Volume 120, Issue 2, 08 January 2004
 COMMUNICATIONS


Bias in the temperature of helium nanodroplets measured by an embedded rotor
View Description Hide DescriptionThe rovibrational spectra of molecules dissolved in liquidnanodroplets display rotational structure. Where resolved, this structure has been used to determine a temperature that has been assumed to equal that of the intrinsic excitations of the helium droplets containing the molecules. Consideration of the density of states as a function of energy and total angular momentum demonstrates that there is a small but significant bias of the rotor populations that make the temperature extracted from a fit to its rotational level populations slightly higher than the temperature of the ripplons of the droplet. This bias grows with both the total angular momentum of the droplet and with the moment of inertia of the solute molecule.
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 ARTICLES

 Theoretical Methods and Algorithms

From transition paths to transition states and rate coefficients
View Description Hide DescriptionTransition states are defined as points in configuration space with the highest probability that trajectories passing through them are reactive (i.e., form transition paths between reactants and products). In the highfriction (diffusive) limit of Langevin dynamics, the resulting ensemble of transition states is shown to coincide with the separatrix formed by points of equal commitment (or splitting) probabilities for reaching the product and reactant regions. Transition states according to the new criterion can be identified directly from equilibrium trajectories, or indirectly by calculating probability densities in the equilibrium and transitionpath ensembles using umbrella and transitionpath sampling, respectively. An algorithm is proposed to calculate rate coefficients from the transitionpath and equilibrium ensembles by estimating the frequency of transitions between reactants and products.

The impact of the selfinteraction error on the density functional theory description of dissociating radical cations: Ionic and covalent dissociation limits
View Description Hide DescriptionSelfinteraction corrected density functional theory was used to determine the selfinteraction error for dissociating oneelectron bonds. The selfinteraction error of the unpaired electron mimics nondynamic correlation effects that have no physical basis where these effects increase for increasing separation distance. For short distances the magnitude of the selfinteraction error takes a minimum and increases then again for decreasing R. The position of the minimum of the magnitude of the selfinteraction error influences the equilibrium properties of the oneelectron bond in the radical cations and which differ significantly. These differences are explained by hyperconjugative interactions in 2 and 3 that are directly reflected by the selfinteraction error and its orbital contributions. The density functional theory description of the dissociating radical cations suffers not only from the selfinteraction error but also from the simplified description of interelectronic exchange. The calculated differences between ionic and covalent dissociation for 1, 2, and 3 provide an excellent criterion for determining the basic failures of density functional theory, selfinteraction corrected density functional theory, and other methods. Pure electronic, orbital relaxation, and geometric relaxation contributions to the selfinteraction error are discussed. The relevance of these effects for the description of transition states and charge transfer complexes is shown. Suggestions for the construction of new exchangecorrelation functionals are given. In this connection, the disadvantages of recently suggested selfinteraction errorfree density functional theory methods are emphasized.

A reinterpretation of the nature of the Fermi hole
View Description Hide DescriptionA reinterpretation of the Boyd–Coulson [R. J. Boyd and C. A. Coulson, J. Phys. B 7, 1805 (1974)] definition of the Fermi hole is presented. Through this reinterpretation, which makes no reference to the hypothetical Hartree level, we are able to show the essentially identical character of the Boyd–Coulson definition with the one based on a conditional probability analysis. The basisset dependence of the Fermi hole is emphasized and the effect of canonical, localized and delocalized Kohn–Sham and Hartree–Fock basis sets is examined for selected atoms and molecules.

Mapped grid methods for longrange molecules and cold collisions
View Description Hide DescriptionThe paper discusses ways of improving the accuracy of numerical calculations for vibrational levels of diatomic molecules close to the dissociation limit or for ultracold collisions, in the framework of a grid representation. In order to avoid the implementation of very large grids, Kokoouline et al. [J. Chem. Phys. 110, 9865 (1999)] have proposed a mapping procedure through introduction of an adaptive coordinate x subjected to the variation of the local de Broglie wavelength as a function of the internuclear distance R. Some unphysical levels (“ghosts”) then appear in the vibrational series computed via a mapped Fourier grid representation. In the present work the choice of the basis set is reexamined, and two alternative expansions are discussed: Sine functions and Hardy functions. It is shown that use of a basis set with fixed nodes at both grid ends is efficient to eliminate “ghost” solutions. It is further shown that the Hamiltonian matrix in the sine basis can be calculated very accurately by using an auxiliary basis of cosine functions, overcoming the problems arising from numerical calculation of the Jacobian of the coordinate transformation.

Fast vibrational selfconsistent field calculations through a reduced mode–mode coupling scheme
View Description Hide DescriptionWe present a new methodology to perform fast correlationcorrected vibrational selfconsistent field (CCVSCF) calculations using ab initio potential energy points calculated on the fly. Our method is based on the replacement of allelectron basis sets with a pseudopotential basis for heavy atoms, and on an efficient reduction of the number of paircoupling elements used in the CCVSCF procedure. The method is applied to several test systems: and where it proves to be efficient, providing a speedup factor of 2 compared to a standard CCVSCF calculation. We also apply our technique to the simulation of the vibrational spectrum of ethane and show that very accurate results can be obtained with a substantial speedup for this system.

Spectral differences in realspace electronic structure calculations
View Description Hide DescriptionRealspace grids for electronic structure calculations are efficient because the potential is diagonal while the second derivative in the kinetic energy may be sparsely evaluated with finite differences or finite elements. In applications to vibrational problems in chemical physics a family of methods known as spectral differences has improved finite differences by several orders of magnitude. In this paper the use of spectral differences for electronic structure is studied. Spectral differences are implemented in two electronic structure programs PARSEC and HARES which currently employ finite differences. Applications to silicon clusters and lattices indicate that spectral differences achieve the same accuracy as finite differences with less computational work.

Semiclassical representations of electronic structure and dynamics
View Description Hide DescriptionWe use a new formulation of the semiclassical coherent state propagator to derive and evaluate several different approximate representations of electron dynamics. For each representation we examine: (1) its ability to treat quantum effects and electron correlation, (2) its expected scaling with system size, and (3) the types of systems for which it can be used. We also apply two of the methods to a pair of model problems, namely the minimal basis electron dynamics in and the magnetization dynamics in a cluster model of the Kagomè lattice, in order to verify the feasibility of these approaches for realistic systems. Based on all these criteria, we find that the representation that takes the electron spins as the classical variables is particularly promising for the quantitative and qualitative description of large systems.

Design and application of a multicoefficient correlation method for dispersion interactions
View Description Hide DescriptionA new multicoefficient correlation method (MCCM) is presented for the determination of accurate van der Waals interactions. The method utilizes a novel parametrization strategy that simultaneously fits to very highlevel binding, Hartree–Fock and correlation energies of homo and heteronuclear rare gas dimers of He, Ne, and Ar. The decomposition of the energy into Hartree–Fock and correlation components leads to a more transferable model. The method is applied to the krypton dimer system, rare gas–water interactions, and threebody interactions of rare gas trimers and For the latter, a very highlevel method that corrects the raregas twobody interactions to the total binding energy is introduced. A comparison with highlevel CCSD(T) calculations using large basis sets demonstrates the MCCM method is transferable to a variety of systems not considered in the parametrization. The method allows dispersion interactions of larger systems to be studied reliably at a fraction of the computational cost, and offers a new tool for applications to raregas clusters, and the development of dispersion parameters for molecular simulation force fields and new semiempirical quantum models.

A new method for solving the quantum hydrodynamic equations of motion: Application to twodimensional reactive scattering
View Description Hide DescriptionThe de Broglie–Bohm hydrodynamicequations of motion are solved using a meshless method based on a moving least squares approach and an arbitrary Lagrangian–Eulerian frame of reference. A regridding algorithm adds and deletes computational points as needed in order to maintain a uniform interparticle spacing, and unitary time evolution is obtained by propagating the wave packet using averaged fields. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. The methodology is applied to a twodimensional model collinear reaction with an activation barrier. Reaction probabilities are computed as a function of both time and energy, and are in excellent agreement with those based on the quantum trajectory method.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Modespecific photoelectron scattering effects on vibrations
View Description Hide DescriptionUsing highresolution photoelectron spectroscopy, we have determined the energy dependent vibrational branching ratios for the symmetric stretch bend and antisymmetric stretch as well as several overtones and combination bands in the photoionization of Data were acquired over the range from 20–110 eV, and this wide spectral coverage highlighted that alternative vibrational modes exhibit contrasting behavior, even over a range usually considered to be dominated by atomic effects. Alternative vibrational modes exhibit qualitatively distinct energy dependences, and this contrasting modespecific behavior underscores the point that vibrationally resolved measurements reflect the sensitivity of the electron scatteringdynamics to welldefined changes in molecular geometry. In particular, such energydependent studies help to elucidate the mechanism(s) responsible for populating the symmetry forbidden vibrational levels [i.e., (001), (030), and (110)]. This is the first study in which vibrationally resolved data have been acquired as a function of energy for all of the vibrational modes of a polyatomic system. Theoretical Schwinger variational calculations are used to interpret the experimental data, and they indicate that a shape resonance is responsible for most of the excursions observed for the vibrational branching ratios. Generally, the energy dependent trends are reproduced well by theory, but a notable exception is the symmetric stretch vibrational branching ratio. The calculated results display a strong peak in the vibrational branching ratio while the experimental data show a pronounced minimum. This suggests an interference mechanism that is not accounted for in the singlechannel adiabaticnuclei calculations. Electronic branching ratios were also measured and compared to the vibrational branching ratios to assess the relative contributions of interchannel (i.e., Herzberg–Teller) versus intrachannel (i.e., photoelectronmediated) coupling.

Variational transition state theory calculations for the rate constants of the hydrogen scrambling and the dissociation of using the multiconfiguration molecular mechanics algorithm
View Description Hide DescriptionThe molecule contains a weak twoelectronthreecenter bond and it requires extremely high level of theories to calculate the energy and structure correctly. The potential energy of the hydrogen scrambling in has been generated by the multiconfiguration molecular mechanics algorithm with 15 highlevel Shepard interpolation points, which would be practically impossible to obtain otherwise. The highlevel interpolation points were obtained from the multicoefficient correlated quantum mechanical methods. The more highlevel points are used, the better the shape of the potential energy surface. The rate constants are calculated using the variational transition state theory including multidimensional tunneling approximation. The potential energy curve for the dissociation has also been calculated, and the variational transition state was located to obtain the dissociation rate constants. Tunneling is very important in the scrambling, and there is large variational effect on the dissociation. The rate constants for the scrambling and the dissociation are and at 300 K, respectively, which suggests that the dissociation is three orders of magnitude faster than the scrambling.

The groundstate tunneling splitting of various carboxylic acid dimers
View Description Hide DescriptionCarboxylic acid dimers in gas phase reveal groundstatetunneling splittings due to a double proton transfer between the two subunits. In this study we apply a recently developed accurate semiclassical method to determine the groundstatetunneling splittings of eight different carboxylic acid derivative dimers (formic acid, benzoic acid, carbamic acid, fluoro formic acid, carbonic acid, glyoxylic acid, acrylic acid, and N,Ndimethyl carbamic acid) and their fully deuterated analogs. The calculated splittings range from to 0.13 cm^{−1} (for the deuterated species from to thus indicating a strong substituent dependence of the splitting, which varies by more than two orders of magnitude. One reason for differences in the splittings could be addressed to different barriers heights, which vary from 6.3 to 8.8 kcal/mol, due to different mesomeric stabilization of the various transition states. The calculated splittings were compared to available experimental data and good agreement was found. A correlation could be found between the tunneling splitting and the energy barrier of the double proton transfer, as the splitting increases with increased strength of the hydrogen bonds. From this correlation an empirical formula was derived, which allows the prediction of the groundstatetunneling splitting of carboxylic acid dimers at a very low cost and the tunneling splittings for parahalogen substituted benzoic acid dimers is predicted.

Potential energy curves of diatomic molecular ions from highresolution photoelectron spectroscopy. I. The first six electronic states of
View Description Hide DescriptionHighresolution photoelectron spectroscopic data have been used to determine the potential energy curves of the first six electronic states of The potential energy functions properly include the effects of the longrange interactions and of the spin–orbit interaction and are of spectroscopic accuracy over a wide range of internuclear distances. The total number of adjustable parameters could be reduced to only 12 by truncating the longrange interaction series after the term and assuming an independent spin–orbit coupling constant. This assumption was verified to be valid to an accuracy of over the range of internuclear distances between 3.0 and 4.6 Å. The interaction potential proposed by Siska [P. E. Siska, J. Chem. Phys. 85, 7497 (1986)] was generalized to a form that is expected to be sufficiently flexible to describe chemical bonding in other diatomic molecular ions. The potential energy curves are more accurate than the best available ab initio curves by two orders of magnitude and provide quantitative information on dissociation energies and equilibrium internuclear distances. The local maximum between the two potential wells of the state was determined to lie below the dissociation limit, and the state is found to be significantly more bound than previously assumed.

Highlevel ab initio computations of structures and interaction energies of naphthalene dimers: Origin of attraction and its directionality
View Description Hide DescriptionThe intermolecular interactionenergies of naphthalene dimers have been calculated by using an aromatic intermolecular interaction model (a model chemistry for the evaluation of intermolecular interactions between aromatic molecules). The CCSD(T) (coupled cluster calculations with single and double substitutions with noniterative triple excitations) interactionenergy at the basis set limit has been estimated from the secondorder Møller–Plesset perturbation interactionenergy near saturation and the CCSD(T) correction term obtained using a mediumsize basis set. The estimated interactionenergies of the set of geometries explored in this work show that two structures emerge as being the lowest energy, and may effectively be considered as isoenergetic on the basis of the errors inherent in out extrapolation procedure. These structures are the slippedparallel structure (−5.73 kcal/mol) and the cross structure (−5.28 kcal/mol). The Tshaped and sandwich dimers are substantially less stable (−4.34 and −3.78 kcal/mol, respectively). The dispersion interaction is found to be the major source of attraction in the naphthalene dimer. The electrostaticinteraction is substantially smaller than the dispersion interaction. The large dispersion interaction is the cause of the large binding energies of the cross and slippedparallel dimers.

Photodissociation dynamics of the Kr–HBr cluster: The effect of the rare gas atom substitution
View Description Hide DescriptionThe ultraviolet photolysisdynamics of is investigated by means of wave packet calculations, focusing on the fragmentation pathway Photolysis is simulated by starting from two different cluster initial states, namely the ground van der Waals (vdW) and an excited vdW bending state, associated with the Kr–H–Br and Kr–Br–H isomers, respectively. The results show that, for the two initial states of the cluster, the Kr–Br product yield is lower than that of Ar–Br radicals found in previous studies on Ar–HBr photolysis. Despite this decrease, the Kr–Br yield is found to be still rather high, in particular for the initial excited vdW state of In addition, the Kr–Br product state distributions exhibit a remarkably higher excitation (mainly rotational) than the corresponding Ar–Br distributions. The lower yield and higher excitation of Kr–Br as compared to Ar–Br, are attributed to a larger share of the energy available for the radical going to internal excitation in the case of the Kr–Br product. The different partition of the energy available for Kr–Br also causes significant deviations in the photolysis behavior of Kr–HBr when compared to that of Ar–HBr, in the case of the initial excited vdW state of both clusters. A common feature of the photodissociation of Kr–HBr and Ar–HBr is the manifestation of quantum interferenceeffects in the Kr–Br and Ar–Br rotational state distributions, in the form of pronounced structures of supernumerary rotational rainbows.

Manybody effects in molecular photoionization in intense laser fields; timedependent Hartree–Fock simulations
View Description Hide DescriptionThe time evolution of the reduced single electron density matrix for eight electrons in a onedimensional finite box potential driven by an intense laser field is calculated by numerically integrating the timedependent Hartree–Fock equations. We study the effects of the Coulomb interaction, field intensity, and frequency on the time profile of the ionization process. Our computed saturation ionization intensity is in good agreement with experimental results for decatetraene [Ivanov et al. J. Chem. Phys. 117, 1575 (2002)].

Structures of mixed goldsilver cluster cations Ion mobility measurements and densityfunctional calculations
View Description Hide DescriptionThe collision cross sections of cluster ions were determined. For bimetallic clusters, we observe a significant intracluster charge transfer leaving most of the ions positive charge on the silver atoms. The mixed trimeric ions and are triangular like the pure gold and silver trimers. Most of the tetrameric clusters are rhombus shaped, with the exception of which has a Y structure with the gold atom in the center. Among the pentamers we find distorted X structures for all systems. For we find an additional isomer which is a trigonal bipyramid. These findings are in line with predictions based on densityfunctional theory calculations, i.e., all these structures either represent the global minima or are within less than 0.1 eV of the predicted global minimum.

Dipolebound anions of highly polar molecules: Ethylene carbonate and vinylene carbonate
View Description Hide DescriptionResults of experimental and theoretical studies of dipolebound negative ions of the highly polar molecules ethylene carbonate (EC, and vinylene carbonate (VC, are presented. These negative ions are prepared in Rydbergelectron transfer (RET) reactions in which rubidium (Rb) atoms, excited to ns or ndRydberg states, collide with EC or VC molecules to produce or ions. In both cases ions are produced only when the Rb atoms are excited to states described by a relatively narrow range of effective principal quantum numbers, the greatest yields of and are obtained for and respectively. Charge transfer from lowlying Rydberg states of Rb is characteristic of a large excess electron binding energy of the neutral parent; employing the previously derived empirical relationship the electron binding energies are estimated to be for EC and for VC. Electron photodetachment studies of show that the excess electron is bound by in excellent agreement with the RET results, lending credibility to the empirical relationship between and Vertical electron affinities for EC and VC are computed employing augccpVDZ atomcentered basis sets supplemented with a set of diffuse Gaussian primitives to support the dipolebound electron; at the CCSD(T) level of theory the computed electron affinities are 40.9 and 20.1 meV for EC and VC, respectively.

Spectroscopy of highly excited vibrational states of HCN in its ground electronic state
View Description Hide DescriptionAn experimental technique based on a scheme of vibrationally mediated photodissociation has been developed and applied to the spectroscopic study of highly excited vibrational states in HCN, with energies between 29 000 and 30 000 cm^{−1}. The technique consists of four sequential steps: in the first one, a high power laser is used to vibrationally excite the sample to an intermediate state, typically (0,0,4), the mode being approximately equivalent to the C–H stretching vibration. Then a second laser is used to search for transitions between this intermediate state and highly vibrationally excited states. When one of these transitions is found, HCN molecules are transferred to a highly excited vibrational state. Third, a ultraviolet laser photodissociates the highly excited molecules to produce H and CN radicals in its electronic state. Finally, a fourth laser (probe) detects the presence of the photofragments by means of an laser induced fluorescence scheme. The spectra obtained with this technique, consisting of several rotationally resolved vibrational bands, have been analyzed. The positions and rotational parameters of the states observed are presented and compared with the results of a stateoftheart variational calculation.