Volume 121, Issue 20, 22 November 2004
 ARTICLES

 Theoretical Methods and Algorithms

Molecular potential energy surfaces by interpolation: Strategies for faster convergence
View Description Hide DescriptionA method for interpolating molecular potential energy surfaces introduced [Ischtwan and Collins, J. Chem. Phys. 100, 8080 (1994)] and developed as an iterative scheme has been improved by different criteria for the selection of the data points. Refinements in the selection procedure are based on the variance of the interpolation and the direct exploration of the interpolation error, and produce more accurate surfaces than the previously established scheme for the same number of data points.

Comparison of methods for finding saddle points without knowledge of the final states
View Description Hide DescriptionWithin the harmonic approximation to transition state theory, the biggest challenge involved in finding the mechanism or rate of transitions is the location of the relevant saddle points on the multidimensional potential energy surface. The saddle point search is particularly challenging when the final state of the transition is not specified. In this article we report on a comparison of several methods for locating saddle points under these conditions and compare, in particular, the wellestablished rational functionoptimization (RFO) methods using either exact or approximate Hessians with the more recently proposed minimum mode following methods where only the minimum eigenvalue mode is found, either by the dimer or the Lanczos method. A test problem involving transitions in a sevenatom Pt island on a Pt(111) surface using a simple Morse pairwise potential function is used and the number of degrees of freedom varied by varying the number of movable atoms. In the full system, 175 atoms can move so 525 degrees of freedom need to be optimized to find the saddle points. For testing purposes, we have also restricted the number of movable atoms to 7 and 1. Our results indicate that if attempting to make a map of all relevant saddle points for a large system (as would be necessary when simulating the long time scale evolution of a thermal system) the minimum mode following methods are preferred. The minimum mode following methods are also more efficient when searching for the lowest saddle points in a large system, and if the force can be obtained cheaply. However, if only the lowest saddle points are sought and the calculation of the force is expensive but a good approximation for the Hessian at the starting position of the search can be obtained at low cost, then the RFO approaches employing an approximate Hessian represent the preferred choice. For small and medium sized systems where the force is expensive to calculate, the RFO approaches employing an approximate Hessian is also the more efficient, but when the force and Hessian can be obtained cheaply and only the lowest saddle points are sought the RFO approach using an exact Hessian is the better choice. These conclusions have been reached based on a comparison of the total computational effort needed to find the saddle points and the number of saddle points found for each of the methods. The RFO methods do not perform very well with respect to the latter aspect, but starting the searches further away from the initial minimum or using the hybrid RFO version presented here improves this behavior considerably in most cases.

Scaled oppositespin second order Møller–Plesset correlation energy: An economical electronic structure method
View Description Hide DescriptionA simplified approach to treating the electron correlation energy is suggested in which only the αβ component of the second order Møller–Plesset energy is evaluated, and then scaled by an empirical factor which is suggested to be 1.3. This scaled oppositespin second order energy (SOSMP2), where MP2 is Møller–Plesset theory, yields results for relative energies and derivative properties that are statistically improved over the conventional MP2 method. Furthermore, the SOSMP2 energy can be evaluated without the fifth order computational steps associated with MP2 theory, even without exploiting any spatial locality. A fourth order algorithm is given for evaluating the opposite spin MP2 energy using auxiliary basis expansions, and a Laplace approach, and timing comparisons are given.

Realtime linear response for timedependent densityfunctional theory
View Description Hide DescriptionWe present a linearresponse approach for timedependent densityfunctional theories using timeadiabatic functionals. The resulting theory can be performed both in the time and in the frequency domain. The derivation considers an impulsive perturbation after which the Kohn–Sham orbitals develop in time autonomously. The equation describing the evolution is not strictly linear in the wave function representation. Only after going into a symplectic realspinor representation does the linearity make itself explicit. For performing the numerical integration of the resulting equations, yielding the linear response in time, we develop a modified Chebyshev expansion approach. The frequency domain is easily accessible as well by changing the coefficients of the Chebyshev polynomial, yielding the expansion of a formal symplectic Green’s operator.

Parallel replica dynamics with a heterogeneous distribution of barriers: Application to nhexadecane pyrolysis
View Description Hide DescriptionParallel replica dynamics simulation methods appropriate for the simulation of chemical reactions in molecular systems with many conformational degrees of freedom have been developed and applied to study the microsecondscale pyrolysis of nhexadecane in the temperature range of 2100–2500 K. The algorithm uses a transition detection scheme that is based on molecular topology, rather than energetic basins. This algorithm allows efficient parallelization of small systems even when using more processors than particles (in contrast to more traditional parallelization algorithms), and even when there are frequent conformational transitions (in contrast to previous implementations of the parallel replica algorithm). The parallel efficiency for pyrolysis initiation reactions was over 90% on 61 processors for this 50atom system. The parallel replica dynamics technique results in reaction probabilities that are statistically indistinguishable from those obtained from direct molecular dynamics, under conditions where both are feasible, but allows simulations at temperatures as much as 1000 K lower than direct molecular dynamics simulations. The rate of initiation displayed Arrhenius behavior over the entire temperature range, with an activation energy and frequency factor of and respectively, in reasonable agreement with experiment and empirical kinetic models. Several interesting unimolecular reaction mechanisms were observed in simulations of the chain propagation reactions above 2000 K, which are not included in most coarsegrained kinetic models. More studies are needed in order to determine whether these mechanisms are experimentally relevant, or specific to the potential energy surface used.

Nonperturbative modeling of twophoton absorption in a threestate system
View Description Hide DescriptionThe physics of the twophoton absorption process is investigated for a threestate system. The densitymatrix equations for the twophoton interaction are solved in the steadystate limit assuming that the pump laser radiation is monochromatic. Collisional broadening, saturation, and Stark shifting of the twophoton resonance are investigated in detail by numerical solution of the steadystate densitymatrix equations. Analytical expressions for the saturation intensity and the Stark shift are derived for the case where the singlephoton transitions between the intermediate state and the initial and final states are far from resonance with the pump laser. For this case, it is found that the direction of the Stark shift is dependent on the relative magnitudes of the dipolemoment matrix elements for the singlephoton transitions that couple the intermediate state with the initial and final states. Saturation and Stark shifting are also investigated for the case where the singlephoton transitions between the intermediate state and the initial and final states are close to resonance with the pump laser.

Spatial distributions of angular momenta in quantum and quasiclassical stereodynamics
View Description Hide DescriptionWe have recently reported a derivation of the relationship between the quantum and classical descriptions of angular momentumpolarization [M. P. de Miranda and F. Javier Aoiz, Phys. Rev. Lett. 93, 083201 (2004)]. This paper presents a detailed account of the derivation outlined in that paper, and discusses the implications of the new results. These include (i) a new expression of the role of the uncertainty principle in the broadening of angular momentum distributions, (ii) the attribution of azimuthal fluctuations of angular momentum distributions to spatialquantum beats, (iii) the definition of a new Fourier transform of the density matrix, distinct from those suggested in the past, that provides an alternative view of how the quantum description of angular momentumpolarization approaches the classical one in the correspondence principle limit, (iv) a prescription for the determination of a quasiclassical angular momentumdistribution function that does not suffer from problems encountered with its purely classical counterpart, and (v) a description of how angular momentum distributions commonly visualized with recourse to the classical vector model can be depicted with exact and welldefined quantum mechanics.

Efficiency considerations in the construction of interpolated potential energy surfaces for the calculation of quantum observables by diffusion Monte Carlo
View Description Hide DescriptionA modified Shepard interpolation scheme is used to construct global potential energy surfaces (PES) in order to calculate quantum observables—vibrationally averaged internal coordinates, fully anharmonic zeropoint energies and nuclear radial distribution functions—for a prototypical loosely bound molecular system, the water dimer. The efficiency of PES construction is examined with respect to (a) the method used to sample configurational space, (b) the method used to choose which points to add to the PES data set, and (c) the use of either a one or twopart weight function. The most efficient method for constructing the PES is found to require a quantum sampling regime, a combination of both hweight and rms methods for choosing data points and use of the twopart weight function in the interpolation. Using this regime, the quantum diffusionMonte Carlozeropoint energy converges to the exact result within addition of 50 data points. The vibrationally averaged O–O distance and O–O radial distribution function, however, converge more slowly and require addition of over 500 data points. The methods presented here are expected to be applicable to both other loosely bound complexes as well as tightly bound molecular species. When combined with high quality ab initio calculations, these methods should be able to accurately characterize the PES of such species.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Photoionization and photodissociation dynamics of the and states of and
View Description Hide DescriptionThe photoionization and photodissociationdynamics of and in selected rovibrational levels of the and states have been investigated by velocity map ion imaging. The selected rotational levels of the and states are prepared by threephoton excitation from the ground state. The absorption of fourth photon results in photoionization to produce or photodissociation to produce a groundstate atom and an excited H atom with The ion can be photodissociated by absorption of a fifth photon. The resulting or ion images provide information on the vibrational state dependence of the photodissociationangular distribution of the molecular ion. The excited atoms produced by the neutral dissociation process can also be ionized by the absorption of a fifth photon. The resulting ion images provide insight into the excited state branching ratios and angular distributions of the neutral photodissociation process. While the experimental ion images contain information on both the ionic and neutral processes, these can be separated based on constraints imposed on the fragment translational energies. The angular distribution of the rings in the ion images indicates that the neutral dissociation of molecular hydrogen and its isotopes is quite complex, and involves coupling to both doubly excited electronic states and the dissociation continua of singly excited Rydberg states.

Transition state dynamics of OHF on several electronic states: Photodetachment spectrum of and conical intersections
View Description Hide DescriptionWave packet simulations of the photodetachment spectrum of are performed on several electronic adiabatic states, two triplets and four singlets of neutral OHF. The transition moments to these six states have been approximated using the ab initio electronic wave functions of and OHF calculated at the equilibrium configuration of the parent anion. In a first step, twodimensional simulations of the spectrum are performed on new twodimensional potential energy surfaces (PESs) of the neutral in a OHF collinear geometry. The resulting simulated spectrum is in rather good agreement with the experimental one, reproducing all the structures from 0 to 2.5 eV electron kinetic energies. At energies below 0.5 eV, all calculated states, singlets and triplets, contribute to the total spectrum. At higher energies, however, only the triplet states participate. In a second step, to improve the description of the spectrum, threedimensional wave packet simulations of the spectrum are performed, getting an excellent agreement with the experiment. The collinear and states split in two and one New adiabatic PESs are used in this work for the and states, while the one recently proposed was used for the ground It is found that the minimum energy paths of the and states cross twice at collinear geometry, so that at the transition state the ground state corresponds to while is the lowest state otherwise. Such conical intersections are expected to give rise to important ΣΠ vibronic effects, requiring a complete threedimensional model of coupled diabatic states to improve our understanding of the reaction dynamics in this kind of systems.

Relaxation behavior of rovibrationally excited in a rarefied expansion
View Description Hide DescriptionThe evolution of the rotational and vibrational distributions of molecular hydrogen in a hydrogen plasma expansion is measured using laser induced fluorescence in the vacuumUV range. The evolution of the distributions along the expansion axis shows the relaxation of the molecular hydrogen from the high temperature in the upstream region to the low ambient temperature in the downstream region. During the relaxation, the vibrational distribution, which has been recorded up to is almost frozen in the expansion and resembles a Boltzmann distribution at However, the rotational distributions, which have been recorded up to in and up to in cannot be described with a single Boltzmann distribution. In the course of the expansion, the lower rotational levels adapt quickly to the ambient temperature while the distribution of the higher rotational levels is measured to be frozen in the expansion at a temperature between 2000 and 2500 K. A model based on rotationtranslation energy transfer is used to describe the evolution of the rotational distribution of vibrational level in the plasma expansion. The behavior of the low rotational levels is described satisfactory. However, the densities of the higher rotational levels decay faster than predicted.

Microwave Fourier transform spectrum of the watercarbonyl sulfide complex
View Description Hide DescriptionThe microwave spectrum of the watercarbonyl sulfide complex was observed with a pulsedbeam, FabryPerot cavity Fouriertransform microwave spectrometer. In addition to the normal isotopic form, we also measured the spectra of HDO–SCO, and The rotational constants are and for and for and for and for and for and for and for for HDO–SCO; for and for with uncertainties corresponding to one standard deviation. The observed rotational constants for the sulfur34 complexes are generally higher than those for the corresponding sulfur32 isotopomers. The heavier isotopomers have smaller effective moments of inertia due to the smaller vibrational amplitude of the vibration (zero point) as compared to the making the effective bond slightly shorter. Stark effect measurements for give a dipole moment of [2.6679(28) D]. The most probable structure of is near planar with the oxygen of water bonded to the sulfur of carbonyl sulfide. The oxygensulfur van der Waals bond length is determined to be 3.138(17) Å, which is very close to the ab initio value of 3.144 Å. The structures of the isoelectronic complexes and are compared. The first two are linear and the others are T shaped with an O–C/O–N van der Waals bond, i.e., the oxygen of water bonds to the carbon and nitrogen of and respectively.

Dissociative electron attachment to dinitrogen pentoxide,
View Description Hide DescriptionElectron attachment was studied in gaseous dinitrogen pentoxide, for incident electron energies between a few meV and 10 eV. No stable parent anion was observed but several anionic fragments and were detected using quadrupolemass spectrometry. Many of these dissociative pathways were found to be coupled and provide detailed information on the dynamics of fragmentation. Estimates of the cross sections for production of each of the anionic fragments were made and suggest that electron attachment to is amongst the most efficient attachment reactions recorded for nonhalogenated polyatomic systems.

Different approaches for the calculation of electronic excited states of nonstoichiometric alkali halide clusters: The example of
View Description Hide DescriptionThe electronic structure and excited states of the cluster are investigated using different approximate, but numerically efficient, computational schemes, such as a hybrid quantum/classical pseudopotential model with fullconfiguration interaction or timedependent densityfunctional theory. Various quantities such as geometries and transition energies are compared with results previously obtained by multireference configuration interaction calculations, taken as reference data. The potential energy surfaces of the lowest excited states are investigated and the finitetemperature absorption spectra are calculated. The good agreement with recent beam experiments [J.M. L’Hermite, V. Blanchet, A. Le Padellec, B. Lamory, and P. Labastie, Eur. Phys. J. D 28, 361 (2004)] leads to the conclusion that the absorptionspectrum observed experimentally corresponds to the lowest energy isomer which has a planar rhombic geometry.

Ultrafast excited state dynamics of the cluster: Quantum wave packet and classical trajectory calculations compared to experimental results
View Description Hide DescriptionShorttime, excitedstatedynamics of the lowest isomer of the cluster is studied theoretically in order to interpret the features of recent timeresolved pumpprobe ionizationexperiments [J. M. L’Hermite, V. Blanchet, A. Le Padellec, B. Lamory, and P. Labastie, Eur. Phys. J. D 28, 361 (2004)]. In the present paper, we propose an identification of the vibrational motion responsible for the oscillations in the ion signal, on the basis of quantum mechanical wave packet propagations and classical trajectory calculations. The good agreement between experiment and theory allows for a clear interpretation of the detected dynamics.

Magnitude and orientation dependence of intermolecular interaction of perfluoropropane dimer studied by highlevel ab initio calculations: Comparison with propane dimer
View Description Hide DescriptionIntermolecular interaction energies of 12 orientations of dimers were calculated with electron correlation correction by the secondorder MøllerPlesset perturbation method. The antiparallel dimer has the largest interaction energy Electron correlation correction increases the attraction considerably. Electrostatic energy is not large. Dispersion is mainly responsible for the attraction. Orientation dependence of the interaction energy of the dimer is substantially smaller than that of the dimer. The calculated interaction energy of the dimer at the potential minimum is 78% of that of the dimer whereas the interaction energies of the and dimers are larger than those of the and dimers. The intermolecular separation in the dimer at the potential minimum is substantially larger than that in the dimer. The larger intermolecular separation due to the steric repulsion between fluorine atoms is the cause of the smaller interaction energy of the dimer at the potential minimum. The calculated intermolecular interaction energy potentials of the dimers using an all atom model OPLSAA (OPLS all atom model) force field and a united atom model force field were compared with the ab initio calculations. Although the two force fields well reproduces the experimental vapor and liquid properties of perfluoroalkenes, the comparison shows that the united atom model underestimates the potential depth and orientation dependence of the interaction energy. The potentials obtained by the OPLSAA force field are close to those obtained by the ab initio calculations.

Density functional study of the adsorption of propene on silver clusters, +1)
View Description Hide DescriptionDensity functional theory has been used to investigate the binding of propene to small Ag clusters in the gas phase. The binding mechanism based on frontier orbital theory, which we used previously to describe the binding between propene and the Au clusters, works for the pure Ag clusters as well. Among other things, it explains the trends of the desorption energy of propene as a function of the Ag cluster size. We show that one can predict the binding site of propene by examining the shape of the lowest unoccupied molecular orbitals (LUMOs) of the bare clusters and correlate the strength of the bond to the orbital energies of the LUMOs of the bare cluster.

Density functional study of the adsorption of propene on mixed goldsilver clusters, Propensity rules for binding
View Description Hide DescriptionWe use density functional theory to investigate the binding of propene to small mixed Au–Ag clusters, in the gas phase. We have found that the rules proposed by us for propene binding to Au and Ag clusters, also work for binding to mixed Au–Ag clusters. The rules state that propene binds to those sites on the edge of the cluster where the equal density plots of the LUMO of the naked cluster protrude into the vacuum. Furthermore, the desorption energy of propene correlate with the LUMO energy: the lower the LUMO energy, the stronger the propene bond. We have also found an additional rule that is specific to mixed clusters. We call active the atoms on which the LUMO of the naked cluster protrude in the vacuum, and inactive those for which such protrusions do not exist. To define the rules we use the following notation: A is an active site to which propene is bound B is another active site, and C is an inactive site. If the atom in C (Ag or Au) is replaced with another atom (Au or Ag) propene desorption energy changes very little. If we replace the atom B with a more electronegative atom (i.e., we replace Ag by Au) the propene bond to A becomes stronger. If we replace the atom B with a less electronegative atom (i.e., we replace Au by Ag) the propene bond to A becomes weaker.

Opticaloptical double resonance photoionization spectroscopy of Rydberg states of nitric oxide
View Description Hide DescriptionThe spectra of vibrationally excited Rydberg states of nitric oxide were recorded by monitoring the photoion current produced using twophoton double resonance excitation via the NO state followed by photoexcitation of the Rydberg state that undergoes autoionization. The optical transition intensities from NO A state to Rydberg states were calculated, and the results agree closely with experiment. These results combined with circular dichroism measurements allow us to assign rotational quantum numbers to the Rydberg states even in a spectrum of relatively low resolution. We report the positions of these Rydberg levels converging to the NO and 2 ionization limits where N is the total angular momentum excluding electron and nuclear spin and represents the rotational quantum number of the ion core. Our twocolor opticaloptical double resonancemeasurements cover the range of N from 15 to 28, from 14 to 29, and the principal quantum number n from 9 to 21. The electrostatic interaction between the Rydberg electron and the ion core is used to account for the rotational fine structure and a corresponding model is used to fit the energy levels to obtain the quadrupole moment and polarizability of the core. Comparison with a multichannel quantum defect theory fit to the same data confirms that the model we use for the electrostatic interaction between the Rydberg electron and the ion core of NO well describes the rotational fine structure.

Collisional deexcitation of optically allowed excited atoms by axially symmetric molecules
View Description Hide DescriptionThe deexcitation process of an atom in an optically allowed excited state by a collision with an axially symmetric molecule is considered. In order to make a precise comparison with experimental data that have recently been obtained, we extend previous work for a Penning ionization process [T. Watanabe and K. Katsuura, J. Chem. Phys. 47, 800 (1967)]. Using the straightline trajectory impact parameter method, the probability of deexcitation in the incident atom is described by a discretecontinuum excitation transfer mechanism. The effects of the ionization yield η in molecular target and of the molecular anisotropicproperty of the optical transition dipole are considered. The crosssection formula σ is presented by a similar formula for Penning ionization of the atomic target by introducing a stereo factor as Here, is the relative velocity of the colliding system and λ is given by the ratio where μ, are the transitiondipole moments of an excited atom, those of a molecule at energy E for the perpendicular component and the parallel component with respect to molecular axis. Applications to (or (or systems and systems of the same projectiles on (or molecules are made. The results for hydrogen molecules are compared with the experimental data.