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Volume 92, Issue 7, 01 April 1990

Exotic exciton–phonon states and bottleneck for self‐trapping
View Description Hide DescriptionIn a previous paper the conventional barrier model of excitonic self‐trapping has been shown to display divergencies. In the present work we report on novel ‘‘exotic’’ exciton–phonon states, which have not been noted so far. These states are of non‐self‐trapping nature, and by way of their small extension in Q space they may acquire a ‘‘bottleneck’’ role in the process of energy dissipation. This seems to allow for a new explanation of the fast luminescence found in rare gas and other crystals.

Wave packet theory of dynamic absorption spectra in femtosecond pump–probe experiments
View Description Hide DescriptionThe large spectral width of ultrashort optical pulses makes it possible to measure the complete time‐resolved absorptionspectrum of a sample with a single pulse, offering simultaneously high resolution in both the time and frequency domains. To quantitatively interpret these experiments, we start with the usual perturbative density matrix theory for the third‐order susceptibility of a multilevel system. However, the theory is formulated in terms of four‐time correlation functions which are interpreted as the time‐dependent overlap of bra and ket vibrational wave packets propagating independently on the ground and excited electronic statepotential surfaces. This approach captures the critical distinction between electronic population decay and pure dephasing processes, while retaining the intuitive physical picture offered by the time‐dependent wave packet theories of molecular spectroscopy. A useful simplification is achieved by considering the absorption of the probe pulse as the f i r s t ‐ o r d e rspectroscopy of the n o n s t a t i o n a r y state created by the pump pulse. In this case, the dynamic spectrum is obtained through the Fourier transform of the time‐dependent overlap of the initial wave packet propagating on its potential surface and a second wave packet, created by the probe pulse, which evolves simultaneously on the final surface. Calculations for model systems using harmonic surfaces and δ‐function pulses are presented to illustrate the application of this theory and to clarify the unique spectral behavior of the nonstationary states created in femtosecond pump–probe experiments. Finally, we demonstrate the practical application of the theory for anharmonic surfaces and finite pulses by analyzing the dynamic spectroscopy of the excited state torsional isomerization of the bacteriorhodopsin chromophore.

Spectroscopy of the 1 ^{2}Π_{ u } state of Na^{+} _{2}
View Description Hide DescriptionWe report here the first experimental observation of bound–bound transitions between the ground X ^{2}Σ^{+} _{ g } and excited 1 ^{2}Π_{ u } states of Na^{+} _{2}. The basis of our experiment is to study doubly excited Rydberg states of Na_{2} by preparing a well‐defined n d ^{1}Λ_{ g } singly excited Rydberg state of Na_{2} and then, by exciting the Na^{+} _{2} core with a tunable laser. In this paper, we show that the ionic transitions may be directly deduced from the doubly excited Rydberg states spectra [C. Bordas, J. L. Vialle, and M. Broyer (submitted)]. We demonstrate that this technique is one of the most powerful to study the excited states of diatomic ions which are not predissociated. A detailed spectroscopic analysis of the 1 ^{2}Π_{ u } state has been performed and the results are compared with the more recent a b i n i t i o and pseudo‐ (or model‐) potential calculations.

Improved analysis of the infrared spectrum of D_{2}H^{+}
View Description Hide DescriptionThe rotational analysis of the Coriolis‐coupled ν_{2}/ν_{3} bands in the infrared spectrum of the D_{2}H^{+} molecular ion has been reexamined. By making four reassignments and adding one new transition, it has been possible to achieve a much better fit of the bands using fewer molecular parameters. The reassigned ν_{2}/ν_{3} data were combined in a simultaneous least‐squares analysis with existing ν_{1} band infrared data and with two newly measured pure rotational transitions. The resulting molecular parameters and calculated energy levels are the best currently available for this fundamental molecular ion.

Vibrational level structure of highly excited SO_{2} in the electronic ground state. II. Vibrational assignment by dispersed fluorescence and stimulated emission pumping spectroscopy
View Description Hide DescriptionThe dispersed fluorescence (DF) spectra for the fluorescence emitted from eight single rovibronic levels in the C̃ ^{1} B _{2} state are observed. The vibrational quantum numbers for these levels are (v ^{’} _{1},v _{2},v ^{’} _{3}) =(0,0,0), (0,1,0), (0,2,0), (0,0,2), (1,0,0), (1,1,0), (1,2,2), and (3,1,0). The 484 vibrational levels distributed between 4300 and 21 600 cm^{−1} in the electronic ground stateX̃ ^{1} A _{1} are identified based on the assignment of the 1388 transitions in the DF spectra. The vibrational level energy is expressed by an anharmonic expansion with 19 coefficients and the vibrational quanta for the three normal modes. The combination analysis of the DF and stimulated emission pumping spectra having the same upper rovibronic level clarifies the vibrational level structure in the vibrationally highly excited region above 17 000 cm^{−1}.

Optically heterodyned polarization spectroscopy. Measurement of the orientational correlation function
View Description Hide DescriptionPolarizationspectroscopy has been developed as a useful method for the investigation of molecular reorientation in both liquid phase solutions and in the gas phase. This technique has the advantage of measuring a single particle orientational correlation function directly but the disadvantage of averaging over rotation in all electronic states. Described and characterized herein is a variant of this technique, optically heterodyned polarizationspectroscopy, which is able to disentangle various contributions to the signal and determine the rotational relaxation of the solute molecule in different electronic states independently. This work also demonstrates the measurement of the normalized value of the orientational correlation function at time zero, r(0), without extensive normalization of laser parameters. Lastly, various technical advantages of the optically heterodyned method are discussed.

The rotational spectrum of the CH radical in its a ^{4}Σ^{−} state, studied by far‐infrared laser magnetic resonance
View Description Hide DescriptionThe CH radical has been detected in its a ^{4}Σ^{−} state by the technique of laser magnetic resonance at far‐infrared wavelengths. Spectra relating to different spin components of the first three rotational transitions have been recorded. The molecule was generated either by the reaction of F atoms with CH_{4}, with a trace of added oxygen or by the reaction of O atoms with C_{2}H_{2}. The observed resonances have been analyzed and fitted to determine the parameters of an effective Hamiltonian for a molecule in a ^{4}Σ state. The principal quantities determined are the rotational constantB _{0}=451 138.434(94) MHz and the spin–spin parameter λ_{0}=2785.83(18) MHz. Proton hyperfine parameters have also been determined.

Ultraviolet photoemission study of oligothiophenes: π‐band evolution and geometries
View Description Hide DescriptionUltraviolet photoelectron spectroscopy (UPS) has been applied to the investigation of the electronic structure of oligothiophenes with 4–8 thiophene rings. In a series of α‐linked oligomers (α_{ n } with n being the number of rings), a systematic evolution of the π band is observed. Several peaks which correspond to the π band are observed in the region of 0.7–3 eV below the Fermi level (E _{ F }), and the bandwidth becomes broader with increasing n. The nonbonding π band is observed at 3.5 eV below E _{ F } and its energy is almost independent of the number of thiophene units. UPS spectra of α_{7} and α_{8} are fairly similar to the spectra of polythiophene, showing that these oligomers are good model compounds of the polymer. The ionization threshold energy of α_{7} and polythiophene was observed to be 5.3 eV. The effect of irregularity on the π‐electron system was also studied by using oligomers which contain a β linkage or a vinylene group at the middle of the molecule. The UPS spectra showed that the β linkages significantly affect the electronic structure of polythiophene, while the vinylene group does not. In order to analyze the UPS spectra and to investigate the electronic structures of oligomers, the orbital energies and the geometries of these oligomers are calculated by the semiempirical MNDO‐SCF‐MO (modified neglect of diatomic overlap self‐consistent‐field molecular orbital) method. Theoretically simulated spectra of these oligothiophenes derived from the obtained orbital energies by Gaussian broadening are compared with the observed ones. The agreement between the observed and calculated spectra is very good, particularly in the π region. It is shown from the optimized geometry that (1) α_{ n } ’s have planar structure and π electrons are delocalized, (2) the oligomer with β linkages has nonplanar structure leading to limited delocalization of π electrons, and (3) the oligomers with a vinylene group are almost planar and the disturbance by the vinylene group on the delocalization is small.

One‐ and two‐color polarization effects induced in emission and absorption spectra of monomeric and dimeric chlorophyll a in solution
View Description Hide DescriptionThe results of polarization measurements are reported for a chlorophyll a dimer in solution. The experiments were conducted with a single laser beam (depolarization measurements) and two laser beams. In the latter case, the wavelength of one of the lasers is tuned to an absorption band of one of the constituent molecules of the dimer, that of the other is tuned to the absorption band of the other molecule. One of these beams produces effective population saturation of an excited state of one of the molecules of the dimer which has an appropriate transition moment parallel to the electric vector of the pump beam. The other, but weaker, laser beam probes either the resonance Raman or the absorptionspectrum of the other molecule of the loosely bonded dimer. As a direct result of the slow rotational relaxation time of the dimer in comparison to the duration of the laser pulse, an anisotropy is created in the absorption as well as the resonance Raman spectrum probed with the weaker laser beam. The anisotropy measurements yield information on the direction of the principal axes of polarizability and transition moments of the constituent molecules of the dimer. In turn, this information can be used to predict structural properties of the dimer.

Two‐dimensional microwave Fourier transform spectroscopy
View Description Hide DescriptionNew two‐dimensional correlation techniques in the field of pulsed microwaveFourier transform spectroscopy are presented. Five different pulse sequences were used to demonstrate connections between rotational transitions with well separated or with closely spaced frequencies. The introduction of two‐ and four‐step phase cycles to select the desired coherence transfer pathways simplified the two‐dimensional spectra considerably. Experiments were performed on methyl formate, norbornadiene, 1‐chloro‐1‐fluoroethene, and vinyl cyanide. A theoretical treatment is given in terms of the density matrix formalism. The relationship between our experiments and similar nuclear magnetic resonance(NMR) techniques is also discussed.

The benzene ground state potential surface. V. Criteria for theoretical modeling of the B _{2u } harmonic force field
View Description Hide DescriptionWe demonstrate that fundamental frequencies provide a poor criterion of the benzene B _{2u } force field accuracy and that two‐photon cross sections of the b _{2u } fundamental bands in the ^{1} B _{2u }↔^{1} A _{1g } electronic transition, which can be directly related to skeletal displacement magnitudes in the two b _{2u } modes, provide an insightful physical criterion of harmonic force field quality. Another valid criterion for force field quality is isotopic frequency shifts c o m b i n e d with the fundamental frequencies. The frequency‐generated force field of part II accurately predicts the measured cross sections and isotopic frequency shifts, indicating that the B _{2u } force constants are known to ±0.01 mdyn/Å. These constants are used as benchmark quantities for calibratingtheoretically modeled force fields.
A systematic series of a b i n i t i o B _{2u } harmonic force fields for ground state benzene using theoretical geometries are generated at Hartree–Fock and correlated second, third, and fourth order (with single, double, triple, and quadruple excitation) Mo/ller–Plesset perturbation theory (MP2, MP3, MP4SDTQ) and configuration interactiontheory with all single and double excitation (CISD) levels using basis sets from minimal double zeta to triple zeta plus diffuse and polarized functions. These theoretical models of the B _{2u } force field all provide poor predictions for the three criteria: fundamental frequency accuracy 2%–3%; isotopic frequency shift accuracy 10%–300%; two‐photon cross section accuracy 300%–1200% with the sense of isotopic effects on two‐photon cross sections in some cases incorrectly predicted. The MP2 calculations, even using the largest basis set, are incapable of meeting any of the criteria, hence higher order approaches to the correlation problem are required. The inadequacies in frequencies, isotopic shifts, and mode forms arise because both the diagonal and off‐diagonal force constants are not predicted by a b i n i t i o calculations with the sufficient 10^{−} ^{2} mdyn/Å accuracy required for reasonably accurate frequency and intensity predictions. A feature of the a b i n i t i o calculations is that carbon and hydrogen displacement phases for the b _{2u } modes are unchanged by the basis set size or correlation level. The unmeasured ^{1} ^{3}C_{6}D_{6}ν_{1} _{4} two‐photon cross section and iosotope frequency shift from ^{1} ^{2}C_{6}H_{6} are predicted to be larger than for any of the other D _{6h } symmetry benzenes (∼30% higher than in C_{6}H_{6} for the former and 72 cm^{−} ^{1} for the latter) by the benchmark field of part II.

Solvation shell effects and spectral diffusion: Photon echo and optical hole burning experiments on ionic dyes in ethanol glass
View Description Hide DescriptionResults of picosecond photon echo and optical hole burning experiments are reported for four ionic dyes in ethanol glass. At low temperatures, the dephasing times deduced from the hole widths are as much as nine times shorter than those measured by the two‐pulse echo because of the effect of spectral diffusion. The temperature dependences found are of the form a T ^{α}+b exp (−ΔE/k T) due to glass two level system dynamics (T<4 K) and a process that activates exponentially at higher temperatures, possibly from a pseudolocal mode or glass optical phonon. Comparing the ratios of echo to hole burningmeasureddephasing times for the four dyes suggests that the dephasing is influenced by the existence of distinct local ethanol solvation shells in addition to the dynamics of the bulk solvent. A theoretical description of solvent shell effects is achieved through the use of a two spatial domain model of the glass dynamics. Calculations of dynamic perturbations from distinct solvation shell and bulk solvent regions show that the observed differences between the dyes’ dephasing ratios can be explained if the ionic chromophores alter glass dynamics locally.

Optical nonlinearity of a proposed quantum‐confined semiconductor colloid
View Description Hide DescriptionOptical saturation and degenerate four‐wave mixing were observed in a bismuth tri‐iodide (BiI_{3}) colloid, which has been reported to exhibit quantum confinement effects. A third‐order optical nonlinearity ‖χ^{(3)} _{eff}‖=1.4×10^{−10} esu was measured at 364 nm with ∼500 ps pulses. The temporal decay of the nonlinear mixing signal is slow (>6 ns) and shows acoustic oscillations. All results were found to be consistent with the formation of tri‐iodide ions I^{−} _{3} only, and the effects could be explained by photochemicaldissociation. The four‐wave mixing signal is thermal in origin.

Two‐level systems and low‐temperature glass dynamics: Spectral diffusion and thermal reversibility of hole‐burning linewidths
View Description Hide DescriptionIntermediate time‐scale time‐dependent hole‐burning measurements are reported on three glassy organic systems which undergo spectral diffusion: cresyl violet in ethanol at 1.30 and 2.13 K, resorufin in ethanol at 2.13 K, and resorufin in glycerol at 2.13 K. The hole width is observed to broaden on a log time scale from 0.1 to 5000 s for each ethanol system while no broadening is observed in the system of resorufin in glycerol. A detailed theoretical treatment is introduced which allows the raw data to be converted to the fluctuation rate distribution of the underlying modes responsible for dephasing. Using this theory, the broadening in ethanol is found to be the result of a distribution of glassy modes which is Gaussian on a log R scale with a center rate at ∼0.02 s^{−} ^{1}. In addition, temperature cycling hole‐burning results are reported on the system cresyl violet in ethanol. A hole is burned at 1.30 K and detected before, during, and after a temperature cycle to 2.13 K and back. The hole width is observed to broaden at the high temperature and then narrow again in a completely reversible manner when the temperature is again lowered. Theoretical calculations show this behavior to be entirely consistent with the tunneling two‐level‐system (TLS) model of glass dynamics but incompatible with other models such as particle or defect diffusion. The cycling data is shown to fall exactly on the theoretical curve calculated from the TLS model using no adjustable parameters.

Electronic excitation transfer in a mixed dimer of p‐xylene and p‐difluorobenzene
View Description Hide DescriptionThe fluorescence excitation and dispersed fluorescence spectra of a mixed dimer of p‐difluorobenzene (p d f) and p‐xylene h _{1} _{0} (p x) or p‐xylene d _{1} _{0} (p x d) formed in a supersonic expansion have been studied in the spectral region of the monomers origins. The excitation spectrum of p d f–p x dimer exhibits two kinds of features, one being red shifted from p x0^{0} _{0} and the other blue shifted from p d f 0^{0} _{0} . Deuteration of the p x moiety does not modify the observed shifts of the heterodimer absorptions with respect to each monomer 0^{0} _{0} transition, and allows assignment of each absorption to the localized excitation of either the p x or the p d f half of the complex. Dispersed fluorescence resulting from the excitation of the p‐xylene moiety in the complex (p d f–p x* or p d f–p x d*) exhibits two components which may indicate a geometry change in the p d f–p x* (or p d f–p x d*) excited complex. Dispersed fluorescence resulting from the excitation of the p‐difluorobenzene half of the p d f–p x complex (p d f*–p x) is similar to that of p d f–p x* excited state, i.e., displays the characteristics of p‐xylene 0^{0}fluorescence. The p d f*–p x d excited complex fluorescence shows the superposition of the resonance fluorescence from the initially excited level (which is characteristic of the p‐difluorobenzene 0^{0}fluorescence) together with the p d f–p x d* emission. These results give evidence that electronic excitation has been transfered within the excited complex from the p d f moiety to the p x (p x d) moiety.

Time‐dependent treatment of scattering: Integral equation approaches using the time‐dependent amplitude density
View Description Hide DescriptionThe time‐dependent form of the Lippmann–Schwinger integral equation is used as the basis of several new wave packet propagation schemes. These can be formulated in terms of either the time‐dependent wave function or a time‐dependent amplitude density. The latter is nonzero only in the region of configuration space for which the potential is nonzero, thereby in principle obviating the necessity of large grids or the use of complex absorbing potentials when resonances cause long collision times (leading, consequently, to long propagation times). Transition amplitudes are obtained in terms of Fourier transforms of the amplitude density from the time to the energy domain. The approach is illustrated by an application to a standard potential scattering model problem where, as in previous studies, the action of the kinetic energy operator is evaluated by fast Fourier transform (FFT) techniques.

Application of hyperspherical coordinates to four‐atom reactive scattering: H_{2}+CN→H+HCN
View Description Hide DescriptionWe develop the use of Delves’ hyperspherical coordinates to study the reactive scattering of four‐atom systems within the collinear approximation. We present quantum mechanical calculations of reaction probabilities for the collinear exothermic reaction H_{2}+CN →H+HCN. We use a potential energy surface which reproduces the essential characteristics of the reaction. The effect of freezing the CN bondlength to its equilibrium value during the reaction is also investigated and is found to be a good approximation. It is found that HCN product vibrational states with the C–H stretch excited are produced preferentially in the reaction.

Deactivation rate constants and product branching in collisions of the Xe(6p) states with Kr and Ar
View Description Hide DescriptionThe quenching kinetics of the Xe(6p[1/2]_{0} ), Xe(6p[3/2]_{2} ), and Xe(6p[5/2]_{2} ) states have been studied in Kr and Ar buffer gas at room temperature using the two‐photon, laser‐excitation technique. The total quenching rate constants and the primary product distributions were measured to obtain state‐to‐state rate constants. Collisions between Xe[1/2]_{0} and Kr mainly gave energy transfer to Kr(5s,^{3} P _{2} ) rather than relaxation to the Xe(6p or 5d) levels. The transfer of energy from Kr(5s,^{3} P _{2} ) back to the Xe(6p) manifold also was observed. The collisional coupling between Xe[1/2]_{0} and Xe(3d _{5} ) in Ar, reported previously, was confirmed. The collisions of Kr and Ar with Xe[3/2]_{2} and Xe[5/2]_{2} atoms gave intramultiplet relaxation; observation of the time dependence of the primary products, the Xe[3/2]_{1}, [5/2]_{3}, and [1/2]_{1} states, permitted assignment of some state‐to‐state rate constants for these states. The flow of energy through the Xe(6p) manifold is discussed.

Effects of interchannel coupling on the photoionization cross sections of carbon dioxide
View Description Hide DescriptionThe photoionization cross sections of CO_{2} leading to the first four electronic states of CO^{+} _{2} have been computed including the effects of interchannel coupling. The results were obtained in the Tamm–Dancoff approximation using the Padé‐approximant C̃‐functional method to solve the resulting scattering equations. All of the required matrix elements have been computed using single‐center expansions and numerical integration of the resulting radial functions. An alternative approach for computing products of single‐center‐expanded functions is presented where the functions are transformed into a coordinate representation, then the product is computed, and finally the product is transformed back into the angular momentum representation. The computational effort required in this approach depends on the second power of the number of partial waves in contrast to the third power dependence found in methods used previously. The photoionization cross sections are obtained in the mixed dipole representation which ensures that the Thomas–Reiche–Kuhn sum rule is satisfied. In the coupled‐channel approximation, the shape resonance in the 4σ_{ g }→kσ_{ u } channel is found to remain at the same energy and have the same width as was found in earlier single‐channel calculations.
Both the total cross section in the (4σ_{ g })^{−1} channel and the photoelectron asymmetry parameter are somewhat less affected by the resonance than in the single‐channel approximation, but there is still a substantial disagreement with experimental data. The kσ_{ u } shape resonance is found to modify the cross sections and asymmetry parameters in the other channels, with the largest effect being in the (3σ_{ u })^{−1}ionization channel. The full coupled‐channel results, which include coupling among the 1π_{ g }→kπ_{ u },1π_{ u }→kπ_{ g },3σ_{ u }→kσ_{ g }, and 4σ_{ g }→kσ_{ u } channels, are found to significantly modify the cross section in the 1π_{ g }→kπ_{ u } channel leading to good agreement between theory and experiment for the total ionization cross section in the (1π_{ g })^{−1} channel. However, this coupling is found to significantly perturb the other channels, and in the case of the asymmetry parameters in the (3σ_{ u })^{−1} channel, this leads to relatively poor agreement with experimental data.

Vibrational energy transfers in ozone from infrared double‐resonance measurements
View Description Hide DescriptionVibrational energy transfer processes in pure ozone have been studied by means of a time‐resolved infrared double‐resonance technique using two CO_{2} lasers. The intermode transfer between the Coriolis‐coupled ν_{1} and ν_{3} modes has been observed for the first time and its rate constant measured. The near‐resonant vibrational energy transfer populating the ν_{2}+ν_{3} state has been also directly observed, as well as the vibrational deexcitation of the ν_{1} and ν_{3} states including the transfer process to the ν_{2} mode and the direct V‐T,R processes. From a kinetic analysis of the vibrational relaxation, a numerical model was formulated allowing by comparison to the experiments to determine the rate coefficients for the processes. A rate coefficient of 2.4×10^{6} s^{−1} Torr^{−1} was obtained for the intermode transfer between the Coriolis coupled ν_{1} and ν_{3} modes. Also a rate coefficient of 7×10^{5} s^{−1} Torr^{−1} was derived for the process populating the ν_{2}+ν_{3} state. The rate coefficient corresponding to the intermode transfer from ν_{1} and ν_{3} to ν_{2} was found to be (2800±500) s^{−1} Torr^{−1}, a value clearly smaller than that obtained in previous studies. Finally the direct deexcitation from the ν_{1} and ν_{3} states, not taken into account in previous works, was found to be rather efficient, its rate coefficient being not negligible (∼600 s^{−1} Torr^{−1}) as compared to the deexcitation coefficient from the ν_{2} state which was found equal to (2250±300) s^{−1} Torr^{−1}.