Volume 114, Issue 8, 22 February 2001
 ARTICLES

 Theoretical Methods and Algorithms

On product state distributions in triatomic unimolecular reactions: Beyond phase space theory and the adiabatic assumption
View Description Hide DescriptionOur goal is to derive a simple dynamically corrected statistical treatment of state distributions in the products of triatomic unimolecular reactions involving efficient energy transfers between rotation and translation motions en route to products. For, phase space theory or the adiabatic channel model—the only statistical approaches of final state distributions—may not be applicable to such processes. We thus analyze and model how the departing atom perturbs the rotation of the diatomic molecule. Since the general problem is intricate, we limit our study to the basic, yet realistic and instructive case where the bending force is harmonic and the total angular momentum is zero. A remarkable fact is the onetoone relation between the perturbation and a coefficient χ, related in a simple way to the mechanical parameters of the system. Transition state theory combined with our model—the linear transformation model—leads to the desired treatment of product state distributions. Its predictions are in good agreement with dynamical calculations. We also show that there is a close relation between the final shape of state distributions and the angular dependence of the potential energy at the transition state.

Nature of polarized excitons
View Description Hide DescriptionThe electromagnetic interaction energy of a molecular aggregate consisting of pointlike molecules in the presence of an electromagnetic field is derived. The corresponding Hamiltonian consists of three parts; describes the aggregate in the absence of the electromagnetic field, describes the interaction of the molecules with the external field, and corresponds to the inducedinteraction between the molecules. Based on this Hamiltonian we derive a selfconsistent equation of motion for a quasiparticle, which we refer to as a polarized exciton. The equation has the same form as the one in classical dipole theory. The polarized exciton model is based on a timedependent perturbative treatment and corresponds to the assumption Our model is compared to standard exciton theory, which is based on the assumption In particular the differences and similarities are illustrated for a direct example, a finite linear chain. We advocate the use of polarized excitons to fully account for the physics in these systems.

Dynamical theory of timeresolved fluorescence with pulse excitation
View Description Hide DescriptionA uniform theory of timeresolvedresonancefluorescence and resonance Raman with pulse excitation is developed and an approach describing the evolution of a wave packet during vibrational relaxation is given. Then, the theory is applied to the spontaneous emission of a model system with two harmonic electronic states. The evolution of the wave packet during vibrational relaxation obtained leads to the changing of fluorescence signal with time.

Dipole moments of adiabatic excited states using the Fock space multireference coupledcluster analytic response approach
View Description Hide DescriptionTheoretical evaluation of molecular properties of excited states is extremely necessary as the lifetime of the excited states is too low for experimental probing. High level of theoretical treatment is an attractive option for the study of such states. However, theoretical calculation of this is a challenging task and in this paper we have presented such calculation using the analytic Fock space multireference coupled cluster linear response approach in a one hole–one particle model space. The results for the dipole moments of the adiabatic excited states of the water molecule are presented in this paper. The Sadlej basis set optimized for the property evaluation is used for the calculation and we address the adiabatic singlet and triplet excited states. The results using both the finitefield and the analytic response approach are presented. Full effective Hamiltonian including the three body terms in a singles and doubles approximation has been used for the calculation.

A method for ab initio nonlinear electrondensity evolution
View Description Hide DescriptionA numerical method is given for effecting nonlinear local density functional evolution. Within a given time interval, Chebyshev quadrature points are used to sample the evolving orbitals. An implicit equation coupling wave functions at the different time points is then set up. The equation is solved iteratively using the “direct inversion in iterative space” acceleration technique. Spatially, the orbitals are represented on a Fourier grid combined with soft pseudopotentials. The method is first applied to the computation of the adiabatic potential energy curves of Next, the electronic dynamics of a toy molecular wire is studied. The wire consists of a molecule connected via sulfur atoms to two gold atoms, the “electrodes.” The molecule is placed in a homogeneous electric field and a dynamical process of charge transfer is observed. By comparing the transient with that of a resistancecapacitance circuit, an effective Ohmic resistance and capacitance is estimated for the system.

NonBorn–Oppenheimer calculations on the LiH molecule with explicitly correlated Gaussian functions
View Description Hide DescriptionWe report the first ever nonBorn–Oppenheimer variational calculations on the ground state of a four electron molecular system. The basis set used in the calculations consists of explicitly correlated Gaussians multiplied by powers of the internuclear distance. To accelerate the optimization of the many nonlinear variational parameters involved in the variational wave function, we performed the calculations on a cluster of Linux workstations using MPI and a parallel implementation of the formulas. Results for the nonadiabaticground state energy of LiH, as well as expectation values for the kinetic and potential energies, the internuclear and square of the internuclear distance, the virial coefficient, and the square of the energy gradient norm are reported.

Exchange energy in a doublewell potential profile from fluctuation theory
View Description Hide DescriptionThis article shows that the asymptotic quantum mechanical exchange energies and wave functions in a bistable potential can be obtained by computing the complexvalued firstpassage time across the potential barrier from a transient state endowed with Smoluchowski boundary conditions, whose probability density is concentrated on one side of the barrier. This interpretation is validated by one of the authors’ previous work on diffusion in a random field, showing that this model yields a diffusion equation equivalent to quantum mechanical equations.

Correlation consistent valence basis sets for use with the Stuttgart–Dresden–Bonn relativistic effective core potentials: The atoms Ga–Kr and In–Xe
View Description Hide DescriptionWe propose largecore correlationconsistent (cc) pseudopotential basis sets for the heavy pblock elements Ga–Kr and In–Xe. The basis sets are of ccpVTZ and ccpVQZ quality, and have been optimized for use with the largecore (valenceelectrons only) Stuttgart–Dresden–Bonn (SDB) relativistic pseudopotentials. Validation calculations on a variety of thirdrow and fourthrow diatomics suggest them to be comparable in quality to the allelectron ccpVTZ and ccpVQZ basis sets for lighter elements. Especially the SDBccpVQZ basis set in conjunction with a core polarization potential (CPP) yields excellent agreement with experiment for compounds of the later heavy pblock elements. For accurate calculations on Ga (and, to a lesser extent, Ge)compounds, explicit treatment of 13 valence electrons appears to be desirable, while it seems inevitable for In compounds. For Ga and Ge, we propose correlation consistent basis sets extended for (3d) correlation. For accurate calculations on organometallic complexes of interest to homogenous catalysis, we recommend a combination of the standard ccpVTZ basis set for first and secondrow elements, the presently derived SDBccpVTZ basis set for heavier pblock elements, and for transition metals, the smallcore Stuttgart–Dresden basis setrelativistic effective core potential combination supplemented by functions with exponents given in the Appendix to the present paper.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

emission induced by laser excitation of neutral CO at 230 nm
View Description Hide DescriptionWe observed emission from electronically excited after laser excitation of groundstate CO with a picosecond dye laser. The laser frequency was tuned to the CO twophoton transition at 230 nm, resulting in resonanceenhanced ionization of CO with production of followed by resonant excitation of the onephoton transition in We provide direct evidence for this process by detecting emission after the laser excitation. An analysis of the pulseenergy and pressure dependence of the emission is presented to derive collisional quenching rate coefficients for

Electron scattering from gaseous Comparing calculations with experiments
View Description Hide DescriptionThe dynamical observables associated with lowenergy electron scattering from molecules in the gasphase, e.g., elastic differential cross sections, integral elastic cross sections and momentum transfer cross sections, are computed using quantum methods and describing the full interaction between the molecule and the impinging electron without empirical parameters. The above quantities are obtained over an energy interval ranging from a few meV up to 100 eV and the results are compared with the available experiments. Various aspects of the theoretical method employed are analyzed in relation to their agreement with the experimental data discussed in this work.

Exploring the transition state for the Li+HF→LiF+H reaction through the absorption spectrum and stimulated emission pumping
View Description Hide DescriptionThe first excited electronic state of LiHF has been calculated (about 3300 points at MRDCI level) and an analytical fit of the global potential energy surface is presented. The absorptionspectrum is simulated at 10 K between 9000 and 13 000 what involves the calculation of excited bound states for moderately high total angular momentum. These quasibound levels of the A state can only decay by electronic predissociation (EP) towards the ground state, since the spontaneous radiative emission is considered to be very slow. The decay of such states has been estimated using a perturbative approach and it is found that LiF products are produced with a high efficiency The stimulated emission pumping spectra is simulated for several initial quasibound levels. These spectra allow the examination of the reaction dynamics specially near the transition state region, and the first photon excitation may act as a rotational filter, reducing the problem of the partial wave average involved in reactive collisions. The high reaction efficiency of this last process is also discussed.

Energetics and dissociative photodetachment dynamics of superoxide–water clusters:
View Description Hide DescriptionThe dissociativephotodetachment of was studied at 388 and 258 nm using photoelectron–multiplephotofragment coincidence spectroscopy.Photoelectron spectra for the series indicate a significant change in the energetics of sequential solvation beyond the fourth water of hydration. Photoelectron–photofragment kinetic energy correlation spectra were also obtained for permitting a determination of the first and second energies of hydration for to be 0.85±0.05 and 0.70±0.05 eV, respectively. The correlation spectra show that the peak photofragment kinetic energy release in the dissociativephotodetachment of and are 0.12 and 0.25 eV, respectively, independent of the photon and photoelectron kinetic energies. The molecular frame differential cross section for the threebody dissociativephotodetachment: is also reported. The observed partitioning of momentum is consistent with either a sequential dissociation or dissociation from a range of initial geometries.

Angular trapping and rotational dissociation of a diatomic molecule in an optical centrifuge
View Description Hide DescriptionWe perform a detailed quantum study of forced molecular rotation in an optical centrifuge, recently proposed by J. Karczmarek [Phys, Rev. Lett. 82, 3420 (1999)]. The approach uses strong nonresonant laser fields with chirped frequency to induce efficient rotational excitation of anisotropic molecules via a sequence of Raman transitions. Quantum calculations firstly of angular confinement (angular trapping) of a molecule in the early stages of the centrifuge evolution and secondly of the resulting rotational dissociation process are carried out herein. The trapping calculations include both angular degrees of freedom while the dissociation calculations include one vibrational and one rotation degree of freedom. Diatomic is used as a test case. An extension of the scheme outlined by Karczmarek et al. is proposed as a method of producing molecules in a single selected level.

Directfitting approach to the analysis of highresolution optical spectra: Monte Carlo and experimental studies of spectra
View Description Hide DescriptionThe traditional approach for analyzing highresolution optical spectra involves locating and measuring line frequencies, then assigning and fitting these to an appropriate model for the molecular energy levels. The alternative approach of fitting the spectrum directly is particularly appealing in the case of congested spectra with many overlapped features. The capabilities and limitations of direct fitting are explored in application to the 0–0 band of the transition, as recorded on a chargecoupleddevice array using a highpressure Tesla discharge source. Monte Carlo calculations confirm that for Poisson (counting) data, the parameter errors from the variance–covariance matrix are trustworthy, unless weights are neglected, in which case the error estimates can be wildly optimistic. In the fitting of actual spectra, a major barrier is the derivation of a suitable instrumental lineshape function. In particular, the often adopted triangular slit function is grossly inadequate. A systematic procedure has been devised for obtaining the line shape as a sum of Gaussian and Lorentzian components. This method has facilitated the analysis of experimental spectra spanning the region 3071–3103 Å. A model having 46 adjustable parameters determines the temperature (320 K) of the levels of the state with and corroborates theoretical intensity branching ratios within 2%. It also determines within the contribution to the emission from OD, which is present in natural abundance in the source.

Reaction of the ethynyl radical, with methylacetylene, under single collision conditions: Implications for astrochemistry
View Description Hide DescriptionThe reaction between the ethynyl radical, and methylacetylene which yields ethynylallene, pentadiyne, and butadiyne, has been studied at the density functional (B3LYP/6311+G^{*} ^{*}) and coupled cluster(coupledcluster single double perturbative triple/ccpVTZ) levels of theory. These results agree with data from crossed molecular beam experiments where ethynylallene (10) and pentadiyne (13) have been observed. The radical initially attacks the π system of methylacetylene (2) without an entrance barrier to form Z1ethynylpropen2yl (3) or Z2ethynylpropen1yl (4) in highly exothermic reactions. Geometric considerations as well as the computed enthalpies suggest Z1ethynylpropen2yl (3) to be the dominant initial intermediate. Assuming single collision conditions as found in cold molecular clouds in the interstellar medium and distinct planetary atmospheres, numerous rearrangements may ensue the initial reaction step before ejection of a hydrogen atom or a methyl group releases the accumulated reaction energy.

Chemical dynamics of d1methyldiacetylene and d1ethynylallene formation from reaction of with methylacetylene,
View Description Hide DescriptionThe crossed beam reaction of the d1ethynyl radical with methylacetylene, was investigated at an average collision energy of 39.8 kJ mol^{−1}. Our experimental results were combined with electronic structure calculations. The chemical reactiondynamics are indirect, involve three distinct channels, and are initiated via a barrierless addition of to the acetylenic bond through long lived cis and trans 1ethynylpropen2yl, intermediates. The reduced cone of acceptance of the carbon atom holding the methyl group favors a carbon–carbon σ bond formation at the carbon atom adjacent to the acetylenic hydrogen atom. A crossed beam experiment of with partially deuterated methylacetylene, shows explicitly that the reactive intermediates decompose to form both methyldiacetylene, (channel 1, 70%–90%), and to a minor amount ethynylallene, (channel 2; 10%–30%), isomers through exit transition states located 7–15 kJ mol^{−1} above the products. The computed reaction energies to form both isomers are −135 and −107 kJ mol^{−1}, respectively, with respect to the separated reactants. A minor reaction pathway involves a H shift in to an 1ethynylpropen1yl radical which fragments to methyldiacetylene via a barrier of 8.8 kJ mol^{−1} (channel 3). Neither methyl group elimination nor the formation of the carbene was observed in our experiments. The experimentally observed “sideways scattering” and ab initio investigation verify our conclusions of a predominate formation of the methyldiacetylene isomer. These electronic structure calculations depict a hydrogen atom loss in the exit transition state to methyldiacetylene almost parallel to the total angular momentum vector J as found in our centerofmass angular distribution. Since the title reaction and the corresponding reaction of the radical with both have no entrance barriers, are exothermic, and all the involved transition states are located well below the energy of the separated reactants, the assignment of the ethynyl versus H atom exchange suggests the formation of both isomers under single collision conditions in extraterrestrial environments such as cold, molecular clouds as well as the atmosphere of Saturn’s moon Titan.

Highly excited vibronic eigenfunctions in a multimode nonadiabatic system with Duschinsky rotation
View Description Hide DescriptionWe study the characteristics of vibronic eigenfunctions of a multidimensional nonadiabatic system and their consequences in the quantum spectra. As an illustrative example, we investigate the properties of highly excited eigenfunctions of Heller’s multimode nonadiabatic system. The system consists of two diabatic states and twodimensional (twomode) harmonic potentials that are nonadiabatically coupled with the Condon approximation and with an appropriate magnitude of the Duschinsky angle. “Quantum chaos” thus produced has no classical counterpart. In addition to rather characterless chaotic eigenfunctions that are uniformly widespread in configuration space, we have found highly excited localized eigenfunctions of two extreme types which favor either the diabatic picture or adiabatic picture. As a result, the features of the associated quantum spectra are strongly affected by the initial preparation of a wave packet. This finding suggests that one can control the rate of nonadiabatic transitions such as that for electron transfer by using laser techniques or by choosing appropriate solvents.

Perturbationallowed rotational transitions and splitting transitions in the ground, and vibrational states of observed by microwave Fourier transform spectroscopy: Extension of the effective hyperfine Hamiltonian
View Description Hide DescriptionUsing the technique of Fourier transformmicrowave spectroscopy in the range 1–14 GHz Qbranch rotational transitions have been observed for and in the ground, and vibrational states with an accuracy of 0.1–100 kHz. splitting transitions for in the ground state, ±9 in and for −2, +4 in the vibrational state have been observed. We also measured perturbationallowed transitions with selection rule in the ground vibrational state for with selection rules in the state for 0↔±3, ±2↔∓4, ±2↔∓7, and 0↔±9 and in the state for +2↔+6, and +3↔+5. The transitions show hyperfine structures due to the quadrupole and spinrotation coupling of the nuclear spin and the rotational angular momentum J . Hyperfine structures in the dyad have been analyzed using an effective Hamiltonian extended to higher order spinrotation coupling terms and including spinvibration coupling. A total of 21 hyperfine parameters has been determined for each isotopomer including quadrupole and spinrotation constants of the (2,2), and (2,−1) interactions. A similar analysis has been performed for the ground vibrational state yielding 7 (6) hyperfine parameters for including the (0,3) interaction constants. Splittings of transitions between Estates involving basis states with have been observed in the ground, and vibrational states. This splitting has been unequivocally explained as lifting of parity degeneracy by proton hyperfine interactions. From the analysis of the ground state hyperfine doublets, tensorial constants of the H spinrotation coupling and the Sb–H spin–spin interaction have been accurately determined.

Proton transfer and tautomerization in clusters: Structure and energetics at the selfconsistent field level
View Description Hide DescriptionThe structures and energetics of 23 different clusters with are investigated using ab initio calculations at the level. Clusters based on both the enol and keto tautomers of 7hydroxyquinoline (7HQ) are investigated, as well as ionpair (zwitterionic) clusters resulting from proton transfer from 7HQ to the cluster. In all cases, the solvent cluster forms hydrogen bonds at both the OH and N positions of 7HQ. For ammoniachain clusters are found, for additional hydrogenbond topologies appear such as bifurcated chains, cycles and mixed chain/cycles. Although the bare keto 7HQ is calculated to be 17 kcal/mol less stable than the enol form, the energy difference decreases continuously to 11 kcal/mol for with increasing n. For one of the enol clusters involving six molecules, proton transfer can occur from either the OH or NH group to the cluster, yielding a locally stable zwitterion cluster For the keto tautomer, locally stable ionpair clusters were found for 5, and 6, but these are calculated to be considerably less stable than the neutral enol forms.

Investigation of J dependence of line shift, line broadening, and line narrowing coefficients in the absorption band of acetylene
View Description Hide DescriptionLine shift coefficients, line broadening coefficients, and line narrowing coefficients have been measured in the band of acetylene using a diode lasersystem operating at 788 nm and a multipass Herriot absorption cell. Experimental data have been obtained for 20 lines of the P and R branches broadened by air, and the rare gases He, Ne, Ar, Kr, and Xe. The observed line shapes could successfully be reproduced by employing Galatry and Rautian functions which include the phenomenon of Dicke narrowing. Our results for the line broadening coefficients are in good agreement with the values reported previously for other vibrational bands. Thus, the present work confirms the vibrational independence of the broadening coefficients. On the other side, we observed a clear dependence of the narrowing coefficients on rotation in a vibrational transition of acetylene for the first time. In addition, the line center frequencies have been determined with improved accuracy.