Volume 111, Issue 1, 01 July 1999
 COMMUNICATIONS


Femtosecond timeresolved photoelectron–photoion coincidence imaging studies of dissociation dynamics
View Description Hide DescriptionWe present the first results using a new technique that combines femtosecond pump–probe methods with energy and angleresolved photoelectron–photoion coincidence imaging. The dominant dissociativemultiphoton ionization (DMI) pathway for at 375.3 nm is identified as threephoton excitation to a repulsive potential surface correlating to followed by onephoton ionization to Dissociation along this surface is followed on a femtosecond timescale.

Competing atomic and molecular hydrogen pathways in the photodissociation of methanol at 157 nm
View Description Hide DescriptionPhotofragment translational spectra at 3(HD), and have been obtained for and at 157 nm excitation. Analysis of the timeofflightspectra reveals two different atomic H loss channels: hydroxyl H elimination, and methyl H elimination. While the hydroxyl H elimination seems to be a single fast process, the methyl H loss exhibits clearly two significantly different mechanisms: one fast and one slow. Experimental results also show two molecular hydrogen elimination channels: threecenter elimination from the methyl group, which displays two different micropathways, and fourcenter elimination involving hydrogen atoms on both the C and O sites. The relative branching of the atomic versus molecular hydrogen elimination channels was found to be 1:0.15. These results present a uniquely clear picture of methanol photodissociation at 157 nm, and thus provide an excellent case for quantitative theoretical investigations.

Electric field induced lateral instability in a simple autocatalytic front
View Description Hide DescriptionThe effect of ionic drift caused by small constant electric field on autocatalytic reaction fronts of ionic species is studied both theoretically and numerically. Besides varying the velocity of propagation, the electric field parallel to the direction of propagation may induce lateral instability in planar fronts resulting in the emergence of cellular structures. The difference in the diffusivities at the onset of instability are lowered when the electric field tends to separate the species spatially. The predictions of the linear stability analysis based on a thinfront approximation are confirmed by the numerical integration of the full twodimensional system.

Surface vibrational coherence at the /air interface: Vibrational wave packet dynamics as a probe of interface inhomogeneity
View Description Hide DescriptionVibrational wave packet dynamics from a monolayercovered surface are reported. These dynamics reflect surface vibrational coherence in a monolayer of amphiphilic molecules deposited at the /air interface. The induced macroscopic polarization following coherent excitation of adsorbate vibrational modes displays quantum interferenceeffects (quantum beats) and decays on a time scale dependent on the nature of the interfacial environment. These observations provide a link between the degree of interfacial order and the vibrational coherence lifetime and demonstrate that monitoring interfacial wave packet dynamics represents a new method for characterizing these important chemical regions.
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 THEORETICAL METHODS AND ALGORITHMS


Kinetic energy conserving integrators for Gaussian thermostatted SLLOD
View Description Hide DescriptionA new integration scheme is developed for nonequilibrium molecular dynamics simulations where the temperature is constrained by a Gaussian thermostat. The utility of the scheme is demonstrated by its application to the SLLOD algorithm which is the standard nonequilibrium molecular dynamics algorithm for studying shear flow. Unlike conventional integrators, the new integrators are constructed using operatorsplitting techniques to ensure stability and that little or no drift in the kinetic energy occurs. Moreover, they require minimum computer memory and are straightforward to program. Numerical experiments show that the efficiency and stability of the new integrators compare favorably with conventional integrators such as the Runge–Kutta and Gear predictor–corrector methods.

Thirdorder nonlinear optical response of energy transfer systems
View Description Hide DescriptionThe thirdorder nonlinear optical response of energy transfersystems is theoretically investigated. A system composed of two chromophores having the same electronic transition energies is considered. The dynamics of energy transfer between the two chromophores is assumed to occur via a hopping (incoherent) mechanism. We introduce new types of pathways incorporating the hopping processes occurring while the system is in population states and reconstruct a thirdorder response function which is computationally viable. The nuclear propagators in the electronic population states are written as convolution integrals between those of the nonreactive twostate system weighted by some factors for the energy transfer. The response function is given by multitime correlation functions and these are analyzed by the cumulant expansion method. Based on this approach, the threepulse photon echo peak shift for several models of energy transfersystems is discussed. It is shown that the rephasing capability of the induced signal is reduced by the memory loss due to resonantenergy transfer. A previous model which incorporates resonantenergy transfers in an intuitive way is reviewed and modified to supplement the loss of dynamic correlation of nuclear motion within the framework of the theory. The response function obtained by our new approach gives a more accurate description than the existing theory and a comparative discussion is given. The effect of inhomogeneity in rate constants on the thirdorder signal is discussed and the temperature dependence of the echo signal is examined.

The conical intersection effects and adiabatic singlesurface approximations on scattering processes: A timedependent wave packet approach
View Description Hide DescriptionUsing a quasiJahnTeller model and an extended version of the approximate BornOppenheimer (BO) single surface equations, Baer, Charutz, Kosloff, and Baer [J. Chem. Phys. 105, 9141 (1996)] have performed timeindependent scattering calculations to study a direct effect on the symmetry of the nuclear wave function due to conical intersections between BO potential energy surfaces. In this article, we have addressed the same problem using the same model by introducing either a vector potential in the nuclear Hamiltonian or by incorporating a phase factor in the nuclear wave function. The scattering calculations have been carried out by using a timedependent wave packet approach.

The Hermite correction method for nonadiabatic transitions
View Description Hide DescriptionWe have performed molecular dynamics simulations on a system where electronic transitions are allowed anywhere in configuration space among any number of coupled states. A classical path theory based on the Hermite correction to the Gaussian wave packet expansion, proposed by Gert D. Billing [J. Chem. Phys. 107, 4286 (1997)] has been used. The calculations are carried out on the same model used by J. C. Tully [J. Chem. Phys. 93, 1061 (1990)] and the transition probabilities agree well with corresponding exact quantum mechanical results.

Roles of nuclear attraction and electron repulsion energies in the relative stability of atomic terms
View Description Hide DescriptionNumerical Hartree–Fock values of the electron–nucleus attraction and electron–electron repulsion energies are examined for 2392 spectroscopic terms of 170 electronic configurations (with two or more terms) arising in 80 different neutral atoms of the periodic table. For 161 configurations, it is confirmed that a lower energy term has smaller and larger than a highenergy term, as considered to be general in the literature. In particular, the ground term has the smallest and the largest The differences and between two terms arising from a configuration are found to have a good linear correlation with the corresponding difference in the total energy. However, peculiar exceptions are observed for nine electronic configurations with two open subshells. In five configurations, the ground term has the smallest but not the largest In four configurations, the ground term has neither the smallest nor the largest

Gradients for the similarity transformed equationofmotion coupledcluster method
View Description Hide DescriptionA derivation of gradients for the similarity transformed equationofmotion coupledcluster singles and doubles method is presented. Algebraic operator equations for all of the terms which appear in the equations are given, with a discussion about the procedure for solving the equations.

Flow of zeropoint energy and exploration of phase space in classical simulations of quantum relaxation dynamics
View Description Hide DescriptionNecessary conditions under which a classical description will give the correct quantum relaxation behavior are analyzed. Assuming a nonequilibrium preparation, it is shown that the longtime mean values of observables can be expressed in terms of the spectral density and statespecific level densities of the system. Any approximation that reproduces these quantities therefore yields the correct expectation values at long times. Apart from this rigorous condition, a weaker but more practical criterion is established, that is, to require that the total level density is well approximated in the energy range defined by the spectral density. Since the integral level density is directly proportional to the phasespace volume that is energetically accessible to the system, the latter condition means that an appropriate classical approximation should explore the same phasespace volume as the quantum description. In general, however, this is not the case. A wellknown example is the unrestricted flow of zeropoint energy in classical mechanics. To correct for this flaw of classical mechanics, quantum corrections are derived which result in a restriction of the classically accessible phase space. At the simplest level of the theory, these corrections are shown to correspond to the inclusion of only a fraction of the full zeropoint energy into the classical calculation. Based on these considerations, a general strategy for the classical simulation of quantum relaxation dynamics is suggested. The method is (i) dynamically consistent in that it refers to the behavior of the ensemble rather than to the behavior of individual trajectories, (ii) systematic in that it provides (rigorous as well as minimal) criteria which can be checked in a practical calculation, and (iii) practical in that it retains the conceptional and computational simplicity of a standard quasiclassical calculation. Employing various model problems which allow for an analytical evaluation of the quantities of interest, the virtues and limitations of the approach are discussed.

Flow of zeropoint energy and exploration of phase space in classical simulations of quantum relaxation dynamics. II. Application to nonadiabatic processes
View Description Hide DescriptionThe unphysical flow of zeropoint energy (ZPE) in classical trajectory calculations is a consequence of the fact that the classical phasespace distribution may enter regions of phase space that correspond to a violation of the uncertainty principle. To restrict the classically accessible phase space, we employ a reduced ZPE whereby the quantum correction γ accounts for the fraction of ZPE included. This ansatz is based on the theoretical framework given in Paper I [G. Stock and U. Müller, J. Chem. Phys. 111, 65 (1999), preceding paper], which provides a general connection between the level density of a system and its relaxation behavior. In particular, the theory establishes various criteria which allows us to explicitly calculate the quantum correction γ. By construction, this strategy assures that the classical calculation attains the correct longtime values and, as a special case thereof, that the ZPE is treated properly. As a stringent test of this concept, a recently introduced classical description of nonadiabatic quantum dynamics is adopted [G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997)], which facilitates a classical treatment of discrete quantum degrees of freedom through a mapping of discrete onto continuous variables. Resulting in negative population probabilities, the quasiclassical implementation of this theory significantly suffers from spurious flow of ZPE. Employing various molecular model systems including multimode models with conically intersecting potentialenergysurfaces as well as several spinbosontype models with an Ohmic bath, detailed numerical studies are presented. In particular, it is shown, that the ZPE problem indeed vanishes, if the quantum correction γ is chosen according to the criteria established in Paper I. Moreover, the complete time evolution of the classical simulations is found to be in good agreement with exact quantummechanical calculations. Based on these studies, the general applicability of the method, the performance of the classical description of nonadiabatic quantum dynamics, as well as various issues concerning classical and quantum ergodicity are discussed.

Definition and properties of the emission anisotropy in the absence of cylindrical symmetry of the emission field: Application to the light quenching experiments
View Description Hide DescriptionWe considered the properties of the fluorescenceanisotropy when the cylindrical symmetry of the fluorescence emission field is absent due to the effects of polarized light quenching. By light quenching we mean stimulated emission by a second longer wavelength pulse following the excitation pulse. In these experiments one observes the excited state population which remains following stimulated emission. When cylindrical symmetry is not present the generally known definition of the emission anisotropy cannot be applied. A generalized theory of anisotropy was described previously by Jabloński. However, we found this formalism to be inadequate for the expected experimental results of light quenching. An extension of this concept, which we call an anisotropy vector, appears capable of describing the expected orientation under all conditions of light quenching. We found that the anisotropy vector can exist within a plane defined by two projections and The projection is comparable to the classical steady state or timedependent anisotropy with cylindrical symmetry. The projection has no direct analogue in classical anisotropy theory. The interesting behavior of the anisotropy vector is that all possible points are placed inside a certain triangle, which we call a triangle of anisotropy. For symmetrical molecules, or for molecules which display isotropic depolarizing rotations, the anisotropy vector is expected to decay on the anisotropy triangle along straight lines towards the origin. The concept of the anisotropy vector should allow predictions of the effect of polarized light quenching on the anisotropy decays, and suggests experimental methods to study anisotropy decays in the presence of light quenching. Further work is needed to apply these concepts to anisotropic rotators.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Ultraviolet photodissociation of furan probed by tunable synchrotron radiation
View Description Hide DescriptionThe photodissociationdynamics of furan at 193 nm have been studied using photofragment translational spectroscopy with tunable vacuum ultraviolet (VUV) probe provided by synchrotron radiation on the Chemical Dynamics Beamline at the Advanced Light Source. Three primary channels are observed: and The evidence suggests that the two closedshell channels occur on the groundstatepotential energy surface (PES) following internal conversion, while the radical channel likely takes place on an excited PES. All channels exhibit a barrier for dissociation with the channel having the largest value at about 25 kcal/mol. Angular distribution measurements show anisotropy only for the radical channel. These findings are consistent with a rapid excited state dissociation for the radical channel and slow dissociation for the other two pathways. The two groundstatedissociation channels— and acetylene+ketene—should be important in the thermal decomposition of furan as was found in pyrolytic studies [A. Lifshitz, M. Bidani, and S. Bidani, J. Phys. Chem. 90, 5373 (1986)] and theoretical investigations [R. Liu, X. Zhou, and L. Zhai, J. Comput. Chem. 19, 240 (1998)].

Positron and positronium chemistry by quantum Monte Carlo. IV. Can this method accurately compute observables beyond energy?
View Description Hide DescriptionMany different properties of the positron containing systems PsH, LiPs, and were computed using both variational Monte Carlo and fixed nodediffusionMonte Carlo methods, and explicitly correlated trial wave functions. Our results show that these techniques can accurately compute not only energy values, but also other observables. Our values for PsH, and LiPs are in good agreement with the most recent state of the art correlated calculations, while for our calculations are the first to give reliable results.

Energy partitioning in two kinds of NO molecules generated from the reaction of with Vibrational state distributions of “new” and “old” NO’s
View Description Hide DescriptionThe reaction of with produces two kinds of NO molecules, the “old” one which originally exists in and the “new” one which includes the attacking O atom. Using the isotopically labeled reagent, we determined the vibrational state distributions of these NO’s ( ) separately. To obtain the distributions, two types of experiments were performed with the laserinduced fluorescence(LIF) technique via the NO and transitions. First, the relative populations of NO molecules (the sum of the two kinds of NO’s) in levels were measured with unlabeled reagents. Then, isotopically labeled reaction, was utilized to determine the relative ratio between the two kinds of NO’s in the vibrational levels of and 12–15. Combining the above results with previously determined vibrational state distribution of NO in high vibrational levels [J. Chem. Soc., Faraday Trans. 94, 1575 (1998)], we were able to obtain a complete set of vibrational state distributions. It was found that the old NO dominantly populated in and 1 whereas the new NO extended its population toward higher vibrational levels However, in high vibrational levels, the old NO still have a considerable population due to the rapid energy transfer to the old NO. The observed efficient energy transfer to the old NO is attributed to the absence of light atoms in the present reacting system. Compared with the system including hydrogen atoms, the state density and the momentum coupling among the vibrational modes are much larger and accelerate the energy redistribution in spite of the short lifetime.

The spectroscopy and intramolecular vibrational energy redistribution dynamics of HOCl in the region, probed by infraredvisible double resonance overtone excitation
View Description Hide DescriptionWe use infraredvisible double resonance overtone excitation to promote HOCl molecules to single, wellcharacterized rotational levels of high OH stretching states just above the dissociation threshold on the ground potential energy surface. Double resonance spectra are monitored by laser induced fluorescence detection of the OH dissociation products. We present here the results obtained in the region of where we have studied states with J ranging from 4 to 25, from 0 to 5 and energy up to 300 cm^{−1} above the dissociation threshold. In the spectra for states, the zerothorder level is split by mixing with a nearby dark state. Because the two states have very different Arotational constants, their separation increases with but the effects of the mixing remain observable in the spectrum up to Comparison with preliminary results from together with analysis of the rotational constants, allows us to identify the perturbing state as (4,4,2). The lack of further strong perturbations compared to the average density of states allows us to infer that most of the matrix elements for couplings between the (6,0,0) bright state and other dark states are less than ∼0.1 cm^{−1}. The average intramolecular vibrational energy redistribution (IVR) rate implied by these matrix elements is two orders of magnitude longer than the predictions of statistical rate theory, indicating that IVR is likely to be the rate limiting step in the unimolecular dissociation process from (6,0,0). The present work provides the spectroscopic foundation for direct timeresolved studies of the unimolecular dissociation dynamics presented in a forthcoming paper.

Resonant twophoton ionization spectra of van der Waals complexes p, m,
View Description Hide DescriptionWe have studied the resonant twophotonionization (R2PI) spectra of three van der Waals (vdW) complexes p, m, through the transition with mass selectivity. The stretching frequencies of the three vdW complexes were found to be quite close (86 cm^{−1}). From the photodissociation mechanism and the relationship between anharmonicity of the stretching vibration and the dissociation energy, we estimated the dissociation energies of all the three vdW complexes in the and states. A quantum ab initio calculation on at the level gave the following geometry: The N atom of is located on the symmetry axis (Zaxis) and 3.53 Å above the benzene ring; the axis of is at an angle of 52.5° with the Zaxis of with one of the hydrogen atoms pointing towards the benzene ring; the rotation of around the Zaxis is nearly free. The calculated bond dissociation energies and the expectation of internal rotation are consistent with our experimental results.

Symmetry and structure of rotating
View Description Hide DescriptionWe present a global study of how the relative equilibria of the ion change as the angular momentumJ increases. A relative equilibrium is a classical trajectory for which the molecule rotates about a stationary axis without changing its shape. The study confirms previous results which show that the geometry of the minimum energy relative equilibria changes from an equilateral triangle to a symmetric linear configuration at around The series of bifurcations and stability changes that accompany this transition is presented in detail. New results include the discovery that the rotating equilateral triangle remains linearly stable for a large range of angular momentum values beyond the point where it ceases to be a minimum of the total energy. A third type of relative equilibrium, a rotating isosceles triangle, is also found to be linearly stable in the approximate range Both the equilateral and isosceles triangle configurations lose stability via Hamiltonian–Hopf bifurcations. The frequencies and symmetry species of the normal modes of the stable relative equilibria are computed and harmonic quantization is used to predict how the symmetries of the lowest lying quantum states will change as J increases. Energy level clustering due to tunneling between symmetryequivalent relative equilibria is described.

Doppler line shapes in the photolysis of laser excited, aligned molecules: Application to the vibrationally mediated photodissociation of
View Description Hide DescriptionA general expression for the Doppler profile for fragments produced in the photodissociation of laser excited, aligned molecules, as in vibrationally mediated photodissociation (VMP), is presented. In contrast to onephoton dissociation, for which the Doppler profile depends only on the second moment of the fragment molecularframe angular distribution, the profile in the case of VMP is sensitive to several moments of the angular distribution, up to In addition, the profile for a nearprolate molecule depends on the angle between the electronic transition moment μ and the a inertial axis. This theory is applied to the analysis and interpretation of Doppler profiles in the laser fluorescence detection of fragments, of rotational angular momenta and 10, from the 532 nm VMP of excited to the second N–H stretch overtone level For both Λdoublets of these rotational levels, the second moment of the molecularframe angular distribution was found to be positive, in agreement with previous results for highJ fragments from onephoton photolysis of The profiles are consistent with a value of ∼0° for the angle These values for and are inconsistent with simple expectations based on planar, prompt dissociation upon excitation to the lowest singlet excited state and suggest the importance of nonplanar geometries in the dissociation dynamics.
