belong to one molecule the hole‐burning signal could be analyzed via fluorescence from one of the chromophores.

Magnetic‐field induced N_{2}(B→A) emission from a beam of metastable nitrogen molecules and precise term energy of the N_{2}(A′ ^{5}Σ^{+} _{ g }) state
View Description Hide DescriptionMagnetic field anticrossing measurements have been made in order to identify unambiguously the N_{2}(A′ ^{5}Σ^{+} _{ g }) level responsible for the recently observed perturbation of the N_{2}(B ^{3}Π_{ g }, v=10, ^{3}Π^{ e } _{2}(12)) level [Ch. Ottinger and A. F. Vilesov, J. Chem. Phys. 100, 4862 (1994)]. When a weak magnetic field (H=0–3000 G) was applied across the N_{2} metastable beam, new field‐induced perturbations were observed in B,v=11, which were ascribed to interactions with A′, v=2. This multiple perturbation pattern permits a determination of the relative energy of the A′ and B states with a precision of 0.02 cm^{−1}.

Solvent effects on first‐order molecular hyperpolarizability: A study based on vibrational observables
View Description Hide DescriptionUsing a recently developed method, we show here that solvent effects on the first molecular hyperpolarizabilities of push‐pull polyenes can be predicted by evaluation of the relaxation contribution β^{ r } to the hyperpolarizability from vibrational infrared and Raman intensities and vibrational frequencies. The molecules studied in this work are a few organic polymethine dyes with different donor and acceptor groups. The analysis of their vibrational spectra confirms the key role played by the structural parameters of the polyene chain in determining the nonlinear optical response.

Detection of CH in an oxyacetylene flame using two‐color resonant four‐wave mixing technique
View Description Hide DescriptionCH free radicals in an oxyacetylene flame at atmospheric pressure were detected by means of the two‐color resonant four‐wave mixing technique. Ground‐state grating schemes with ω_{1}=ω_{2} (pump) and ω_{3} (probe)=ω_{4} (signal) were used; ω_{1}(=ω_{2}) and ω_{3} are in resonance with distinct rovibronic transitions of B ^{2}Σ^{−}−X ^{2}Π and A ^{2}Δ−X ^{2}Π of CH, respectively. Varying the relative polarization of the pump and probe beams significantly affects the ratio of signal to noise. Two schemes with cross polarization pairs (ω_{1}⊥ω_{2}) and (ω_{3}⊥ω_{4}) produced results best suited to detect trace species in the luminous, dense medium; the relative J dependence observed for these schemes agrees with theoretical predictions. The double‐resonance feature of this technique, advantageous to identify congested lines, is also demonstrated. When an A–X transition line is employed as a probe, previously unobserved predissociative levels of B ^{2}Σ^{−} are detected; the R(12) line of B←X (1,0) transion has a halfwidth greater than 10 cm^{−1}, corresponding to a lifetime of 0.5 ps.

Theoretical study of the unimolecular dissociation HO_{2}→H+O_{2}. I. Calculation of the bound states of HO_{2} up to the dissociation threshold and their statistical analysis
View Description Hide DescriptionThis is the first of a series of papers in which we investigate the unimolecular dissociation of hydroperoxyl. Using the DMBE IV potential energy surface [Pastrana et al., J. Phys. Chem. 94, 8073 (1990)], in the present study 726 bound states of HO_{2}(X̃) up to the H+O_{2}dissociation threshold are calculated in an attempt to access the extent of the coupling between the modes of the system. The first approach involves an analysis of the nodal structure of the wave functions. While the wave functions for the lowest states are regular and assignable, the degree of mixing and complexity rapidly increases with energy. The wave functions close to the dissociation threshold are mostly irregular without any clear cut nodal structure and fill the entire coordinate space available. Nevertheless, a small number of regular states, that are associated with large excitation in the O_{2} stretching coordinate and no or only little excitation in the other modes, are found even at high energies. The second approach used to study the degree of intramolecular coupling is an analysis of the energy spectrum. The nearest neighbor level spacing distribution, which probes the short‐range correlation, as well as the Σ^{2} and Δ_{3} statistics, which are sensitive to the long‐range correlations in the spectrum, are investigated and compared to the distributions predicted for regular and irregular spectra. Both of these approaches indicate that the system is almost totally irregular with a Brody parameter of about 92%. In addition, the sum of states at a particular energy, which is extremely important in all statistical models for unimolecular dissociation, is approximately calculated from the volume of classical phase space and found to be in excellent agreement with the exact quantum mechanical result.

Reaction of SiC^{+} _{ n } (n=1–6) and SiC^{−} _{ n } (n=2–4) with O_{2} molecules in a radio frequency ion trap
View Description Hide DescriptionIon‐molecule reactions of silicon‐carbon binary cluster ions SiC^{+} _{ n } (n=1–6) and SiC^{−} _{ n } (n=2–4) with O_{2} molecules were studied by using an rf ion trap. For all selected positive and negative parent ions, only SiC_{ n }O^{+} or SiC_{ n }O^{−} were produced, respectively. The rate constants for the oxidation of these clusters were determined for the first time. The size dependence of the reactivities are discussed, and the presence of the ring form positive ions for n=3 and 5 are suggested.

Electron nuclear dynamics of H^{+}+H_{2} collisions at E _{lab}=30 eV
View Description Hide DescriptionProtoncollisions with hydrogen molecules at 30 eV in the laboratory frame is a simple ion‐molecule system exhibiting a number of distinct processes such as inelastic scattering,charge transfer, rearrangement, and dissociation. The electron nuclear dynamics (END) theory which allows full electron nuclear coupling and which does not restrict the system from reaching any of the possible product channels, is applied to this sytem to produce transition probabilities, differential, and integral (vibrationally resolved) cross sections. Comparisons with experiment demonstrate that END, even in its simplest implementation, with a single determinantal state for the electrons and with classical nuclei, yields results that are competitive with other theoretical approaches.

State‐specific unimolecular dissociation dynamics of HFCO. II. CO rotational distribution and Doppler widths
View Description Hide DescriptionRovibrational state distributions and Doppler widths of CO fragments formed from unimolecular dissociation of HFCO in its ground electronic state are measured by vacuum ultraviolet laser‐induced fluorescence, following state‐selective preparation of the molecule in a single quantum state in the energy region of 2000 to 3000 cm^{−1} above the dissociation threshold by stimulated emission pumping. CO fragments are rotationally hot and distributed over J≤15 to J=63 with distributions peaking at J=45 to 50 depending upon the initial HFCO dissociative state. Although CO rotational distributions are significantly different for different initial states, about 20% of the total available energy is released on average as rotational energy of CO for all three initial states studied. The yield of CO(v=1) fragments is determined to be about 10% and CO(v≥2) fragments are not observed. The average Doppler width of CO fragments is 0.85 cm^{−1}, which indicates that ∼50% of the total available energy is released as translation. The CO product state distributions and Doppler widths may be rationalized using a modified impulsive model with the ab initio transition state geometry. The dependence of product state distributions on the initial HFCO quantum state may reflect incomplete intramolecular vibrational energy redistribution.

Charge‐transfer dynamics in ion–polyatomic molecule collisions: X^{+}+H_{2}O (X=N,Kr) luminescence study
View Description Hide DescriptionH_{2}O^{+} Ã ^{2} A _{1}–X̃ ^{2} B _{1}luminescencespectra are presented for the X^{+}+H_{2}O (X=N,Kr) charge‐transfer systems at collision energies ranging between 0.4 and 130 eV (c.m.). The luminescence is attributed to bending vibrational states near‐resonant with N^{+}(^{3} P)+H_{2}O and Kr^{+}(^{2} P _{1/2})+H_{2}O reactants, in agreement with energy resonance and Franck–Condon predictions. H_{2}O^{+} Ã‐state product vibrational distributions are obtained from spectral simulations. The energy dependence of vibrational state‐to‐state cross sections is determined for the N^{+}(^{3} P)+H_{2}O charge‐transfer system, where the integral charge‐transfer cross section is known. The cross sections are related to semiclassical charge‐transfer models. Exothermic product states are interpreted to be primarily governed by curve crossings along the bending coordinate of H_{2}O, while endothermic levels can be rationalized using a Demkov‐type mechanism. The Kr^{+}(^{2} P _{1/2})+H_{2}O luminescence study, for which state‐selected cross sections are not available, provides product state distributions consistent with this interpretation. The higher optical resolution in that experiment, however, enables a K‐substate resolved analysis, as well as an approximate assessment of the product rotational temperature. The observed rotational temperatures are near thermal, implying long‐range processes governed by large impact parameters.

On the propensity rules for inelastic NH_{3}–rare gas collisions
View Description Hide DescriptionThe observed and ab initio calculated propensity rules for collisions of NH_{3} with rare gas atoms are found to be in reasonable agreement for NH_{3}–Ar, whereas for NH_{3}–He they show large discrepancies. In order to examine these discrepancies we have calculated state‐to‐state integral cross sections for collisions of NH_{3} with He using the close coupling method. The NH_{3}–He interaction potential has been obtained from SCF calculations, augmented by a multipole‐expanded damped dispersion energy. Our calculations show that the discrepancies can be accounted for if the cross sections are corrected for the imperfect initial state preparation in the experiment. They also clarify why the discrepancies do not occur to the same extent for NH_{3}–Ar. After comparing our new theoretical results with the experimental data we found that for one experimental cross section for NH_{3}–He the earlier assignment must be corrected.

Newtonian propagation methods applied to the photodissociation dynamics of I_{3} ^{−}
View Description Hide DescriptionA uniformly convergent propagation scheme designed for non‐hermitian Hamiltonian operators is presented. The method is based on a Newtonian interpolationpolynomial which is created by a recursive application of the Hamiltonian operator on an initial wavefunction. The interpolation points used to construct the Newtonian polynomial are located in the complex eigenvalue space of the Hamiltonian. A new algorithm is developed to construct the interpolation points. Both time dependent and time independent quantities can be obtained using the same polynomial expansion. The method is particularly useful when negative imaginary potentials are used. The photodissociation dynamics of I_{3} ^{−} is studied as an example of the utility of the scheme to gain insight on a dynamical encounter. The bond cleavage is followed in time simultaneously with the calculation of the Raman spectra. The study addresses the role of vibrational excitation of the reactant I_{3} ^{−} on the nascent I_{2} ^{−}spectral modulations and Raman spectra.

Classical description of nonadiabatic photoisomerization processes and their real‐time detection via femtosecond spectroscopy
View Description Hide DescriptionA classical‐path approach to the description of photoinduced isomerizationdynamics as well as the interrelated electronic and vibrational relaxation processes is outlined. Adopting a three‐mode model of photoisomerization that has been recently proposed by Seidner and Domcke (Chem. Phys. 186, 27 (1994)), we perform detailed numerical studies and compare the results of the classical simulations to available exact quantum‐mechanical results. It is shown that the classical model reproduces semiquantitatively time‐dependent diabatic and adiabatic electronic population probabilities, state‐specific torsional wave functions, and energy contents of vibrational degrees of freedom. Furthermore it is demonstrated that the classical approach is able to simulate at least qualitatively time‐ and frequency‐resolved pump‐probe spectra of these processes. In accordance with exact quantum calculations, the classical simulations reveal the decay of the stimulated emission of the reactants and the delayed onset of the absorption of the photoproducts. To demonstrate the capability of the classical approach, the three‐mode model of Seidner et al. is augmented by a hundred weakly‐coupled harmonic modes. This allows to roughly simulate the relaxation dynamics of a chromophore interacting with a solvent. The simulations reveal that the time evolution of the full system within the first few hundred femtoseconds is quite similar to the case of the bare three‐mode model. For later times, however, the dynamics of the three‐mode model becomes quasistationary, whereas the calculations for the full system reflect the redistribution of the excess energy of the reaction mode into the bath nuclear degrees of freedom. It is found that the quantum yield of the cis‐trans photoreaction depends to a large extent on the specific chromophore‐solvent coupling employed, as it governs directly the competition of the various relaxation pathways. Simulations of the corresponding time‐ and frequency‐resolved pump‐probe spectra reveal that the cooling of the vibrationally hot photoproducts in the solvent is mainly reflected in a blue shift and a narrowing of the width of the absorptionspectrum.

Quantum time evolution in time‐dependent fields and time‐independent reactive‐scattering calculations via an efficient Fourier grid preconditioner
View Description Hide DescriptionA numerical scheme is suggested for accurate large‐scale quantum dynamics simulations. The time‐dependent Schrödinger equation with finite time‐dependent interaction terms is replaced by an inhomogeneous equation with imaginary boundary operators applied along the time axis. This equation is solved globally for a finite time interval using recent Krylov subspace‐based iterative methods that are accelerated by a Fourier grid preconditioner. The same scheme is applied also to time‐independent reactive‐scattering calculations with absorbing boundary operators where the operation of the Green’s function is carried out by solving an inhomogeneous time‐independent equation. The scheme is economic in terms of both memory requirement and computation time. It is especially favorable when high grid densities are required, e.g., for representation of highly oscillatory fields or high‐energy wave functions. Illustrative applications are given for representative models of bound and dissociative systems driven by time‐dependent pulsed fields, and for time‐independent calculations of the cumulative reaction probability for the generic reactionH+H _{2} at high collision energies.

Dynamic reaction path analysis based on an intrinsic reaction coordinate
View Description Hide DescriptionWe propose two methods that may be used to describe the dynamic reaction path (DRP) based on an intrinsic reaction coordinate (IRC) or minimum energy path, to examine how the actual dynamics proceeds relative to the IRC path. In the first of these, any point on the DRP is expressed in terms of the IRC and the distance from the IRC path. In the second method, any DRP point is expressed in terms of the IRC, the curvature coordinate, and the distance from a two‐dimensional ‘‘reaction plane’’ determined by the IRC path tangent and curvature vectors. The latter representation is based on the fact that the 3N−8 dimensional space orthogonal to the reaction plane is independent of an internal centrifugal force caused by the motion along the IRC path. To analyze the relation between geometrical features of the IRC path and the dynamics, we introduce a function that estimates the variation of the reaction plane along the IRC path. As demonstrations, the methods are applied to the dissociationreaction of thiofolmaldehyde (H_{2}CS→H_{2}+CS).

Monomer‐excimer kinetics in solution. III. Generalized Smoluchowski approach
View Description Hide DescriptionA generalized Smoluchowski approach developed in A. Molski, Chem. Phys. 182, 203 (1994) is employed to study reversible excimer formation in solution. For contact excimer formation, relations among the rate coefficients are analyzed for three modes of excitation; initially pulsed, steady‐state, and periodic. A new kinetic Laplace transform relation for the frequency domain is demonstrated in the linear harmonic regime. The Laplace transform relations between the time domain and steady states, derived in W. Naumann and A. Molski, J. Chem. Phys. 100, 1511, 1520 (1994) for interaction‐free models, are shown to be also valid when the interaction forces are included.

Spin density in first‐row diatomic hydrides from the Hiller–Sucher–Feinberg identity
View Description Hide DescriptionThe delta function and Hiller–Sucher–Feinberg (HSF) operators are compared for calculation of electronic spin density at the nucleus. New methods are designed and implemented for evaluation of the difficult molecular integrals over the HSF operator. Calculations are carried out with wave functions that include spin polarization effects using Gaussian basis sets and, to estimate the complete basis set limit, with a seminumerical procedure. Results are reported for the diatomic hydrides CH, NH, and OH in their ground states. While the HSF operator gives much better total densities at the heavy atoms, the delta function and HSF operators are found to perform overall about equally well for spin densities.

CaOH has a second linear structure HCaO
View Description Hide DescriptionThe energy surface of CaOH has been studied and an isomer of the form of HCaO with an electronic state of ^{2}Σ^{+} symmetry has been found. It is linear with H–Ca and Ca–O bond lengths of 2.021 and 2.002 Å, respectively, at the CISD level with a basis set of triple‐zeta plus double polarization quality. The overall electronic structure is largely ionic and can be described as H(1s ^{2})Ca(4s ^{0})O(2s ^{2}2p ^{2} _{ x }2p ^{2} _{ y }2p ^{1} _{ z }) (H^{−}Ca^{2+}O^{−}). The minimum on the energy surface is well defined and the harmonic vibrational frequencies have been calculated. The O–H bond length and stretching frequency and the bending frequency of CaOH have also been calculated and compared with experiment.

Bound states and resonances of the hydroperoxyl radical HO_{2}: An accurate quantum mechanical calculation using filter diagonalization
View Description Hide DescriptionAn accurate calculation of bound and resonance spectra of the non‐rotating odd O_{2} exchange symmetry HO_{2} radical is presented. The calculation has been carried out by a recently developed iterative technique which uses filter diagonalization of a sparse matrix of the system Hamiltonian with absorbing boundary conditions. We were able to obtain 361 bound states and some 232 isolatable resonances (Γ<0.01 eV) in a wide energy range corresponding to the HO_{2}→H+O_{2} unimolecular decomposition reaction. It is shown that all resonances found have the same nature as the bound states in that they all are localized in the same region of space over the deep potential well, and moreover the extrapolated smoothed density of the bound states merges easily with the smoothed density of the resonance states. The level statistics for both bound and resonance states indicates a highly chaotic regime consistent with the random matrix theory. Strong mode mixing makes assignments of most bound and resonance states impossible because the corresponding wave functions do not show any simple pattern. Interestingly, the randomly fluctuating high resolution density of states after smoothing shows a structure resembling two basic frequencies corresponding to the O_{2} stretch and HOO bend motion of the HO_{2} molecule.