Volume 123, Issue 10, 08 September 2005
 ARTICLES

 Theoretical Methods and Algorithms

Pathintegral virial estimator based on the scaling of fluctuation coordinates: Application to quantum clusters with fourthorder propagators
View Description Hide DescriptionWe first show that a simple scaling of fluctuation coordinates defined in terms of a given reference point gives the conventional virial estimator in discretized path integral, where different choices of the reference point lead to different forms of the estimator (e.g., centroid virial). The merit of this procedure is that it allows a finitedifference evaluation of the virial estimator with respect to temperature, which totally avoids the need of higherorder potential derivatives. We apply this procedure to energy and heatcapacity calculations of the and clusters at low temperature using the fourthorder TakahashiImada [J. Phys. Soc. Jpn.53, 3765 (1984)] and Suzuki [Phys. Lett. A201, 425 (1995)] propagators. This type of calculation requires up to thirdorder potential derivatives if analytical virial estimators are used, but in practice only firstorder derivatives suffice by virtue of the finitedifference scheme above. From the application to quantum clusters, we find that the fourthorder propagators do improve upon the primitive approximation, and that the choice of the reference point plays a vital role in reducing the variance of the virial estimator.

On the equivalence between the energy and virial routes to the equation of state of hardsphere fluids
View Description Hide DescriptionThe energy route to the equation of state of hardsphere fluids is ill defined since the internal energy is just that of an ideal gas, and thus it is independent of density. It is shown that this ambiguity can be avoided by considering a squareshoulder interaction and taking the limit of vanishing shoulder width. The resulting hardsphere equation of state coincides exactly with the one obtained through the virial route. Therefore, the energy and virial routes to the equation of state of hardsphere fluids can be considered as equivalent.

Pathintegral computations of tunneling processes
View Description Hide DescriptionThe application of the pathintegral methodology of Chandler and Wolynes [D. Chandler and P. G. Wolynes, J. Chem. Phys.74, 4078 (1981)] to the calculation of oneelectrontunneling probabilities is revisited. We show that the evaluation of the kink free energy that is related to the tunneling splitting is associated with “polymer bead” distributions over a continuous distribution of scaled barriers, which makes both the calculation and its physical interpretation relatively difficult. In particular, we find that relative to other available techniques the method converges slowly and suffers from inaccuracies associated with the finitetemperature aspect of the calculation, and that past tentative identification of the bead distribution over the barrier with a physical picture of a “tunneling path” should be reassessed.

Effect of the onebody potential on interelectronic correlation in twoelectron systems
View Description Hide DescriptionThe correlationenergies of the helium isoelectronic sequence (IS) and of Hooke’s IS are very similar and are both weakly increasing upon increasing the nuclear charge∕force constant, respectively. However, their separation into radial and angular correlations shows interesting differences. First, for intermediate (and high) values of the force constant radial correlation in Hooke’s IS is surprisingly low. Second, both systems exhibit a decrease in the relative contribution of radial versus angular correlation upon strengthening the onebody attractive potential; however, unlike the helium IS, in Hooke’s IS the radial correlationenergy increases in absolute value upon strengthening the attractive onebody potential. The contribution of radial correlation to the Coulomb hole is examined and the asymptotic behavior at both strong and weak attractive potentials is considered. Radial correlation in Hooke’s IS is found to constitute about 9.3% of the total correlationenergy when the spring constant approaches the limit , but 100% of the total correlationenergy for . Our results highlight both the similarities and the differences between the helium and Hooke’s ISs.

Large systems at ab initio multireference level: A cheap treatment thanks to a division into fragments
View Description Hide DescriptionThanks to the use of localized orbitals and the subsequent possibility of neglecting longrange interactions, the linearscaling methods have allowed to treat large systems at ab initio level. However, the limitation of the number of active orbitals in a complete active space self consistentfield (CASSCF) calculation remains unchanged. The method presented in this paper suggests to divide the system into fragments containing only a small number of active orbitals. Starting from a guess wave function, each orbital is optimized in its corresponding fragment, in the presence of the other fragments. Once all the fragments have been treated, a new set of orbitals is obtained. The process is iterated until convergence. At the end of the calculation, a set of active orbitals is obtained, which is close to the exact CASSCF solution, and an accurate CASSCF energy can be estimated.

Measure of accuracy for multicanonical moleculardynamics simulation
View Description Hide DescriptionA measure of the flatness of the energy probability distribution for multicanonical moleculardynamics (MMD) simulation is presented. It (the flatness measure) can be introduced by a slight change in the renewing scheme of the MMD potential energy. Our proposed measure is applied to liquid Ar with a LennardJones potential system in order to investigate the influence of flatness on the simulation results such as internal energy and specific heat at constant volume. We find that the accuracy of MMD simulation is influenced not only by the flatness of the energy probability distribution but also by the width of the energy region that is accessible during the MMD simulation.

A comparative study between dissipative particle dynamics and molecular dynamics for simple and complexgeometry flows
View Description Hide DescriptionThe purpose of this study is to compare the results from moleculardynamics and dissipative particle dynamics (DPD) simulations of LennardJones (LJ) fluid and determine the quantitative effects of DPD coarse graining on flow parameters. We illustrate how to select the conservative force coefficient, the cutoff radius, and the DPD time scale in order to simulate a LJ fluid. To show the effects of coarse graining and establish accuracy in the DPD simulations, we conduct equilibrium simulations, Couette flow simulations, Poiseuille flow simulations, and simulations of flow around a periodic array of square cylinders. For the last flow problem, additional comparisons are performed against continuum simulations based on the spectral/hp element method.

A new algorithm for predicting triplettriplet energytransfer activated complex coordinate in terms of accurate potentialenergy surfaces
View Description Hide DescriptionThe new algorithm presented here allows, for the first time, the determination of the optimal geometrical distortions that an acceptor molecule in the triplettriplet energytransfer process undergoes, as well as the dependence of the activation energy of the process on the triplet energy difference of donor and acceptor molecules. This algorithm makes use of the complete potentialenergysurfaces (singlet and triplet states), and contrasts with the firstorder approximation already published [L. M. Frutos, O. Castaño, J. L. Andrés, M. Merchán, and A. U. Acuña, J. Chem. Phys.120, 1208 (2004)] in which an expansion of the potentialenergysurfaces was used. This algorithm is gradient based and finds the best trajectory for the acceptor molecule, starting from groundstate equilibrium geometry, to achieve the maximum variation of the singlettriplet energy gap with the minimum energy of activation on . Therefore, the algorithm allows the determination of a “reaction path” for the triplettriplet energytransfer processes. Also, the algorithm could also serve eventually to find minimumenergy crossing (singlettriplet) points on the potentialenergysurface, which can play an important role in the intersystem crossing process for the acceptor molecules to recover their initial capacity as acceptors. Also addressed is the misleading use of minimumenergy paths in to describe the energytransfer process by comparing these results with those obtained using the new algorithm. The implementation of the algorithm is illustrated with different potentialenergysurfacemodels and it is discussed in the frame of nonvertical behavior.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

A new ab initio interaction energy surface and highresolution spectra of the van der Waals complex
View Description Hide DescriptionA new fourdimensional intermolecular potentialenergysurface for the complex is presented. The ab initio points have been computed on a fivedimensional grid including the dependence on the H–H separation (the C–O separation was fixed). The surface has then been obtained by averaging over the intramolecular vibration of . The coupledcluster supermolecular method with single, double, and noniterative triple excitations has been used to calculate the interaction energy. The correlation part of the interaction energy has been obtained from extrapolations based on calculations in a series of basis sets. An analytical fit of the ab initiopotentialenergysurface has the global minimum of at the intermolecular separation of for the linear geometry with the C atom pointing toward the molecule. For the other linear geometry, with the O atom pointing toward , the local minimum of has been found for the intermolecular separation of . The potential has been used to calculate the rovibrational energy levels of the complex. The results agree very well with those observed by McKellar [A. R. W. McKellar J. Chem. Phys.108, 1811 (1998)]: the discrepancies are smaller than . The calculated dissociation energy is equal to and significantly smaller than the value of estimated from the experiment. Predictions of rovibrational energy levels for have also been done and can serve as a guidance to assign recorded experimental spectra. The interaction second virial coefficient has been calculated and compared with the experimental data.

Highresolution absorption spectrum of jetcooled between 70 000 and : New assignments
View Description Hide DescriptionThe absorptionspectrum of jetcooled was photographed from (or , ) at a resolution limit of ( or ). Even in the best structured region of the spectrum, from , observed bandwidths (full width at half maximum) are large, from . No rotational feature could be resolved. The spectrum is dominated by two strong bands near , , the and bands of Mulliken [J. Chem. Phys.8, 382 (1940)] or the spectral region of Price [J. Chem. Phys.4, 539 (1936)]. Their relative intensity is incompatible with previous assignments, namely, to a triplet and a singlet state belonging to the same configuration. On the basis of the present ab initio calculations, those bands are now assigned to two singlet states, the and excited states resulting from the Rydberg configuration. The present calculations also reveal that the two states issued from and are quasidegenerate and strongly mixed. They should be assigned to the two broad bands near , , the and bands of Mulliken and Price. Three vibrational modes are observed to be active: the CCl bond stretch , and the umbrella and rocking vibrations, respectively, and . The fundamental frequencies deduced are well within the ranges defined by the corresponding values in the neutral and ion ground states. The possibility of a dynamical Jahn–Teller effect induced by the vibrational mode in the Rydberg states is discussed.

Recombination of polycyclic aromatic hydrocarbon photoions with electrons in a flowing afterglow plasma
View Description Hide DescriptionA new technique, flowing afterglow with photoions (FIAPI), has been developed to measure the rate coefficient for the recombination of complex ions, and, in particular, polycyclic aromatic hydrocarbon(PAH) cations with electrons. The method is based on the flowing afterglowLangmuir probe  mass spectrometer apparatus at the University of Rennes I. A helium plasma is generated by a microwave discharge in a He buffer gas and downstream, a small amount of argon gas is injected to destroy any helium metastables. A very small amount of neutral PAH molecules is added to the afterglow plasma by evaporation from a plate coated with the PAH to be studied. PAH ions are then produced by photoionization of the parent molecule using a pulsed UV laser (157 nm). The laser beam is oriented along the flow tube and so a constant spatial concentration of photoions is obtained. The electron concentration along the flow tube is measured by means of a movable Langmuir probe. Ion concentration decay in time is measured at a fixed position using a quadrupole mass spectrometer which is triggered by the laser pulse. The recombination of anthracene and pyrene cations has been studied using this technique and we have found a recombination rate of for anthracene and for pyrene.

The effect of substituents on electronic states’ ordering in metaxylylene diradicals: Qualitative insights from quantitative studies
View Description Hide DescriptionEquationofmotion spinflip coupledcluster method with single and double substitutions (EOMSFCCSD) is employed to study how substituents affect the electronic states’ ordering in metaxylylene diradicals. The electronegativity of substituents and the incorporation of a heteroatom are found to have a negligible effect. The effect of charges on energy gaps is much more pronounced, in agreement with the proposal of Dougherty and coworkers [J. Am. Chem. Soc.118, 1452 (1996)]. Resonancestructuretheory and molecular orbital analysis are employed to explain this phenomenon. The changes in the exocyclic C–C bond length in substituted metaxylylenes, derived from equilibrium structures calculated by using analytic gradients for the EOMSFCCSD method, support the original resonancetheory explanation by West et al. However, a similar resonancetheorybased reasoning fails to explain the quantitative difference between positively and negatively charged systems as well as the observed strong stabilization of an openshell singlet state in the Noxidized pyridinium analog of metaxylylene.

Photofragment translation spectroscopy of at 248 nm: Determination of the primary and secondary dissociation pathways
View Description Hide DescriptionPhotofragmentation translational spectroscopy was used to identify the primary and secondary reaction pathways in the KrF laser (248 nm) photodissociation of chlorine azide under collisionfree conditions. Both the molecular channel producing NCl and the radical channel producing Cl were analyzed in detail. Consistent with previously reported velocity map ion imaging experiments [N. Hansen and A. M. Wodtke, J. Phys. Chem. A107, 10608 (2003)] a bimodal translational energy distribution is seen when Cl atoms are monitored at . Momentummatched counterfragments can be seen at . The characteristics of the observed radicalchannel data reflect the formation of linear azide radical and another highenergy form of (HEF) that exhibits many of the characteristics one would expect from cyclic . HEF can be directly detected by electronimpact ionization more than after its formation. Products of the unimolecular dissociation of HEF are observed in the and data. Anisotropy parameters were determined for the primary channels to be for the NCl forming channel and and for the linear and HEF forming channels, respectively. There is additional evidence for secondary photodissociation of and of NCl.

NonBorn–Oppenheimer calculations of the pure vibrational spectrum of
View Description Hide DescriptionVery accurate calculations of the pure vibrational spectrum of the ion are reported. The method used does not assume the Born–Oppenheimer approximation, and the motion of both the electrons and the nuclei are treated on equal footing. In such an approach the vibrational motion cannot be decoupled from the motion of electrons, and thus the pure vibrational states are calculated as the states of the system with zero total angular momentum. The wave functions of the states are expanded in terms of explicitly correlated Gaussian basis functions multipled by even powers of the internuclear distance. The calculations yielded twelve bound states and corresponding eleven transition energies. Those are compared with the pure vibrational transition energies extracted from the experimental rovibrational spectrum.

A densityfunctional study on aromatic interaction: Benzene dimer and naphthalene dimer
View Description Hide DescriptionThe longrange correction (LC) scheme of densityfunctional theory(DFT) was applied to the calculation of the aromatic interaction of the benzene dimer and naphthalene dimer. In previous calculations, it was confirmed that the LC scheme [Iikura et al., J. Chem. Phys.115, 3540 (2001)] gives very accurate potential energysurfaces (PESs) of small van der Waals (vdW) complexes by combining with the AndersonLangrethLundqvist (ALL) vdW correlation functional [Andersson et al., Phys. Rev. Lett.76, 102 (1996)] . In this study, method was examined by calculating a wide range of PES of the benzene dimer including parallel, Tshaped, and paralleldisplaced configurations. As a result, we succeeded in reproducing very accurate PES within the energy deviance of less than in comparison with the results of highlevel ab initio molecularorbital methods at all reference points on the PES. It was also found that gave accurate results independent of exchangecorrelation functional used, in contrast with the strong functional dependencies of conventional pure functionals. This indicates that both exchange repulsion and van der Waals attractive interactions should be correctly incorporated in conventional pure functionals in order to calculate accurate aromatic interactions. We also found that method has a low basisset dependency in the calculations of aromatic interactions. The present scheme was also successfully applied to the stacking interactions of naphthalene dimer. This may suggest that method would be a powerful tool in the calculations of large molecules such as biomolecules.

Freeelectron attachment to coronene and corannulene in the gas phase
View Description Hide DescriptionElectron attachment to the polyaromatic hydrocarbons coronene and corannulene is studied in the electron energy range of about using a highresolution crossed electronneutral beam setup. The major anions observed are the parent anions peaking at about with cross sections of and , respectively. The only fragment anions formed in coronene and corannulene are the dehydrogenated coronene and corannulene anions. Other anions observed in the negative mass spectra at about can be ascribed to impurities of the sample. Highlevel quantummechanical studies are carried out for the determination of electron affinities, hydrogen binding energies, and structures of both molecules. The behavior of coronene and corannulene upon electron attachment is compared with that of other polyaromatic hydrocarbons studied previously.

The role of rotation in the vibrational relaxation of water by hydrogen molecules
View Description Hide DescriptionVibrational relaxation cross sections of the bending mode by molecules are calculated on a recent highaccuracy ab initio potentialenergy surface using quasiclassical trajectory calculations. The role of molecular rotation is investigated at a collisional energy of and it is shown that initial rotational excitation significantly enhances the total (rotationally summed) vibrational relaxation cross sections. A strong and complex dependence on the orientation of the water angular momentum is also observed, suggesting the key role played by the asymmetry of water. Despite the intrinsic limitations of classical mechanics, these exploratory results suggest that quantum approximations based on a complete decoupling of rotation and vibration, such as the widely used vibrational closecoupling (rotational) infiniteordersudden method, would significantly underestimate rovibrationally inelastic cross sections. We also present some rationale for the absence of dynamical chaos in the scattering process.

Nonresonant ionization of oxygen molecules by femtosecond pulses: Plasma dynamics studied by timeresolved terahertz spectroscopy
View Description Hide DescriptionWe show that optical pumpterahertz probe spectroscopy is a direct experimental tool for exploring laserinduced ionization and plasma formation in gases. Plasma was produced in gaseous oxygen by focused amplified femtosecond pulses. The ionization mechanisms at 400 and 800nm excitation wavelengths differ significantly being primarily of a multiphoton character in the former case and a strongfield process in the latter case. The generation of the plasma in the focal volume of the laser and its expansion on subnanosecond time scale is directly monitored through its densitydependent susceptibility. A Drude model used to evaluate the plasma densities and electronscattering rates successfully captures the observations for a wide range of pump intensities. In addition, rotational fingerprints of molecular and ionic species were also observed in the spectra.

Energytransfer dynamics of highpressure rovibrationally excited molecular
View Description Hide DescriptionThe energytransfer dynamics of highpressure molecular gas initially prepared in the state using stimulated Raman pumping are probed with rotational Raman scattering. A computer simulation that incorporates the effects of collisioninduced vibrational energy transfer is described and used to fit the experimental Raman scattering results obtained as a function of the pump/probe delay time. The vibrational energytransfer rate for decay from the state compares well with other lowerpressure studies.

Stabilization and rovibronic spectra of the shaped and linear groundstate conformers of a weakly bound raregas–homonuclear dihalogen complex:
View Description Hide DescriptionLaserinduced fluorescence spectra of entrained in a He supersonic expansion have been recorded in the , 80, 120, and 210 spectral regions at varying downstream distances, and thus different temperature regimes. Features associated with transitions of the shaped and linear complexes are identified. The changes in the relative intensities of the shaped and linear features with cooling in the expansion indicate that the linear conformer is energetically more stable than the shaped conformer. A ab initiopotentialenergysurface, computed at the coupled cluster level of theory with a large, flexible basis set, is used to calculate the binding energies of the two conformers, 15.8 and for the shaped and linear complexes, respectively. This potential and an excitedstate potential [M. P. de LaraCastells, A. A. Buchachenko, G. DelgadoBarrio, and P. Villareal, J. Chem. Phys.120, 2182 (2004)] are used to calculate the excitation spectra of in the , 120 region. The calculated spectra are used to make spectral assignments and to determine the energies of the excitedstate intermolecular vibrational levels accessed in the observed transitions. Temperaturedependent laserinduced fluorescence spectra and a simple thermodynamic model [D. S. Boucher, J. P. Darr, M. D. Bradke, R. A. Loomis, and A. B. McCoy, Phys. Chem. Chem. Phys.6, 5275 (2004)] are used to estimate that the linear conformer is more strongly bound than the shaped conformer. Twolaser action spectroscopy experiments reveal that the binding energy of the linear conformer is , and that of the shaped conformer is then , in good agreement with the calculated values.