Volume 128, Issue 19, 21 May 2008
 COMMUNICATIONS


UVinduced protonation of molecules adsorbed on ice surfaces at low temperature
View Description Hide DescriptionUVirradiation of icefilms adsorbed with methylamine molecules induces protonation of the adsorbate molecules at low temperature . The observation indicates that longlived protonic defects are created in the icefilm by UV light, and they transfer protons to the adsorbate molecules via tunneling mechanism at low temperature. The methylammonium ion formed by proton transfer remains to be stable at the icesurface. It is suggested that this solidphase protonation might play a significant role in the production of molecular ions in interstellar clouds.

Energy difference space random walk to achieve fast free energy calculations
View Description Hide DescriptionA method is proposed to efficiently obtain free energy differences. In the present algorithm, free energy calculations proceed by the realization of an energy difference space random walk. Thereby, this algorithm can greatly improve the sampling of the regions in phase space where target states overlap.

Probing intermolecular couplings in liquid water with twodimensional infrared photon echo spectroscopy
View Description Hide DescriptionTwodimensional infrared photon echo and pump probe studies of the OH stretch vibration provide a sensitive probe of the correlations and couplings in the hydrogen bond network of liquid water. The nonlinear response is simulated using numerical integration of the Schrödinger equation with a Hamiltonian constructed to explicitly treat intermolecular coupling and nonadiabatic effects in the highly disordered singly and doubly excited vibrational exciton manifolds. The simulated twodimensional spectra are in close agreement with our recent experimental results. The high sensitivity of the OH stretch vibration to the bath dynamics is found to arise from intramolecular mixing between states in the twodimensional anharmonic OH stretch potential. Surprisingly small intermolecular couplings reproduce the experimentally observed intermolecular energy transfer times.

Fragility and glassy dynamics of under pressure: Molecular dynamics simulations
View Description Hide DescriptionMolecular dynamics simulations of the glassforming liquid (CKN) were performed from high temperature liquid states down to low temperature glassy states at six different pressures from . The temperature dependence of the structuralrelaxation time indicates that the fragility of liquid CKN changes with pressure. In line with recent proposal [Scopigno et al., Science302, 849 (2003)], the change on liquid fragility is followed by a proportional change of the nonergodicity factor of the corresponding glass at low temperature.
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 ARTICLES

 Theoretical Methods and Algorithms

Eckart axis conditions, Gauss’ principle of least constraint, and the optimal superposition of molecular structures
View Description Hide DescriptionThe relation of the Eckart axis conditions for polyatomic vibrating molecules to the problem of optimal superposition of molecular structures has been pointed out recently [J. Chem. Phys.122, 224105 (2005)]. Here, it is shown that both problems are intimately related to Gauss’ principle of least constraint, for which a concise derivation is presented. In the context of this article, Gauss’ principle leads to a rotational superposition problem of the unconstrained atomic displacements and the corresponding displacements due to a molecular rigidbody motion. The Eckart axis conditions appear here as necessary conditions for a minimum of the constraint function. The importance of Eckart’s problem for extracting the internal motions of macromolecules from simulated molecular dynamics trajectories is pointed out, and it is shown how the case of coarsegrained sampled trajectories can be treated.

Maximum Caliber: A variational approach applied to twostate dynamics
View Description Hide DescriptionWe show how to apply a general theoretical approach to nonequilibrium statistical mechanics, called Maximum Caliber, originally suggested by E. T. Jaynes [Annu. Rev. Phys. Chem.31, 579 (1980)], to a problem of twostate dynamics. Maximum Caliber is a variational principle for dynamics in the same spirit that Maximum Entropy is a variational principle for equilibrium statistical mechanics. The central idea is to compute a dynamical partition function, a sum of weights over all microscopic paths, rather than over microstates. We illustrate the method on the simple problem of twostate dynamics, , first for a single particle, then for particles. Maximum Caliber gives a unified framework for deriving all the relevant dynamical properties, including the microtrajectories and all the moments of the timedependent probability density. While it can readily be used to derive the traditional master equation and the Langevin results, it goes beyond them in also giving trajectory information. For example, we derive the Langevin noise distribution rather than assuming it. As a general approach to solving nonequilibrium statistical mechanics dynamical problems, Maximum Caliber has some advantages: (1) It is partitionfunctionbased, so we can draw insights from similarities to equilibrium statistical mechanics. (2) It is trajectorybased, so it gives more dynamical information than populationbased approaches like master equations; this is particularly important for fewparticle and singlemolecule systems. (3) It gives an unambiguous way to relate flows to forces, which has traditionally posed challenges. (4) Like Maximum Entropy, it may be useful for data analysis, specifically for timedependent phenomena.

Comparison of algorithms for the calculation of molecular vibrational level densities
View Description Hide DescriptionLevel densities of vibrational degrees of freedom are calculated numerically with formulas based on the inversion of the canonical vibrational partition function. The calculated level densities are compared with other approximate equations from literature and with the exact Beyer–Swinehart values, for which a simplified but equivalent version is given. All approximate equations agree at high excitation energies, but our results are vastly superior at low energies for large molecules. The results presented here are therefore of particular relevance for thermal processes of very large molecules, e.g., of biological nature, for which the exact state counting can be prohibitively slow. Furthermore, it is valid for situations where anharmonic motion significantly influences the thermal properties.

Parallel implementation of electronic structure energy, gradient, and Hessian calculations
View Description Hide DescriptionACES III is a newly written program in which the computationally demanding components of the computational chemistry code ACES II [J. F. Stanton et al., Int. J. Quantum Chem.526, 879 (1992); [ACES II program system, University of Florida, 1994] have been redesigned and implemented in parallel. The highlevel algorithms include Hartree–Fock (HF) selfconsistent field (SCF), secondorder manybody perturbation theory [MBPT(2)] energy, gradient, and Hessian, and coupled cluster singles, doubles, and perturbative triples [CCSD(T)] energy and gradient. For SCF, MBPT(2), and CCSD(T), both restricted HF and unrestricted HF reference wave functions are available. For MBPT(2) gradients and Hessians, a restricted openshell HF reference is also supported. The methods are programed in a special language designed for the parallelization project. The language is called super instruction assembly language (SIAL). The design uses an extreme form of objectoriented programing. All compute intensive operations, such as tensor contractions and diagonalizations, all communication operations, and all inputoutput operations are handled by a parallel program written in C and FORTRAN 77. This parallel program, called the super instruction processor (SIP), interprets and executes the SIAL program. By separating the algorithmic complexity (in SIAL) from the complexities of execution on computer hardware (in SIP), a software system is created that allows for very effective optimization and tuning on different hardware architectures with quite manageable effort.

Generalized gradient approximation model exchange holes for rangeseparated hybrids
View Description Hide DescriptionWe propose a general model for the spherically averaged exchange hole corresponding to a generalized gradient approximation (GGA) exchange functional. Parameters are reported for several common GGAs. Our model is based upon that of Ernzerhof and Perdew [J. Chem. Phys.109, 3313 (1998)]. It improves upon the former by precisely reproducing the energy of the parent GGA, and by enabling fully analytic evaluation of rangeseparated hybrid density functionals. Analytic results and preliminary thermochemical tests indicate that our model also improves upon the simple, localdensitybased exchange hole model of Iikura et al. [J. Chem. Phys.115, 3540 (2001)].

A spherical electron cloud hopping model for studying product branching ratios of dissociative recombination
View Description Hide DescriptionA spherical electron cloud hopping (SECH) model is proposed to study the product branching ratios of dissociative recombination (DR) of polyatomic systems. In this model, the fast electroncaptured process is treated as an instantaneous hopping of a cloud of uniform spherical fractional point charges onto a target ion (or molecule). The sum of point charges simulates the incident electron. The sphere radius is determined by a critical distance between the incoming electron and the target, at which the potential energy of the system is equal to that of the electroncaptured molecule in a symmetryallowed electronic state with the same structure as . During the hopping procedure, the excess energies of electron association reaction are dispersed in the kinetic energies of atoms to conserve total energy. The kinetic energies are adjusted by linearly adding atomic momenta in the direction of driving forces induced by the scattering electron. The nuclear dynamics of the resultant molecule are studied by using a direct ab initio dynamics method on the adiabatic potential energy surface of , or together with extra adiabatic surface(s) of . For the latter case, the “fewest switches” surfacehopping algorithm of Tully was adapted to deal with the nonadiabaticity in trajectory propagations. The SECH model has been applied to study the DR of both and . The theoretical results are consistent with the experiment. It was found that water molecules play an important role in determining the product branching ratios of the molecular cluster ion.

Cholesky decomposition of the twoelectron integral matrix in electronic structure calculations
View Description Hide DescriptionA standard Cholesky decomposition of the twoelectron integral matrix leads to integral tables which have a huge number of very small elements. By neglecting these small elements, it is demonstrated that the recursive part of the Cholesky algorithm is no longer a bottleneck in the procedure. It is shown that a very efficient algorithm can be constructed when family type basis sets are adopted. For subsequent calculations, it is argued that twoelectron integrals represented by Cholesky integral tables have the same potential for simplifications as density fitting. Compared to density fitting, a Cholesky decomposition of the twoelectron matrix is not subjected to the problem of defining an auxiliary basis for obtaining a fixed accuracy in a calculation since the accuracy simply derives from the choice of a threshold for the decomposition procedure. A particularly robust algorithm for solving the restricted Hartree–Fock (RHF) equations can be speeded up if one has access to an ordered set of integral tables. In a test calculation on a linear chain of beryllium atoms, the advocated RHF algorithm nicely converged, but where the standard direct inversion in iterative space method converged very slowly to an excited state.

The accuracy of rotational constants predicted by highlevel quantumchemical calculations. I. molecules containing firstrow atoms
View Description Hide DescriptionA statistical analysis of the accuracy of theoretically predicted rotational constants is presented based on the data for a total of and 97 isotopologues. Special focus is given on the treatment of electron correlation by using coupledcluster methods up to quadruple excitations, core correlation, basisset effects, zeropoint vibrational corrections, and the electronic contribution to the rotational constants. The high accuracy achieved in the present investigation is demonstrated by the fact that at our best theoretical level, termed as , the mean absolute error is 0.04% and the standard deviation is 0.07% in comparison with the available experimental data. The importance of higher excitations, core correlation, and zeropoint vibrational effects is emphasized, while the electronic contribution is found to be less important.

Using a nondirect product discrete variable representation for angular coordinates to compute vibrational levels of polyatomic molecules
View Description Hide DescriptionIn this paper we test a nondirect product discrete variable representation (DVR) method for solving the bend vibration problem and compare it with wellestablished direct product DVR and finite basis representation approaches.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Separation of longrange and shortrange interactions in Rydberg states of diatomic molecules
View Description Hide DescriptionObservation and analysis of the , , and Rydberg series of CaF in the range is presented. Simultaneous analysis of the , , and Rydberg series of CaF, combined with significant improvements to the longrange model for nonpenetrating Rydberg states, provides a generally applicable scheme for separating the effects of the longrange (electric multipole and polarization) and shortrange (core penetration) interactions between the Rydberg electron and ion core in diatomic molecules. Techniques for rigorous assignment of nonpenetrating states, as well as extensions of the longrange model, are discussed. Explicit formulas for the first and secondorder matrix elements of the first four anisotropic electric multipole interactions (electric dipole, quadrupole, octupole, and hexadecapole) are given. The discrepancies between the observed behavior and that predicted by the longrange model, which are particularly significant for the series, are shown to be due to penetration of the Rydberg electron wavefunction within the ion core. We show that these penetration effects can be understood within the framework of ligand field theory and conclude with a discussion of the relative contributions of the long and shortrange interactions to the quantum defects of the corepenetrating “,” “,” and “” series of CaF.

Theoretical study of the dynamics of the and reactions using a specificreactionparameter semiempirical Hamiltonian
View Description Hide DescriptionWe present a theoretical study of the reactions of hydrogen atoms with methane and ethane molecules and isotopomers. Highaccuracy electronicstructure calculations have been carried out to characterize representative regions of the potentialenergy surface (PES) of various reaction pathways, including H abstraction and H exchange. These ab initio calculations have been subsequently employed to derive an improved set of parameters for the modified symmetricallyorthogonalized intermediate neglect of differential overlap (MSINDO) semiempirical Hamiltonian, which are specific to the family of reactions. The specificreactionparameter (SRP) Hamiltonian has then been used to perform a quasiclassicaltrajectory study of both the and reactions. The calculated values of dynamics properties of the reaction and isotopologues, including alkyl product speed distributions, diatomic product internalstate distributions, and cross sections, are generally in good agreement with experiment and with the results provided by the ZBB3 PES [Z. Xie et al., J. Chem. Phys.125, 133120 (2006)]. The results of trajectories propagated with the SRP Hamiltonian for the reaction also agree with experiment. The level of agreement between the results calculated with the SRP Hamiltonian and experiment in both the and reactions indicates that semiempirical Hamiltonians can be improved for not only a specific reaction but also a family of reactions.

The reaction: A triple oxygen isotope perspective on the reaction dynamics and atmospheric implications for the transfer of the ozone isotope anomaly
View Description Hide DescriptionAtmospheric nitrate shows a large oxygen isotope anomaly , characterized by an excess enrichment of over , similar to the ozone molecule. Modeling and observations assign this specific isotopic composition mainly to the photochemical steady state that exists in the atmosphere between ozone and nitrate precursors, namely, the nitrogen oxides . However, this transfer is poorly quantified and is built on unverified assumptions about which oxygen atoms of ozone are transferred to , greatly weakening any interpretation of the nitrate oxygen isotopic composition in terms of chemical reaction pathways and the oxidation state of the atmosphere. With the aim to improve our understanding and quantify how nitrate inherits this unusual isotopic composition, we have carried out a triple isotope study of the reaction. Using ozone intramolecular isotope distributions available in the literature, we have found that the central atom of the ozone is abstracted by NO with a probability of at room temperature. This result is at least qualitatively supported by dynamical reaction experiments, the nonArrhenius behavior of the kinetic rate of this reaction, and the kinetic isotope fractionation factor. Finally, we have established the transfer function of the isotope anomaly of to , which is described by the linear relationship , with and . Such a relationship can be easily incorporated into models dealing with the propagation of the ozoneisotope anomaly among oxygenbearing species in the atmosphere and should help to better interpret the oxygen isotope anomaly of atmospheric nitrate in terms of its formation reaction pathways.

Size and chargedependent geometric and electronic structures of clusters by firstprinciples simulations
View Description Hide DescriptionNeutral and negatively chargedbismuth clusters, and , are investigated by firstprinciples simulations with the scalarrelativistic projectoraugmented wave potential and the spinpolarized generalized gradient approximation. Both types of clusters show sizedependent oddeven oscillations in stability, density of states, and vertical and adiabatic electron affinities, in close agreement with experiment. The negative charge thoroughly reverses the oscillations and considerably influences the geometricstructures, particularly of the oddsized clusters. We note that most atoms in the ground states and the lowlying isomers are three coordinated with a quasilayerlike growth mode based on pentagon units, due to a weak hybridization. The cluster is found to prefer a small elongated tubelike structure with the surface consists of six curvedpentagon rings and two triangular facets, which may be the basis for the formation of bismuth nanotubes experimentally reported.

Topology of magneticfield induced electron current density in the cubane molecule
View Description Hide DescriptionA spatial model of the electronic current density induced in the cubane molecule by applying an external magneticfield has been constructed employing quantum mechanical methods at the Hartree–Fock level of accuracy. The topological features of the current densityvector field are described via a stagnation graph that shows the isolated points and the lines at which the current vanishes. Shielding density maps based on the differential Biot–Savart law, along with a collection of current density maps, explain magnetic shielding at hydrogen and carbon nuclei, and virtual shielding at ring and cage centers.

Electron impact ionization of size selected hydrogen clusters : Ion fragment and neutral size distributions
View Description Hide DescriptionClusters consisting of normal molecules, produced in a free jet expansion, are size selected by diffraction from a transmission nanograting prior to electron impact ionization. For each neutral cluster , the relative intensities of the ion fragments are measured with a mass spectrometer. is found to be the most abundant fragment up to . With a further increase in , the abundances of , , , and first increase and, after passing through a maximum, approach each other. At , they are about the same and more than a factor of 2 and 3 larger than for and , respectively. For a given neutral cluster size, the intensities of the ion fragments follow a Poisson distribution. The fragmentation probabilities are used to determine the neutral cluster size distribution produced in the expansion at a source temperature of and a source pressure of . The distribution shows no clear evidence of a magic number as predicted by theory and found in experiments with pure paraclusters. The ion fragment distributions are also used to extract information on the internal energy distribution of the ions produced in the reaction, which is initiated upon ionization of the cluster. The internal energy is assumed to be rapidly equilibrated and to determine the number of molecules subsequently evaporated. The internal energy distribution found in this way is in good agreement with data obtained in an earlier independent merged beam scattering experiment.

Time dependent quantum dynamics study of the proton transfer reaction
View Description Hide DescriptionThe proton transferreaction was studied using the time dependent real wave packet quantum dynamics method at the helicity decoupling level, considering the molecular ion in the (, ) vibrorotational states and a wide collision energy interval. The calculated reaction probabilities and reaction cross sections were in a rather good agreement with reanalyzed previous exact quantum dynamics results, where a much smaller collision energy interval was considered. Also, a quite good agreement with experimental data was found. These results suggested the adequacy of the approach used here to describe this and related systems.