Volume 112, Issue 19, 15 May 2000
 ARTICLES

 Theoretical Methods and Algorithms

Ground and excited Hubbard states for buckminsterfullerene with uniform and alternating bond strengths
View Description Hide DescriptionA detailed investigation on the electronic ground and lowest excited g and usymmetrical singlet and triplet states of icosahedral is performed in the framework of the semiempiricalHubbard model using single and double excited configuration interaction (SDCI) upon an appropriately chosen reference space constructed out of Hartree–Focktype molecular orbitals. We present SDCI results for energies, wavefunction symmetries, bond orders and spin–spin correlations for these states. For the ground state, second order Mo/ller–Plesset (MP2) and sizeconsistency corrected energies are presented and compared with Monte Carlo results. We also examine the influence of bond length alternation on the calculated properties. It is shown that within the Hubbard model the lowest excited g and u singlet and triplet states of give very similar overall bond orders and spin–spin correlations.

Semiclassical approximations to realtime quantummechanical effects in correlation functions of complex molecular systems
View Description Hide DescriptionSemiclassical approximation of realtime quantum effects is analyzed with the aid of the semiclassical initial value representation (SCIVR) and Wigner distribution functions. We utilize these two ingredients to propose a new version of the semiclassical correlation function that contains, in principle, all quantummechanical effects. The advantage of this formulation is that it allows for a stepwise approximation specifically for realtime quantum effects based on a gradual inclusion of more degrees of freedom into the integral responsible for interference. From numerical calculations, this procedure does not seem to depend significantly on the choice coordinates if all degrees of freedom are coupled. This freedom from the coordinate choice removes possible ambiguities in applying this method. Several example cases are presented to demonstrate the usefulness of this approach.

A method for molecular dynamics simulation of confined fluids
View Description Hide DescriptionWe report the development of a simulation method, with advantages for simulating fluids confined between solid substrates and in equilibrium with bulk fluids. For moleculardynamics simulations, the isothermal–isobaric constraint method is modified to implement this method. Longrange corrections to the pressure tensor for simple confined systems are also derived and included. Consistent with previous studies employing the grandcanonical ensemble, confined LennardJones and modeldecane fluids investigated with this method show layering induced by the confining surfaces, oscillatory surfaceforce profiles, and steplike dependencies of the number of confined molecules on surface separation. For a confined LennardJones fluid, increasing the bulk pressure at a fixed temperature enhances layering, increases the effect of surface structure on the surfaceforce profile, and causes the surface forces to be more repulsive.

Testing the identifiability of a model for reversible intermolecular twostate excitedstate processes
View Description Hide DescriptionThe modeling of excitedstate processes in photophysics can conveniently be done within the framework of compartmental analysis. In compartmental analysis substantial attention has been devoted to the study of deterministic identifiability, which verifies whether it is possible to determine the parameters of the compartmental model from errorfree data. In this paper the similarity transformation approach is applied to the identifiability problem of the photophysical model for reversible intermolecular twostate excitedstate processes. This method provides straightforward relations between the true and alternative sets of the system parameters. This allows one to explore directly the parameter space for identifiability. Since absolute values for the spectral parameters associated with excitation and emission are not available from timeresolved fluorescence experiments, the original similarity transformation approach to the identifiability problem was reformulated in terms of normalized spectral parameters, which are experimentally accessible. It is shown that six decay traces—measured at two coreactant concentrations and three emission wavelengths—are required for the model to be locally identifiable. Two sets of rate constants and associated spectral parameters may be found under these conditions. Enclosure in the analysis of the monoexponential decay at very low coreactant concentration results in global identifiability. The nonnegativity requirement of the spectral parameters also can lead to the unique solution. If the fluorescence decays are independent of the emission wavelength, additional information about the photophysical system is necessary for identifiability.

Electricfielddependent empirical potentials for molecules and crystals: A first application to flexible water molecule adsorbed in zeolites
View Description Hide DescriptionA general method to include electricfielddependent terms in empirical potential functions representing interatomic interactions is proposed. It is applied to derive an intramolecular potential model for the water molecule able to reproduce the effects of an electric field on its geometry and dynamics: to enlarge the HOH angle, to increase slightly the OH bond lengths, to redshift the stretching vibrational frequencies, and to blueshift slightly the bending mode frequency. These effects have been detected experimentally for water adsorbed in zeolites and have been confirmed by quantum mechanical calculations. The electricfielddependent intramolecular potential model for water has been combined with a newly refined intermolecular potential for bulk water and with new potentials representing cation–water and aluminosilicate–water interactions in order to simulate, by classical molecular dynamics (MD) technique, the behavior of water adsorbed in zeolites. The performances of the model have been checked by a MD simulation of liquid water at room temperature, by the structural and vibrational properties of the water dimer, and by test MD calculations on a hydrated natural zeolite (natrolite). The results are encouraging, and the simulations will be extended to study the behavior of water adsorbed in other zeolites, including diffusion and some aspects of ion exchange processes.

Density functional calculations of nuclear quadrupole coupling constants in the zeroorder regular approximation for relativistic effects
View Description Hide DescriptionThe zerothorder regular approximation (ZORA) is used for the evaluation of the electric field gradient, and hence nuclear quadrupole coupling constants, in some closed shell molecules. It is shown that for valence orbitals the ZORA4 electron density, which includes a small component density (“picturechange correction”), very accurately agrees with the Dirac electron density. For hydrogenlike atoms exact relations between the ZORA4 and Dirac formalism are given for the calculation of the electric field gradient. Density functional(DFT) calculations of the electric field gradients for a number of diatomic halides at the halogen nuclei Cl, Br, and I and at the metallic nuclei Al, Ga, In, Th, Cu, and Ag are presented. Scalar relativistic effects, spin–orbit effects, and the effects of picturechange correction, which introduces the small component density, are discussed. The results for the thallium halides show a large effect of spin–orbit coupling. Our ZORA4 DFT calculations suggest adjustment of some of the nuclear quadrupole moments to and which should be checked by future highly correlated ab initio relativistic calculations. In the copper and silver halides the results with the used gradient corrected density functional are not in good agreement with experiment.

Diffusion of reactive species tuned by modulated external fields: Application to high performance chromatography
View Description Hide DescriptionIn order to improve the separation of any given chemical species from a mixture of compounds with close thermodynamic and kinetic properties, we propose a new chromatography procedure in the presence of a uniform timeperiodic field. In the framework of a macroscopic reaction–diffusion model in an external field, we prove that the apparent motion of the chemical species is of diffusion type and determine an approximate analytical expression for the effective diffusion coefficient. Considering this coefficient as a function of the rate constants and maximizing it leads to specific relations between rate constants and field properties interpreted as stochastic resonances. In the case of an electric field, we show that these constraints are compatible with typical experimental values.

On the importance of an accurate representation of the initial state of the system in classical dynamics simulations
View Description Hide DescriptionA definition of a quantumtype phasespace distribution is proposed in order to represent the initial state of the system in a classical dynamics simulation. The central idea is to define an initial quantum phasespace state of the system as the direct product of the coordinate and momentum representations of the quantum initial state. The phasespace distribution is then obtained as the square modulus of this phasespace state. The resulting phasespace distribution closely resembles the quantum nature of the system initial state. The initial conditions are sampled with the distribution, using a grid technique in phase space. With this type of sampling the distribution of initial conditions reproduces more faithfully the shape of the original phasespace distribution. The method is applied to generate initial conditions describing the threedimensional state of the Ar–HCl cluster prepared by ultraviolet excitation. The photodissociationdynamics is simulated by classical trajectories, and the results are compared with those of a wave packet calculation. The classical and quantum descriptions are found in good agreement for those dynamical events less subject to quantum effects. The classical result fails to reproduce the quantum mechanical one for the more strongly quantum features of the dynamics. The properties and applicability of the phasespace distribution and the sampling technique proposed are discussed.

On the diffusioninfluenced reversible trapping problem in one dimension
View Description Hide DescriptionThe exact Green function for a particle moving between two static reversible traps in one dimension is obtained for the continuous diffusion model. From this function, we derive the exact expressions of various survival probabilities, which are the key elements in devising the efficient Brownian dynamics algorithm. An exact expression of the mean survival probability is also obtained for the periodic distribution of reversible traps both for the crossingallowed and crossingforbidden cases. For the random distribution of reversible traps, the exact mean survival probability is obtained only for the crossingforbidden case and its long time behavior is compared with that of the crossingallowed case. We find, in this case, that not only the long time asymptotic relaxation behavior but also the equilibrium concentration itself can be changed from the classical results due to the fluctuation effect of the trap density.

On the independence of nonadiabatic coupling elements on the choice of origin of the coordinate system
View Description Hide DescriptionA finitedifference approach is employed to demonstrate the manner in which the values of nonadiabatic radial coupling matrix elements vary with the choice of origin of the nuclear coordinate system. Configuration interaction (CI) calculations for a series of excited states of the HCl molecule verify that such results do not depend on the location of the center of mass as long as it is held fixed during the differentiation process. The reason that radial coupling matrix elements are found to vary with the choice of origin of the coordinate system in standard scattering formulations is that the corresponding motion is not purely internal but rather has a definite translational component, namely a linear dependence of on the bond distance R is assumed. An identity which relates variations of such (mixed internaltranslational motion) nonadiabatic coupling elements to the value of the electric dipole transition moment when the latter prescription is employed for choosing the origin of the nuclear coordinate system is also verified by the present CI calculations.

Accurate wave packet propagation for large molecular systems: The multiconfiguration timedependent Hartree (MCTDH) method with selected configurations
View Description Hide DescriptionThe multiconfiguration timedependent Hartree (MCTDH) method is a general, accurate algorithm for wave packet propagation calculations. Its efficiency is due to the use of an optimally small timedependent basis set which evolves with the wave packet. The method however suffers from an exponential scaling of the required effort with system size, though with a much lower base than the exponential scaling of the standard propagation scheme. Here, we present a method to reduce the computational resources required for MCTDH calculations on large systems by selecting and propagating only the most important configurations for the representation of the wave function. At the same time the properties of the MCTDH method, such as convergence against numerically exact solutions, are retained.

The generalized Kramers theory for nonequilibrium open onedimensional systems
View Description Hide DescriptionThe Kramers theory of activated processes is generalized for nonequilibrium open onedimensional systems. We consider both the internal noise due to thermal bath and the external noise which are stationary, Gaussian and are characterized by arbitrary decaying correlation functions. We stress the role of a nonequilibrium stationary state distribution for this open system which is reminiscent of an equilibrium Boltzmann distribution in calculation of rate. The generalized rate expression we derive here reduces to the specific limiting cases pertaining to the closed and open systems for thermal and nonthermal steady state activation processes.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Stereodynamics of the reactions of with saturated hydrocarbons: The dependences on the collision energy and the structural features of hydrocarbons
View Description Hide DescriptionStateselected differential cross sections (DCSs) have been measured for the OH radicals produced from the reactions of with saturated hydrocarbons by utilizing Dopplerresolved polarizationspectroscopy. Stereodynamics in the reactions of secondary and tertiary hydrogen atoms are discussed based on the dependences of the DCSs on the collision energy and the structure of these hydrocarbons. For the reaction, the DCS of the shows predominant intensities in the backward hemisphere with reference to the incident atom at a mean collision energy of When the collision energy is raised to the OH radicals scattered in the forward hemisphere grow almost to match those in the backward hemisphere. The observed increase in the forward scattering implies that the collision energy makes the large impact parameter collisions contribute to the reactive scattering. At a similar collision energy of the forward scattering component in the DCS of the reaction does not exceed that of the This shows that the cone of acceptance is not enlarged in the reaction from that in the reaction, as opposed to the expectation based on the height of activation barrier. The absence of the enlargement of the cone of acceptance can be attributed to a large steric hindrance caused by the three bulky methyl groups surrounding the reactive tertiary C–H bond of The difference in the steric hindrance can explain the difference in the temperaturedependent preexponential factors of the macroscopic reaction rates between the abstraction of the secondary and tertiary C–H bonds. The collision energy dependence of the DCS as well as the internal excitation of alkyl radical products reveal that the reactions are not always dominated by the simple rebound mechanism, which has long been believed.

Timeresolved dissociative intenselaser field ionization for probing dynamics: Femtosecond photochemical ring opening of 1,3cyclohexadiene
View Description Hide DescriptionThe concerted photochemical ring opening of 1,3cyclohexadiene was investigated in the gas phase by lowintensity pumping at 267 nm and subsequent probing by highintensity photoionization at 800 nm and massselective detection of the ion yields. We found five different time constants which can be assigned to traveling times along consecutive parts of the potential energy surfaces. The molecule is first accelerated in the spectroscopic state 1B along Franck–Condon active coordinates, then alters direction before changing over to the dark state 2A. All constants including that for leaving the 2A surface are below 100 fs. These times are shorter than appropriate vibrational periods. Such a maximum speed is evidence that the pathway is continuous leading from surface to surface via real crossings (conical intersections) and that the molecule is accelerated right into the outlet of the 2A/1A funnel. On the ground state it arrives as a compact wave packet, indicating a certain degree of coherence. The experimental method promises a high potential for investigating dynamics, since many consecutive phases of the process can be detected. This is because the fragmentation pattern depends on the location on the potential energy surface, so that monitoring several different ions permits to conclude on the population flow through these locations. Ionization at the intensities used is normally considered to be an effect of the electric field of the radiation. But in our case it is enhanced by resonances in the neutral molecule and in particular in the singly positive ion, and it is not sensitive for the length of the molecule (different conformers of the product hexatriene). The ionic resonances explain why hexatriene has a much richer fragmentation pattern than cyclohexadiene. Coulomb explosion is observed from an excited state of a doubly positive ion. Its mechanism is discussed.

Photoinduced nucleation: A novel tool for detecting molecules in air at ultralow concentrations
View Description Hide DescriptionThis paper describes the development of a novel detection method and the demonstration of its capability to detect substances at concentrations as small as a few parts per trillion. It is shown that photoinduced nucleation is not in itself a nucleation process; rather, supersaturated vapor condenses onto longlasting clusters formed by chemical reaction of photoexcited molecules. The role of the supersaturated vapor is to increase the size of these photoproducts by condensation to a size readily detectable by light scattering. Furthermore, the measured nucleation rate variation with illumination wavelength exactly matches the substance’s vaporphase UV light absorption wavelength dependence, thus providing species identification. The ability to detect and identify molecules of substances at extremely low concentrations from ambient air is useful for detecting and monitoring pollutants, and for detecting explosives such as TNT.

Line strengths, selfbroadening, and line mixing in the branch of carbon dioxide
View Description Hide DescriptionUsing a difference frequency spectrometer we have measured the to transitions of carbon dioxide at 296 K and pressures up to 15 kPa. These low pressure spectra were analyzed using both the Voigt model, and an empirical line shape that blends together a hard collision model and a speed dependent Lorentzian profile. The broadening coefficients were obtained with an accuracy of 1% or better. The low density or first order low pressure line mixing parameters were also determined. We have compared both our measured low pressure linemixing parameters and the complete band spectrum at high pressures with those predicted by a relaxation matrix calculated from an EPG fitting law. Spectra at the highest pressures were recorded using both the difference frequency spectrometer and an FTIR spectrometer, the temperature for the latter experiments being 303 K. The vibrational band intensity and linear pressure shift of the branch as a whole were also measured.

Accurate ab initio nearequilibrium potential energy and dipole moment functions of the ground electronic state of ozone
View Description Hide DescriptionWe report a highly correlated multireference configuration interaction calculation of the nearequilibrium potential energy surface of ozone using a large correlation consistent basis set. Threedimensional analytical expressions are obtained for the potential energy and dipole moment functions using leastsquares fits to ab initio points near the equilibrium geometry. Lowlying vibrational band origins of and some of its isotopic variants are calculated using the ab initiopotential energy function. The calculated fundamental frequencies for the symmetric stretching and bending vibrations are within about of the observed values, while that for the antisymmetric stretch deviates from experiment by about The agreement with experiment can be significantly improved if the ab initiopotential energy function is scaled in the antisymmetric stretching coordinate. Absolute infrared absorption intensities are also calculated using ab initioelectric dipole moment functions and in good agreement with the available experimental data.

Quantized dynamical bottlenecks and transition state control of the reaction of D with Effect of varying the total angular momentum
View Description Hide DescriptionAccurate quantum mechanical scattering calculations for the reaction of D with are analyzed for evidence that quantized transition states control the reaction dynamics over a wide range of total angular momenta. We find that quantized transition states control the chemical reactivity up to high energy and for values of the total angular momentum up to at least nine. We show that the average transmission coefficient for individual dynamical bottlenecks up to 1.6 eV is greater than 90% for all four of the values of considered We assign energies, widths, levelspecific transmission coefficients, and quantum numbers to eleven transition state levels for and two for and we show how a separable rotation approximation (SRA) based on these data predicts thermal rate constants for temperatures between 500 and 1500 K that are within 0.3%–5.0% of the values obtained from accurate quantal scattering calculations up to high This implementation of the SRA enables us to quantify the contribution of each transition state level to the thermal rate constant, and to separately quantify the influence of recrossing and of quantum mechanical tunneling and nonclassical reflection on the thermal rate constant. Finally, we demonstrate the influence of two supernumerary transition states on both the overall and the stateselected dynamics.

Spectroscopy of Mg atoms solvated in helium nanodroplets
View Description Hide DescriptionWe have measured the laserinduced fluorescence excitation spectra of the transition of Mg atoms solvated in heliumnanodroplets. The observed blue shifts and line broadenings mirror the shifts and broadenings observed in studies of Mg atoms solvated in bulk liquid helium. This similarity allows us to conclude that Mg atoms reside in the interior of the helium droplet. The transition shows a splitting which we attribute to a quadrupolelike deformation of the cavity which forms around the solute atom after excitation. Temporal evolution of the fluorescence from the solvated Mg yields a longer lifetime (2.39±0.05 ns) than found in vacuum (1.99±0.08 ns). This difference can be accounted for quantitatively by evaluation of the anisotropic distribution of the helium density in the neighborhood of the excited Mg atom. The question of solvation vs surface location for the guest atoms is also discussed in light of the model of Ancilotto et al. [F. Ancilotto, P. B. Lerner, and M. W. Cole, J. Low Temp. Phys. 101, 1123 (1995)], of existing metal atom–helium potential energy functions, and of our own calculations for the MgHe and CaHe ground states. While the Ancilotto model successfully predicts solvation (or lack of it) if the solvation parameter of the guest atom is not too near the threshold of 1.9, the present knowledge of the interatomic potentials is not precise enough to test the model in the neighborhood of the critical value.

The electronic spectrum of germanium methylidyne (GeCH), the prototypical organogermanium compound
View Description Hide DescriptionThe electronic transition of jetcooled germanium methylidyne has been recorded in the 730–555 nm region by laserinduced fluorescence techniques. The radical was produced in a pulsed electric discharge using tetramethylgermane as the precursor. The band system consists of perpendicular and vibronically induced parallel bands with upper state frequencies of and for GeCH/GeCD. The components of the bands of GeCH and GeCD and the band of GeCH have been recorded with sufficient resolution to assign the transitions of the and isotopomers. The rotational constants of the various hydrogen and germanium isotopomers were used to derive the following molecular structures: and The ground state germanium–carbon bond length is typical for a double bond, but in the excited state it corresponds to a triple bond. This is a consequence of promotion of an electron from a nonbonding σ orbital to a π bonding orbital to form the excited state. In this study we provide the first experimental value for the length of the germanium–carbon triple bond.