Volume 124, Issue 7, 21 February 2006
 COMMUNICATIONS


Molecular geometry and polarizability of small cadmium selenide clusters from allelectron ab initio and Density Functional Theory calculations
View Description Hide DescriptionWe have calculated molecular geometries and electric polarizabilities for small cadmium selenide clusters. Our calculations were performed with conventional ab initio and density functional theory methods and Gaussiantype basis sets especially designed for . We find that the dipole polarizability per atom converges rapidly to the bulk value.

Dissociation energy of ekaplutonium fluoride E126F: The first diatomic with molecular spinors consisting of atomic spinors
View Description Hide DescriptionOur ab initio allelectron fully relativistic DiracFock (DF) and nonrelativistic (NR) HartreeFock (HF) selfconsistent field (SCF) calculations predict the superheavy diatomic ekaplutonium fluoride E126F to be bound with the calculated dissociation energy of 7.44 and at the predicted E126F bond lengths of 2.03 and , respectively. The antibinding effects of relativity to the dissociation energy of E126F are . The predicted dissociation energy with both our NR HF and relativistic DF SCF wave functions is fairly large and is comparable to that for very stable diatomics. This is the first case, where in a diatomic, an atom has orbital occupied in its ground state electronic configuration and such superheavy diatomics would have occupied molecular spinors (orbitals) consisting of atomic spinors (orbitals). This opens up a whole new field of chemistry where atomic spinors (orbitals) may be involved in electronic structure and chemical bonding of systems of superheavy elements with .
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 ARTICLES

 Theoretical Methods and Algorithms

Extended BornOppenheimer equation for a threestate system
View Description Hide DescriptionWe present explicit forms of nonadiabatic coupling (NAC) elements of nuclear Schrödinger equation (SE) for a coupled threestate electronic manifold in terms of mixing angles of real electronic basis functions. If the adiabaticdiabatic transformation (ADT) angles are the mixing angles of electronic bases, ADT matrix transforms away the NAC terms and brings diabatic form of SE. ADT and NAC matrices are shown to satisfy a curl condition with nonzero divergence. We have demonstrated that the formulation of extended BornOppenheimer (EBO) equation from any threestate BO system is possible only when there exists a coordinateindependent ratio of the gradients for each pair of mixing angles. On the contrary, since such relations among the mixing angles lead to zero curl, we explore its validity analytically around conical intersection(s) and support numerically considering two nuclearcoordinatedependent three surface BO models. Numerical calculations are performed by using newly derived diabatic and EBO equations and expected transition probabilities are obtained.

On the relationship between the local tracking procedures and monotonic schemes in quantum optimal control
View Description Hide DescriptionNumerical simulations of (bilinear) quantum control often rely on either monotonically convergent algorithms or tracking schemes. However, despite their mathematical simplicity, very limited intuitive understanding exists at this time to explain the former type of algorithms. Departing from the usual mathematical formalization, we present in this paper an interpretation of the monotonic algorithms as finite horizon, local in time, tracking schemes. Our purpose is not to present a new class of procedures but rather to introduce the necessary rigorous framework that supports this interpretation. As a byproduct we show that at each instant, estimates of the future quality of the current control field are available and used in the optimization. When the target is expressed as reaching a prescribed final state, we also present an intuitive geometrical interpretation as the minimization of the distance between two correlated trajectories: one starting from the given initial state and the other backward in time from the target state. As an illustration, a stochastic monotonic algorithm is introduced. Numerical discretizations of the two procedures are also presented.

A unified electrostatic and cavitation model for firstprinciples molecular dynamics in solution
View Description Hide DescriptionThe electrostatic continuum solvent model developed by [Fattebert and Gygi J. Comput. Chem.23, 662 (2002); Int. J. Quantum Chem.93, 139 (2003)] is combined with a firstprinciples formulation of the cavitation energy based on a natural quantummechanical definition for the surface of a solute. Despite its simplicity, the cavitation contribution calculated by this approach is found to be in remarkable agreement with that obtained by more complex algorithms relying on a large set of parameters. Our model allows for very efficient CarParrinello simulations of finite or extended systems in solution and demonstrates a level of accuracy as good as that of established quantumchemistry continuum solvent methods. We apply this approach to the study of tetracyanoethylene dimers in dichloromethane, providing valuable structural and dynamical insights on the dimerization phenomenon.

Substitution and chemical environment effects on the absorption spectrum of indigo
View Description Hide DescriptionThe UV/visible spectra of a series of indigo derivatives have been evaluated by using ab initio methods. The combination of the Polarizable continuum model for estimating bulk solvent effects with the level of approximation, leads to an accurate description of the wavelength of maximum absorption of indigoïds compounds. Using this procedure, we have assessed the effects of both the surroundings (solvent and solid state) and the substitution pattern. For the latter, we obtained a mean absolute deviation of only 7 nm (0.02 eV) compared to experiment, for a set of 86 molecules/solvents.

Mesoscale modeling of complex binary fluid mixtures: Towards an atomistic foundation of effective potentials
View Description Hide DescriptionThis paper is devoted to equilibrium moleculardynamics (MD) simulations of a fully atomistic model of binary mixtures of water (component 1) and ethanol (component 2). We investigate ways to extract from these simulations effective, pairwise additive potentials suitable to describe the interactions between coarsegrained molecules (i.e., beads) in corresponding mesoscale dissipative particledynamics simulations. The fully atomistic model employed in MD simulations is mapped onto an implicit water model, where the internal degrees of freedom of ethanol and all the degrees of freedom of water are integrated out. This gives us an effective onecomponent system consisting only of ethanol beads. The effective interaction potential between a pair of ethanol beads, , is approximated at three levels of sophistication. At the lowest one, we approximate by the potential of mean force between the centers of mass of two ethanol beads calculated in the fully atomistic MD simulations; at the second level, we take to be the potential linked to total and direct correlation functions in the hypernettedchain closure of the OrnsteinZernike equation. At the third level we approximate numerically by improving it iteratively through the Boltzmann inversion scheme. Our results indicate that the levelone approach works only at the lowest (8 wt %) concentration; the leveltwo approach works only up to intermediate ethanol concentrations (ca. 50 wt %). Only the Boltzmann inversion scheme works for all, up to the highest concentration considered (70 wt %).

Dipole and quadrupole moments of molecules in crystals: A novel approach based on integration over Hirshfeld surfaces
View Description Hide DescriptionElegant expressions are derived for the computation of dipole and quadrupole moments of molecules using the electrostatic potential and electric field evaluated on an oriented molecular surface. These expressions are implemented for Hirshfeld surfaces, applied to various molecular crystals, and compared with the results from the quantum theory of atoms in molecules. The effect of intermolecular interactions is also explored by examining the differences between electrostatic moments derived from a periodic HartreeFock electron density and an electron density resulting from a superposition of noninteracting molecules. The enhancement of the dipole moment for hydrogen bonded molecular crystals is typically 30%–40% and shown to be largely independent of the partitioning scheme. Dipole moments calculated from Hirshfeld surfaces systematically underestimate those from zeroflux surfaces, a result attributed to the translation of the Hirshfeld surface relative to the zeroflux surfaces for these molecules. For acetylene and benzene, the differences between a crystal calculation and the sum of noninteracting molecules are small, and both partitioning schemes yield quadrupole and second moment results in close agreement.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Absolute rate coefficients for the reactions of and at 298 K in a selectedion flow tube instrument
View Description Hide DescriptionThe absolute rate coefficients at 298 K for the reactions of and have been determined in a selectedion flow tube instrument. O atoms are generated by the quantitative titration of N atoms with NO, where the N atoms are produced by microwavedischarge on . The experimental procedure allows for the determination of rate constants for the reaction of the reactant ion with and . The rate coefficient for is found to be , a factor of 2 slower than previously determined. In addition, it was found that the reaction proceeds by two different reaction channels to give (1) and (2) . The second channel was not reported in the previous study and accounts for ca. 35% of the reaction. An overall rate coefficient of was determined for , which is slightly faster than previously reported. Branching ratios for this reaction were determined to be and .

Direct identification of propargyl radical in combustion flames by vacuum ultraviolet photoionization mass spectrometry
View Description Hide DescriptionWe have developed an effusive laser photodissociation radical source, aiming for the production of vibrationally relaxed radicals. Employing this radical source, we have measured the vacuum ultraviolet (VUV)photoionization efficiency (PIE) spectrum of the propargyl radical formed by the excimer laserphotodissociation of propargyl chloride in the energy range of using highresolution (energy ) multibunch synchrotron radiation. The VUVPIE spectrum of thus obtained is found to exhibit pronounced autoionization features, which are tentatively assigned as members of two vibrational progressions of in excited autoionizing Rydberg states. The ionization energy of determined by a small steplike feature resolved at the photoionization onset of the VUVPIE spectrum is in excellent agreement with the IE value reported in a previous pulsed field ionizationphotoelectron study. We have also calculated the FranckCondon factors (FCFs) for the photoionization transitions . The comparison between the pattern of FCFs and the autoionization peaks resolved in the VUVPIE spectrum of points to the conclusion that the resonanceenhanced autoionization mechanism is most likely responsible for the observation of pronounced autoionization features. We also present here the VUVPIE spectra for the mass 39 ions observed in the VUV synchrotronbased photoionization mass spectrometric sampling of several premixed flames. The excellent agreement of the IE value and the pattern of autoionizing features of the VUVPIE spectra observed in the photodissociation and flames studies has provided an unambiguous identification of the propargyl radical as an important intermediate in the premixed combustionflames. The discrepancy found between the PIE spectra obtained in flames and photodissociation at energies above the suggests that the PIE spectra obtained in flames might have contributions from the photoionization of vibrationally excited and/or the dissociative photoionization processes involving larger hydrocarbon species formed in flames.

Monobridged
View Description Hide DescriptionThe rotational spectrum of a new monobridged isomer of , denoted here as , has been detected by Fourier transform microwave spectroscopy of a supersonic molecular beam through the discharge products of silane. On the basis of highlevel coupled clustertheory, this isomer is calculated to lie only above disilene , the most stable isomeric arrangement of , and to be fairly polar, with a calculated dipole moment of . The rotational spectrum of exhibits closely spaced line doubling, characteristic of a molecule undergoing highfrequency inversion. Transition state calculations indicate that inversion probably occurs in two steps: migration of the bridged hydrogen atom to form silylsilylene, , and then internal rotation of the group, followed by the reverse process. The potential energy surface for this type of inversion is quite shallow, with a barrier height of only . Searches for the rotational lines of silylsilylene, calculated to be of comparable stability to but about five times less polar , have also been undertaken, so far without success, even though strong lines of have been detected. The favorable energetics and high polarity of monobridged with respect to either disilene or silylsilylene make it a plausible candidate for radioastronomical detection in sources such as , where comparably large silicon molecules such as SiS, , and have already been discovered.

A lineshape function in terms of changes in both molecular structure and force constants: A Gaussian approximation
View Description Hide DescriptionWe propose a new expression of a lineshape function (LSF) including the effects of changes in both force constants and the molecular structure within the harmonicoscillator approximation. This expression enables us to calculate the LSF using only the data on molecular structures, force constants, and electronic energies in the initial and final electronic states without solving the eigenvalue equation for the normal vibration of a molecule. To derive the LSF expression, we consider onephoton emission from a polyatomic molecule thermalized in an electronic excited state, and derive the intensity distribution function for onephoton emission using not Lax and Kubo and Toyozawa’s [J. Chem. Phys.20, 1752 (1952); Prog. Theor. Phys.13, 160 (1955)] generating function method but rather the densitymatrix method. As a simple application, a Gaussian approximate LSF is applied to . As a result, it is found that the effect of change in force constants between the initial and final electronic states cannot be ignored, nor can the effect of change in the molecular structure between these two states. The LSF expression obtained is applicable to studies of not only radiative transition but also of electrontransfer and energytransfer processes where both changes in molecular structure and force constants between the initial and final electronic states cannot be disregarded.

Theoretical rate coefficients for the exchange reaction
View Description Hide DescriptionIn this work quasiclassical trajectory calculations were carried out to determine directly the rate coefficients for the isotopic exchange reaction,, using a potentialenergysurface that carefully accounts for the longrange interactions. The calculated thermal rate coefficients are in good agreement with the experimental results.

Evidence of and produced from photodissociation of 1,3trimethylene oxide at
View Description Hide DescriptionWe investigated the dissociativeionization of formaldehyde and ethene produced from photolysis of 1,3trimethylene oxide at using a molecularbeam apparatus and vacuumultraviolet radiation from an undulator for direct ionization. The product suffers from severe dissociativeionization to ( and ) even though photoionizationenergy is as small as . Branching ratios of fragmentation of and following ionization are revealed as a function of kinetic energy of products using ionizing photons from . Except several exceptions, branching ratios of daughter ions increase with increasing photonenergy but decrease with increasing kinetic energy. The title reaction produces and mostly on electronic ground states but a few likely on triplet states; seems to have a yield greater than . The distinct features observed at small kinetic energies of daughter ions are attributed to dissociativeionization of photoproducts and . The observation of triplet products indicates that intersystem crossing occurs prior to fragmentation of 1,3trimethylene oxide.

Collisioninduced dissociation of transition metaloxide ions: Dynamics of collision with Xe
View Description Hide DescriptionThe collisioninduced dissociation of by Xe has been studied by the use of classical dynamics procedures on LondonEyringPolanyiSato potentialenergy surfaces in the collision energy range of . The dissociation threshold behavior and the dependence of reaction cross sections on the collision energy closely follow the observed data with the threshold energy of . The principal reaction pathway is and the minor pathway is . At higher collision energies, the former reaction preferentially occurs near the collinear and perpendicular alignments, but the latter only occurs near the perpendicular alignment. At lower energies close to the threshold, the reactions are found to occur near the collinear configuration. No reaction occurs in the collinear alignment . The high and low energytransfer efficiencies of the collinear alignments and are attributed to the effects of mass distribution. The activation of the bond toward the dissociation threshold occurs through a translationtovibration energy transfer in a strong collision on a time scale of about .

Dynamics of the reaction at low temperatures: Comparison of quasiclassical trajectory with quantum scattering calculations
View Description Hide DescriptionQuasiclassical trajectory and quantummechanical scattering calculations are reported for the reaction at energies close to the reaction threshold. The dynamics of the reaction have been investigated for zero total angular momentum using the lowest potentialenergy surface developed by Rogers et al. [J. Phys. Chem. A104, 2308 (2000)] and its recent extensions by Brandão et al. [J. Chem. Phys.121, 8861 (2004)] which provide an improved description of the van der Waals interaction. Good agreement is observed for this system between quasiclassical and quantal results for incident kinetic energies above the tunneling regime. Quantummechanical calculations also confirm recent theoretical predictions of a strong collisionenergy dependence of the product branching ratio in the reaction, which explains the differences observed in vibrational populations between experiments using different sources.

Highresolution studies of tropolone in the and electronic states: Isotope driven dynamics in the zeropoint energy levels
View Description Hide DescriptionRotationally resolved microwave (MW) and ultraviolet (UV) spectra of jetcooled tropolone have been obtained in and electronic states using Fouriertransform microwave and UVlaser/molecularbeam spectrometers. In the ground electronic state, the MW spectra of all heavyatom isotopomers including one and four isotopomers were observed in natural abundance. The OD isotopomer was obtained from isotopically enriched samples. The two lowest tunneling states of each isotopomer except have been assigned. The observed inversion splitting for the OD isotopomer is 1523.227(5) MHz. For the asymmetric structures, the magnitudes of tunnelingrotation interactions are found to diminish with decreasing distance between the heavy atom and the tunneling proton. In the limit of closest approach, the state of was well fitted to an asymmetric rotor Hamiltonian, reflecting significant changes in the tautomerization dynamics. Comparisons of the substituted atom coordinates with theoretical predictions at the MP2/augccpVTZ level of theory suggest the localized and wave functions of the heavier isotopes favor the C–OH and forms of tropolone, respectively. The only exception occurs for the and structures which correlate to the and states, respectively. These preferences reflect kinetic isotope effects as quantitatively verified by the calculated zeropoint energy differences between members of the asymmetric atom pairs. From rotationally resolved data of the and bands in , lineshape fits have yielded Lorentzian linewidths that differ by 12.2(16) MHz over the interval in . The fluorescence decay rates together with previously reported quantum yield data give nonradiative decay rates of and for the and levels of the state of tropolone.

Threshold ionpair production spectroscopy of HCN
View Description Hide DescriptionThe spectroscopic technique of threshold ionpair production spectroscopy (TIPPS) has been applied to the triatomic molecule HCN. We have recorded the total ionpair yield and TIPP spectra for the process using coherent vacuum ultraviolet excitation. From the simulation of our highresolution TIPP spectrum we have precisely measured the HCN ionpair threshold to be . This value could be used to determine the bond dissociation energy to unprecedented accuracy. Our fitting result also showed that rotationally excited instead of cold fragment is favored as the ionpair dissociation product in the threshold region.

Energetics and dynamics of threshold photoionpair formation in
View Description Hide DescriptionThreshold ionpair production spectroscopy (TIPPS) has been applied to two isotopomers, HF and DF. From the high resolution TIPP spectra, the ionpair thresholds of have been precisely measured. Combined with the ionization energy of H(D), the electron affinity of F, and the zero point energies of , the difference between their classical bond dissociation energies was obtained as . Our result provides an experimental estimate of the BornOppenheimer breakdown in the ground electronic state. The present work also measured the total ionpair yield spectra of HF and DF in the threshold region, and the ionpair formation mechanisms of these two molecules were discussed in light of the high resolution results.

Quasiclassical trajectory calculations comparing the reactivity and dynamics of symmetric and asymmetric stretch and the role of the bending mode excitations of methane in the reaction
View Description Hide DescriptionTo analyze the effects of the symmetric and asymmetric stretch mode excitations and the role played by the “umbrella” bending mode excitation in the reactivity and the dynamics of the gasphase reaction, an exhaustive dynamics study was performed. Quasiclassical trajectory(QCT) calculations, including corrections to avoid zeropoint energy leakage along the trajectories, were used in this work on an analytical potential energy surface previously developed by EspinosaGarcia et al. [J. Chem. Phys. (to be published)]. First, with respect to the reactivity, we found that the mode excitation is more reactive than the mode by a factor of 1.20, in agreement with the experimental tendency between these modes. The inclusion of the bending mode practically does not affect this relative reactivity, . Second, with respect to the dynamics (rotovibrational and angular distributions of the products), the two stretch modes, and , give very similar pictures, reproducing the experimental behavior, and the “umbrella” mode does not affect the dynamics. The satisfactory reproduction (always qualitatively acceptable and sometimes even quantitatively) of a great variety of experimental data by the QCT study presented here lends confidence to the potential energy surface constructed by EspinosaGarcia et al. [J. Chem. Phys. (to be published)].