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Volume 118, Issue 5, 01 February 2003
 COMMUNICATIONS


Controlling molecular groundstate dissociation by optimizing vibrational ladder climbing
View Description Hide DescriptionTo achieve large population transfer to high vibrational levels in a selected groundstate mode of a polyatomic molecule we apply chirped femtosecond midinfrared laser pulses at to optimize vibrational ladder climbing as an energy deposition mechanism, which in turn controls the outcome of a unimolecular dissociation process. Its dependence on excitation parameters (frequency, intensity, chirp) is investigated and found to be in excellent agreement with a theoretical calculation. In particular, it is shown that optimizing vibrational ladder climbing allows for coherently controlled excitation even in a polyatomic molecule.

 ARTICLES

 Theoretical Methods and Algorithms

A concerted variational strategy for investigating rare events
View Description Hide DescriptionA strategy for finding transition paths connecting two stable basins is presented. The starting point is the Hamilton principle of stationary action; we show how it can be transformed into a minimum principle through the addition of suitable constraints like energy conservation. Methods for improving the quality of the paths are presented: for example, the Maupertuis principle can be used for determining the transition time of the trajectory and for coming closer to the desired dynamic path. A saddle point algorithm (conjugate residual method) is shown to be efficient for reaching a “true” solution of the original variational problem.

Computation of molecular Hartree–Fock Wigner intracules
View Description Hide DescriptionThe computation of molecular Wigner intracules from Hartree–Fock wave functions using Gaussian basis functions is described. The Wigner intracule is a new type of intracule that contains information about both the relative position and momentum of the electrons. Two methods for evaluating the required integrals are presented. The first approach uses quadrature while the second requires summation of an infinite series.

Continuum description of solvent dielectrics in moleculardynamics simulations of proteins
View Description Hide DescriptionWe present a continuum approach for efficient and accurate calculation of reaction field forces and energies in classical moleculardynamics (MD) simulations of proteins in water. The derivation proceeds in two steps. First, we reformulate the electrostatics of an arbitrarily shaped molecular system, which contains partially charged atoms and is embedded in a dielectric continuum representing the water. A socalled fuzzy partition is used to exactly decompose the system into partial atomic volumes. The reaction field is expressed by means of dipole densities localized at the atoms. Since these densities cannot be calculated analytically for general systems, we introduce and carefully analyze a set of approximations in a second step. These approximations allow us to represent the dipole densities by simple dipoles localized at the atoms. We derive a system of linear equations for these dipoles, which can be solved numerically by iteration. After determining the two free parameters of our approximate method we check its quality by comparisons (i) with an analytical solution, which is available for a perfectly spherical system, (ii) with forces obtained from a MD simulation of a solubleprotein in water, and (iii) with reaction field energies of small molecules calculated by a finite difference method.

A new concise expression for the free energy of a reaction coordinate
View Description Hide DescriptionFor processes that can be parametrized by a reaction coordinate, the calculation of the free energy against this coordinate is the first step towards equilibrium constants and transition rates. We present a new concise expression for the free energy that is computed from data sampled at a fixed (constrained) reaction coordinate. It is consistent with previous theories and satisfies a more general criterion for free energy profiles.

Locally coupled coherent states and Herman–Kluk dynamics
View Description Hide DescriptionAn exact analysis of coupled coherent state (CCS) theory in the moving locally quadratic Hamiltonian approximation is shown to reproduce both the linearized coherent state matrix element of the Herman–Kluk propagator and the coherent state overlap with Heller’s thawed Gaussian wave function. The derivation is applicable to anharmonic as well as harmonic systems, because the quadratic approximation is taken to apply only in the vicinity of a particular classical trajectory. New compact expressions for the linearized Herman–Kluk coherent state matrix element are given, and improvements for the practical application of CCS theory are discussed.

Gradientfree and gradientdependent approximations in the total energy bifunctional for weakly overlapping electron densities
View Description Hide DescriptionWe analyze the performance of gradientfree local density approximation(LDA) and gradientdependent generalized gradient approximation (GGA) functionals in a density functional theory variational calculations based on the total energy bifunctional These approximations are applied to the exchangecorrelation energy and to the nonadditive component of the kinetic energy of the complex. Benchmark ab initiointeractionenergies taken from the literature for 25 intermolecular complexes for which the interactionenergies fall into the 0.1–3.0 kcal/mol range are used as reference. At the GGA level, the interactionenergies derived from are more accurate than the Kohn–Sham ones. LDA leads to very good interactionenergies for such complexes where the overlap is very small (NeNe, ArAr, for instance) but it is not satisfactory for such cases where the overlap is larger. Introduction of gradientdependent terms into the approximate part of improves significantly the overall accuracy of the interactionenergies. Gradientdependent functionals applied in lead to the average error and the average absolute error of the interactionenergies amounting to 0.08 kcal/mol and 0.29 kcal/mol, respectively.

Equivalent core model: Extended theory and applications
View Description Hide DescriptionThe ability of the recently developed corrected equivalent core model (cECM) to predict properties of core hole states is examined for the CO molecule. It is shown that systematic corrections derived in this approach significantly improve the results of the conventional equivalent core model (ECM). This opens new possibilities to apply the equivalent core formalism to calculate the energy of core hole states which cannot be usefully done by the ECM itself. On the selfconsistentfield level the predictions of geometry changes upon core ionization made by the cECM and those of direct core hole calculations are found to be very similar to each other. There exists, however, an appreciable difference between the total energies of the core hole states obtained in both approaches. A new procedure enabling us to improve the results of the cECM, in particular, to reduce this energy difference is proposed. In contrast to the cECM, where the corrections to the ECM energy are found by deriving the Hamiltonian of the Z system from the Hamiltonian of the system, the corrections are straightforwardly obtained in this new method by deriving from The importance of the various systematic corrections to the ECM is discussed.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Timedependent interplay between electron emission and fragmentation in the interatomic Coulombic decay
View Description Hide DescriptionThe electronic decay of the cation by electron emission is studied. This interatomic Coulombic decay (ICD) follows inner valence ionization of the neon dimer and the decay rate depends strongly on the internuclear distance. The timedependent theory of wave packet propagation is applied allowing to follow the evolution of the decay process in time. The impact of nuclear dynamics on the decay spectrum is investigated. Among others, the spectrum corresponding to the decay of the electronic state of the cation is calculated at different times. Its characteristics are found to be influenced considerably by the nuclear motion. A pronounced oscillatory structure appears: Its origin is explained and related to the interatomic nature of the ICD process. Particularly enlightening for the understanding of the ICD process is the analysis of the total energy distribution in the final system resulting after the fragmentation of the dication, produced by the ICD of

Photoelectron spectroscopy of clusters (n=1–130)
View Description Hide DescriptionPhotoelectron spectra of cold anion clusters for n=1–130 were investigated at four detachment photon energies: 532, 355, 266, and 193 nm. Improved spectral resolution provides wellresolved electronic structures of the clusters, and the spectral evolution as a function of cluster size was probed systematically. Narrow and wellresolved spectral features were observed at n=13, 19, and 55, consistent with the high symmetry icosahedral structures proposed for these clusters. The measured electron affinities as a function of size in the studied size range do not extrapolate to the bulk work function, indicating that Ti clusters with n=130 may not assume the bulk structure.

Structural and electronic properties of small titanium clusters: A density functional theory and anion photoelectron spectroscopy study
View Description Hide DescriptionDensity functional theory calculations using the generalizedgradient approximation have been carried out on the structural and electronic properties of and clusters for n=3–8 and 13. Many lowlying states, of different spins and geometries, were found for each and species. We observed that the calculated density of states (DOS) and the adiabatic electron binding energies for the ground state of a given anion are in good agreement with experimental photoelectron spectroscopy (PES) data, lending credence to the assignments of the ground state structures. Comparison between the calculated DOS and the PES data for other lowlying states made it possible to affirm contributions of these states to the spectra, allowing the characterization of the ensemble or composition of a given system. We found that all the clusters possess highly compact structures, and and have distorted pentagonal bipyramidal and icosahedral structures, respectively. From the ground state spin states, insight into the magnetic properties of the clusters and their evolution with size was also obtained. Small Ti clusters with n<5 are highly magnetic, but the magnetic moment drops rapidly with size.

Spectroscopically determined potential energy surface of up to 25 000 cm^{−1}
View Description Hide DescriptionA potential energy surface for the major isotopomer of water is constructed by fitting to observed vibration–rotation energy levels of the system using the exact kinetic energy operator nuclear motion program DVR3D. The starting point for the fit is the ab initio Born–Oppenheimer surface of Partridge and Schwenke [J. Chem. Phys. 106, 4618 (1997)] and corrections to it: both one and twoelectron relativistic effects, a correction to the height of the barrier to linearity, allowance for the Lamb shift and the inclusion of both adiabatic and nonadiabatic nonBorn–Oppenheimer corrections. Fits are made by scaling the starting potential by a morphing function, the parameters of which are optimized. Two fitted potentials are presented which only differ significantly in their treatment of rotational nonadiabatic effects. Energy levels up to 25 468 cm^{−1} with 2, and 5 are fitted with only 20 parameters. The resulting potentials predict experimentally known levels with with a standard deviation of 0.1 cm^{−1}, and are only slightly worse for for which rotational nonadiabatic effects are significant. The fits showed that around 100 known energy levels are probably the result of misassignments. Analysis of misassigned levels above 20 000 cm^{−1} leads to the reassignment of 23 transitions.

The reaction Implications for the heat of formation of
View Description Hide DescriptionFor some years there has been a dispute concerning the appearance energy of from or alternatively, the ionization energy of or the heat of formation of In an earlier work [M. Tichy, G. Javahery, N. D. Twiddy, and E. E. Ferguson, Int. J. Mass Spectrom. Ion Processes 79, 231 (1987)] the reaction between was used to support a low value, A remeasurement of this reaction over the temperature range 173–500 K shows that the original study was in error, both in the reported rate constant and the ion product. In the present work, the rate constant was found to be collisional, producing The rate constant for thermal decomposition of into was measured in the course of this work. These new measurements bring into harmony obtained from the reaction and the value reported by R. L. Asher and B. Ruscic [J. Chem. Phys. 106, 210 (1997)].

Semiclassical calculation of thermal rate constants in full Cartesian space: The benchmark reaction
View Description Hide DescriptionSemiclassical (SC) initialvalue representation (IVR) methods are used to calculate the thermal rate constant for the benchmark gasphase reaction In addition to several technical improvements in the SCIVR methodology, the most novel aspect of the present work is use of Cartesian coordinates in the full space (six degrees of freedom once the overall centerofmass translation is removed) to carry out the calculation; i.e., we do not invoke the conservation of total angular momentumJ to reduce the problem to fewer degrees of freedom and solve the problem separately for each value of J, as is customary in quantum mechanical treatments. With regard to the SCIVR methodology, we first present a simple and straightforward derivation of the semiclassical coherentstate propagator of Herman and Kluk (HK). This is achieved by defining an interpolation operator between the Van Vleck propagators in coordinate and momentum representations in an a priori manner with the help of the modified Filinov filtering method. In light of this derivation, we examine the systematic and statistical errors of the HK propagator to fully understand the role of the coherentstate parameter γ. Second, the Boltzmannized flux operator that appears in the rate expression is generalized to a form that can be tuned continuously between the traditional halfsplit and Kubo forms. In particular, an intermediate form of the Boltzmannized flux operator is shown to have the desirable features of both the traditional forms; i.e., it is easy to evaluate via path integrals and at the same time it gives a numerically wellbehaved flux correlation function at low temperatures. Finally, we demonstrate that the normalization integral required in evaluating the rate constant can be expressed in terms of simple constrained partition functions, which allows the use of wellestablished techniques of statistical mechanics.

Absolute total and partial cross sections for the electron impact ionization of diborane
View Description Hide DescriptionWe measured absolute partial cross sections for the formation of all singly charged positive ions formed by electron impact on diborane from threshold to 200 eV using a timeofflightmass spectrometer. The absolute total ionization cross section of was obtained as the sum of all measured partial ionization cross sections. Dissociativeionization resulting in thirteen different fragment ions was found to be the dominant ionization process, although we found evidence of the presence of the parent ion. The ion spectrum at all impact energies including in the energy region below 40 eV, which is of special interest for lowtemperature plasma technology, is dominated by and fragment ions. The fragment ion has the largest partial ionization cross section with a maximum value of at 60 eV. We also observed and fragment ions, but no ion signals were found that can be attributed to the formation of doubly charged ions. Additional measurements using a sectorfield mass spectrometer revealed that all fragment ions containing one boron atom and are formed with significant excess kinetic energy. The mass spectrum of ions formed by electron impact on at 70 eV in our experiments revealed distinctly larger abundances of the fragment ions and than earlier mass spectrometric measurements.

Bondforming reactions of dications: Production of and in the reaction of with
View Description Hide DescriptionWe present cross sections as a function of the collision energy for the bondforming reactions of argon dications with oxygen molecules, producing and respectively. Both the reactions are exothermic, and have cross sections much smaller than those of the competitive chargetransfer processes. The lowlying electronic states of have been calculated at the MR–AQCC/ccpV5Z level. In contrast to previous results we found that the ground state has a local minimum. However, the estimated lifetime of this metastable state is too short to be detected in our setup. Thus the observed ions must be in the higherlying or states.

Oxygen isotopic fractionation during UV and visible light photodissociation of ozone
View Description Hide DescriptionStratosphericozone is essentially in a steady state due to the simultaneous formation and dissociation and found to be enriched (massindependently) in heavy oxygen isotopes. Though there have been a number of experimental and theoretical studies on the mechanism(s) associated with the formation of isotopically heavy ozone, the decomposition processes were not studied in necessary detail. Here we report a novel feature in the isotopic fractionation of ozone during photodissociation in the UV and visible wavelengths. Photodissociation of ozone produces isotopically light oxygen, enriching the leftover ozone pool. Interestingly, the isotopic fractionation patterns are not similar in the two wavelength regions. Dissociation at visible wavelengths displays a massdependent slope whereas UVdissociation shows a massindependent character photodissociation in UV wavelengths is normally associated with another effective channel of dissociation, i.e., It is demonstrated for the first time that pure UVphotodissociation of ozone [i.e., without the channel] gives a slope of unity intriguingly similar to that obtained in the ozone formation process. A combination of the two processes i.e., mass dependent reaction and pure UVphotodissociation is responsible for the observed slope of 0.63.

The excited electronic state of the silver–ammonia complex
View Description Hide DescriptionThe first excited electronic state of the silver–ammonia 1:1 complex was studied by resonantly enhanced twophotonionization. The complex was formed using laser ablation and cooled in a free jet expansion. The origin of the band system located at 467 nm is redshifted by 8142 cm^{−1} from the corresponding transition of Ag, indicating a significant stabilization upon electronic excitation. The splitting of the origins of the spin–orbit substates, and was determined to be 805 cm^{−1}. The intermolecular stretching overtones and their combination bands with the intermolecular bending mode are observed for the state, whereas only the mode appears in the bands. The vibronic assignment was supported by the spectrum of its deuterated isotopomer, The vibrational frequencies of the and mode in the state of were determined to be 371 and 185 cm^{−1}, respectively. The anomalously small frequency of the mode is explained as a result of Jahn–Teller interaction and spin–orbit interaction in the state.

Ferromagnetic spin coupling in the manganese trimer ion evidenced by photodissociation spectroscopy
View Description Hide DescriptionThe optical spectrum of the manganese trimer ion, was obtained by measurement of the photodissociation cross section in the photonenergy range between 1.43 and 4.13 eV. Analysis of the spectrum by quantumchemical calculations derived its electronic and geometric structures. The geometric structure was found to be an isosceles triangle with bond lengths of 3.03 Å and an apex angle of The ground electronic state was found to be The electronic structure of the valence orbitals indicates that the chemical bond is formed weakly by the electrons. The electrons are localized on the atomic sites, as is suggested by the nonbonding nature of the nearly degenerate occupied orbitals. All of the local spins are in the majorityspin state, and give rise to a total spin magnetic moment as large as The ferromagnetic nature is due to the weak binding among constituent atoms and to the strong exchange interaction in the manganese atom. This finding is in marked contrast to the antiferromagnetism of bulk manganese.

Quantal study of the exchange reaction for using an ab initio potential energy surface
View Description Hide DescriptionThe exchange rate is calculated using a timedependent quantum dynamics method on a newly determined ab initiopotential energy surface (PES) for the ground state. This ab initio PES shows a double barrier feature in the interaction region with the barrier height at 47.2 kcal/mol, and a shallow well between these two barriers, with the minimum at 43.7 kcal/mol. A quantum dynamics wave packet calculation has been carried out using the fitted PES to compute the cumulative reaction probability for the exchange reaction of The shift method is then employed to obtain the rate constant for this reaction. The calculated rate constant is compared with experimental data and a recent quasiclassical calculation using a London–Eyring–Polanyi–Sato PES. Significant differences are found between the present and quasiclassical results. The present rate calculation is the first accurate threedimensional quantal dynamics study for the reaction system and the ab initio PES reported here is the first such surface for