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Volume 106, Issue 19, 15 May 1997

Simulation of atomic zinc luminescence in rare gas solids: A localized pair potentials approach
View Description Hide DescriptionThe luminescence spectroscopy of atomic zinc isolated in the solid rare gases (Zn/RG) is compared with theoretical predictions obtained from the sum of diatomic Zn⋅RG and RG⋅RG pair potentials. In particular the existence of pairs of emission bands, both of which are assigned to the same gas phase electronic transition, is examined with the use of diatomic pair potentials to simulate the potential energy surfaces of the Jahn–Teller active vibrational modes of Zn in the solid rare gases Ar, Kr, and Xe. Simulations of the solid state Zn/RG luminescence are developed from a consideration of the excited state van der Waals cluster species in the gas phase. The maximum binding energy of the clusters is found in the cluster having a square planar structure at the energy minimum. Based on the results of the cluster calculations, lattice distortions which led to a dominant interaction between the Zn atom and four of its host atoms were sought to simulate the solid state luminescence. Two such vibronic modes were identified; one a lattice mode in which four rare gas atoms contract on a single plane toward the Zn atom, referred to as the waist mode, and the other a motion of the Zn atom toward an octahedral interstitial site of the lattice, the body mode. Energy calculations of these modes were carried out for rigid and relaxed rare gas lattices allowing identification of the high energy emission bands in the Zn/RG systems as arising from the waist mode, while the lower energy bands are associated with the body mode. The model also rationalizes the differences exhibited in the timeresolved behavior of the pairs of singlet emission bands in the Zn/Ar and Zn/Kr systems, whereby the lower energy band of a given system shows a risetime of a few hundred picoseconds while the higher energy band exhibits direct feeding. The steep gradient calculated on the waist mode, feeding the high energy band, and the flat gradient found on the body mode, feeding the lower energy emission, are consistent with the existence of a risetime in the latter and its absence in the former. The close agreement found between theory and experiment indicates the validity of using pair potentials in analysis of matrix zinc spectroscopy and thereby indicates that the luminescence is controlled by localized guest–host interactions.

Longrange interaction of the ^{39}K(4s)+ ^{39}K(4p) asymptote by photoassociative spectroscopy. I. The pure longrange state and the longrange potential constants
View Description Hide DescriptionThis paper reports on a comprehensive study of the longrange interaction of the asymptotic system. We present a detailed discussion of the dependent angular momentum couplings and correlation between the Hund’s case (a) and case (c) molecular states. Analytical expressions for the 16 adiabatic Hund’s case (c) longrange potential curves are derived including the higher order dispersion forces and the effects of retardation. Experimentally, six Hund’s case (c) longrange molecular states ( and dissociating to the asymptote and and to the limit) are observed with rovibrational resolution by photoassociative spectroscopy of ultracold atoms in a high density magnetooptical trap(MOT). Among the six observed longrange states, the upper “pure longrange” state has negligible shortrange chemical exchange contributions and the measured molecular binding energies are used to precisely determine the longrange potential constants of the interaction. We determine: and Molecular constants for the three special pure longrange states, the and (dissociating to the limit and with potential minimum) and the (dissociating to the and with potential maximum), are reported. The internal consistency of the theoretical model used in this work is confirmed by the excellent agreement between the longrange potential curve of the state obtained in present work (from the state) and the longrange portion of the RKR potential curve of the state previously determined by conventional molecular spectroscopy. The radiative lifetime of the K state derived from the dipole–dipole interaction constant is also in excellent agreement with a recent fastbeam measurement.

Xray and neutron scattering studies of the temperature and pressure dependence of the structure of liquid formamide
View Description Hide DescriptionA structural investigation of liquid formamide was performed by neutron scattering at pressures of up to 4 kbar. We have also deduced the molecular pair correlation functions from xray studies at ambient pressure and in the 263–326 K temperature range. The spectra obtained are consistent with the presence of hydrogenbonded open chains of molecules in the liquid state. The effect of both pressure and temperature on the hydrogenbond network is examined.

Probing solute–solvent electrostatic interactions: Rotational diffusion studies of 9,10disubstituted anthracenes
View Description Hide DescriptionThe rotational diffusion of 9,10disubstituted anthracenes is studied in various solvents. By systematic variation of the anthracene functionalities the influence of the electrostatic properties of the solute on the solute–solvent frictional coupling is investigated. These studies explore the range of validity of continuum based dielectricfriction models for describing the frictional coupling. It is found that a continuum model of the solvent with an extended charge distribution for the solute is adequate in unassociated solvents, but does not adequately describe the friction in the associated solvent, benzyl alcohol.

Theoretical study of vibrational overtone spectroscopy and dynamics of methanol
View Description Hide DescriptionExperimentally observed coupling between OH and CH stretching modes in the high overtone region has been modeled successfully in terms of a curvilinear internal coordinate Hamiltonian including harmonic coupling between anharmonic OH and CH stretching oscillators and cubic Fermi resonance kinetic and potential energy couplings between CH stretches and HCH bends. The Hamiltonian matrices have been set up in block diagonal forms including only resonant states. The potentialenergy parameters have been optimized by the leastsquares method using experimental vibrational term values as data. The OH/CH stretch interaction parameter obtained agrees well with the one calculated by perturbation theory from a published ab initio harmonic force field. The model has reproduced well experimental band origins in the OH stretching overtone region, and it has provided assignments for the bending overtones in the CH stretching fundamental region. Finally, a unitary transformation is found from the internal coordinate representation to the corresponding normal coordinate representation providing a set of normal coordinate parameters like diagonal anharmonicity parameters, Darling–Dennison resonance constants and cubic Fermi resonance force constants. The results confirm the experimental finding of energy redistribution between the OH and CH stretching modes on subnanosecond time scale at

Internal dynamics contributions to the CH stretching overtone spectra of gaseous nitromethane
View Description Hide DescriptionThe methyl CH stretching overtone spectra of gaseous nitromethane have been recorded with Fourier transform infrared conventional near infrared spectroscopy in the regions and by intracavity laser photoacoustic spectroscopy in the and 6 regions. They all exhibit a complex structure with, at and 2, a characteristic asymmetric top vibrationrotation profile which vanishes as vibrational energy increases. In addition, in these two lower energy spectra, the perpendicular stretching vibrations exhibit a widely spaced fine structure profile resulting from a Coriolis coupling induced by the methyl internal rotation. These excited spectra have been analyzed with a theoretical model which takes into account, in the adiabatic approximation, the coupling of the anharmonic CH stretch vibrations, described by a Morse potential, with the quasifree internal rotation of the methyl group and with isoenergetic combination states involving methyl bending modes. Till the theoretical treatment yields normal modes. From the third overtone, the vibrational energy is seen to be localized and thus the calculations proceed in a local mode basis from Most of the parameters of this model and their variation with the internal rotation coordinate θ are the same as those used to account for the overtone spectra of the monohydrogenated species. Fermi resonance phenomena, also modeled with θ dependent parameters, lead to only weak IVR localized at the second overtone where only the two first tiers are effective and at the third overtone where three tiers must be considered to give a good reproduction of the experimental spectral features. This simple calculation successfully describes the relative intensity and frequency of each peak within a given overtone.

Spectroscopy of high Rydberg states of the triatomic deuterium molecule
View Description Hide DescriptionWe report first investigations of high principal quantum number Rydberg states of the neutral triatomic deuterium molecule. The experiments were performed using a fast neutral beamphotoionization spectrometer recently developed at Freiburg. A fast beam of metastable molecules was created by charge transfer of a beam in cesium. Rydberg states of were analyzed by pulsedlaser excitation using twophoton resonanceenhanced ionization, electric field ionization and autoionization. Our data identify the state of to be metastable with a lifetime of about 1 s. The spectral lines following excitation in the ultraviolet spectral range were assigned to type and type Rydbergseries converging to vibrational ground state, symmetric stretch excited and degenerate mode excited ion states. By a combination of vibrationally diagonal and nondiagonal transitions, we determined the ionization potential, the symmetric stretch and degenerate mode vibrational frequencies of the state in . The data give insight into the influence of the coupling between the Rydberg electron and the ion core on the potential energy surface.

Evidence for heavy atom large amplitude motions in RGcyclopropane van der Waals complexes ( Ar, Kr) from rotationtunneling spectroscopy
View Description Hide DescriptionRotationtunneling spectra of the van der Waals complex Necyclopropane, and pure rotational spectra of Arcyclopropane and Krcyclopropane, were measured with a Fourier transformmicrowave spectrometer in the frequency range from 4–19 GHz. The observed transitions are all of type and are in accord with those of prolate symmetric top molecules where the rare gas atom is positioned on the axis of the cyclopropane subunit above its symmetry plane. Altogether transitions of five isotopomers of the Ne complex with values ranging from 0 to 4 and K values from 0 to 1 were measured. Three isotopomers of the Ar complex ( from 1 to 5 and from 0 to 2) and nine isotopomers of the Kr complex ( from 1 to 8 and from 0 to 2) were observed. Effective separations between the centerofmass of cyclopropane and the rare gas atoms were obtained from the ground state rotational constants and were found to be 3.673, 3.802, and 3.906 Å for the Ne, Ar, and Krcontaining complexes, respectively. The derived centrifugal distortion constants indicate that the complexes are comparatively rigid in the radial coordinate. Transitions of two isomers were observed for complexes that contain monodeuterated cyclopropane. The intensities of transitions of the Dbonded species were considerably higher compared to those of the Hbonded isomers indicating that the angular motion of the rare gas atom is much less restricted. In the case of the parent Necyclopropane complex, and its  and mono isotopomers, all transitions appeared as doublets. This is attributed to a tunneling internal rotation motion of the cyclopropane unit within the complex.

Laser photofragmentation and collisioninduced reactions of and
View Description Hide DescriptionLaser photofragmentation processes of the doubly charged ions and are studied at 1064, 532, and 355 nm. The observed photoproducts are compared with those of the reaction pathways induced by the collisions of these dications with the rare gases. Photodissociation, via absorption of a single photon occurs readily for both dications, and the photoion yields are dominated by the products of neutralloss pathways: from and from A minor contribution from photoinduced charge separation is also observed. For a neutralloss pathway forming the atomic dication is also detected at higher photon energies. The excitation energy required for this fragmentation process is determined to be Collisions of and with He and Ne are also dominated by neutralloss reactions. With the heavier rare gases, charge transfer is exothermic and dominates the product ion yield, although neutralloss reactions still occur. Interpretation of the charge transfer results using Landau–Zener theory suggests that two electronic states of lying at and above the ground state of the neutral molecule, are present in the dication beam. Ab initio calculations reveal that adopts an equilibrium geometry of symmetry with one elongated bond. Hence, electron capture by results in the formation of in an energetically unfavorable conformation. By taking account of these geometry differences in the Landau–Zener algorithm, a satisfactory rationalization of the ion yields from the charge transferreactions of is achieved.

Photodesorption of Na atoms from rough Na surfaces
View Description Hide DescriptionWe investigate the desorption of Na atoms from large Na clusters deposited on dielectricsurfaces. Highresolution translational energy distributions of the desorbing atoms are determined by three independent methods, twophoton laserinduced fluorescence, as well as singlephoton and resonanceenhanced twophoton ionization techniques. Upon variation of surface temperature and for different substrates (mica vs lithium fluoride) clear nonMaxwellian timeofflight distributions are observed with a angular dependence and most probable kinetic energies below that expected of atoms desorbing from a surface at thermal equilibrium. The halfwidth of the timeofflight distribution decreases with increasing surface temperature. A quantitative description of the energy and angular distributions is presented in terms of a model which assumes that following the initial surface plasmon excitation neutral atoms are scattered by surface vibrations. Recent experiments providing time constants for the decay of the optical excitations in the clusters support this model. The excellent agreement between experiment and theory indicates the importance of both absorption of the laser photons via direct excitation of surface plasmons as well as energy transfer with the substrate during the desorption process.

Femtosecond photoassociation: Coherence and implications for control in bimolecular reactions
View Description Hide DescriptionA theoreticalanalysis of the recent femtosecond photoassociation spectroscopy (FPAS) experiment on mercury [U. Marvet and M. Dantus, Chem. Phys. Lett. 245, 393 (1995)] is presented. It is shown that when a thermal distribution of diatom collision pairs is excited from a free to a bound electronic state on a time scale shorter than molecular vibration, an ensemble of coherent wave packets is produced. The dynamics of these wave packets created by the photoassociation pulse can be observed by firing a second probe pulse at variable time delays, and the depletion of the first excited bound state by the probe pulse is detected via fluorescence of the remaining population. Simulations of the FPAS experiment, using both wave packet propagation techniques and perturbation theory, clearly show the vibrational dynamics of the photoassociated transients. It is also demonstrated how the FPAS technique may be used as a tool for controlling the energy, impact parameter, and orientation in bimolecular reactions.

Matrixtheoretical analysis in the Laplace domain for the time lags and mean first passage times for reactiondiffusion transport
View Description Hide DescriptionSiegel’s matrix analysis of membrane transport in the Laplace domain [J. Phys. Chem. 95, 2556 (1991)], which is restricted to zero initial distribution, has been extended to including the case of nonzero initial distribution. This extension leads to a more general transport equation with Siegel’s results as a special case. The new transport equation allows us to formulate the meanfirstpassage time for various boundary conditions, if the initial distribution is stipulated to be of the Dirac deltafunction type; and the steadystate permeability and time lag if zero initial distribution is employed. Based on this matrix analysis we also propose an algorithm for quick and effective numerical computations of and Examples are given to demonstrate the application of this algorithm, and the numerical results are compared with the theoretical ones. The validity of the transport equation is also checked by a Green’s function.

Protonordered models of ordinary ice for quantummechanical studies
View Description Hide DescriptionA periodic HartreeFock ab initio study is presented concerning two protonordered structures of ordinary ice: one ferroelectric ice), the other antiferroelectric ice). The calculated energies are practically coincident, and in good agrement with the experimental stability of disordered ice Ih. Slabs are cut out from these crystals in order to formulate a model for studying the surface properties of ordinary ice. The stability of these twodimensional periodic systems is discussed, and the relaxation of the ice slab formed by two bilayers parallel to the (001) face is considered. Finally, an embedded cluster method is adopted to calculate geometric and energetic properties of KOH and NaOH dissolved in  and ice at low concentration. This study permits us to discuss the role of KOH in promoting the transition from disordered Ih to ordered ice, which has been observed to occur at 72 K [Leadbetter et al., J. Chem. Phys. 82, 424 (1985)].

On the ab initio evaluation of Hubbard parameters. I. The analytical approach in the absence of orbital relaxation
View Description Hide DescriptionA theoretical approach is considered for the ab initio derivation of the parameters contained in the Hubbard Model, under the fundamental assumption that the orbital relaxation represents a negligible effect for the system of interest. The approach is based on a onetoone mapping between the states of a general empirical twoelectron Hamiltonian and the results of ab initio calculations on a dimeric unit. The localization of the ab initio orbitals and its consequences are discussed in the Appendix. The analysis is carried out by distinguishing two main cases: (a) the symmetric case, in which it is possible to derive the values of the empirical parameters from a limited set of selfconsistent calculations, and (b) the asymmetric case, in which several parameters have to be estimated by resorting to frozenorbital calculations. The dependence of the effective value of the onsite Hubbard repulsion on the chemical environment is discussed. Finally, making contact with an alternative approach, based on the expansion of the Hamiltonian matrix in series of overlaps between nonorthogonal functions centered on neighboring sites, the reliability of the standard Hubbard Model is investigated. It is found that offdiagonal electronelectron interaction terms such as and can become nonnegligible, even in the absence of orbital relaxation, due to special geometrical arrangements. A discussion of the capabilities and limitations of the approach, as compared with more rigorous methods, is also included.

On the ab initio evaluation of Hubbard parameters. II. The crystal
View Description Hide DescriptionA previously proposed approach for the ab initio evaluation of Hubbard parameters is applied to BEDTTTF dimers. The dimers are positioned according to four geometries taken as the first neighbors from the experimental data on the crystal. RHFSCF, CASSCF and frozenorbital calculations using the 631G^{*} ^{*} basis set are performed with different values of the total charge, allowing us to derive all the relevant parameters. It is found that the electronic structure of the BEDTTTF planes is adequately described by the standard Extended Hubbard Model, with the offdiagonal electronelectron interaction terms and of negligible size. The derived parameters are in good agreement with available experimental data. Comparison with previous theoretical estimates shows that the values compare well with those obtained from Extended Hückel Theory (whereas the minimal basis set estimates are completely unreliable). On the other hand, the values exhibit an appreciable dependence on the chemical environment.

Coupled cluster response functions revisited
View Description Hide DescriptionWe introduce an inherently real coupled cluster timedependent expectation value of a Hermitian operator. Based on the expansion of this expectation value in orders of the generally timedependent perturbation, we subsequently identify the coupled cluster timeindependent expectation value, the linear response function, and the quadratic response function. The response functions and their residues behave physically correctly. Spectroscopic observables are identified as residues, whereas the identification of individual transition matrix elements is prohibited. Thus the unphysical behavior of previously published coupled cluster response functions may be viewed not as a consequence of the projection, but rather that identifications are made on the basis of an unphysical expectation value or quasienergy.

Theoretical study of the potential energy surfaces and dynamics of CaNC/CaCN
View Description Hide DescriptionPotential energy surfaces for the ground and two lowlying electronically excited states of CaNC/CaCN, are calculated using the ab initio molecular orbital (MO) configuration interaction (CI) method. The absorption and emission spectra of the system are computed by performing timedependent quantum dynamical calculations on these surfaces. The most stable geometries for the two lowest lying and electronic states correspond to the calcium isocyanide (CaNC) structure. These two states are characterized by ionic bonding and the potential energy curves along the bending coordinate are relatively isotropic. The result of our wave packet dynamics shows that the characteristics of the experimental spectra observed by the laserinduced fluorescence spectroscopy can be explained by the Renner–Teller splitting.

Model potentials for main group elements Li through Rn
View Description Hide DescriptionModel potential (MP) parameters and valence basis sets were systematically determined for the main group elements Li through Rn. For alkali and alkalineearth metal atoms, the outermost core electrons were treated explicitly together with the valence electrons. For the remaining atoms, only the valence and electrons were treated explicitly. The major relativistic effects at the level of Cowan and Griffin’s quasirelativistic Hartree–Fock method (QRHF) were incorporated in the MPs for all atoms heavier than Kr. The valence orbitals thus obtained have inner nodal structure. The reliability of the MP method was tested in calculations for and =Br, I, and At) at the SCF level and the results were compared with the corresponding values given by the numerical HF (or QRHF) calculations. Calculations that include electroncorrelation were done for and ( and Br) at the SDCI level and for at the CASSCF and MRSDCI levels. These results were compared with those of allelectron (AE) calculations using the welltempered basis sets. Close agreement between the MP and AE results was obtained at all levels of the treatment.

Electronic states and nature of bonding in the molecule MoC by all electron ab initio calculations
View Description Hide DescriptionIn the present work all electron ab initio multiconfiguration selfconsistentfield (CASSCF) and multireference configuration interaction (MRCI) calculations have been carried out to determine the lowlying electronic states of the molecule MoC. The relativistic corrections for the one electron Darwin contact term and the relativistic massvelocity correction have been determined in perturbation calculations. The electronic ground state is predicted as The spectroscopic constants for the electronic ground state and eight lowlying excited states have been derived by solving the Schrödinger equation for the nuclear motion numerically. Based on the results of the CASSCF calculations the ground state of MoC is separated from the excited states and by transition energies of 4500, 6178, 7207, 9312, 10 228, 11 639, and respectively. The transition energy between the ground state and the state as derived in the MRCI calculations is For the ground state the equilibrium distance has been determined as 1.688 Å, and the vibrational frequency as The chemical bond in the electronic ground state has triple bond character due to the formation of delocalized bonding π and σ orbitals. The chemical bond in the MoC molecule is polar with charge transfer from Mo to C, giving rise to a dipole moment of 6.15 D at 3.15 a.u. in the ground state.

New statistical mechanical treatment of systems near surfaces. II. Polydisperse linear and branched polymers in an athermal solution
View Description Hide DescriptionWe apply a recently developed analytic but approximate method to study the behavior of polydisperse linear and branched polymers in an athermal solution and near various kinds of surfaces. We consider equilibrium polydispersity controlled by a set of activities. The method allows us to account for polymer connectivity and excludedvolume effects and goes beyond the random mixing approximation. The density profiles of various kinds exhibit oscillations for bulk densities larger than some threshold bulk density The origin of these oscillations is related to the decreasing branch of the recursion function, as explained in the text. The correlation length ξ related to these oscillations increases as increases. On the other hand, the correlation length ξ controlling the approach of various density profiles to their respective bulk values in the range increases as decreases. The free energy and the entropy are uniquely determined. Various surface properties are also easily determined. We demonstrate the existence of surfacepolymerization transition in the case of linear chains as surface interactions are varied, even though there is no bulk transition. The method allows us to probe the entire density range which is not possible in a Monte Carlo simulation. Our computations are ultrafast by at least three orders of magnitude compared to rival methods and easy to implement. Our results agree with Monte Carlo simulations but disagree with the meanfield predictions.