Volume 109, Issue 6, 08 August 1998
 COMMUNICATIONS


Stateresolved twophoton laser induced fluorescence detection of BrO
View Description Hide DescriptionIn the present work we report stateresolved detection of radicals generated in reactive collision processes using twophoton excitation with subsequent monitoring of the vacuumultraviolet fluorescence. product excitation spectra extending in the spectral range between 348 and 363 nm were obtained from both the reaction and The spectra indicate the existence of a hitherto unobserved highlying radiative C state at an energy of around

Silicide formation by hightemperature reaction of Rh with model films
View Description Hide DescriptionThe metal–support interaction between rhodium and silica has been studied by xray photoelectron spectroscopy for a model system. This system consists of a thin silicon oxide layer, prepared by chemical vapor deposition on molybdenum with a nominal load of one monolayerrhodium. Heating in ultrahigh vacuum (UHV) results in changes of the cluster size and binding energies of surface species. Thermal treatments above 850 K in UHV results in the formation of a rhodium silicide, which has not been reported so far. For the formation of this new phase a surface reaction mechanism is proposed.
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 THEORETICAL METHODS AND ALGORITHMS


A strictly variational procedure for cluster embedding based on the extended subspace approach
View Description Hide DescriptionEven if an isolated defect results only in a local perturbation of the electron density, the wave function and the firstorder reduced density matrix may still exhibit a longrange response to the defect. We present an axiomatic approach to the construction of a generalpurpose embedding scheme which is able to cope with this problem. We start from a list of requirements, which we consider pertinent to an accurate embedding technique, and we proceed to demonstrate that the extended subspace approach recently proposed by Head and Silva [J. Chem. Phys. 104, 3244 (1996)] is the minimal realization of such an embedding scheme. The variational principle, strict fulfillment of the Pauli exclusion principle, a finite dimensional parameter space, and the possibility to perform the minimization by a standard SCF (selfconsistent field) procedure are the key requirements which lead to a constrained SCF procedure. Selfembedding consistency and local completeness of the Hilbert space can then be realized by a mathematically very simple construction principle for the active subspace which can be formulated independent of any basis set. We analyze the spatial structure of the resulting minimal orbital space by means of tightbinding model Hamiltonians. For metal systems, we find active and frozen constrained SCF spaces to necessarily interlock in a strong and complicated fashion.

Identifying collective dynamical observables bearing on local features of potential surfaces
View Description Hide DescriptionA singular value decomposition of dynamical sensitivities provides insight into the relationship between a data set and the potential which is often not evident from the sensitivities of individual observables. An illustration is treated consisting of data sets drawn from reactive transition probabilities as a function of energy for the collinear system. While the sensitivities of individual reactive transition probabilities to the twodimensional potential are highly structured functions of the potential coordinates, a set of reactive transition probabilities is identified which collectively has localized sensitivity primarily to the saddle point region and secondarily to the slope along the symmetric stretch line in the outer corner tunneling region and to the width of the barrier. Information of this type garnered from a principal component sensitivity analysis can be especially valuable when attempting to use dynamics data to refine potential surfaces.

Inflection spacing symmetry of diatomic potential curves
View Description Hide DescriptionMolecular ground states are found to have an approximate symmetry related to equally spaced inflection points from Morse, KratzerCoulomb, Rydberg, exp–exp, and cubicanharmonic potentials turn out to have exact equal spacing of all inflection points out to dissociation. Equal spacing near equilibrium is consistent with the rule connecting the hardsphere radius and the point of maximum attractive bonding force to the equilibrium bond length. In theoretical and experimental molecular curves, the rule tends to be exact at high reduced force constant with symmetry breaking over related to covalent, ionic, and van der Waals bonding character. Scaling preserves spacing symmetry, and maps twoterm potentials into a universal exp–exp limit, including the potential into the Morse potential. Scaled spacing parameters for different molecules are nearly constant. Anharmonic shape parameters for “tilt” and “width” of the well are linked to empirical correlations of Dunham constants [J. L. Graves and R. G. Parr, Phys. Rev. A 31, 1 (1985)], and RKR analysis suggests correlations induced by equalspacing constraints. The inflection structure is linked to threshold singularities in the inverse Born–Oppenheimer potential which predicts the potential as a first approximation.

Path integrals for Fokker–Planck dynamics with singular diffusion: Accurate factorization for the time evolution operator
View Description Hide DescriptionFokker–Planck processes with a singular diffusion matrix are quite frequently met in Physics and Chemistry. For a long time the resulting noninvertability of the diffusion matrix has been looked as a serious obstacle for treating these Fokker–Planck equations by various powerful numerical methods of quantum and statistical mechanics. In this paper, a pathintegral method is presented that takes advantage of the singularity of the diffusion matrix and allows one to solve such problems in a simple and economic way. The basic idea is to split the Fokker–Planck equation into one of a linear system and an anharmonic correction and then to employ a symmetric decomposition of the short time propagator, which is exact up to a high order in the time step. Just because of the singularity of the diffusion matrix, the factors of the resulting product formula consist of well behaved propagators. In this way one obtains a highly accurate propagation scheme, which is simultaneously fast, stable, and computationally simple. Because it allows much larger time steps, it is more efficient than the standard propagation scheme based on the Trotter splitting formula. The proposed method is tested for Brownian motion in different types of potentials. For a harmonic potential we compare to the known analytic results. For a symmetric double well potential we determine the transition rates between the two wells for different friction strengths and compare them with the crossover theories of Mel’nikov and Meshkov and Pollak, Grabert, and Hänggi. Using a properly defined energy loss of the deterministic particle dynamics, we obtain excellent agreement. The methodology is outlined for a large class of processes defined by generalized Langevin equations and processes driven by colored noise.

A new inhomogeneity parameter in densityfunctional theory
View Description Hide DescriptionDensityfunctional exchange–correlation approximations depending on spin densities and their gradients have proven remarkably accurate in recent thermochemical tests [e.g., A. D. Becke, J. Chem. Phys. 107, 8554 (1997)]. With the inherent limitations of firstorder gradient corrections now in sight, however, we investigate here a class of inhomogeneity corrections based on a new secondorder gradient parameter. The new parameter is logically motivated by previous work on Taylor expanded exchange hole densities, and generates exchange–correlation functionals more accurate than those containing firstorder gradients only.

A nonequilibrium statistical grandcanonical ensemble: Description in terms of flux operators
View Description Hide DescriptionIn the domain of Statistical Mechanics of nonequilibriumnonlinear (dissipative) systems based on a generalized Gibbs–Boltzmann ensemble formalism, it may be highlighted the socalled Nonequilibrium Statistical Operator Method, and, particularly, Zubarev’s approach. We report here a detailed analysis of a case consisting in a generalized nonequilibrium grandcanonical ensemble. Its construction requires to introduce besides the traditional densities of energy and the particle number their nonconservingdissipative fluxes of all order. The description is quite appropriate to provide a framework for the construction of a nonclassical thermohydrodynamics, which is briefly described.

Gustavson’s procedure and the dynamics of highly excited vibrational states
View Description Hide DescriptionThe wellknown Birkhoff–Gustavson canonical perturbation theory has been used so far to obtain a reasonable approximation of model systems near the bottom of the well. It is argued in the present work that Gustavson’s calculation procedure is also a powerful tool for the study of the dynamics of highly excited vibrational states, as soon as the requirement that the transformed Hamiltonians be in Birkhoff’s normal form is dropped. Mathematically, this amounts to modifying the content of Gustavson’s null space. Physically, the transformed Hamiltonians are of the single or multiresonance type instead of just trivial Dunham expansions, even though no exact resonance condition is fulfilled. This idea is checked against 361 recently calculated levels of HCP up to above the bottom of the well and involving up to 30 quanta in the bending degree of freedom. Convergence up to 13th order of perturbation theory and an average absolute error as low as are reported for a tworesonance Hamiltonian, whereas the Dunham expansion converges only up to 4th order at an average error of The principal advantages of the resonance Hamiltonians compared to the exact one rely on its remaining good quantum numbers and classical action integrals. Discussions of the limitations of the method and of the connections to other canonical perturbation theories, like Van Vleck or Lie transforms, are also presented.

A comparison of the efficiency of Fourier and discrete timepath integral Monte Carlo
View Description Hide DescriptionWe compare the efficiency of Fourier and discrete time path integral Monte Carlo (PIMC) methods on a cluster of 22 hydrogen molecules at 6 K. The discrete time PIMC with a pair density matrix approximation to the path action is shown to be the most efficient for evaluating all the observables studied here. The Fourier PIMC technique has a comparable efficiency for observables diagonal in the coordinates but is significantly worse for estimating the kinetic and total energies. The superior performance of the discrete time PIMC is shown to be due to the more accurate treatment of the path action using the pair density matrix approach; the discrete time PIMC simulation within the primitive approximation is much less efficient. Complete details of the implementation of all algorithms are given.

Effective Hamiltonian for neardegenerate states in relativistic direct perturbation theory. II. like systems
View Description Hide DescriptionThe recently developed effective Schrödingerlike Hamiltonian equation (EHA) in a model space of neardegenerate nonrelativistic twocomponent spinors is applied to the relativistic energy corrections at first, second, and third order of within the framework of relativistic direct perturbation theory (DPT). The dominant singular part of the total relativistic correction is already recovered by the lowestorder effective Hamiltonian in the spirit of degenerate perturbation theory, while the perturbative expansion needs to account for only the small remaining part. Numerical results for groups of excited potential curves of the oneelectron like quasimolecule are presented and discussed. In general the most efficient approach is firstorder EHADPT for the set of states, followed by singlestate DPT of higher orders.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


( Ne, Ar) interactions: Ab initio potentials and collision properties
View Description Hide DescriptionThe lowest states of Σ and Π symmetry of Rg⋯Cl ( Ne, Ar) complexes were investigated using the coupled cluster approach with single, double, and noniterative triple excitations (CCSD(T)) in an extended basis set including bond functions. The Σ states possess deeper minima at shorter interatomic distances than the corresponding Π states. The ΣΠ splittings, which for He⋯Cl and Ar⋯Cl are significantly larger than previously deduced, are mainly due to differences in the exchange repulsion terms. The total energies were dissected into electrostatic, exchange, induction, and dispersion components. The calculated potentials have been used in the calculations of collision properties of Rg⋯Cl systems. Absolute total cross sections, spinorbit quenching rate constants, and diffusion coefficients were evaluated from both the ab initio and previously available empirical potentials. The performance of ab initio potentials in these calculations proved to be very reasonable.

Electron bombardment matrix isolation of Rg/Rg^{′}/methanol mixtures (Rg= Ar, Kr, Xe): Fouriertransform infrared characterization of the protonbound dimers and in Ar matrices and and in Kr matrices
View Description Hide DescriptionMatrices formed by subjecting methanol vapor diluted in argon/krypton mixtures to electron bombardment and subsequent matrix isolation (EBMI) reveal a new feature at 885.3 which is assigned to the fundamental of the triatomic cation In samples containing about 5% krypton, the fundamental of is also observed in a predominantly solid argon environment. These assignments are supported by annealing experiments and by density functional theory calculations reported in a separate paper. Similar experiments with xenon diluted in argon yield infrared spectra showing the and bands of , and of in predominantly argon environments. EBMI of methanol diluted in krypton in the presence of xenon gives rise to infrared bands assigned to the and fundamentals and combination bands of both and isolated in predominantly krypton environments. The energetics and plausible mechanisms to the formation of these homogenous and mixed protonbound raregas dimers are considered.

Density functional theory study of the protonbound raregas dimers and ( Kr, Xe): Interpretation of experimental matrix isolation infrared data
View Description Hide DescriptionDensity functional theory calculations have been performed on the various protonbound raregas dimers and ( Kr, or Xe, and ) employing the BP86 method coupled with either a Gaussian split valence basis set (DZVP) or a numerical split valence basis set The calculations with the basis represent the first calculations in which correct qualitative agreement is obtained with respect to the trend in experimental data for the antisymmetric stretching wavenumbers of the three cations. Good qualitative agreement is also obtained for the antisymmetric stretching wavenumber of the mixedraregas species For the xenoncontaining mixedraregas cations, the agreement with experimental wavenumbers is not good as is the case for the DZVP basis set with any of the aforementioned cations. This is believed to be due to the inability of these basis sets to predict some physical and chemical properties for these species. Quantitative agreement between theory and experiment with respect to the antisymmetric stretch of the cations is improved when four radial argon atoms are placed at a fixed distance from the central H, intended to mimic the matrix environment. Based on these calculations, an inverse hydrogenisotope dependence for the dissociation energy of these species is predicted. No center atom isotope dependence is predicted for the symmetric stretching vibration. Employing a polyatomic model, we have reanalyzed previously published combination band data for and and concluded that there is no evidence for an inverse isotope dependence for the symmetric stretching vibrations of these species.

Intermolecular interaction potential of the carbon dioxide dimer
View Description Hide DescriptionThe energy profile of the lowest energy path connecting the slipped parallel and Tshaped dimers of carbon dioxide was investigated using a reasonably large basis set with the MP2 level electron correlation correction and with the counterpoise correction. There was no inversion barrier and the Tshaped dimer was a transition state connecting the two slipped parallel dimers. The calculated interaction energies of the two dimers (−1.290 and −1.072 kcal/mol) were larger than those reported previously. The calculated energy difference of the two dimers (0.218 kcal/mol) was also larger than the previous values (less than 0.1 kcal/mol). The effects of basis set, electron correlation, and basis set superposition error were studied in detail. The secondorder Mo/ller–Plesset (MP2) interaction energies of the two dimers were close to the coupled cluster calculations using single and double substitutions including noniteratively triple excitations [CCSD(T)] ones. The choice of the basis set greatly affected the calculated interaction energies. Small basis sets underestimated the attractive interaction energies. Diffuse polarization functions were essential to evaluate the attractive interaction. The calculated MP2 interaction energies of the two dimers with the counterpoise correction increased by the augmentation of the diffuse polarization functions to the basis set. These values were close to the estimated MP2 interaction energies at the complete basis set (−1.362 and −1.140 kcal/mol). The basis set was reasonably large to evaluate the attractive interactions. Although the basis set augmented with diffuse polarization functions had large basis set superposition error (BSSE), the calculated interaction energies with the counterpoise correction were close to those calculated with the nearly BSSE free ccpV5Z and augccpVQZ basis sets and to the expected values at the complete basis set.

Molecular dynamics study of the cluster using an ab initio manybody model potential
View Description Hide DescriptionA general approach to construct a model potential with parameters fitted to ab initio energy surfaces, including manybody nonadditive effects, developed in our previous works is applied to the cluster. A molecular dynamics study of structural and dynamical properties of this cluster is performed using such a potential. Two new stable twodimensional isomers with and symmetries are identified as local minima of the potential surface using the simulated quenching technique. An analysis of the thermal stability as a function of the cluster temperature reveals interesting features in the meltinglike transition of . A twostep isomerization phenomenon is observed: at temperatures around 300 K, the cluster structures fluctuate among twodimensional isomers, at higher temperatures (500 K), fast transitions occur between two and threedimensional cluster configurations. The simulation was extended up to the cluster fragmentation which is observed through dimer evaporation.

The 16 valence electronic states of nitric oxide dimer
View Description Hide DescriptionSixteen electronic states of nitric oxide dimer are investigated using various ab initio levels of theory and various orientations of the dimer. These are the states which arise from the mixing of the singly occupied orbitals of the monomers, and include all eight states which directly correlate to the ground states of the monomers. Twelve of the sixteen states are significantly multiconfigurational in character, which cause incorrect state orderings at low levels of theory. At several plausible geometries, eight lowlying states are predicted (four singlets and four triplets) within a 1 eV span, hence corresponding to excitations in the infrared, while the other eight states (six singlets and two triplets) lie much higher in the far ultraviolet, and in the realm of numerous other electronic states. The results imply, but do not confirm, that the only potential minimum lying below the lowest dissociation asymptote is the cisONNO geometrical conformation of the ground state.

Resonant coherent hyperRaman scattering (CHRS). II. A theory on the general relationship between CHRS and coherent Raman scattering (CRS) processes
View Description Hide DescriptionA theoretical description of the resonant coherent hyperRaman scattering for an arbitrary system–bath interaction is presented. Particularly the relationship between the coherent hyperRaman scattering (CHRS) and coherent Raman scattering (CRS) signals is established without alluding to any specific model of optical broadening. The permanent dipole moment difference between the excited and ground states of a given chromophore is shown to be proportional to the ratio of the CHRS to CRS signals, and it is proved that this result is valid regardless of the model for the chromophore–bath interaction.

A theoretical characterization of the quartet states of the molecular ion
View Description Hide DescriptionThe quartet states of the molecular ion are described theoretically using the internally contracted multireference configuration interaction approach and natural orbitals generated from a stateaveraged density matrix. Correlationconsistent polarizedvalence quadruplezeta atomic functions are used in the expansion of the oneelectron basis. Potential energy curves are presented for all the states, and solutions of the radial Schrödinger equation allowed the determination of vibrational energy differences and spectroscopic constants. For the state, this study corroborates the available experimental data and extends the spectroscopic information to regions not yet accessed experimentally; an alternative explanation for the predissociation mechanism is also suggested. For the state, our data and analysis are indicative that the vibrational spectroscopic constants derived from the photoelectron spectra might be underestimated. It also leaves open the possibility that the experimental vibrational level numbering might have to be increased by one unit. Transition probabilities as given by the Einstein coefficients, and Franck–Condon factors are also provided to help analyze the experimental data. Of immediate relevance to the direct ionfragment spectroscopy, this study predicts the existence of a new bound state in the energy range of photons used in these experiments. This new state crosses the curve very close to where it was supposed to be crossed by the and its repulsive side runs almost parallel to this latter state. Our theoretical prediction places the state still lower than it was inferred experimentally. For the transition we have also computed the transition moment function and showed that its constancy assumed in the simulation of the experimental intensity data is not valid.

Vuv photolysis of hydrazoic acid: Absorption and fluorescence excitation spectra
View Description Hide DescriptionThe vuvabsorption of the isotopomers and the formation of NH/ND photofragments in the and states were studied. Tunable synchrotron radiation and several atomic resonance lines were used as light sources. The absorptionspectrum, which shows more features than reported earlier, was analyzed by means of extensive quantum chemical ab initio calculations. The internal energies of the observed photofragments were estimated as a function of the photolysis wavelength by emission spectroscopy. The fragment is formed with a rather constant quantum yield below 147 nm, while the relative production yield of increases with decreasing wavelength. Although can be formed directly via a spin forbidden process at long wavelengths, it is more efficiently produced by reactions of the three different triplet states with The variation of the vibrational distribution of the radicals indicates that various production mechanisms exist.
