Volume 123, Issue 9, 01 September 2005
 ARTICLES

 Theoretical Methods and Algorithms

Quasiclassical determination of reaction probabilities as a function of the total angular momentum
View Description Hide DescriptionThis article presents a quasiclassical trajectory(QCT) method to determine the reaction probability as a function of the total angular momentum for any given value of the initial rotational angular momentum. The proposed method is based on a discrete sampling of the total and orbital angular momenta for each trajectory and on the development of equations that have a clear counterpart in the quantummechanical (QM) case. The reliability of the method is illustrated by comparing QCT and timedependent wavepacket QM results for the reaction. The small discrepancies between both sets of calculations, when they exist, indicate some genuine quantum effects. In addition, a procedure to extract the reaction probabilities as a function of when trajectories are calculated in the usual way using a continuous distribution of impact parameters is also described.

Towards accurate allelectron quantum Monte Carlo calculations of transitionmetal systems: Spectroscopy of the copper atom
View Description Hide DescriptionIn this work we present allelectron fixednode diffusionMonte Carlo (FNDMC) calculations of the lowlying electronic states of the copper atom and its cation. The states considered are those which are the most relevant for the organometallic chemistry of coppercontaining systems, namely, the , , and electronic states of Cu and the ground state of . We systematically compare our FNDMC results to CCSD(T) calculations using very large atomicnaturalorbitaltype allelectron basis sets. The FNDMC results presented in this work provide, to the best of our knowledge, the most accurate nonrelativistic allelectron correlation energies for the lowestlying states of copper and its cation. To compare our results to experimental data we include the relativistic contributions for all states through numerical DiracFock calculations, which for copper provide almost the entire relativistic effects. It is found that the fixednode errors using HartreeFock nodes for the lowest transition energies of copper and the first ionization potential of the atom cancel out within statistical fluctuations. The overall accuracy achieved with quantum Monte Carlo for the nonrelativistic correlation energy (statistical fluctuations of about and near cancelation of fixednode errors) is good enough to reproduce the experimental spectrum when relativistic effects are included. These results illustrate that, despite the presence of the large statistical fluctuations associated with core electrons, accurate allelectron FNDMC calculations for transition metals are nowadays feasible using extensive but accessible computer resources.

Time autocorrelation function analysis of master equation and its application to atomic clusters
View Description Hide DescriptionWe derive the energy fluctuation , and the time autocorrelation and its Fourier transformation—the fluctuation spectra—of the masterequation transition matrix. The contribution from each eigenmode of the transition matrix to these fluctuation quantities reveals the relevant importance of the individual mode in the relaxation processes. The time scales associated with these relaxation processes are determined by the corresponding eigenvalues. Unlike traditional time evolution analysis, the autocorrelation function and fluctuation spectraanalysis does not involve an arbitrary initial population. It is also more suitable for analyzing the underlying dynamic, kinetic behavior near the equilibrium and the behavior of the longtimescale rare events. We utilize our technique to analyze the solidliquid phase coexistence of the 13atom Morse cluster and the fcctoicosahedral structure transition of the 38atom LennardJones cluster. For the processes studied, the fluctuation spectra from the master equation simplify the analysis of the transition matrix, and the important relaxation modes are easily extracted.

Efficient transition path sampling for systems with multiple reaction pathways
View Description Hide DescriptionA new algorithm is developed for sampling transition paths and computing reaction rates. To illustrate the use of this method, we study a twodimensional system that has two reaction pathways: one pathway is straight with a relatively high barrier and the other is roundabout with a lower barrier. The transition rate and the ratio between the numbers of the straight and roundabout transition paths are computed for a wide range of temperatures. Our study shows that the harmonic approximation for fluctuations about the steepestdescent paths is not valid even at relatively low temperatures and, furthermore, that factors related to entropy have to be determined by the global geometry of the potentialenergysurface (rather than just the local curvatures alone) for complex reaction systems. It is reasonable to expect that this algorithm is also applicable to higher dimensional systems.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Imaging photoninitiated reactions: A study of the reaction
View Description Hide DescriptionThe hydrogen or deuterium atom abstraction reactions between and methane, or its deuterated analogues and , have been studied at mean collision energies around 0.34 eV. The experiments were performed in a coexpansion of molecular chlorine and methane in helium, with the atomic Cl reactants generated by polarized laser photodissociation of at 308 nm. The Clatom reactants and the methyl radical products were detected using resonantly enhanced multiphoton ionization, coupled with velocitymap ion imaging. Analysis of the ion images reveals that in singlebeam experiments of this type, careful consideration must be given to the spread of reagent velocities and collision energies. Using the reactions of Cl with , , and , as examples, it is shown that the data can be fitted well if the reagent motion is correctly described, and the angular scattering distributions can be obtained with confidence. New evidence is also provided that the radicals from the reaction possess significant rotational alignment under the conditions of the present study. The results are compared with previous experimental and theoretical works, where these are available.

Intensity and wavelength control of a single molecule reaction: Simulation of photodissociation of coldtrapped
View Description Hide DescriptionPhotodissociation of cold magnesium hydride ions leading to either or is simulated from first principles. The purpose is to study the possibility of single molecule control of the products in the presence of two laser fields. The system evolves on four electronic potentialenergy curves, , , , and . These potentialenergy curves are calculated from first principles using multireference selfconsistent field theory. The accuracy of the electronic potential curves has been checked by calculating the energies of the rovibrational eigenstates and comparing them to experimental findings. The photodissociation dynamics has furthermore been simulated by solving the timedependent Schrödinger equation. It is shown that the branching ratio of the two dissociation channels, or , can be controlled by changing the intensity and wavelength of the two driving laser fields.

Frequencydependent hyperpolarizabilities of the Ne, Ar, and Kr atoms using the approximate coupled cluster triples model CC3
View Description Hide DescriptionThe frequencydependent electric fieldinduced second harmonic generation (ESHG) second hyperpolarizabilities of neon, argon, and krypton are calculated using the approximate coupled cluster triples model CC3. Systematic basis set investigations are carried out to establish basis set limits, and scalar relativistic effects are accounted for by direct perturbation theory. To estimate higherorder correlation effects, full configurationinteraction results are used to benchmark the accuracy of CC3. The best theoretical estimates obtained thereby for the static second hyperpolarizabilities are 107.4, 1159, and 2589 a.u. for neon, argon, and krypton, respectively. These values as well as the results for the dispersion curve of the parallel component agree well with the latest experimental values from electric fieldinduced second harmonic generation. In addition, the dispersion of the perpendicular component and the hyperpolarizability ratios has been studied for the first time on a consistently correlated ab initio level. The analysis of the results indicates that, in particular for neon and krypton, the presently available experimental values are flawed.

Reaction dynamics study of with crossed beams and densityfunctional theory calculations
View Description Hide DescriptionThe reactions between and have been studied using the crossedbeam technique and densityfunctional theory(DFT) calculations in the collision energy range from 0.35 to 1.5 eV . Both proton transfer and C–O bond formation are observed. The proton transfer channel forming is the dominant pathway. The centerofmass flux distributions of the product ions are highly asymmetric, with maxima close to the velocity and direction of the precursor acetylene beam, characteristic of direct reactions. The reaction quantitatively transforms the entire reaction exothermicity into internal excitation of the products, consistent with mixed energy release in which the proton is transferred in a configuration in which both the breaking and the formingbonds are extended. The C–O bond formation channel producing displays a distinctive kinematic picture in which the product distribution switches from predominantly forward scattering with a weak backward peak to sideways scattering as the collision energy increases. At low collision energies, the reaction occurs through an intermediate that lives a significant fraction of a rotational period. The asymmetry in the distribution leads to a lifetime estimate of 600 fs, in reasonable agreement with DFT calculations showing that hydrogenatom migration is rate limiting. At higher collision energies, the sidewaysscattered products arise from repulsive energy release from a bent transition state.

: Saturnlike fullerene derivatives (, Cl, Br)
View Description Hide DescriptionBased on the recently reported , the geometries and stabilities of its Saturnlike derivatives (, Cl, Br) have been investigated by DFT method. Compared with , the equatorial carbon atoms in have been saturated by halogens and change to hybridization to release the large angle strain. Because the equatorial carbon atoms have been taken out of the system by the halogens “ring,” the system has been split into two welldelocalized conjugated annulene subunits, and then the electronic stabilization has been enhanced.

High resolution electronic spectra of 7azaindole and its Ar atom van der Waals complex
View Description Hide DescriptionRotationally resolved fluorescence excitation spectra of the origin band of 7azaindole and its argon atom van der Waals complex have been recorded and assigned. The derived rotational constants give information about the geometries of the two molecules in both electronic states. The equilibrium position of the argon atom in the azaindole complex is considerably different from its position in the corresponding indole complex. Furthermore, the argon atom moves when the UV photon is absorbed. There are significant differences in the intermolecular potential energy surfaces in the two electronic states. A large, vibrationstatedependent rotation of the electronic transition moment vector of 7azaindole relative to that of indole suggests that these differences have their origin in electronic state mixing in the isolated molecule, a mixing that is enhanced by nitrogen substitution in the sixmembered ring.

On the theory of the reaction, including H and C kinetic isotope effects
View Description Hide DescriptionThe effect of pressure, temperature, isotopes, and C isotopes on the kinetics of the reaction are investigated using RiceRamspergerKasselMarcus theory.Pressureeffects are treated with a stepladder plus steadystate model and tunnelingeffects are included. New features include a treatment of the C isotope effect and a proposed nonstatistical effect in the reaction. The latter was prompted by existing kinetic results and molecularbeam data of Simons and coworkers [J. Phys. Chem. A102, 9559 (1998);J. Chem. Phys.112, 4557 (2000);113, 3173 (2000)] on incomplete intramolecular energy transfer to the highest vibrational frequency mode in . In treating the many kinetic properties two small customary vertical adjustments of the barriers of the two transition states were made. The resulting calculations show reasonable agreement with the experimental data on (1) the pressure and temperature dependence of the effect, (2) the pressuredependent isotope effect, (3) the strong nonArrhenius behavior observed at low temperatures, (4) the hightemperature data, and (5) the pressure dependence of rate constants in various bath gases. The kinetic carbon isotopic effect is usually less than 10 per mil. A striking consequence of the nonstatistical assumption is the removal of a major discrepancy in a plot of the ratio versus pressure. A prediction is made for the temperature dependence of the reaction in the lowpressure limit at low temperatures.

A closecoupling study of vibrationalrotational quenching of CO by collision with hydrogen atoms
View Description Hide DescriptionQuantummechanical scattering calculations were performed for the rovibrational relaxation of CO in collisions with H atoms using the closecoupling approach for collision energies between and . We adopted the H–CO interaction potential of Werner, Keller, and Schinke and computed the statetostate and total cross sections for the quenching of the , levels of CO. Numerous resonances, as a consequence of the van der Waals potential, are observed and the cross sections are found to approach the Wigner limit at low energies. Also, by averaging the cross sections over a Boltzmann distribution of velocities of the incoming atom, quenching rate coefficients are obtained and found to be consistent with previous infiniteorder sudden approximation calculations for temperatures between 100 and .
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Lowfrequency Raman spectra of sub and supercritical : Qualitative analysis of the diffusion coefficient behavior
View Description Hide DescriptionWe report the results of the lowfrequency Raman experiments on which were carried out in a wide density range, along the liquidgas coexistence curve in a temperature range of 293–303 K, and on the critical isochore of in a temperature range of 304–315 K. In our approach, the qualitative behavior of the diffusion coefficient is predicted, assuming the following: first, that the lowfrequency Raman spectra can be interpreted in terms of the translation rotation motions; second, that the random force could be replaced by the total force to calculate the friction coefficient; and finally, that the Einstein frequency is associated with the position of the maximum of the lowfrequency Raman spectrum. The results show that the diffusion coefficient increases along the coexistence curve, and its values are almost constant on the critical isochore. The predicted values reproduce qualitatively those obtained by other techniques. The values of were also calculated by moleculardynamics simulation and they qualitatively reproduce the behavior of .

Heterodyned fifthorder twodimensional IR spectroscopy: Thirdquantum states and polarization selectivity
View Description Hide DescriptionA heterodyned fifthorder twodimensional (2D) IR spectrum of a model coupled oscillator system, , is reported. The spectrum is generated by a pulse sequence that probes the eigenstate energies up to the second overtone and combination bands, providing a more rigorous potentialenergy surface of the coupled carbonyl local modes than can be obtained with thirdorder spectroscopy. Furthermore, the pulse sequence is designed to generate and then rephase a twoquantum coherence so that the spectrum is line narrowed and the resolution improved for inhomogeneously broadened systems. Features arising from coherence transfer processes are identified, which are more pronounced than in thirdorder 2D IR spectroscopy because the transition dipoles of the second overtone and combination states are not rigorously orthogonal, relaxing the polarization constraints on the signal intensity for these features. The spectrum provides a stringent test of cascading signals caused by thirdorder emitted fields and no cascading is observed. In the Appendix, formulas for calculating the signal intensities for resonant fifthorder spectroscopies with arbitrarily polarized pulses and transition dipoles are reported. These relationships are useful for interpreting and designing polarization conditions to enhance specific spectral features.

Thermally activated escape rate for the Brownian motion of a fixed axis rotator in an asymmetrical doublewell potential for all values of the dissipation
View Description Hide DescriptionThe Kramers theory of the escape rate of a Brownian particle from a potential well as extended by Mel’nikov and Meshkov, [J. Chem. Phys.85, 1018 (1986)] is used to evaluate the relaxation times and the dynamic susceptibility for the rotational Brownian motion of fixed axis rotators in an asymmetric doublewell potential. An expression for the escape rate valid for all values of the dissipation including the very low damping (VLD), very high damping (VHD), and crossover regimes is derived. It is shown that this expression provides a good asymptotic estimate of the inverse of the smallest nonvanishing eigenvalue of the underlying FokkerPlanck operator calculated by using the matrixcontinued fraction method. For low barriers, where the Mel’nikov and Meshkov approach is not applicable, analytic equations for the correlation time of the longitudinal dipole correlation function in the VLD and VHD limits are derived and a simple extrapolating equation valid for all values of the damping is proposed.

Rotational motion in the molecular crystals meta and orthocarborane studied by deuteron nuclear magnetic resonance
View Description Hide DescriptionSpinlattice and spinspinrelaxation times, one and twodimensional spectra as well as two and fourtime correlation functions were measured for the molecular crystals ortho and metacarborane using deuteron nuclear magnetic resonance. It is found that in their noncubic phases these crystals exhibit highly anisotropic motions. In order to allow for a quantitative description of the motional geometry of the carboranes several stochastic models are formulated. By comparison of the model calculations with the experimental results it is found that the dynamics of these quasiicosahedrally shaped molecules is governed by a composite reorientation process. Here the molecules perform threefold jumps around a moleculefixed axis which itself can be tilted in four different directions with respect to a crystalfixed axis. The tilt angle increases significantly with increasing temperature. On the basis of measurements of fourtime stimulatedecho functions, implications for dynamic heterogeneity also in comparison with that of supercooled liquids are discussed.

Phase changes in LennardJones mixed clusters with composition
View Description Hide DescriptionWe have carried out parallel tempering Monte Carlo calculations on the binary sixatom mixed LennardJones clusters, . We have looked at the classical configurational heat capacity as a probe of phase behavior. All three clusters show a feature in the heat capacity in the region of . The cluster exhibits a further peak in the heat capacity near . We have also investigated dynamical properties of the cluster as a function of temperature using molecular dynamics. We report the interbasin isomerization rate and the bond fluctuation parameter obtained from these calculations. At , the isomerization rate is on the order of ; at , the isomerization rate is greater than . Furthermore, at , the bond fluctuation parameter is less than 3%; at , it is in the range of 10–15% (depending on the sampling time used). Using this information, together with Monte Carlo quenching data, we assign the feature in the heat capacity to a solidliquidphase change and the peak to a solidsolidphase change. We believe this is the smallest LennardJones cluster system yet shown to exhibit solidsolidphase change behavior.

Density functional theory based moleculardynamics study of aqueous iodide solvation
View Description Hide DescriptionWe study the solvation of iodide in water using density functional theory based moleculardynamics simulations. Detailed analysis of the structural and dynamical properties of the first solvation shell is presented, showing a disruptive influence of the ion on the local waterstructure. Iodidewater hydrogen bonding is weak, compared to waterwater hydrogen bonds. This effective repulsive ionwater interaction leads to the formation of a quite unstructured solvation shell. The dynamics of water molecules surrounding the iodide is relatively fast. The intramolecular structural and electronical properties of water molecules around the ion are not affected.

Moleculardynamics simulations of alkalineearth metal cations in water by atombond electronegativity equalization method fused into molecular mechanics
View Description Hide DescriptionIntermolecular potential for alkalineearth metal (, , and ) cations in water has been derived using the atombond electronegativity equalization method fused into molecular mechanics (ABEEM/MM), and it is consistent with what was previously applied to the hydration study of the monovalent cations. Parameters for the effective interaction between a cation and a water molecule were determined, reproducing the ab initio results. The static, dynamic, and thermodynamic properties of , , and were studied using these potential parameters. requires a more complicated form of the potential function than and in order to obtain better fits. Strong influences of the twofold charged cations on the structures of the hydration shells and some other properties of aqueous ionic solutions are discussed and compared with the results of a previous study of monovalent cations in water. At the same time, comparative study of the hydration properties of each cation is also discussed. This work demonstrates that ABEEM/MM provides a useful tool in the exploration of the hydration of doublecharged cations in water.

Temperatureinduced dynamical conformational disorder in 4vinyl benzoic acid molecular crystals: A molecular simulation study
View Description Hide DescriptionExtensive molecular simulations are carried out as a function of temperature to understand and quantify the conformational disorder in molecular crystals of 4vinyl benzoic acid. The conformational disorder is found to be dynamic and associated with a flipflop motion of vinyl groups. The population of minor conformer is less than 3% up to and is 13.2% at and these results are consistent with the experimental observations. At still higher temperatures, the population of minor conformer increases up to 25%. The evolution of structure at both molecular and unitcell level of the molecular crystal as a function of temperature has been characterized by various quantities such as radial distribution functions, average cell parameters, volume, and interaction energies. The van’t Hoff plot shows a nonlinear behavior at lower temperatures as it has been reported recently by Ogawa and coworkers in the case of stilbene, azobenzene [J. Am. Chem. Soc.126, 3539 (2004)], and (4methylbenzylidene)4methylaniline [Acta Crystallogr, Sect. B. Struct. Sci.B60, 589 (2004)] molecular crystals. A set of rigid body simulations were also carried out to quantify the effect of conformational disorder on structural quantities such as unitcell volume and interaction energy. The anomalous shrinkage of vinyl bond length as a function of temperature has been explained by combining the results of simulations and a set of constrained optimizations using ab initio electronic structure calculations for various molecular structures differing in torsional angle.