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Volume 104, Issue 4, 22 January 1996

Optimal control of population transfer in an optically dense medium
View Description Hide DescriptionWe apply the optimal control technique (OCT) to design an optical pulse pair that controls the population transfer in a medium of three‐level atoms. The absorption and reshaping of the controlling pulses by the medium are taken into account. The efficiency of the population transfer is improved significantly compared with designs that do not incorporate pulse absorption and reshaping.

Rotational spectra for off‐center endohedral atoms at C_{60} fullerene
View Description Hide DescriptionRotational spectra for endohedral Li^{+}@C_{60} and Na^{+}@C_{60} are calculated at different temperatures. Most of the features in these spectra are related with the degree of anisotropy in the atom–cage interaction. While the low anisotropy for Na^{+}@C_{60} results in rather simple spectra with the 2B oscillation typical of a diatomic molecule, the more eccentric and anisotropic Li^{+}@C_{60} produces complex spectra with rotational and librational bands. Some interesting effects are induced by the cage rotation, which has been incorporated through a semiclassical formalism.

Application of an inverse method to the determination of a two‐dimensional intermolecular potential energy surface for the Ar–OH(A ^{2}Σ^{+}, v=0) complex from rovibrational spectra
View Description Hide DescriptionA stable inversion method of determining molecular potentials from a finite number of spectroscopic data is presented. Molecular inverse problems are often underdetermined, unstable, and nonlinear. Specifically, the measured spectra contains only partial information of the sought‐after potential and even a small error in the data may cause a large variation in the inverted solution. Moreover, the underlying potential is a complicated nonlinear functional of the spectral data. The inversion algorithm, based on the Tikhonov regularization method, resolves all of the above predicaments and yields accurate sought‐after potentials with proper analytic properties. The method is applied to extract two‐dimensional Ar–OH(A ^{2}Σ^{+}, v=0) potential energy surfaces from the rotational–vibrational spectral data. Two versions of the recovered potential energy surfaces are obtained using two slightly different sets of rovibrational data. These two potentials are basically equivalent, except in the regions to which the data are insensitive, and possess physically acceptable smooth features with the correct long‐range behavior. Both recovered potentials reproduce the observed spectra, the estimated rotational constants, and the binding energy within the experimental accuracy.

Mode‐specific hydrogen tunneling in tropolone: An instanton approach
View Description Hide DescriptionCalculations are reported of hydrogen and deuterium tunneling splittings in the ground stateS _{0} (X̃,^{1} A _{1}) and the first excited singlet state S _{1} (Ã,^{1} B _{2}) of tropolone‐d _{0} and ‐d _{1}. The main focus of the calculations is on the splittings observed in vibrationally excited levels of S _{1}, some of which are larger while others are smaller than the zero‐point splitting. To account for these observations, a potential‐energy surface is constructed by standard quantum‐chemical methods and the dynamics on this surface is treated by a method derived from the instanton approach. The potential‐energy surface is a complete multidimensional surface resulting from the combination of a potential‐energy curve along the tunneling coordinate with a harmonic force field calculated at the stationary points. The level of calculation adopted is HF/6‐31G** for S _{0} and CIS/6‐31G** for S _{1}. A few other, nominally more accurate, methods were tried but proved to be unsatisfactory. To deal with the dynamics, the instanton method, used previously for the calculation of zero‐point level splittings, is modified so as to make it applicable to excited levels. As expected, it is found that excitation of the tunneling mode strongly promotes hydrogen transfer. The effects of exciting modes that are symmetric or antisymmetric with respect to the symmetric transition state are evaluated for all such modes with assigned splittings by a straightforward generalization of the correction terms previously derived for zero‐point splittings. Of special interest are out‐of‐plane modes, some of which show up as overtones with splittings smaller than the zero‐point splitting, despite the fact that there is no linear coupling between these modes and the tunneling mode. The effect is ascribed to anharmonic coupling and an effort is made to calculate the required anharmonicities quantum‐chemically. In general the agreement between theory and experiment is satisfactory for modes that are linearly coupled while the situation is less clear for anharmonically coupled modes.

Mass‐resolved two‐photon spectra of ArXe in the region of Xe*(6p)
View Description Hide Description(2+1) resonantly enhanced multiphoton ionization (REMPI) spectra of ArXe have been recorded between ≊78 000 and 80 110.0 cm^{−1}. Single isotopomer data was obtained using a time‐of‐flight (TOF)mass spectrometer. Vibrational analyses for several transitions involving ArXe excited states that dissociate to Ar(^{1} S _{0})+Xe*(6p) are presented, in some instances, for the first time. In addition to vibrational numbering and constants, excited state symmetries were deduced from separate REMPI/TOF spectra recorded with linearly and circularly polarized light, while excited state bond lengths were derived from Franck–Condon factor calculations. Some of the excited states were found to have potential humps and/or unusual vibrational band intensity distributions. Where possible, the nature of the perturbations is discussed.

Self‐consistent determination of fullerene binding energies BE (C^{+} _{ n }–C_{2}), n=58⋅ ⋅ ⋅44
View Description Hide DescriptionUsing recently measured accurate relative partial ionization cross section functions for production of the C_{60} fragment ions C^{+} _{58} through C^{+} _{44} by electron impact ionization, we have determined the respective binding energies BE(C^{+} _{ n }–C_{2}), with n=58,...,44, using a novel self‐consistent procedure. Appearance energies were determined from ionization efficiency curves. Binding energies were calculated from the corresponding appearance energies with the help of the finite heat bath theory. Then using these binding energies we calculated with transition state theory(TST), the corresponding breakdown curves, and compared these calculated ones with the ones derived from the measured cross sections. The good agreement between these breakdown curves proves the consistency of this multistep calculation scheme. As the only free parameter in this procedure is the binding energy C^{+} _{58}–C_{2}, we studied the influence of different transition states chosen in the determination of this binding energy via TSTtheory and iterative comparison with breakdown curve measurements. Based on this study we can conclude that extremely loose transition states can be confidently excluded, and that somewhat looser transition states than those used earlier result in an upward change of the binding energy of less than 10% yielding an upper limit for the binding energy C^{+} _{58}–C_{2} of approximately 7.6 eV.

Cooperative optical bistability in the dimer system Cs_{3}Y_{2}Br_{9}:10% Yb^{3+}
View Description Hide DescriptionIn single crystals of the dimer compound Cs_{3}Y_{2}Br_{9}:10% Yb^{3+} below 31 K, both visible (VIS) and near‐infrared (NIR)luminescence intensities were found to exhibit hysteresis as a function of incident NIR intensity and temperature. The optical bistability is intrinsic to Cs_{3}Y_{2}Br_{9}:10% Yb^{3+} and not a result of an external feedback. Lowering the temperature to 11 K strongly enhances the all‐optical switching behavior. The switching on VIS cooperative upconversion and NIRluminescence transitions occurs simultaneously and with opposite polarity reflecting the competition of both emission processes. On/Off switching ratios of up to 4.8 and 1.7 were observed for VIS and NIRluminescence intensities. Using NIRluminescence spectroscopy, differences in the internal sample temperature of up to 7 K were found between the upper and lower branches of the hystereses. A two‐level density‐matrix model is developed which includes ground‐ and excited‐state interactions and shows that the intrinsic bistability due to a local field different from the external field is strongly amplified by the nonlinear cooperative upconversion process. Alternatively, a rate‐equation model is presented which takes the multilevel nature of the ions into account but is more phenomenological in nature. Formally, the two models are shown to be equivalent, and they qualitatively explain all major experimental observations. It is found both theoretically and experimentally that increasing the coupling within Yb^{3+} dimers and/or decreasing energy migration through the Yb^{3+} lattice enhances switching and renders it easier to observe intrinsic optical bistability.

Conformational disorder of conjugated polymers: Implications for optical properties
View Description Hide DescriptionA physical picture of a conjugated chain as a collection of almost planar segments, separated by large angular breaks arises from a microscopic model which includes conjugation and steric interactions. The conjugation part of the standard phenomenological Hamiltonian for torsional motion is also derived from the model. We obtain a probability distribution of the length of segments between those breaks as the relevant factor for the behavior of the chain. We also perform numerical simulations of the structure and properties of these chains; the results of this are in agreement with our analytic predictions. In explaining experimental data for optical properties, such as the second hyperpolarizability, γ, our theory provides improved agreement over previous models.

Raman intensities from Kohn–Sham calculations
View Description Hide DescriptionRaman intensity calculations have been performed for nine small main‐group molecules using the Kohn–Sham density functional method. A combination of numerical and analytic derivation techniques was used as implemented in the program package DEMON. The effect of the applied functional, the basis set augmentation, and the numerical fitting of the exchange‐correlation potential have been investigated along with other aspects of the computations. The results obtained at the local level using valence triple‐zeta plus 2 polarization functions (VTZP+) basis sets compare well with experiment and with the results obtained from the Hartree–Fock and correlation methods using large basis sets, whereas nonlocal corrections did not yield improvements in the predicted local Raman intensities. Systematic analysis proved the sensitivity of the results obtained with the gradient corrected nonlocal functional to the numerical fitting applied in the calculations of the exchange‐correlation terms. We demonstrated that omitting the fitting procedure from nonlocal calculations improves the quality of the Raman intensities while the grid used for fitting does not have an influence on the Raman intensities. Effects of the reference geometry, step size for evaluating the numerical derivatives and the threshold of energy convergence were also tested.

Rotational spectra in the ν_{2} vibrationally excited states of MgNC
View Description Hide DescriptionThe pure rotational spectra of MgNC in the ν_{2} (bending) vibrationally excited states were observed in the 310–380 GHz region to study the linearity of the molecule. The observed 90 spectral lines were assigned to the transitions in the v _{2}=1–5 states and analyzed to determine a set of molecular constants in each state. The bending vibrational frequency was estimated to be 86 cm^{−1} from the l‐type doubling constant of the v _{2}=1 state. The interval of the Φ and Π states in v _{2}=3 was determined to be 29.2280(24) cm^{−1}, giving the anharmonicity constant x _{ ll }=3.8611(9) cm^{−1} with one standard deviation in parentheses, which indicates that the molecule has a linear form. However, somewhat peculiar properties were recognized in dependence of the observed l‐type resonance and vibration‐rotation constants on the v _{2} vibrational quantum number, suggesting an effect of anharmonicity.

Nanosecond time‐resolved degenerate four‐wave mixing measurements of small Pd particles: Thermal phase grating analysis
View Description Hide DescriptionReflection by the thermal phase grating formed in methanol containing small Pd metal particles has been measured by using a degenerate four‐wave mixing optics equipped with a nanosecond Nd:YAG laser and a streak camera. Although the integrated intensity of the reflection depended on the cubic power of the laser intensity, the temporal profile of the reflection in a pulse duration showed the delayed response, the theoretical profile of which has been formulated by considering the formation of thermal phase grating. The theoretical calculation based on heat conduction equation was in good agreement to the experimental results with respect to the shape of the profile, the intensity, and the polarization dependence.

Toward preresonant impulsive Raman preparation of large amplitude vibrational motion
View Description Hide DescriptionThis article investigates a new approach to the optical generation of large‐amplitude coherent molecular vibrations in condensed media. On the basis of analytical results using pulse propagators in the classical Franck approximation, we are led to investigate the efficacy of driving vibrational motion in the electronic ground state by impulsive stimulated Raman scattering with a timed sequence of electronically preresonantfemtosecond laser pulses. Numerically exact computations are performed on a model system of dilute molecular Iodine in a low‐temperature host crystal. Vibrational relaxation is incorporated via Redfield theory. The results indicate that under a variety of conditions, chemically significant (greater than 0.1 Å) displacements can be produced in a Raman active mode with a fair measure of control over wave packet spreading, and without substantial population loss due to electronic absorption.

Solvation energies and electronic spectra in polar, polarizable media: Simulation tests of dielectric continuum theory
View Description Hide DescriptionA dielectric continuum theory for the solvation of a polar molecule in a polar, polarizable solvent is tested using computer simulations of formaldehyde in water. Many classes of experiments, for example those which measure solvent‐shifted vertical transition energies or electron transfer rates, require an explicit consideration of the solvent electronic polarization. Due to the computational cost of simulating a polarizable solvent, many simulation models employ non‐polarizable solute and solvent molecules and use dielectric continuum theory to relate the properties of the non‐polarizable system to the properties of a more realistic polarizable system. We have performed simulations of ground and excited state formaldehyde in both polarizable and non‐polarizable water, and the solvation energies and solvent‐shifted electronic spectra we obtained are used to test dielectric continuum, linear response predictions. Dielectric continuum theory correctly predicts that free energy differences are the same in polarizable and non‐polarizable water. The theory wrongly predicts that the reorganization energy in a polarizable solvent is 30% smaller than the reorganization energy in a polar, non‐polarizable solvent; in the simulations, the reorganization energies differ by only 6%. We suggest that the dielectric continuum theory fails because it assumes that both solute electronic states exist in the same size cavity in the solvent, whereas in the simulation the cavity radius increases by 20% after the electronic transition. We account for the change in the cavity size by adding a non‐linear solute–solvent coupling to the dielectric continuum theory, and find that the resulting predictions are just outside the error bounds from the simulation. The cavity size corrections have the undesired and incorrect side‐effect of predicting fluctuations far smaller than seen in the simulations. This reveals the inherent difficulty in devising a simple, fully self‐consistent dielectric continuum theory for solvation.

Equations‐of‐motion method for the spin–orbit coupling of aromatic molecules: Application to the phosphorescence lifetime of benzene
View Description Hide DescriptionA phosphorescence theory for aromatic molecules is formulated in terms of the equations‐of‐motion method. The theory is applied to the INDO/S calculations on the lowest triplet radiative lifetime of benzene. All the calculations are performed within the spin‐same‐orbit interaction approximation. The random‐phase approximations are found to give better results than the Tamm–Dancoff approximation (or the singly excited CI). The importance of the spin‐other‐orbit interactions contributing to the phosphorescence lifetime is discussed from the formula derived in an Appendix.

State‐resolved inelastic collisions of single rotational, fine‐structure, and Λ doublet levels of NH(A ^{3}Π) with helium: A combined experimental and theoretical study
View Description Hide DescriptionA comprehensive set of single‐collision state‐to‐state rate constants for the relaxation of NH(A ^{3}Π, v=0,N,F _{ i },e/f ) levels in collisions with helium are presented. These rate constants were extracted from measuredfluorescence intensities of isolated A→X rotational lines in the presence of He subsequent to laser excitation of individual levels in the A state. There is no indication of the collisional propensities predicted for a Hund’s case (a) ^{3}Π state, most likely because NH(A) represents an intermediate coupling case. With increasing N, NH(A) rapidly approaches the Hund’s case (b) limit. For high initial N, rotational relaxation proceeds predominantly through ΔN=−1 fine‐structure conserving transitions to Λ doublet levels with Π(A′) reflection symmetry. In addition, a propensity to conserve the Π(A′)/Π(A″) symmetry of the initial level is found for ΔN=0 fine‐structure changing transitions. The observed propensities have been interpreted by comparison with full quantum close‐coupling and coupled‐states calculations of cross sections based on ab initiopotential energy surfaces (PES’s). The propensity for forming Π(A′)Λ doublet levels in ΔN=−1 collisions of high N initial levels is found to be facilitated by approach in a ‘‘helicopterlike’’ orientation on the more attractive HeNH(A)A′ PES, followed by curve crossing to the more repulsive A″ PES which correlates adiabatically to the next lower rotational manifold. In addition, thermal rate constants derived from the calculated cross sections agree extremely well with those obtained from a deconvolution of the experimental spectra.

The reaction of Cs(8^{2} P) and Cs(9^{2} P) with hydrogen molecules
View Description Hide DescriptionThe reactions of Cs(n ^{2} P _{ J }), n=8, 9, J=1/2, 3/2 with H_{2} were studied by laser induced fluorescence of the nascent product. No difference was found in the reactivity of the J=1/2 and 3/2 states. The energies available to the reaction products were 11.5 and 16.9 kcal/mol for the n=8 and 9 states, respectively. CsH was found in the v=0 and 1 states but could not be detected in any higher vibrational state. The v=0/v=1 population ratios were 1/0.33 (n=8) and 1/0.42 (n=9). The products rotational temperatures were approximately the same as the ambient temperature of the reaction cell. Thus about 90% of the available energy is released as translation. From these data the following picture is derived. The mechanism is a primarily collinear abstraction and not an insertion. The large translational energy release is caused by a sudden switching on of repulsion when the H atoms are still close to each other. The reaction involves electron transfer, but at Cs–H distances not far from the equilibrium bond length and is therefore not a harpoon reaction in the usual sense.

Multimode Floquet theory for atomic and molecular laser‐modified collision processes
View Description Hide DescriptionWe outline a multimode‐Floquet‐based approach to the analysis of atomic and molecular laser‐modified collision processes. The approach depends upon Fourier decomposition of the radiation field and identification of time‐independent laser‐interaction elements in the Floquet representation. The corresponding time‐independent Floquet dynamical equations are solved and S‐matrix elements between the various Floquet channels collected to determine the transition probabilities of interest. The approach is examined for laser excitation in a model energy transfer system. Results are compared with ones obtained conventionally, i.e., by explicitly following the time dependence of the field amplitude. We conclude that the Floquet method nicely complements the conventional.

Vector correlation studies of HO_{2} photodissociation at 220 nm
View Description Hide DescriptionThe 220 nm photolysis of the hydroperoxyl radical, HO_{2}, is investigated by probing the ejected OH fragments using Doppler and polarizationspectroscopy. Analysis of the measured line profiles reveals that the OH fragments are predominately (84%) formed with the partner oxygen atom in its electronically excited ^{1} D state with a smaller component (16%) being associated with oxygen atoms in the ^{3} Pground electronic state.Measurement of OH fragment internal state distribution indicates that the 23 200 cm^{−1} of available energy is primarily released as electronic excitation of the oxygen atom (f _{el}=0.57) and to a lesser extent as relative translation of the products (f _{tr}=0.41). The internal degrees‐of‐freedom of the OH fragment receive very little of the available energy and are found to be fairly cold (f _{vib}<0.004 and f _{rot}=0.014). For the primary O(^{1} D) dissociation channel the measured 〈μ ⋅ v〉 correlation is strongly positive (β_{μv }=0.61) indicating a preference for parallel alignment of the electronic transition moment and the recoil velocity vector in HO_{2}, consistent with the excited state being of A″ symmetry. All other bipolar moments are close to zero for this pathway (β_{μJ }=−0.10, β_{ vJ }=−0.04, β_{μvJ }=−0.06) independent of the probed rotational quantum state of the OH fragment. For the minor O(^{3} P) pathway a comparable set of bipolar moments is obtained. An investigation into the source of OH fragment rotation reveals that the combined contributions from out‐of‐plane rotation, generated by initial parent thermal motion about A‐inertial axis, and in‐plane rotation, generated by the combination of bending mode zero‐point energy and final state interaction on the excited potential energy surface, result in negligible 〈v⋅J〉 correlation in the photodissociation of a thermally distributed sample of HO_{2} at 300 K.

Intramolecular vibrational relaxation seen as expansion in phase space. II. Reference ergodic systems
View Description Hide DescriptionThe aim of the paper is to estimate the volume of phase space that is, in principle, available to a nonstationary wave packet during its intramolecular vibrational relaxation. For that purpose, use is made of the maximum entropy method, together with the concept of constrained ergodicity to construct two so‐called reference ergodic systems. The first one concerns thermal excitation processes. In that case, the only two constraints that are imposed on the intramolecular dynamics arise from the normalization of the wave function and from the conservation of energy. These constraints affect the zeroth and first moments of the spectrum. The second reference system concerns a situation where, as an additional constraint, use is made of the information that the system has been prepared spectroscopically, i.e., by a specific excitation process, consisting in the coherent excitation of an initial pure state. Then, the second moment of the spectrum, denoted σ, is shown to provide the appropriate additional constraint. Translated into the time domain, the prior knowledge of the dynamics used as a constraint is limited to an infinitesimally brief period of time [0,dt] with the remaining evolution determined by the maximum entropy method. The spectroscopic reference system constructed in that way can be understood as the one that samples the maximal volume of phase space available to a wave packet having a specified average energy and being put in motion by a specified initial force.
Closed‐form expressions are obtained for the phase space volumes occupied by these two reference systems for various simple parametrizations of the function D(E) that expresses the density of states as a function of the internal energy (power laws or exponential increase). Thermal reference systems are found to sample a larger volume of phase space than their spectroscopic counterparts. The difference between these two cases depends critically on the value of σ, and also on the symmetry characteristics of the excitation process. In general, the volumes occupied by the reference systems, thermal as well as spectroscopic, can be expressed as ηE _{av} D(E _{av}), where E _{av} is the (conserved) average energy of the wave packet and η is a correcting factor that depends on the functional form of D(E) and on the nature of the imposed constraints. In all cases studied, the value of η was found not to greatly differ from 1. The method has been applied to the analysis of three experimental photoelectron spectra presenting different spectralcharacteristics (X̃ ^{2} A _{1} state of NH^{+} _{3}, X̃ ^{2} B _{3} state of C_{2}H^{+} _{4}, and the X̃ ^{2} A″ state of C_{2}H_{3}F^{+}). The fractional occupancy index F defined by Heller as the fraction of the available phase space eventually explored up to the break time T _{ B } could be determined. After a time of the order of 100 fs, F was found to be of the order of a few percent for thermal excitation. When the molecule presents some symmetry, the expansion of the wave packet is restricted to that part of phase space spanned by the totally symmetric wave functions. The use of this additional a priori knowledge increases the fractional index F.

Reaction dynamics of Mg(3s3p ^{1} P _{1}) with CH_{4}: Elucidation of reaction pathways for the MgH product by the measurement of temperature dependence and the calculation of ab initio potential energy surfaces
View Description Hide DescriptionUsing a pump–probe method, we have obtained the nascent bimodal rotational distribution of MgH (v″=0 and 1) products formed in the reaction of Mg(3s3p ^{1} P _{1}) with CH_{4}. The low‐N component of the distribution in the v″=0 state is much larger than that in the v″=1 state, whereas the high‐N component in the v″=0 state is roughly equivalent to that in the v″=1 state. The MgH (v″=0) rotational distributions at three temperatures, 770, 830, and 880 K, were measured. The bimodal distribution does not change with temperature within a small experimental error. The findings suggest that the bimodal nature results from the same process, supporting a mechanism of Mg insertion into the C–H bond, irrespective of the geometry of the entrance approach. The result is consistent with that of Kleiber et al. using the far‐wing scattering technique, and is supported by Chaquin et al.’s theoretical calculations. We also calculated two‐dimensional potential energy surfaces for the excited and ground states of the reaction system. The calculation suggests that two possible trajectories are responsible for the production of MgH following a nonadiabatic transition. One trajectory, weakly dependent on the bending angle of H–Mg–CH_{3}, is related to formation of the low‐N component. The other trajectory evolves through a linear geometry of the intermediate complex prior to dissociation, causing a strong anisotropy in the PES. This second trajectory corresponds to the population of rotationally and vibrationally hot states. An alternative explanation of the low‐N distribution is also discussed.