Volume 117, Issue 6, 08 August 2002
 ARTICLES

 Theoretical Methods and Algorithms

Spectral difference methods for solving the differential equations of chemical physics
View Description Hide DescriptionSpectral differences [D. A. Mazziotti, Chem. Phys. Lett. 299, 473 (1999)] is a family of techniques for solving differential equations in which the summation in the numerical derivative is accelerated to produce a matrix representation that is not only exponentially convergent like the discrete variable representation (DVR) and other spectral methods but also sparse like traditional finite differences and finite elements. Building upon important work by Boyd [Comput. Methods Appl. Mech. Eng. 116, 1 (1994)] and Gray and Goldfield [J. Chem. Phys. 115, 8331 (2001)], we explore a new class of spectral difference methods which yields solutions that are more accurate than highorder finite differences by several orders of magnitude. With the generating weight for Gegenbauer polynomials we design a new spectral difference method where the limits of an adjustable parameter generate both finite differences emphasizing the low Fourier frequencies, and a truncated sincDVR emphasizing all Fourier frequencies below the aliasing limit of the grid. A range of choices for produces solutions which are significantly better than the equivalent order of finite differences. We compare the Gegenbauerweighted spectral differences with methods by Boyd as well as Gray and Goldfield which employ a hyperbolic secant and a step function as frequency weights, respectively. The solutions from the Gegenbauer and the sechweighted differences are shown to be less sensitive to parameter selection than the stepweighted differences. We illustrate all of the spectral difference methods through vibrational and quantum control calculations with diatomic iodine and the van der Waals cluster NeCO. Spectral differences also have important applications in molecular dynamics and electronic structure as well as other areas of science and engineering.

Boundary conditions and trajectories of diffusion processes
View Description Hide DescriptionThis article constructs trajectories associated with various boundary conditions for the Smoluchowski equation on an interval. Singleparticle diffusion processes are first constructed by taking the diffusion limits of random walks. The diffusion limit gives both boundary conditions which enforce the singleparticle constraint and properties of underlying trajectories at those boundaries. Meanfielddiffusions are then obtained as limits of sums of singleparticle processes. The results help to interpret the application of diffusionmodels to both ion channels and wider pores that facilitate molecular transport across membranes. Potential applications to Brownian dynamics simulations are discussed.

Anomalous behavior of the target decay on small world networks
View Description Hide DescriptionWe investigate on small world networks (SWN’s) the survival probability of immobile targets, which get annihilated by random walkers at first encounter. On SWN’s we find (distinct from regular lattices, Cayley trees, and regular ultrametric spaces) that in general the survival probability cannot be directly related to the average number of distinct sites visited. We underline this finding with arguments related to the structural disorder of SWN’s and through the derivation of a lower bound for the targets’ decay.

Analytical timedependent Hartree–Fock schemes for the evaluation of the hyperRaman intensities
View Description Hide DescriptionTwo analytical procedures based on the timedependent Hartree–Fock (TDHF) scheme are elaborated to evaluate the first derivatives of the dynamic first hyperpolarizability with respect to atomic Cartesian coordinates. In the first scheme, the mixed thirdorder TDHF equations are solved iteratively to obtain the third derivatives of the linear combination of atomic orbitals coefficients twice with respect to external dynamic electric fields and once with respect to atomic Cartesian coordinates. The second takes advantage of the rule and interchange relations to express the first derivatives of the dynamic first hyperpolarizability with respect to atomic Cartesian coordinates in terms of lowerorder derivatives. Both procedures have been implemented in the GAMESS quantum chemistry package. Applications focus on the characterization of the frequency dispersion of the first derivatives of the first hyperpolarizability with respect to vibrational normal coordinates of and as well as on the determination of nonresonant hyperRaman intensities within the double harmonic oscillator approximation.

Assessment of simple exchangecorrelation energy functionals of the oneparticle density matrix
View Description Hide DescriptionAn improved density matrix functional (DMF) combining the properties of the “corrected Hartree” (CH) and “corrected Hartree–Fock” (CHF) approximations is proposed. Functionals of the CH/CHF type and the closely related natural orbital functional of Goedecker and Umrigar (GU) are tested in fully variational finite basis set calculations of light atoms, the lowest energy singlet methylene, and, for the first time, potential energy curves of diatomic molecules. Although CH/CHFstyle DMFs may give reasonable energies for atoms and molecules near equilibrium geometries, they predict unrealistically shallow minima in the potential energy curves for diatomic molecules with more than two electrons. The calculated CH and CHF molecular dissociation curves exhibit the same patterns of over and undercorrelations as the corresponding correlationenergy plots for the homogeneous electron gas undergoing a transition from high to low densities. In contrast, the GU functional yields not only accurate atomic and molecular energies but also plausible dissociation curves. The reasons behind the observed performance are analyzed.

Electrostatics in periodic slab geometries. I
View Description Hide DescriptionWe propose a new method to sum up electrostatic interactions in twodimensional (2D) slab geometries. It consists of a combination of two recently proposed methods: the 3D Ewald variant of Yeh and Berkowitz [J. Chem. Phys. 111, 3155 (1999)] and the purely 2D method MMM2D by Arnold and Holm [Chem. Phys. Lett. 354, 324 (2002). The basic idea involves two steps: First we use a threedimensional summation method whose summation order is changed to sum up the interactions in a slabwise fashion. Second we subtract the unwanted interactions with the replicated layers analytically. The resulting method has full control over the introduced errors. The time to evaluate the layer correction term scales linearly with the number of charges, so that the full method scales like an ordinary 3D Ewald method, with an almost linear scaling in a mesh based implementation. In this paper we will introduce the basic ideas, derive the layer correction term, and numerically verify our analytical results.

Electrostatics in periodic slab geometries. II
View Description Hide DescriptionIn our preceeding Paper I [Ref. 16] a method was developed to subtract the interactions due to periodically replicated charges (or other longrange entities) in one spatial dimension. The method constitutes a generalized “electrostatic layer correction” which adapts any standard threedimensional summation method to slablike conditions. Here the implementation of the layer correction is considered in detail for the standard Ewald (EW3DLC) and the P3M mesh Ewald (P3MLC) methods. In particular this method offers a strong control on the accuracy and an improved computational complexity of for meshbased implementations. We derive anisotropic Ewald error formulas and give some fundamental guidelines for optimization. A demonstration of the accuracy, error formulas and computation times for typical systems is also presented.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Stateresolved radiative lifetimes of the radical and rate constants for the quenching by
View Description Hide DescriptionA reinvestigation of the radiative lifetimes and the quenching rate constants of single excited rotational states of the radical has been performed. The quenching species was the parent molecule The electronically excited radicals are generated by first forming ground state in the ArF laser photolysis of after a delay, is pumped by a dye laser to selected fine structure levels of the state. Both the radiative lifetimes and quenching rate constants were found to be dependent on the rotational level but not on the spin and Λdoublet component. The formation of a blast wave was observed under certain conditions leading to time dependent changes of the number density and temperature in the system. In case of a blast wave, kinetic measurements have to be evaluated with great care.

Statetostate rate constants for the rotational relaxation of radicals in inelastic collisions with
View Description Hide DescriptionA stateresolved experimental investigation of the rotational relaxation of the radical in inelastic collisions with ammonia is presented. Fine structure and Λdoublet resolved, statetostate rate constants were extracted from fluorescence spectra recorded upon laser excitation to individual levels in the state. Relaxation trends are reported with regard to Hund’s coupling (a), (b), and intermediate cases. At low N, the most dominant process is the Λdoublet mixing. For high N, rotational relaxation proceeds predominantly via transitions at conservation of the spin unit and the symmetry. A general tendency of conservation of the spin unit is observed. A comparison of the dipolar collision partner with the spherical He is performed.

Raman and infrared linewidths of CO in Ar
View Description Hide DescriptionWe present measurements of Raman linewidths in the fundamental Q branch of CO for mixtures with Ar at temperatures of 77, 195, and 300 K, recorded using an inverse Raman spectrometer. Starting from a recent ab initiopotential energy surface,theoretical values of Ar broadening coefficients for CO infrared and Raman lines (isotropic and anisotropic components) at temperatures in the range 77 to 1100 K are calculated via quantummechanical methods. The relative merits of the close coupling theoretical results over the coupled states results are underlined. Finally, a comparison of the calculated pressure broadening coefficients is made with the present experimental data as well as with recently available infrared data. There is general agreement between the calculated and measured values of the broadenings for all the temperatures probed. We conclude that the temperature dependence of the infrared and Raman broadening coefficients have been correctly determined theoretically and may be used to test a common temperature scaling law.

Theoretical study of infrared and Raman spectra of hydrated magnesium sulfate salts
View Description Hide DescriptionHarmonic and anharmonic vibrational frequencies, as well as infrared and Raman intensities, are calculated for Electronic structuretheory at the second order Møller–Plesset perturbation theory level with a basis set is used to determine the geometry, energetics, charge distributions, and vibrational spectra of pure and hydrated salts. The direct vibrational selfconsistent field method and its correlation corrected extension are used to determine anharmonic corrections to vibrational frequencies and infrared intensities for the pure and its complex with one water molecule. Very significant differences are found between vibrational spectra of water molecules in complexes with and pure water. Some of the O–H stretching frequencies are shifted to the red very significantly (by up to upon complexation with magnesium sulfate. They should be observed between 1700 and in a region very different from the corresponding O–H stretch frequency region of pure water In addition, the stretching vibrations are found at lower frequency regions than the water vibrations. They can serve as unique identifiers for the presence of sulfate salts. The predicted infrared and Raman spectra should be of valuable help in the design of future missions and analysis of observed data from the ice surface of Jupiter’s moon Europa that possibly contains hydrated salts.

Discovery of longlived excited electronic states of chlorobenzene, bromobenzene, benzonitrile, and phenyl acetylene cations
View Description Hide DescriptionPreviously developed technique of charge exchangeionization in a collision cell outside the ion source, which detects ions originating from the collision gas in the cell, was used to find longlived excited electronic states of monosubstituted benzene cations. The technique is based on the criterion that charge exchange between polyatomic species is efficient only when the energy of reaction is close to zero or negative or the exoergicity rule. The states of chlorobenzene, bromobenzene, benzonitrile, and phenyl acetylene cations were found to have long lifetimes (10 microseconds or longer) while excited electronic states with long lifetime were not detected for fluorobenzene, iodobenzene, toluene, nitrobenzene, and styrene cations. The longlived states found were those displaying wellresolved vibrational structures in the photoelectron spectra. In particular, these were the states generated by removal of an electron from the inplane nonbonding p orbitals of halogens or inplane π orbitals of the triple bonds.

Energy dependence of forward scattering in the differential cross section of the reaction
View Description Hide DescriptionExtensive timeindependent quantum mechanical scattering calculations for the reaction have been performed in the collision energy range 1.39–2.20 eV on the Boothroyd–Keogh–Martin–Peterson potential energy surface. The theoretical differential cross sections (DCS) obtained for the channel of the reaction have been compared with recent measurements by Zare and coworkers over the collision energy range 1.39–1.85 eV using the photoloc technique [S. C. Althorpe et al., Nature (London) 416, 67 (2002)]. An excellent agreement between experiment and theory has been found for most of the collision energies studied. In particular, the appearance and evolution of forward scattering with collision energy observed experimentally has been quantitatively reproduced by the theoretical calculations. An analysis of the theoretical results, including a semiclassical complex angular momentum analysis, have been performed in order to ascertain the origin of the sharp forward peaks in the DCS.

Experimental and theoretical study of the ion–molecule association reaction
View Description Hide DescriptionThe association reaction leading to the protonbound dimer of ammonia, was studied by the CRESU flow technique over the temperature range 15–170 K, in the bath gases Ar, and and over the range of bath gas concentrations The rate coefficients are shown to depend on the temperature, the pressure, and the nature of the bath gas. Theoretical modelling of the reaction involves a combination of ion–molecule capture and unimolecular reaction rate theory. It is shown that the present experiments all correspond to the intermediate falloff regime of the reaction ranging up to the high pressure bimolecular capture limit, whereas earlier experiments between 200 and 350 K were made close to the low pressure termolecular limit. Temperature and pressuredependent rate coefficients over wide ranges of conditions are calculated and compared with experimental results from this and earlier work. For the bath gas under most of the applied conditions, the reaction does not follow the energy transfer mechanism, but proceeds via a radical–complex mechanism. In this case, the reaction rate is determined by the capture of by complexes. The rate of this process is estimated by modified ion–dipole capture theory.

NO angular distributions in the photodissociation of at 213 nm: Deviations from axial recoil
View Description Hide DescriptionAngular distributions of selected rotational states of products obtained in the 213 nm photodissociation of have been determined in a molecular beam by using the photofragment ion imaging technique. Specifically, images of products in 11, and 19 have been recorded, for which the maximum energies available to the products are 2038, 1774, and 1278 cm^{−1}, respectively. The recoil anisotropy parameter of the photofragments, decreases significantly at low centerofmass translational energies from its maximum value of and depends strongly on the rotational angular momentum of the photoproducts. This behavior is described well by a classical model that takes into account the transverse recoil component mandated by angular momentumconservation. For each of the observed N states, highly rotating levels are produced via planar dissociation, and the angular momenta are established at an interfragment separation of about 2.6 Å. For most of the centerofmass translational energy range, both corotating and counterrotating fragments are produced, but at the lowest energies, only the latter are allowed. The correlated rotational energy distributions exhibit deviations from the behavior predicted by phase space theory, suggesting that exitchannel dynamics beyond the transition state influences the product state distributions. In this study, a new method for image reconstruction is employed, which gives accurate angular distributions throughout the image plane.

Ultraviolet photodissociation of bromoform at 234 and 267 nm by means of ion velocity imaging
View Description Hide DescriptionThe photochemistry of bromoform is of considerable importance to understanding the impact of shortlived halogen species on bromine chemistry in the atmosphere. In the present work, the products of the ultraviolet photodissociation of bromoform at 234 and 267 nm are determined by timeofflight mass spectrometry and velocity ion imaging. Both ground Br and spin–orbit excited Br atoms are found to be formed via resonanceenhanced multiphoton ionization detection. Radical products are detected via vacuum ultraviolet photoionization at 118 nm. The results indicate that there is a primary molecule bromine elimination channel consisting of The quantum yields for atomic Br and molecular elimination channels are determined from the timeofflightspectra to be 0.74 and 0.26 at 234 nm, respectively. At 267 nm, they are 0.84 and 0.16, respectively. Energy and angular distributions are deduced from the 2D images of Br, CHBr, and The direct studies described in this paper on the photodissociation of bromoform suggest that the current atmospheric photochemical models that do not anticipate the formation of need to be reinvestigated to determine their implications for atmospheric bromine chemistry.

Infrared spectra of and complexes
View Description Hide DescriptionInfrared spectra of the weakly bound complexes and have been observed using a tunable diode laser to probe a pulsed supersonic jet expansion. The rotational structure of the bands was analyzed using a conventional asymmetric rotor Hamiltonian. The and spectra are mostly a type in structure, with very weak btype transitions, but for the a and btype components are both prominent. The fitted rotational parameters are consistent with roughly Tshaped structures with intermolecular separations around 3.4–3.5 Å for and 3.8–3.9 Å for OCS–He. The angle between the or OCS axis and the He position is about 80° for and 65° for OCS–He. The vibrational band origins are slightly blueshifted from those of the free molecule, with the shifts (+0.2 cm^{−1}) being about twice the magnitude of the OCS–He shifts (+0.1 cm^{−1}). The results are of particular interest since and (especially) OCS have both been used as probes in experiments on ultracold helium nanodroplets.

A global potential energy surface of based on ab initio calculations
View Description Hide DescriptionResults of the ab initio calculations on the ground state of are presented. With accurate method and basis sets, the potential energy surface for the ground state was scanned with more than 7000 points, and an analytic global potential energy surface was constructed based on these points. The properties such as the potential minima, the transition state, and the dissociating paths of were discussed. The influence of the threebody interaction in this system was also investigated, and it is found that a potential based on the twobody additive interaction is not good to represent the system.

Theoretical study of proton transfer in ammonium nitrate clusters
View Description Hide DescriptionProton transfer in ammonia–nitric acid clusters containing up to four component units are subject to theoretical calculation in this work. In a single ammonium nitrate unit, proton transfer between the nitric acid and ammonia unit does not occur but the two molecules are strongly hydrogenbonded. In a cluster of two ammonium nitrate formula units proton transfer does occur and the components are stabilized by ionic interactions. Ammonium nitrate solvated with single ammonia or nitric acid molecules are also studied. Structural changes in the various clusters relative to the free molecules are discussed. Using population analysis, the total electrostatic interaction between the components of each cluster are calculated. It is argued that the magnitude of the total electrostatic interactions within the cluster determines whether proton transfer and ion formation takes place. Binding energies alone do not give a reliable indication of the occurrence of proton transfer.

The effect of intermolecular interactions on the electric properties of helium and argon. III. Quantum statistical calculations of the dielectric second virial coefficients
View Description Hide DescriptionThe second dielectric virial coefficients of helium and argon are investigated using a fully quantum statistical approach and recent accurate ab initio results for the interatomic potentials and the interactioninduced polarizabilities. We thereby extend a preceding investigation based on a semiclassical approach to include quantum effects. For helium the results support the findings of a previous study by Moszynski et al. [J. Chem. Phys. 247, 440 (1995)] that quantum effects are substantial for temperatures below 10 K, while they are practically negligible above 70 K. For argon special care is needed in the numerical integrations carried out in the quantum statistical calculation of the virial coefficients, due to the presence of quasibound states in the continuum and a slow convergence of the summation over the angular momentum. Here quantum effects are practically negligible in the range of temperatures experimentally investigated, i.e., between 243 and 408 K. As far as comparison with experimental data is concerned, large discrepancies are found for some of the lowtemperature experimental measurements of helium. Agreement is also unsatisfactory for high temperatures for argon and experimental redetermination is suggested.