Volume 114, Issue 6, 08 February 2001
 ARTICLES

 Theoretical Methods and Algorithms

On the use of graph invariants for efficiently generating hydrogen bond topologies and predicting physical properties of water clusters and ice
View Description Hide DescriptionWater clusters and some phases of ice are characterized by many isomers with similar oxygen positions, but which differ in direction of hydrogen bonds. A relationship between physical properties, like energy or magnitude of the dipole moment, and hydrogen bond arrangements has long been conjectured. The topology of the hydrogen bond network can be summarized by oriented graphs. Since scalar physical properties like the energy are invariant to symmetry operations, graphical invariants are the proper features of the hydrogen bond network which can be used to discover the correlation with physical properties. We demonstrate how graph invariants are generated and illustrate some of their formal properties. It is shown that invariants can be used to change the enumeration of symmetrydistinct hydrogen bondtopologies, nominally a task whose computational cost scales like where N is the number of configurations, into an process. The utility of graph invariants is confirmed by considering two water clusters, the cage and dodecahedron, which, respectively, possess 27 and 30 026 symmetrydistinct hydrogen bondtopologies associated with roughly the same oxygen atom arrangements. Physical properties of these clusters are successfully fit to a handful of graph invariants. Using a small number of isomers as a training set, the energy of other isomers of the dodecahedron can even be estimated well enough to locate phase transitions. Some preliminary results for unit cells of iceIh are given to illustrate the application of our results to periodic systems.

The conformational behavior of polyglycine as predicted by a density functional model with periodic boundary conditions
View Description Hide DescriptionRepresentative conformations of polyglycine are studied by means of density functional calculations, performing complete geometry optimizations under periodic boundary conditions. The calculated stability order and the equilibrium geometries are in good agreement with the available experimental results. The performance of four density functionals (LSDA, PBE, BLYP, VSXC) are compared both for the dipeptide analogue and for the infinite homopolypeptide. Our results indicate that PBE and BLYP are the models of choice for analyzing conformational equilibriums in polypeptides. While the geometry of the different conformations of polyglycine and the stability order are almost converged at the 6–31G(d) level, the relative energies are not stable until the 6–311++G(2d,2p) basis set level is reached. A comparison between the geometries of glycine dipeptide analogue and of glycine infinite homopolypeptide allows us to gain further insights on the influence of long range effects on the geometry and the stability of the different conformers. This study shows the feasibility of complete high level ab initiooptimizations of infinite polypeptides, paving the route for new interesting applications of reliable quantum mechanical methods to biological systems.

Photoabsorption spectra in the continuum of molecules and atomic clusters
View Description Hide DescriptionWe present linear response theories in the continuum capable of describing photoionizationspectra and dynamic polarizabilities of finite systems with no spatial symmetry. Our formulations are based on the timedependent local density approximation with uniform grid representation in the threedimensional Cartesian coordinate. Effects of the continuum are taken into account either with a Green’s function method or with a complex absorbing potential in a realtime method. The two methods are applied to a negatively charged cluster in the spherical jellium model and to some small molecules (silane, acetylene and ethylene).

Semiclassical description of quantum coherence effects and their quenching: A forward–backward initial value representation study
View Description Hide DescriptionThe forward–backward (FB) version of the semiclassical (SC) initial value representation (IVR) is used to study quantum coherenceeffects in the timedependent probability distribution of an anharmonic vibrational coordinate and its quenching when coupled to a thermal bath. It is shown that the FBIVR accurately reproduces the detailed quantum coherent structure in the weak coupling regime, and also describes how this coherence is quenched with an increase of the system–bath coupling and/or the bath temperature. Comparisons are made with other approximations and the physical implications are discussed.

Semiclassical description of diffraction and its quenching by the forward–backward version of the initial value representation
View Description Hide DescriptionIt is shown that the forward–backward (FB) version of the semiclassical (SC) initial value representation (IVR) is able to describe quantum interference/coherence (i.e., diffraction) of particles transmitted by a twoslit potential. (In contrast, the linearized approximation to the SCIVR, which leads to the classical Wigner model, is unable to do so.) FBIVR calculations are also used to describe the (partial) quenching of this interference structure (i.e., “decoherence”) when the twoslit potential is coupled to a bath of harmonic oscillators.

A Fukui function overlap method for predicting reactivity in sterically complex systems
View Description Hide DescriptionA formalism is given for predicting reactivity of complex systems by combining electronic structure calculations with forcefield calculations within a transition state theory framework. The theory is employed in combination with the Fukui function to produce a simulation method capable of the ensemble sampling needed to examine sterically complex systems. An important linkage between reactivity information and energetic quantities is provided by introduction of the Fukui overlap integral. This spatial overlap integral measures the coincidence of electron donating regions on a nucleophile with electron accepting regions on the corresponding electrophilic reactant. We show that configurations with high values of this overlap integral tend to have lower densityfunctional theory energies. Thus, Fukui functions calculated once on single isolated reactants can be used to quickly estimate the reactivity of configurations generated using conventional forcefieldbased simulations. The correlation between energies and high overlap integrals can also be used to identify initial guess configurations for transition state searches. However, in the present implementation, real transition states are not accessible because intramolecular geometry relaxation is not allowed. The proposed method is tested on electrophilic aromatic alkylation reactions. Simulation results successfully reproduce experimental substituent effects in a series of variously substituted aromatics. Especially encouraging is the ability of the simulations to predict steric effects in the reaction of toluene with a series of electrophiles of varying bulkiness. Further applications, previously inaccessible to simulation, are expected in systems where steric effects play a dominant role in determining reaction selectivity.

The improved virtual orbitalcomplete active space configuration interaction method, a “packageable” efficient ab initio manybody method for describing electronically excited states
View Description Hide DescriptionWe describe a computationally efficient ab initio manybody method that can be used as a “packageable approximation” for computing excited stateproperties for small to large molecular systems, including those of multiconfigurational character. The method is based on first order multireference manybody perturbationtheory (MRMBPT), where the unoccupied valence orbitals are obtained by using an extension of Huzinaga’s improved virtual orbital (IVO) generation technique. Because the method employs a complete active space (CAS) which contains singly, doubly, and higher excited state configurations with respect to the zeroth order ground state configuration, the approach (IVOCASCI) is capable of providing a more accurate description of the excited states than the widely used packageable configuration interaction with singles (CIS) at a fraction of computational labor. Moreover, unlike the CASSCF approach this IVOCASCI method does not require iterations and therefore is more computationally efficient and free of the convergence problems that sometimes plague CASSCF calculations with increasing size of the CAS. Excited state energies are compared with energies from the widely used CIS, MCSCF, and CASSCF methods for the CaOH, cyclic and porphin molecules. The computed IVOCASCI transition energies are generally more accurate than the CASSCF. For example, our energies are comparable to CIS energies for CaOH and porphin, while the and IVOCASCI transition energies are more accurate than the CASSCF and CIS energies.

Nuclear dynamics near conical intersections in the adiabatic representation: I. The effects of local topography on interstate transitions
View Description Hide DescriptionThe local topography of a conical intersection can be represented by four parameters, readily determined from multireference configuration interactionwave functions, describing the pitch and tilt of the double cone. The timedependent Schrödinger equation is solved in the vicinity of a conical intersection in the adiabatic basis using an approach tailored to this representation. It is shown that an adiabatic state treatment, which offers conceptual advantages is, in the appropriate set of internal coordinates, not qualitatively more difficult than the equivalent calculation in a diabatic basis. The present treatment is fully hermitian and takes full account of the geometric phase effect being, for example, gauge invariant (in the infinite basis limit) and could be used to develop a fully adiabatic description of nonadiabatic dynamics. The gauge invariant formulation provides interesting insights into the consequences of neglecting the geometric phase. The algorithm is used to study the effects of the double cone’s topography on the outcome of a nonadiabatic transition. Transitions from both the upper state to the lower state and from the lower state to upper state are considered for representative sets of conical parameters. The effects of the local topography on the outcome of nonadiabatic transitions can be dramatic.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Characterizing the local topography of conical intersections using orthogonality constrained parameters: Application to the internal conversion in HNCO
View Description Hide DescriptionPortions of the seam of conical intersection relevant to the internal conversion of photoexcited isocyanic acid HNCO are analyzed. The topography of the potential energy surfaces, and the derivative coupling, in the vicinity of a conical intersection is described in terms of four conical parameters. These parameters are also used to obtain a local diabatic representation that removes the singularity in the derivative coupling. Continuity is achieved through the use of a recently described orthogonalization procedure. The conical parameters demonstrate that the double cones of concern are significantly tilted, which has important implications for the nuclear dynamics.

Vibrational spectra of the methanol tetramer in the OH stretch region. Two cyclic isomers and concerted proton tunneling
View Description Hide DescriptionSecond order Mo/ller–Plesset perturbation theory and density functional theory are employed to localize several stationary points on the potential energy surface of the cyclic methanol tetramer. Two cyclic isomers are identified: one of symmetry, with methyl groups in updownupdown configuration, and a second one of symmetry, with the methyl groups in upupdowndown configuration. The latter minimum is 360 above the minimum, with a barrier of 475 separating them. These isomers give rise to four asymmetric OH modes around 3300 A model of the concerted proton transfer, is the transition structure), yields an estimate of 0.7 for the tunneling splitting of the totally symmetric OH stretch vibrational fundamental. Raman spectra would show evidence of this fundamental and help to identify admixtures of the isomer.

Continuum state spectroscopy: A high resolution ion imaging study of IBr photolysis in the wavelength range 440–685 nm
View Description Hide DescriptionThe photodissociation of jetcooled IBr molecules has been investigated at numerous excitation wavelengths in the range 440–685 nm using a stateofart ion imaging spectrometer operating under optimal conditions for velocity mapping. Image analysis provides precise threshold energies for the ground, and first excited dissociation asymptotes, the electronic branching into these two active product channels, and the recoil anisotropy of each set of products, as a function of excitation wavelength. Such experimental data have allowed mapping of the partial crosssections for parallel (i.e., and perpendicular (i.e., absorptions and thus deconvolution of the separately measured (room temperature) parent absorptionspectrum into contributions associated with excitation to the and excited states of IBr. Such analyses of the continuous absorptionspectrum of IBr, taken together with previous spectroscopic data for the bound levels supported by the A and B state potentials, has allowed determination of the potential energy curves for, and (R independent) transition moments to, each of these excited states. Further wave packet calculations, which reproduce, quantitatively, the experimentally measured wavelength dependent product channel branching ratios and product recoil anisotropies, serve to confirm the accuracy of the excited state potential energy functions so derived and define the value (120 of the strength of the coupling between the bound and dissociative diabatic states of symmetry.

Ab initio studies of the reactions of and with (M=Cd, Hg)
View Description Hide DescriptionThe interaction of and with were studied by means of Hartree–Fock selfconsistent field (SCF) and multiconfigurational SCF plus variational and multireference second order Möller–Plesset perturbational configuration interaction (CIPSI) calculations, using relativistic effective core potentials. It was found that both metal atoms in their state break spontaneously the Ge–H bond of the germane molecule, giving place to the final products. For both atoms, the state is also inserted in the Ge–H bond and the corresponding interactionsurface shows an avoided crossing with the lowestlying potential surface adiabatically linked with the This interactionleads eventually to the products. The intermediate molecules, diabatically correlated with the which lie 13.6 and 21 kcal/mol, respectively, above the ground state reactants, have been carefully characterized as well as the dissociation channels leading to the and products. These products are reached from the intermediates without activation barriers. Accurate energy differences for all these species are reported. This work suggests that the simultaneous photoexcitation of Cd and Hg atoms in the presence of silane and germane molecules in the gas phase could be used to produce better quality thin films.

Negative ion photoelectron spectroscopy of the group 5 metal trimer monoxides and
View Description Hide DescriptionThe vibrationally resolved 488 nm negative ion photoelectron spectra of and provide measurements of their electron affinities, vibrational frequencies, and lowlying electronic state energies. The electron affinities increase smoothly down the triad with values (eV) of for for and for The metal–oxygen symmetric stretching fundamental frequencies are and respectively, for the neutral clusters and for Lower frequency symmetric modes are also active, with frequencies (±15 cm^{−1}) of 415 and 340 cm^{−1} for 320 cm^{−1} for 225 cm^{−1} for and of 355, 300, and 215 cm^{−1} (±20 cm^{−1}), respectively, for their anions. Weaker transitions also showing vibrational structure are observed to excited states at for and for and and for The spectra indicate that the extra electrons in the anions occupy essentially nonbonding orbitals, and that the neutral and anionic clusters have planar structures with doubly bridging oxygen atoms. Results are discussed in light of previous studies of and the Group 5 and MO molecules, and tentative assignments for the observed and states are proposed.

Differential cross sections for rotationally inelastic scattering of NO from He and
View Description Hide DescriptionState selective differential cross sections for rotationally inelastic scattering of NO 1.5, and from He and measured by crossed molecular beam product imaging are reported. The differential cross sections were extracted from the data images using a new basis image iterative fitting technique. The images typically exhibit a single broad rotational rainbow maximum that shifts from the forward to the backward scattering direction with increasing The angle of the rainbow maximum was lower at a given for than for He as a collision partner. At a collision energy of ∼500 cm^{−1}, primarily the repulsive part of the potential surface is probed, which can be modeled with a twodimensional hard ellipse potential. This model for rotationally inelastic scattering is shown to qualitatively match the experimental differential cross sections. A more advanced correlated electron pair approximation potential energy surface for NO+He does not give substantially better agreement with the experiment. The differences between scattering of He and are partially attributed to their differing structure and partially to a small difference in collision energy used in the two experiments.

Effect of carriergas pressure on barrier to nucleation: Monte Carlo simulation of water/nitrogen system
View Description Hide DescriptionCarrier gases are used in most nucleation experiments for releasing the latent heatgenerated during vapor condensation. In the analysis of experimental data it is often assumed that the carrier gas is inert and would not participate in the nucleation process of the target gas. Several recent nucleation experiments show that the influence of carrier gases to nucleation rate is not negligible under certain conditions. To gain more insight into the carriergas effect, we carry out Monte Carlo simulation to compute the free energy of formation of water clusters in the presence of a nitrogen carrier gas. At fixed temperature (240 K) and chemical potential, it is found that the barrier height to nucleation increases with the carriergas pressure. This barrier enhancement is attributed to the increase of equilibrium vapor pressure of water in the presence of carrier gas, which results in a decrease of supersaturation. It is also found that the simulation results are consistent with the binarynucleation theorem.

A theoretical study of the polarized neutron scattering from
View Description Hide DescriptionSpinorbit interactions play an essential part in elucidating the magnetic structures which are measured by the polarized neutron diffraction technique. This work extends our previous Hartree–Fock theory, with a oneelectron spinorbit term limitation, to incorporate both one and twoelectron terms exactly. This new theory, which is based on the current density, has been applied to calculate the lowtemperature magnetic structure factors of the crystal. The crystal is assumed to be assembled from noninteracting molecular fragments. The calculated structure factors were compared directly with those observed from experiment. The agreement between these theoretical results and the experimental data shows great improvement compared with those from the usual unrestricted Hartree–Fock theory and with those from the previous generalized Hartree–Fock theory including oneelectron terms. To examine the electron correlation effects, we use ab initio wavefunctionbased correlation methods, unrestricted secondorder Møller–Plesset perturbation (UMP2) and quadratic configuration interaction including single and double excitations (QCISD), and also density functionaltheoretical methods, localspin density approximation, generalized gradient approximation, Becke’s threeparameter hybrid methods, and modified halfandhalf hybrid methods, to calculate magnetic structure factors. Results indicate that the effects of spinorbit interactions are comparable to those of electron correlation, and both must be included in reproducing the experimental data. To consider both these effects simultaneously we employed a simple model. With only three parameters, this model reproduced the observed data almost exactly as reflected by a goodness of fit close to unity.

Hydration of a structured excess charge distribution: Infrared spectroscopy of the clusters
View Description Hide DescriptionTo explore how a structured excess charge distribution affects the hydration of an anion, we report midIR, argon predissociationspectra for the hydrated superoxide cluster anions, This size range was chosen to establish the evolution of the structures through the putative shell closing [Weber et al., Science 287, 2461 (2000)] for superoxide hydration at the tetrahydrate. Whereas the observed bonding motifs for are those of single water molecules and dimeric subclusters bound to the ion, the pentahydrate spectrum displays strong bands in the region typically associated with ring modes of the water trimer. The present results reinforce the conclusion that the tetrahydrate adopts an especially robust structure in which each water molecule forms a single ionic H bond to one of the lobes of the π^{*} highest occupied molecular orbital in superoxide.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Raman microprobe polarization measurements as a tool for studying the structure and orientation of molecules and clusters incorporated into cubic zeolites: and rings in zeolite A
View Description Hide DescriptionRaman spectra of molecules or clusters incorporated into cubic zeolites are usually studied using microcrystalline powder samples, light being completely unpolarized because of multiple reflection on microcrystal surfaces. Therefore, all information about symmetry of the Ramanactive vibrations of species and orientation of species in zeolite cavities is lost. In order to save this information, we propose to do Raman microprobe polarization measurements of cubic zeolitesingle crystals containing examined species. We theoretically consider examples of highsymmetry anisotropic species (planelike or rodlike molecules or clusters with the threefold or higher major axes) incorporated into cubic zeolite A. We experimentally study polarization and angular dependencies of Raman spectra of and rings incorporated into zeolite A single crystal. The obtained dependencies correspond to the point group symmetry rings oriented by their fourfold axes along the fourfold axes of zeolite and the point group symmetry rings oriented by their threefold axes along the threefold axes of zeolite. The method applied to the and rings is considered as a new powerful tool for studying the structure and orientation of a wide class of cubiczeoliteconfined species.

Nonexponential dielectric relaxation dynamics in supercooled liquid and glassy states of isoamyl bromide and 2methylpentane mixtures
View Description Hide DescriptionThe dielectric spectra of mixtures of the polar solute isoamyl bromide in 2methylpentane have been investigated in the frequency range 1 mHz to 1 MHz and in the temperature range approaching the glass transitiontemperature. The results obtained from the spectra are compared with those obtained recently [J. Chem. Phys. 111, 10979 (1999)] on pure isoamyl bromide. It is found that on increasing dilution with the nonpolar solvent, the width of the curves of the dielectric spectra increase significantly, and this is reflected in the increase in the nonexponential nature of the relaxation dynamics. This is found to be a consequence of the decrease in the cooperativity of the relaxation dynamics and or an increase in the heterogeneity of the solution. The data are found to fit the Havriliak–Negami equation extremely well. The data at low and high frequencies also fits the “universal law,” since the latter is a low and high frequencies limiting case of the Havriliak–Negami equation. The scaling parameters of this law are calculated for the 25 mol % solution of isoamyl bromide in 2methylpentane, and these are shown to experimentally relate to the H–N parameters. The stretched exponential parameter, γ, is estimated as a function of the temperature and is shown to follow the equation Vogel–Fulcher–Tammann equation fits the data of the relaxation peak frequency as a function of the inverse of absolute temperature for the various mixtures quite well, this being possibly a consequence of the temperature dependence of the stretched exponential parameter. The predictions from the mode coupling theory and those by Bertrand and Souletie are verified with the exception that the exponent is found to be much greater than predicted by these theories. The relative predominance of the Johari–Goldstein process in isoamyl bromide increases initially with dilution with 2methylpentane and then disappears as the number density of the independent relaxors increases with further dilution.

Isotopeedited twodimensional vibrational spectroscopy of trialanine in aqueous solution
View Description Hide DescriptionTwodimensional vibrational spectroscopy is applied to the amide I mode of trialanine and two of its isotopomers dissolved in heavy water. We use sitedirected isotope substitution to change the individual frequencies of the coupled oscillators, and hence to modify specific matrix elements of the molecular Hamiltonian. It is found that all of the results can be well described by an excitonic model for the amide I band, using the same coupling strength and dipole–dipole angle for all three isotopomers. This demonstrates that these two spectral parameters are determined by the secondary structure of the peptide, which remains unchanged upon isotope substitution.