Volume 111, Issue 16, 22 October 1999
 COMMUNICATIONS


A second rhomboidal isomer of
View Description Hide DescriptionA second lowlying cyclic isomer of has been detected in a supersonic molecular beam by Fourier transformmicrowave spectroscopy. Calculated to lie about 5 kcal above the ground state rhomboid, the new isomer is also a planar rhomboid with a transannular bond, symmetry, and a singlet electronic ground state. The transannular bond, however, is between the Si and the opposite C, and the rotational spectrum as a result is that of an oblate, not a prolate, asymmetric rotor. Both rhomboidal isomers of are produced with comparable abundance under a wide range of experimental conditions, which suggests that cyclic isomers of longer siliconcarbides may now be observable with the present techniques. Oblate is a plausible molecule for astronomical detection because it is calculated to be fairly polar, and because radio emission lines of the ground state rhomboid have already been detected in the circumstellar shell of the evolved carbon star

Relative formation rates of and in mixtures
View Description Hide DescriptionTunable diode laser (TDL) and mass spectrometry have been combined to measure relative formation rate coefficients of each of the four channels contributing to ozone of mass 50 u and 52 u produced in mixtures. Only one channel has a large rate coefficient advantage causing almost exclusively the observed isotope enrichment. Collisions to form ozone are endon reactions.Molecular symmetry plays no apparent role in the ozoneisotope enrichment process, regardless, whether or not ozone is produced in collisions with homo or heteronuclear molecular oxygen. The oxygen isotope exchange process may hold a key in explaining the rate coefficient results.

Femtosecond fluorescence depletion spectroscopy of multiphoton dissociation dynamics
View Description Hide DescriptionTwocolor femtosecond pump–probe spectroscopy has been applied to the multiphotondissociation of with a time resolution of fs. At laser intensities in the range and a wavelength of 400 nm, absorbs three photons before dissociation. Nascent NO product in its and 1 vibrational levels is probed by singlephoton fluorescence depletion at 800 nm. Analyses of the ultrafast transient behavior at different intensities leads to an estimate of fs for formation of NO and 1.
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 THEORETICAL METHODS AND ALGORITHMS


Scattering matrix determination by asymptotic analysis of complex scaled resonance wave functions: Model nonadiabatic dynamics
View Description Hide DescriptionIt has previously been shown that partial widths of resonance states can be calculated by the asymptotic analysis of the complex scaled resonance wave function [U. Peskin, N. Moiseyev, and R. Lefebvre, J. Chem. Phys. 92, 2902 (1990)] and by the complex coordinate scattering theory [N. Moiseyev and U. Peskin, Phys. Rev. A 42, 255 (1990)]. Here we use these methods for the first time to calculate complex partial width amplitudes. The complex amplitudes are independent of the complex scaling parameters and are used for calculating the resonance contribution to the scattering matrix (the S matrix) in the case of scattering described by two coupled onedimensional potential energy curves. The background contribution to the S matrix was calculated by the use of one potential energy curve only. The sum of the resonance and the background contributions provides accurate complex S matrix elements and transition probabilities, even at the resonance energy for which total reflection is obtained due to the interference between the two contributions.

Multireference perturbation configuration interaction methods for solvated systems described within the polarizable continuum model
View Description Hide DescriptionWe present a method to include solventeffects described within the polarizable continuum model into the CIPSI multireference perturbation algorithm. In the methodology we have formulated and implemented, solvent interactions are explicitly included in the configuration interaction scheme and in the following perturbative corrections, through proper operators. The nonlinear character induced by such operators leads to an iterative procedure in which solute and solvent can mutually equilibrate. Applications to the electronic excitation spectrum of formamide are considered. In these cases, effects due to an incomplete electrostatic response of the solvent (nonequilibrium model) as well as repulsion interactions between solute and solvent have been included in the quantum mechanical description.

A direct method of calculating sensitivity coefficients of chemical kinetics
View Description Hide DescriptionIn this paper, a new direct method of calculating the firstorder sensitivity coefficients using sparse matrix technology to chemical kinetics is presented. The Gear type procedure is used to integrate a model equation and its coupled auxiliary sensitivity coefficient equations. Because the Jacobian matrix of the model equation is the same as that of the sensitivity coefficient equation with respect to a parameter, it is only necessary to triangularize the matrix related to the Jacobian matrix of the model equation. The FORTRAN subroutines of the model equation, the sensitivity coefficient equations, and their Jacobian analytical expressions are generated automatically from chemical mechanism. This method greatly increases the efficiency of computation by taking advantage of the fact that the auxiliary equations for different sensitivity coefficients are linear and quite similar. Two sets of chemical reactions are used to illustrate this approach: oxidation of formaldehyde in the presence of carbon monoxide and photooxidation of dimethyl sulfide. The accuracy and computational efficiency of the new direct method is demonstrated by comparing the results from the new direct method and from the indirect method.

Simulation of a free energy upper bound, based on the anticorrelation between an approximate free energy functional and its fluctuation
View Description Hide DescriptionThe local states and hypothetical scanning methods enable one to define a series of lower bound approximations for the free energy, from a sample of configurations simulated by any exact method. is expected to anticorrelate with its fluctuation i.e., the better (i.e., larger) is the smaller is where becomes zero for the exact F. Relying on ideas proposed by Meirovitch and Alexandrowicz [J. Stat. Phys. 15, 123 (1976)] we bestfit such results to the function where C, and α are parameters to be optimized, and is the extrapolated value of the free energy. If this function is also convex (concave down), one can obtain an upper bound denoted This is the intersection of the tangent to the function at the lowest measured with the vertical axis at We analyze such simulation data for the square Ising lattice and four polymer chain models for which the correct F values have been calculated with high precision by exact methods. For all models we have found that the expected concavity always exists and that the results for and are stable. In particular, extremely accurate results for the free energy and the entropy have been obtained for the Ising model.

Vector parametrization of the Natom problem in quantum mechanics. III. Separation into two subsystems: Application to
View Description Hide DescriptionIn this work, the vectorial formalism previously developed [Gatti et al., J. Chem. Phys. 108, 8804 (1998); 108, 8821 (1998)] is extended to radial coordinates and to the general study of dimers. This method is general and avoids the direct use of differential calculus in the derivation of the kinetic operator. Moreover, to study the spectrum of an exact and simple kinetic energy operator is proposed. The new system of coordinates (a combination of Jacobi and hyperspherical coordinates) fully displays the permutation symmetry of the three hydrogen atoms. It is adapted to study the umbrella motion and furthermore minimizes the Coriolis terms.

Fully coupled 6D calculations of the ammonia vibrationinversiontunneling states with a split Hamiltonian pseudospectral approach
View Description Hide DescriptionAn efficient pseudospectral method for performing fullycoupled sixdimensional bound state dynamics calculations is presented. A Lanczosbased iterative diagonalization scheme produces the energy levels in increasing energies. This scheme, which requires repetitively acting the Hamiltonian operator on a vector, circumvents the problem of constructing the full matrix. This permits the use of ultralarge molecular basis sets in order to fully converge the calculations. The Lanczos scheme was conducted in a symmetry adapted sixdimensional spectral representation. The Hamiltonian operator has been split into only four different terms, each being Hermitian and symmetryadapted. The potential term is evaluated by a pseudospectral scheme of Gaussian accuracy, which guarantees the variational principle. Spectroscopic levels are computed with this method for one ammonia potential, and compared to experimental results. The results presented below are a direct application of our vector formulation. The latter has shown to be particularly well adapted to the split pseudospectral approach for it yields a compact and symmetryadapted Hamiltonian.

Numerical implementation of a mixed quantum classical rate theory
View Description Hide DescriptionThe recently formulated mixed quantum classical rate theory (MQCLT) is implemented for a model system with two degrees of freedom. In MQCLT, one must compute the Wigner representation of the symmetrized thermal flux operator. This phase space flux distribution is then multiplied by the classical reaction probability to obtain the rate. The major computational difficulty is the multidimensional Fourier transform necessary for obtaining the Wigner distribution. The Fourier transform reintroduces a sign problem when attempting to estimate the MQCLT rate using Monte Carlo methods. Two different methods for overcoming the sign problem are explored in this paper. Numerical results are presented for a model problem of an Eckart barrier coupled bilinearly to a slow oscillator and compared with numerically exact results.

General formulation of the vibrational kinetic energy operator in internal bondangle coordinates
View Description Hide DescriptionA general formulation of the vibrational kinetic energy operator expressed in internal bondangle coordinates is presented. This formulation is based on Podolsky’s expression for the covariant form of the Laplace–Beltrami operator. When a valid set of internal bondangle coordinates is employed, it is possible to adapt a systematic approach to solve for the Jacobian determinant governing the coordinate transformation from Cartesian coordinates. In the general case of an arbitrary Natom system, this Jacobian always factorizes to a simple form. This allows one to evaluate all the terms that contribute to the effective potential that arises from transforming the kinetic energy operator to internal coordinates. We discuss restrictions on the choice of internal vibrational coordinates that may be included in a valid set. We then provide tabular information from which the vibrational kinetic energy operator for any molecular system can be constructed directly with no matrix inversion or chain rule manipulation required.

A new timedependent wave operator approach to the internal eigenstate problems for large matrices
View Description Hide DescriptionA new integration procedure is proposed to solve the nonlinear timedependent waveoperator equation. This procedure can easily be adapted to describe the adiabatic evolution of a system on a longtime scale and also to solve the internal eigenstate problem for large matrices.

Boundary condition determined wave functions for the ground states of one and twoelectron homonuclear molecules
View Description Hide DescriptionSimple analytical wave functions satisfying appropriate boundary conditions are constructed for the ground states of oneand twoelectron homonuclear molecules. Both the asymptotic condition when one electron is far away and the cusp condition when the electron coalesces with a nucleus are satisfied by the proposed wave function. For the resulting wave function is almost identical to the Guillemin–Zener wave function which is known to give very good energies. For the two electron systems and the additional electron–electron cusp condition is rigorously accounted for by a simple analytic correlation function which has the correct behavior not only for and but also for and where is the interelectronic distance and R, the internuclear distance. Energies obtained from these simple wave functions agree within with the results of the most sophisticated variational calculations for all R and for all systems studied. This demonstrates that rather simple physical considerations can be used to derive very accurate wave functions for simple molecules thereby avoiding laborious numerical variational calculations.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Theoretical studies of rotation induced Fermi resonances in HOCl
View Description Hide DescriptionTheoretical investigations of rotation induced Fermi resonances in HOCl are carried out using several different quantum mechanical methods. Due to shape differences of the eigenfunctions, nearby vibrational levels may be energetically tuned to form Fermi (or anharmonic) resonances by varying rotational quantum numbers. Such rotation induced Fermi resonances have been observed experimentally in HOCl, for example, for bright states (3,2,0) and (4,0,0) by Abel et al. [J. Chem. Phys. 104, 3189 (1996) and ibid. 106, 3103 (1997)]. Using an ab initio potential, this work shows that the (3,2,0) state is significantly mixed with the (2,3,3) state near and and and while the (4,0,0) state forms a Fermi pair with (3,2,1) near and The wave functions of the Fermi pairs display significant deformation due to the mixing. Both the rotation induced degeneracy and coupling strength are found to be important.

The chemiionization of for collision energies from 0.003 to 6 eV
View Description Hide DescriptionMeasurements of the collision energy dependence of the chemiionization cross sections of the model systems are presented for the relevant energy range 0.003–6 eV. Except for all systems show a pronounced minimum of ionization at thermal energies. In the hyperthermal range, however, the two spin systems are in sharp contrast to each other: the triplet systems exhibit a broad saturating maximum of ionization, whereas the singlet systems reveal a shallow shaped second minimum (pronounced for Xe) which can be rationalized within the oneelectron model potential calculations of Siska [J. Chem. Phys. 71, 3942 (1979)]. Using an effective singlechannel Schrödinger equation, one finds, for all systems, complex potentials depending on distance only which properly model the measured features. A more profound picture appears when differential elastic cross sections from experiments of other groups are included. In the triplet case, differential elastic and chemiionization data can be adequately described with one complex potential, i.e., the local approximation holds. This is not found for the singlet systems. The hyperthermal minima instead give evidence that the optical singlet potentials are nonlocal. Various aspects of this striking spin dependence of the characteristics of are discussed. In particular, the breakdown of the local approximation in the singlet case can be rigorously derived.

Nondissociative lowenergy electron attachment to and C_{6}F_{6}: Intermediate lifetimes
View Description Hide DescriptionNondissociative electron attachment to and is investigated by measuring the velocity distribution of ions formed via electron transfer in collisions with velocity selected Rydberg atoms and by measuring the decay of the product negative ions during passage to a detector. Collisions with lead to the production of free electrons and of longlived (τ>100 μs) ions. The free electrons, which result from autodetachment, are all created within a very short time period (τ≲15 ps) following initial electron capture. Collisions with result in the formation of ions that have a broad range of lifetimes against autodetachment. A possible reaction model involving competition between autodetachment and intramolecular vibrational relaxation is discussed.

Infrared spectrum and energy levels of the CO dimer: Evidence for two almost isoenergetic isomers
View Description Hide DescriptionThe CO dimer has been studied in the region of the CO stretching vibration (2139–2152 cm^{−1}) with a pulsed supersonic jet and a tuneable diode laser probe. By using both pinhole and slit jet configurations, and varying the distance downstream of the laser probe, the dimer spectrum was obtained over a range of effective rotational temperatures from about 1 to 12 K. Using this temperature dependence and the technique of combination differences, over 120 transitions belonging to 13 subbands were assigned in terms of 24 ground state and 36 excited state rotational energy levels of The levels fall into two groups, corresponding to isomers with effective intermolecular separations of either about 4.4 or 4.0 Å. The 4.4 Å isomer is the ground state, while the 4.0 Å isomer is a lowlying (0.88 cm^{−1}) excited state. This energy ordering is inverted when Previous calculations suggest that both forms are planar and roughly Tshaped, with the 4.4 Å isomer in a Cbonded configuration and the 4.0 Å isomer in an Obonded configuration. Measurements on an isotopically mixed dimer, indicate that C–O vibrational coupling between the monomer units in a dimer is very weak.

Ultrafast photodissociation studies of acetyl cyanide and acetic acid and unimolecular decomposition rates of the acetyl radical products
View Description Hide DescriptionUnimolecular decomposition rates for acetyl radical following the photodissociation of acetyl cyanide and acetic acid near 193 nm have been studied using ultrafast massresolved photoionizationspectroscopy. In both cases, the parent decays with an instrumentally limited lifetime, while the acetyl radical behaves in a manner consistent with an RRKM mechanism, in contrast to our previous results on acetone. It is necessary to convolute the population distribution with the microcanonical RRKM rates in order to achieve this agreement. We have also undertaken an ab initio study of the excited states of acetyl cyanide to clarify the assignments of these states. The state excited at 193 nm arises from a π→π^{*} transition with a calculated transition velocity dipole moment oriented at an angle of 57° with respect to the C–C≡N bond, resulting in an anisotropy parameter of −0.22. This is in reasonable agreement with the previous data of North et al. [J. Phys. Chem. A 101, 9224 (1997)]. The apparent RRKM behavior of the acetyl radical formed by the photodissociation of acetic acid and acetyl cyanide indicates that acetyl radical produced by the photodissociation of acetone at 193 nm may exhibit “extrinsic nonRRKM” effects, i.e., dynamic bottlenecks or mode specific effects.

Electronic absorption spectrum of cold naphthalene cation in the gas phase by photodissociation of its van der Waals complexes
View Description Hide DescriptionThe electronic absorptionspectrum of the naphthalene cation has been obtained in conditions relevant for comparison with the diffuse interstellar bands in astrophysics, i.e., cold species in the gas phase. The novel technique consisting to photodissociate a selectively R2P2CIprepared PAH–argon van der Waals complex in a molecular beam [Ph. Bréchignac and T. Pino, Astron. Astrophys. 343, L49 (1999)] has been used. The various aspects of the method are described in detail. The whole visible range has been explored revealing two electronic transitions displaying 28 vibronic bands. Absolute absorption cross sections have also been measured, and found much larger than reported from rare gas matrices studies. The additional information on the matrixinduced or complexinduced shifts and widths, and on the intramolecular and intermolecular processes involved in these species, is discussed. No definite conclusion about the possible presence of the cation in space can be drawn so far.

Vibrational stateresolved study of the reaction: Isotope effects on the product energy partitioning
View Description Hide DescriptionThe deuterium isotope effect on product energy partitioning in the particle transfer reaction is investigated in a crossed molecular beam experiment. Vibrationalstateresolved angular distributions are measured at six collision energies between 0.20 and 0.77 eV for the reaction and at seven collision energies between 0.22 and 1.20 eV for the reaction. The fraction of the total available energy deposited into product vibration is significantly larger in the deuterium system than in the hydrogen system. This effect is greatest at the lowest collision energies where products are formed with more than twice as much vibrational energy as products. The isotopic systems display similar trends in the product angular distributions, which extend over the full range of scattering angles at low energies and shift towards the forward direction as the collision energy is increased. These observations are discussed in terms of a competition between reaction mechanisms. An insertionmigration mechanism, yielding products with moderate vibrational excitation, is especially important at the lower energies. The insertion process leads to the isotope effect in the product energy partitioning which is explained in terms of Franck–Condon factors. As the energy increases, larger impact parameter collisions are able to proceed through a direct mechanism, yielding more tightly forwardscattered, vibrationally excited products. Since direct mechanisms show isotopically independent energy partitioning, the overall isotope effect diminishes with increasing energy as more collisions become purely direct. Bimodal rotational state distributions help strengthen the claim that two distinct reaction mechanisms produce the particle transfer product.
