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Volume 105, Issue 8, 22 August 1996

Mode suppression in the non‐Markovian limit by time‐gated stimulated photon echo
View Description Hide DescriptionIt is demonstrated that enhanced mode suppression in stimulated photon echo experiments can be obtained by diagonal time gating of the echo. This technique is especially important when the optical dynamics of the system is non‐Markovian. A two‐mode Brownian oscillator model is used to analyze the effect of time gating on the stimulated photon echo. The method is demonstrated on a dye solution of DTTCI in ethylene glycol at room temperature. Experimentally, time gating of the echo is accomplished by means of femtosecond phase‐locked heterodyne detected stimulated photon echo. The vibrational dynamics in this system are explored by conventional stimulated photon echo experiments. Especially stimulated photon echo‐maximum shift measurements are found to be particularly useful.

An ab initio study of solvent shifts in vibrational spectra
View Description Hide DescriptionUsing analytical second derivatives of the generalized conductorlike screening model (GCOSMO) we calculate vibrational frequency shifts for several molecules (acetone, methylamine, formic acid, acetic acid, and trans‐NMA) solvated in water. In these calculations, results from dielectric continuum approach with and without several explicit water molecules are compared with traditional supermolecule approach. The simple GCOSMO model, where all solvent molecules are treated as a continuum medium, reproduces quite accurately solvent shifts in solutes having moderate hydrogen bondings with water, such as acetone and methylamine. To represent strong solvent effects in formic acid and acetic acid, one should add at least one explicit water molecule in GCOSMO calculations. Solvent effects on solute structure correlate well with frequency shifts. Geometry optimizations and frequency calculations in the GCOSMO‐supermolecule approach require only 10%–20% more computational effort than similar calculations in the gas phase. Therefore, this method provides a promising and effective tool for studying reactivity, structural, and spectroscopic properties of realistic solutes.

Time‐dependent coupled cluster approach to multimode vibronic dynamics
View Description Hide DescriptionThe time‐dependent coupled cluster method is used to calculate the dynamics on coupled surfaces. The time‐dependent self‐consistent‐field solution of the initial doorway state is used as the reference state. Autocorrelation functions and spectra of two model systems are presented. It is found that the spurious recurrences in the self‐consistent‐field autocorrelation functions are eliminated in the coupled cluster approach and the spectral features are correctly reproduced at T=T _{1}+T _{2} level of approximation.

Characterization of spin–orbit autoionizing Rydberg states excited via one‐photon absorption from the F ^{1}Δ_{2} Rydberg state of HBr
View Description Hide DescriptionRotationally and parity resolved excitation spectra of autoionizing Rydberg states of HBr in the energy region between the ^{2}Π_{3/2} and ^{2}Π_{1/2} ionic thresholds have been obtained in a double resonant excitation scheme via single rotational levels of the vibrationless F ^{1}Δ_{2}Rydberg state. A cursory examination of these spectra reveals the presence of s, p, d, and fRydberg series. Apart from the f series, which show almost Hund’s case (e) coupling, these series clearly exhibit an angular momentum coupling scheme intermediate between Hund’s case (c) and (e). As a result it is difficult to assign them as converging upon specific ionic rotational thresholds. A detailed analysis of the excitation spectra has consequently been performed employing multichannel quantum defect theory calculations, allowing for a determination of the quantum defects of the Hund’s case (a) basis states and the relevant transition moments, and, concurrently, the assignment of nearly all the observed autoionizing resonances.

Phase control of absorption in large polyatomic molecules
View Description Hide DescriptionThe phenomenon of interference of the amplitude for absorption of one photon of frequency 3ω and the amplitude for absorption of three photons of frequency ω was theoretically predicted by Shapiro, Hepburn, and Brumer. The interference was demonstrated experimentally by varying the relative phase between the tripled frequency photon and three photons with the fundamental frequency by the groups of Elliott and Gordon in atoms and small molecules. In order to see how general this phenomenon is, five compounds were studied, ammonia, trimethylamine, triethylamine, cyclooctatetraene, and 1,1‐dimethylhydrazine. CH_{3}I was used as the tripling gas for light in the range 604–600 nm. Interference was observed in all cases. The last four compounds have low ionization potentials and interference was observed between a 3+1 and a 1+1 ionization process with a maximum modulation of 22%. NH_{3} with a higher ionization potential requires absorption of 3+2 or 1+2 photons and exhibits a maximum modulation of 33%. We conclude that molecular size is no obstacle and that as long as a molecule has sufficiently strong absorption at the tripled frequency, and sufficient vapor pressure, and the laser fundamental beam is very strong, phase control of interference is observable.

Optical pumping magnetic resonance in high magnetic fields: Characterization of nuclear relaxation during pumping
View Description Hide DescriptionThe polarization of ^{129}Xe gas by spin exchange with optically pumped Rb vapor is investigated in high magnetic field. Operation in a high field provides added spectral dispersion via Zeeman shifts of the electronic transitions. This simplifies the physics of the pumping process in such a way as to make it more amenable to treatment with simple rate theory. A relationship between the steady state ^{129}Xe polarization and the applied laser power is derived which agrees with experimental results. This theory serves as a guide to the manufacture of very high polarizations of ^{129}Xe gas.

Temperature effects in the collisional deactivation of highly vibrationally excited pyrazine by unexcited pyrazine
View Description Hide DescriptionTime‐dependent infrared fluorescence (IRF) from the C–H fundamental and overtone bands was used to monitor the vibrational deactivation (by unexcited pyrazine) of pyrazine excited at 308 nm with a pulsed laser. The 1‐color and 2‐color IRF results were modeled with collisional master equation calculations in order to determine the temperature dependence of the energy transfer parameters. The experimental data cannot be modeled without invoking a biexponential collision step size distribution, which implies that ‘‘super collisions’’ are significant. The results show that the energy transfer parameters are essentially constant at temperatures greater than the Lennard–Jones well depth, but at lower temperatures, energy transfer is enhanced. It is likely that vibration–vibration energy transfer dominates in this system.

Vibrational energy transfer from four levels below 410 cm^{−1} in S _{1} p‐difluorobenzene. II. A search for vibration to rotation transfer
View Description Hide DescriptionCollision‐induced vibrational energy transfer has been studied in S _{1} p‐difluorobenzene in a supersonic free jet expansion at ∼30–40 K with the diatomic partners H_{2}, D_{2}, and N_{2}. Transfer has been studied from the initial levels 30^{2} (E _{vib}=240 cm^{−1}), 8^{2} (E _{vib}=361 cm^{−1}), 27^{1} (E _{vib}=403 cm^{−1}) and 6^{1} (E _{vib}=410 cm^{−1}). The diatomic partners provide the possibility for transfer of vibrational motion in p‐difluorobenzene to rotational motion in the diatomic (vibration to rotation transfer) in addition to the ubiquitous transfer of vibrational to translational motion. No compelling evidence is found for vibration to rotation transfer. Consequently, the diatomics are expected to behave analogously to monatomics, for which it has previously been observed that across the He to Kr series there is a substantial increase in multiple quanta (Δυ≳1) transfer. The results for the diatomics are qualitatively in accord with this trend, with increased multiple quanta transfer from H_{2} to D_{2} to N_{2}. However, the diatomics do not always slot into the monatomic series where expected. Furthermore, the particular channels observed to be prominent in the Δυ=2 transfer for the diatomics are in a number of instances different to those seen for the monatomics. There are subtle but clear differences between these two classes of collision partner. The behavior of D_{2} is particularly unusual, and at this stage unexplained. This collision partner has an unexpected preference for transfers involving multiple changes in vibrational quanta. The state‐to‐state branching ratios for transfer from 27^{1} and 6^{1} are very similar, suggesting that the initial vibrational motion and its symmetry play little role in determining the favored destination levels.

Mobilities of Li^{+} in Ne and in N_{2} and Na^{+} in SF_{6}: Effect of inelastic energy loss
View Description Hide DescriptionIon mobility measurements were made for Li^{+} in Ne and in N_{2} and Na^{+} in SF_{6} using a variable‐temperature drift tube. The measurements were made by two different methods: variable‐E/N method at constant T and variable‐T method at constant E/N, where E, N, and T are the electric field strength, the gas number density, and the gas temperature, respectively. Two datasets were compared at the same effective temperature T _{eff}, as calculated from the Wannier equation. For Li^{+} in Ne, the two datasets are put on a single curve in the range 150 K<T _{eff}<10 000 K, indicating that the scaling rule holds well. However, for Li^{+} in N_{2} and Na^{+} in SF_{6} there exists a mobility difference between the two datasets, which is attributed to inelastic energy loss in the variable‐E/N measurement. Using the modified Wannier equation developed by Viehland et al., we determined the inelastic energy loss factor for Na^{+} in SF_{6}.

Solvent‐induced nonadiabatic transitions in iodine: An ultrafast pump–probe computational study
View Description Hide DescriptionThe solvent‐induced electronic predissociation [B→a1_{ g }(^{3}Π)] following an ultrafast X→B transition in molecular iodine is studied using a classical ensemble representation of Heisenberg’s equations of motion. An N electronic state quantum mechanical Hamiltonian is used to derive (coupled) equations of motion for the population (and the coherence) of the different electronic states as well as classicallike coupled equations for the nuclear dynamics (of both the molecule and the solvent) on each electronic state. The ultrafast excitation of the intermediate B state creates a coherent vibrational motion in this bound state. The localized nature of the solvent‐induced B–a1_{ g }(^{3}Π) coupling results in a steplike depletion of the excited B state population and hence in a bulletlike appearance of population on the dissociative a1_{ g }(^{3}Π) state twice per vibrational period. The depletion of the B state population and the appearance of products on the a1_{ g }(^{3}Π) state are discussed as a function of solvent density and polarizability. The magnitude of the nonadiabaticB–a1_{ g }(^{3}Π) coupling depends both on the molecule–quencher separation and on the quencher’s polarizability. It is found that at all reduced densities the small Ar atom is the most effective quencher (when compared to either Kr and/or Xe). We attribute this unexpected trend to the local density of atoms around the solute molecule. For all the rare gas solvents the local density around the iodine molecule does not quite scale with the global one and there is an observed tendency for the solvent to cluster around the solute in a T‐shaped configuration. It is this close‐packed configuration that compensates for the smaller polarizability of the Ar atom and hence provides for a more effective quenching. These arguments are used to explain the experimental results which demonstrate that for a series of homologous alkanes the extent of predissociation scales with the length of the molecular chain although the global polarizability density remains roughly constant.

Moderately dense gas quantum kinetic theory: Aspects of pair correlations
View Description Hide DescriptionA recently formulated density corrected quantum Boltzmann equation emphasizes the need to explicitly include pair correlations and the conversion of kinetic energy to potential energy as important effects in the kinetic theory of moderately dense gases. This paper first considers an appropriate evolution equation for the pair correlations which includes their decay via interactions with other particles in the gas. The molecular description is given of such a gas close to local thermal equilibrium, together with expressions for the associated hydrodynamic variables. Wigner functions are used to uniquely separate macroscopic and microscopic properties. An accompanying paper solves the combination of linearized Boltzmann and correlated pair equations to obtain expressions for the transport coefficients.

Moderately dense gas quantum kinetic theory: Transport coefficient expressions
View Description Hide DescriptionExpressions for the transport coefficients of a moderately dense gas are obtained, based on a recently derived density corrected quantum Boltzmann equation. Linearization of the equations determining the pair correlation and the ‘‘free’’ singlet density operators about local equilibrium is discussed first. The rate of change of the pair correlations is treated as dynamic effects for pairs of particles relaxing to local equilibrium via a relaxation timemodel arising from interactions with ‘‘third particles.’’ In contrast, the singlet density operator satisfies a Boltzmann equation with binary collisions. Spatially inhomogeneous corrections to the collision superoperator are included. Contributions to the transport coefficients arise from the perturbation from local equilibrium through fluxes associated with kinetic, collisional and, for the thermal conductivity, potential energy mechanisms. A comparison is made between the classical limit of the transport coefficient expressions obtained here and the classical expressions previously derived from the Boltzmann equation with the nonlocal collision corrections of Green and Bogoliubov.

Differential cross sections for rotational excitation of NH_{3} by collisions with Ar and He: Close coupling results and comparison with experiment
View Description Hide DescriptionBy means of the close coupling method we have calculated state‐to‐state differential and integral cross sections for rotational excitation and inversion of NH_{3} by collisions with Ar and He. For NH_{3}–Ar we used an empirical and a scaled ab initio potential, for NH_{3}–He an ab initio potential. The differential cross sections for NH_{3}–Ar obtained from the empirical potential have an angular dependence that is in closer agreement with experiment than those obtained from the scaled ab initio potential. The integral cross sections are reproduced equally well by the two potentials. Also for NH_{3}–He the differential cross sections are in accordance with experiment. For the integral cross sections the agreement is good too, except for the very small cross sections to some of the higher rotationally excited states. For both complexes the differential cross sections show a strong dependence on energy, both in their angular dependence and in their relative magnitudes.

Reaction mechanisms and energy disposal in the [C_{2}H_{2}:OCS]^{+} system: A mode‐selective differential cross section study
View Description Hide DescriptionCharge transfer and S‐atom transfer have been studied for reaction of both charge states of the [C_{2}H_{2}:OCS]^{+} system. Reactions have been studied as a function of six different modes of reactant nuclear motion, including relative motion and nine levels of five vibrational modes for the two reactant ions. Integral cross section measurements provide information on how total reactivity and product branching are affected by different forms of reactant excitation. Detailed insight into the reaction mechanism is obtained from differential scattering measurements—the first ever for mode‐selectively excited reactants. The S‐transfer reaction is found to be nearly identical for the two reactant charge states, which appear to be coupled by charge transfer in the collision entrance channel. In both charge states S transfer is dominated by two distinct direct scattering mechanisms, rebound and glancing/stripping, each of which are affected by collision energy and vibrational state. At collision energies below 0.5 eV, complex‐mediated scattering becomes an important mechanism as well. It appears that the cis‐trans symmetry of the C_{2}H^{+} _{2} bending vibration strongly affects formation of [C_{2}H_{2}:OCS]^{+} complexes. Charge transfer goes by very different mechanisms in the two charge states. For C_{2}H^{+} _{2}+OCS, long‐range electron hopping is the dominant mechanism, while for OCS^{+}+C_{2}H_{2} the dominant mechanism requires impulsive collisions.

Electron transfer in the inverted region: Adiabatic suppression and relaxation hindrance of the reaction rate
View Description Hide DescriptionKramers’s model is applied to an electron transferreaction in the inverted region. The reaction rate is considered at different values of the coupling matrix element and the damping, which is a measure of the interaction of the reaction coordinate with the other, nonreactive degrees of freedom of the system. The coupling characterizes overlap of the electron orbits of the donor and acceptor. It is shown that at the low/high damping the reaction rate is controlled by the slowest of the two rates. One is the thermally averaged transition rate (the reaction rate in the intermediate damping regime) and another one is the rate controlled by the energy/spatial diffusion. We demonstrate that the reaction rate as a function of the electron coupling shows a striking difference from the normal region case. The rate passes via maximum and decreases exponentially with the increase of the coupling.

Collisional deactivation of vibrationally highly excited azulene in compressed liquids and supercritical fluids
View Description Hide DescriptionThe collisional deactivation of vibrationally highly excited azulene was studied from the gas to the compressed liquid phase. Employing supercritical fluids like He, Xe, CO_{2}, and ethane at pressures of 6–4000 bar and temperatures ≥380 K, measurements over the complete gas–liquid transition were performed. Azulene with an energy of 18 000 cm^{−1} was generated by laser excitation into the S _{1} and internal conversion to the S _{0} ^{*}‐ground state. The subsequent loss of vibrational energy was monitored by transient absorption at the red edge of the S _{3}←S _{0} absorption band near 290 nm. Transient signals were converted into energy‐time profiles using hot band absorption coefficients from shock wave experiments for calibration and accounting for solvent shifts of the spectra. Under all conditions, the decays were monoexponential. At densities below 1 mol/l, collisional deactivation rates increased linearly with fluid density. Average energies 〈ΔE〉 transferred per collision agreed with data from dilute gas phase experiments. For Xe, CO_{2}, and C_{2}H_{6}, the linear relation between cooling rate and diffusion coefficient scaled collision frequencies Z _{ D } turned over to a much weaker dependence at Z _{ D }≳0.3 ps^{−1}. Up to collision frequencies of Z _{ D }=15 ps^{−1} this behavior can well be rationalized by a model employing an effective collision frequency related to the finite lifetime of collision complexes.

Rovibrational energy levels and equilibrium geometry of HCP
View Description Hide DescriptionThe ground statepotential energy surface for HCP has been investigated theoretically. A large fraction of electron correlation is included by multireference internally contracted configuration interaction from CASSCF reference wave functions using large orbital expansions. The origin of the potential is then shifted and the force constants scaled to reproduce all spectroscopic data available for the four isotopically substituted species. Variational calculations of vibrational and rotational frequencies for transitions up to J = 7 ← 6 have finally been performed, with accuracy which is typically ± 5 cm^{−1} for vibrations and ± 10 MHz for most rotations. By comparison with the results of the perturbation treatment the importance of the ν_{1}:2ν_{3} Fermi interaction for vibrational frequencies and effective rotational constants has been determined. From computed and experimental ground staterotational constants, the molecular equilibrium geometry has also been estimated.

Improved density functional theory results for frequency‐dependent polarizabilities, by the use of an exchange‐correlation potential with correct asymptotic behavior
View Description Hide DescriptionThe exchange‐correlation potentials v _{xc} which are currently fashionable in density functional theory(DFT), such as those obtained from the local density approximation(LDA) or generalized gradient approximations (GGAs), all suffer from incorrect asymptotic behavior. In atomic calculations, this leads to substantial overestimations of both the static polarizability and the frequency dependence of this property. In the present paper, it is shown that the errors in atomic static dipole and quadrupole polarizabilities are reduced by almost an order of magnitude, if a recently proposed model potential with correct Coulombic long‐range behavior is used. The frequency dependence is improved similarly. The model potential also removes the overestimation in molecular polarizabilities, leading to slight improvements for average molecular polarizabilities and their frequency dependence. For the polarizability anisotropy we find that the model potential results do not improve over the LDA and GGA results. Our method for calculating frequency‐dependent molecular response properties within time‐dependent DFT, which we described in more detail elsewhere, is summarized.

Theoretical study of the CH_{4}+F→CH_{3}+FH reaction. I. Ab initio reaction path
View Description Hide DescriptionUsing ab initio information, the reaction path for the CH_{4}+F→CH_{3}+FH reaction was traced and the coupling between the reaction coordinate and normal modes was analyzed along it. The FH product may be vibrationally excited due to the nonadiabatic flow of energy between the reaction coordinate and this bound mode, manifest in the large peak in the coupling term after the saddle point. It was concluded that the variational effects were due only to entropic effects. The rate constants were calculated for the temperature range 100–500 K using the variational transition state theory with different levels of calculation to calibrate the reaction path. Agreement was found with the experimental values when using the QCI/b3 shifted curve, avoiding the errors associated with the use of the single‐point calculation.

Theoretical study of the CH_{4}+F→CH_{3}+FH reaction. II. Semiempirical surfaces
View Description Hide DescriptionWe present two semiempiricalsurfaces for the CH_{4}+F→CH_{3}+FH reaction. One is based on the PM3 semiempirical molecular orbital theory, using parameters specifically calculated for this reaction (SRP method), and the other is based on the analytic function J1 for the CH_{4}+H→CH_{3}+H_{2}reaction, slightly modified (MJ1 surface). To calibrate the first surface we chose as reference data the reactant and product experimental properties, while to fit the second, we also used ab initio calculated saddle‐point information. Experimental rate constants were not used in the calibration because of their uncertainty. Because of the flattening of these surfaces in the saddle‐point zone, the variational effects are important and the location of the transition state is concluded to be due to entropy effects. The kinetic isotope effects (KIEs) at different temperatures were also analyzed showing reasonable agreement with the experimental value for both surfaces. The factor analysis of the KIEs indicates an inverse tunneling contribution originated by the behavior of the V ^{ G } _{ a } curve. The strengths and the weaknesses of these two surfaces, along with the ab initioreaction path studied previously, were also analyzed.