Volume 111, Issue 7, 15 August 1999
 COMMUNICATIONS


Direct observation of nonadiabatic transitions in Na+raregas differential optical collisions
View Description Hide DescriptionWe study the dynamics in optical collisions of Na with Ne, Ar, Kr, and Xe in a differential scattering experiment. We report the observation of nonadiabatic transitions in the excited collisional quasimolecule based on measurements of the population ratio of the and finestructure levels. Comparison with theoretical results shows a generally very good agreement over the range of collision energies (0.01–0.3 eV) scanned in our experiment, using the best available potentials. For the heavier raregas systems a strong influence of the crossing on the population ratios is observed. We further extract a universal function for the nonadiabatic transition probability for these systems. In the thermal energy range, our results are in good qualitative agreement with data from gas phase optical collision experiments.

Crossed beam reaction of the cyano radical, with methylacetylene, Observation of cyanopropyne, and cyanoallene,
View Description Hide DescriptionThe chemical dynamics to form cyanopropyne, and cyanoallene, via the neutral–neutral reaction of the cyano radical, CN with methylacetylene, is investigated under single collision conditions in a crossed molecular beam experiment at a collision energy of 24.7 kJ The laboratory angular distribution and timeofflight spectra of the products are recorded at m/e=65, 64, 63, and 62. The reaction of with CN radicals yields reactive scattering signal at and demonstrating that two distinct H(D) atom loss channels are open. Forwardconvolution fitting of the laboratory data reveal that the reaction dynamics are indirect and governed by an initial attack of the CN radical to the π electron density of the β carbon atom of the methylacetylene molecule to form a long lived collision complex. The latter decomposes via two channels, i.e., H atom loss from the group to yield cyanoallene, and H atom loss from the acetylenic carbon atom to form cyanopropyne. The explicit identification of the CN vs H exchange channel and two distinct product isomers cyanoallene and cyanopropyne strongly suggests the title reaction as a potential route to form these isomers in dark molecular clouds, the outflow of dying carbon stars, hot molecular cores, as well as the atmosphere of hydrocarbon rich planets and satellites such as the Saturnian moon Titan.

Giant enhancement of electroninduced dissociation of chlorofluorocarbons coadsorbed with water or ammonia ices: Implications for atmospheric ozone depletion
View Description Hide DescriptionThe yield produced by dissociative electron attachment of a submonolayer of is enhanced by factors of and when is coadsorbed with waterice and ammonia ice, respectively, on a surface at ∼25 K. Moreover, the magnitude of enhancement increases strongly with decreasing concentration. This enhancement is attributed to dissociation of by capture of electrons selftrapped in polar water or ammonia molecules. This process may be an unrecognized sink for chlorofluorocarbons in the atmosphere. ions produced may be directly or indirectly converted to Cl atoms, which then destroy ozone.

Predicting intense field laser ionization probabilities: The application to species
View Description Hide DescriptionA structurebased tunneling mechanism developed to predict the ionization of molecules subjected to intense, ultrafast irradiation is tested on the series of hydrocarbons: acetylene, ethylene, and ethane. Relative ionization probabilities (1, 4.1, and 8.7 for ethane, acetylene, and ethylene, respectively) are measured upon excitation with 780 nm, 125 fs pulses of and compared to predictions of the model (1, 4.1, and 7.9 for ethane, acetylene, and ethylene, respectively). Ionization probabilities determined via the ADK (Ammosov, Delone, and Krainov) model for atomic ionization (1, 2.7, and 13.1 for ethane, acetylene, and ethylene, respectively) are shown to be near those of the structurebased model.
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 THEORETICAL METHODS AND ALGORITHMS


Extension of path integral quantum transition state theory to the case of nonadiabatic activated dynamics
View Description Hide DescriptionIn this paper, a methodology is introduced by which one may compute rates of nonadiabatic processes for arbitrary potential forms. This method augments the extant pathintegral transition state theory approach in which information about the inherently dynamical rate process is obtained from a static analysis of a free energysurface. The present resulting formula reduces to previous single adiabatic surface results when the adiabatic surface are well separated. Numerical examples show that the method well approximates the exact results in the nonadiabatic limit and over a large range of temperatures for quadratic and for nonquadratic potentials. Corroborating these results, analysis of the rate formula for a singleoscillator spinboson Hamiltonian in the nonadiabatic classicallimit reveals close agreement with the known exact result.

Frequencydependent polarizabilities, hyperpolarizabilities, and excitation energies from timedependent densityfunctional theory based on the quasienergy derivative method
View Description Hide DescriptionA timedependent densityfunctional theory for systems in periodic external potentials in time is formulated on the assumption of the existence of the Floquet states from the quasienergy viewpoint. Coupling strength integration, which connects a noninteracting system with an interacting system, is introduced by using the timedependent Hellmann–Feynman theorem. Coupled perturbed timedependent Kohn–Sham equations are derived from the variational condition to the quasienergy functional with respect to parameters. Explicit expressions for frequencydependent polarizability and first hyperpolarizability are given by the quasienergy derivative method. Excitation energies and transition moments are defined from poles and residues of frequencydependent polarizabilities, respectively. In contrast to the previous theory, our formulation has the following three advantages: (1) The timedependent exchangecorrelation potential is defined by the functional derivative of the exchangecorrelation quasienergy. (2) The formal expression for frequencydependent polarizability, which corresponds to the exact sumoverstates expression, can be obtained. (3) Explicit expressions for response properties which satisfy the rule can be automatically obtained.

Accurate excitation energies from timedependent density functional theory: Assessing the PBE0 model
View Description Hide DescriptionWe analyze the performance of a density functional model obtained by combining the Perdew–Burke–Erzenrhof (PBE) generalized gradient functional with a predetermined amount of exact exchange for predicting vertical electronic excitation energies within a timedependent approach. Four molecules, namely, CO, and have been chosen as benchmark cases. Our results show that this model (PBE0) provides accurate excitations both to valence and Rydberg states. Furthermore, the results are numerically close to those obtained using asymptotically correct exchangecorrelation functionals. The performance of the PBE0 model for predicting excitation energies in larger molecules is assessed for benzene, pyridine, and naphthalene. Here, the PBE0 model provides results which are in fairly good agreement with experimental data and of similar quality to those obtained by more sophisticated (and timeconsuming) postHartree–Fock methods.

Second and thirdorder spinorbit contributions to nuclear shielding tensors
View Description Hide DescriptionWe present analytical calculations of the electronic spin–orbit interaction contribution to nuclear magnetic shieldingtensors using linear and quadratic response theory. The effects of the Fermi contact and the spindipole interactions with both the one and twoelectron spin–orbit Hamiltonians, included as firstorder perturbations, are studied for the ( S, Se, and Te), HX ( Cl, Br, and I), and ( Cl, Br, and I) systems using nonrelativistic multiconfiguration selfconsistent field reference states. We also present the first correlated study of the spin–orbitinduced contributions to shielding tensors arising from the magnetic field dependence of the spin–orbit Hamiltonian. While the terms usually considered are formally calculated using thirdorder perturbation theory, the magneticfield dependent spinorbit Hamiltonian requires a secondorder calculation only. For the hydrogen chalcogenides, we show that contributions often neglected in studies of spin–orbit effects on nuclear shieldings, the spindipole coupling mechanism and the coupling of the twoelectron spin–orbit Hamiltonian to the Fermicontact operator, are important for the spin–orbit effect on the heavyatom shielding, adding up to about half the value of the oneelectron spin–orbit interaction with the Fermicontact contribution. Whereas the secondorder spinorbitinduced shieldings of light ligands are small, the effect is larger for the heavy nuclei themselves and of opposite sign compared to the thirdorder contribution.

Orbital transformations and configurational transformations of electronic wavefunctions
View Description Hide DescriptionTransformations among molecular orbitals are often expedient or illuminating, and sometimes essential in quantum chemical contexts. In order to express the manyelectron wavefunction in terms of the corresponding transformed configurations, full CI calculations used to be repeated in the transformed orbital basis. The configurational transformations can however be obtained directly, as shown by Malmqvist, by a factorization into single orbital transformations. In the present paper, a direct transformation method is presented that is based on the factorization of orbital transformations in terms of Jacobi rotations. Compared to the repetition of a CI calculation, both direct reexpansion methods drastically reduce the computational effort and increase the numerical accuracy. They are, moreover, applicable to wavefunctions whose original construction is not accessible.

Infinite basis limits in electronic structure theory
View Description Hide DescriptionWe have developed a database of 29 molecules for which we have estimated the completeoneelectronbasisset limit of the zeropointexclusive atomization energy for five levels of electronic structuretheory: Hartree–Fock (HF) theory, Mo/ller–Plesset second and fourthorder perturbation theory,coupled clustertheory based on single and double excitations (CCSD), and CCSD plus a quasiperturbative treatment of triple excitations [CCSD(T)], all at a single set of standard geometries. Convergence checks indicate that the estimates are within a few tenths of a kcal/mol of the limit of the basis set sequence. This data is then used to obtain optimized powerlaw exponents for extrapolating to the basissetlimit from correlationconsistent polarized valence double and triple zeta (ccpVDZ and ccpVTZ) basis sets. This allows one to get thermochemical accuracy comparable to polarized quadruple or quintuple zeta (ccpVQZ or ccpV5Z) basis sets with a cost very comparable to polarized triple zeta, which is one order of magnitude less expensive than polarized quadruple zeta and two orders of magnitude less expensive than polarized quintuple zeta.

Approaches to the approximate treatment of complex molecular systems by the multiconfiguration timedependent Hartree method
View Description Hide DescriptionA consistent treatment of environmental effects is proposed in the framework of the multiconfiguration timedependent Hartree (MCTDH) method. The method is extended in view of treating complex molecular systems which require an exact quantum dynamics for a certain number of “primary” modes while an approximate dynamics is adequate for a class of “secondary” modes. The latter may correspond to the weakly coupled modes in a polyatomic molecule, or the first solvent shell in a solutesolvent complex. For these modes, a description in terms of parameterized functions is introduced. The MCTDH working equations are generalized to allow for the nonorthogonality of these functions, which may take, e.g., a multidimensional Gaussian form. The formalism is developed on the level of both the wave function description and the density matrix description. Dissipative effects are accounted for in terms of a stochastic Hamiltonian approach versus master equation approach in the respective descriptions.

Physical and mathematical content of coupledcluster equations. III. Model studies of dissociation processes for various reference states
View Description Hide DescriptionThe structure and physical significance of the full set of solutions to coupledcluster (CC) equations at various stages of the dissociation process and the impact of the choice of reference functions on these solutions have been studied for the first time. The equations for the CC method involving double excitations (CCD) are obtained for the P4 model consisting of two molecules in a rectangular nuclear configuration determined by a geometry parameter We consider equations for the reference states and corresponding to the lowest, highest, and intermediate Hartree–Fock (HF) energies, respectively. The first two states provide a sizeconsistent description of the dissociation process. For the compactmolecule geometries the sets of complete solutions to the standard CCD equations [based on molecular orbitals (MOs) of symmetry] in the spin–orbital and spin–symmetryadapted versions always consist of 20 and 12 entries, respectively. For and in the dissociation limit only for the latter version the solutions can be attained by homotopy method. In this case we have reformulated the standard spin–symmetryadapted CCD equations to a version based on the use of localized orbitals (LO) which is extremely simple and can be solved analytically providing an understanding of the unexpected peculiarities of the solutions for For and there are only two regular solutions. For the remaining 10 solutions, the CCDwave functions are meaningless despite the fact that the corresponding CCD energies are equal to the exact values.

Physical and mathematical content of coupledcluster equations. IV. Impact of approximations to the cluster operator on the structure of solutions
View Description Hide DescriptionThe impact of approximations to the form of the cluster operator on the structure and physical significance of the complete set of geometrically isolated solutions to the coupledcluster (CC) equations has been studied for the first time. To systematically study the correspondence of solutions obtained at various levels of the approximation process, a continuation procedure based on a set of nested equationsNE) has been proposed and applied. Numerical studies based on a homotopy method for obtaining full solutions to sets of polynomialequations have been performed for the H4 and P4 models which belong to the simplest realistic manyelectron modelsystems. Two examples of approximation procedures have been considered. The first one involved, for the P4 model, the approximation leading from the full CC (FCC) method to the CC method based on double excitations (CCD). As a result of this approximations the number of solutions has increased from 8 to 20. In the second example, for H4, we have studied the approximation leading from the CCSD method to the CCD one. To complete these studies, we have for the first time obtained the full set of geometrically isolated solutions for a CCSD equations which consists of 60 solutions. Only a small subset of this set might have some physical significance. During the approximation process considered, the number of solution decreases from 60 to 12. This radical drop of the numbers of solutions is a consequence of the absence of the third and fourth powers of the unknowns in the CCDequations.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Fourier transform spectroscopy and crosssection measurements of the Herzberg II bands of at 295 K
View Description Hide DescriptionFourier transformspectroscopicmeasurements of the absorption bands of the Herzberg II of at 295 K have been made with a resolution of 0.06 cm^{−1} in the wavelength region 240–275 nm. Rotational line positions are determined with an accuracy of 0.005 cm^{−1}, and rotational term values are presented for the vibrational levels, Precise band oscillator strengths of the (7,0)–(16,0) bands are obtained for the first time by direct measurement by summing the cross sections of individual rotational lines of the bands. The rotational line strengths and the branching ratios are also presented for the same bands.

Regularity of the vibrational spectrum of the in the state: Our previous results revisited
View Description Hide DescriptionIn previous experiments, a nearly complete vibrational spectrum of the molecule in the state has been obtained using a laser induced fluorescence method. The statistical tests of the random matrix theory, applied on this spectrum, suggest a transition to quantum chaos. The aim of this letter is to show that these statistical results are biased because of a nonsingle excitation of the molecule. This is experimentally confirmed by highresolution new experiments in supersonic jet, using the powerful laser chain of the french project for the isotopic separation of uranium by laser (SILVA project).

Electronic states of the copper silicide and its ions
View Description Hide DescriptionPotential energy curves and spectroscopic parameters of the ground and exited states of SiCu, and are presented. The calculations were performed by highlevel correlated methods including the relativistic correction for the lowest states. The present results are compared with recent theoretical and experimental studies of SiCu and its ions and support the earlier theoretical conclusions concerning the assignment of the electronic ground state of SiCu. According to calculations presented in this paper the lowest energy states of SiCu, and are and respectively.

The O–H stretching vibrations of glycine trapped in rare gas matrices and helium clusters
View Description Hide DescriptionEmploying molecular beam depletion spectroscopy and Fourier transform infrared matrix spectroscopy, respectively, we have studied the O–H stretching vibrations of the glycine conformers I, II, and III. The glycine molecules were either deposited into large liquid heliumclusters or trapped in various rare gas matrices (Ne, Ar, Kr) at temperatures below 12 K. By extrapolating the experimental data plotted as a function of the square root of the critical temperature of the matrix material, the positions of the gas phase absorption bands were estimated to be 3585±2 cm^{−1} (conformer I), 3295±3 cm^{−1} (conformer II), and 3580±5 cm^{−1} (conformer III). The experimental results are compared with recent ab initio calculations.

Heteronuclear raregas dimer bonding: Understanding the nature of the Rydberg states that dissociate to the highest energy level of the manifold
View Description Hide Descriptionresonance enhanced multiphoton ionization (REMPI) spectra of jetcooled KrXe and ArXe in the vicinity of the high energy atomic line at 83889.99 cm^{−1} were obtained by exciting the neutral dimers with tunable coherent vacuum ultraviolet (VUV)radiation generated by fourwave sum mixing in mercury vapor, and then detecting the resultant ions in a timeofflight(TOF) mass spectrometer. Precise excited state constants were derived from analyses of the resultant vibrational fine structure, while equilibrium bond lengths were estimated from Franck–Condon factor intensity simulations. Excited state symmetries were deduced from separate ultraviolet (UV) (2+1) REMPI spectra recorded with linearly and circularly polarized light. The results of this work confirm a recent model proposed by Lipson and Field, where the states are predicted to be strongly destabilized relative to due to strong lmixing induced by the ground state Rg atom partner making up the dimer. Orbital mixing is also responsible for the observation of appreciably strong spectra in both one and twophoton excitation.

Photodissociation of gas phase using femtosecond photoelectron spectroscopy
View Description Hide DescriptionThe photodissociationdynamics of gas phase following 390 nm excitation are studied using femtosecondphotoelectron spectroscopy. Both and photofragments are observed; the exhibits coherent oscillations with a period of 550 fs corresponding to ∼0.70 eV of vibrational excitation. The oscillations dephase by 4 ps and rephase at 45 and 90.5 ps on the anharmonic potential. The gas phase frequency of ground state is determined from oscillations in the photoelectron spectrum induced by resonance impulsive stimulated Raman scattering. The dynamics of this reaction are modeled using one and twodimensional wave packet simulations from which we attribute the formation of to threebody dissociation along the symmetric stretching coordinate of the excited anion potential. The photodissociationdynamics of gas phase differ considerably from those observed previously in solution both in terms of the vibrational distribution and the production of

Ab initio study of the dipolebound anion
View Description Hide DescriptionThe anion has been studied at the coupled cluster level of theory with single, double, and noniterative, triple excitations whereas lowest energy structures have been determined at the secondorder Mo/ller–Plesset level. The vertical electron detachment energy and the adiabatic electron affinity were found to be 475 and 447 cm^{−1}, respectively, and they agree very well with the maximum of the dominant peak in the photoelectron spectrum of at 436 cm^{−1}, recorded by Bowen and collaborators. Our results indicate that electron correlation contributions to the electron binding energy are important and represent ∼70% of its total value. Both for the neutral and the anion, the two equivalent symmetry minima are separated by a transition state and the energy barrier amounts to only 77 cm^{−1}. Thus the equilibrium structures averaged over vibrations are effectively planar The Franck–Condon (FC) factors, calculated in harmonic approximation, indicate that the neutral complex formed in photoelectron spectroscopy (PES) experiments may be vibrationally excited in both soft intermolecular and stiff intramolecular modes. The theoreticalphotoelectron spectrum based on the calculated FC factors is compared to the experimental PES spectrum of Bowen et al.
