Volume 119, Issue 13, 01 October 2003
 COMMUNICATIONS


Sampling the complex energy landscape of a simple βhairpin
View Description Hide DescriptionThe folding trajectories of a 16residue βhairpin are studied using the activation–relaxation technique with a generic energymodel. From more than 70 trajectories, three folding pathways emerge. All involve a simultaneous optimization of the complete hydrophobic and hydrogen bondinginteractions. The first two follow closely those observed by previous theoretical studies, while the third can be described as a reptation move of one strand of the βsheet with respect to the other. This reptation move indicates that nonnative interactions can play a dominant role in the folding of secondary structures.

Dissociative chemisorption of methane on Ni(100): Threshold energy from eigenstateresolved sticking measurements
View Description Hide DescriptionA threeparameter microcanonical theory of gassurface reactivity is used to model the dissociative sticking of vibrationally excited methane with two quanta of energy in the antisymmetric C–H stretch. An apparent threshold energy for C–H bond cleavage of incident on Ni(100) of 65 kJ/mol is found, in quantitative agreement with ab initio quantum chemistry calculations but 38 kJ/mol less than GGADFT calculations. Successful microcanonical analysis and prediction of recent thermal equilibrium and various nonequilibrium dissociative chemisorption experiments for methane on Ni(100) provide no evidence for modespecific reactivity.

Solvation in molecular ionic liquids
View Description Hide DescriptionSolvation in 1ethyl3methylimidazolium chloride and 1ethyl3methylimidazolium hexafluorophosphate is studied via molecular dynamics simulations by employing a diatomic solute as a probe. It is found that solvent fluctuations are chacterized by at least two distinct dynamics occurring on vastly different time scales—rapid subpicosecond dynamics arising mainly from anion translations and slow relaxation ascribed to anion and cation diffusions. Fast subpicosecond dynamics are responsible for more than 50% of the entire relaxation of solvent fluctuations in the temperature range It is also found that solvent spectral shifts and reorganization free energies in these liquids are comparable to those in ambient water.

First compounds with argon–carbon and argon–silicon chemical bonds
View Description Hide DescriptionArgon is an extremely chemically inert element. HArF is presently the only experimentally known neutral molecule containing a chemically bound argon atom. Ab initio calculations at the MP2 and CCSD(T) levels presented here suggest, however, the existence of whole families of additional molecules. Explicitly predicted are FArCCH, with an argon–carbon bond, and with an argon–silicon bond. These metastable compounds are found to be protected from decomposition by relatively high energy barriers. Other organo–argon and organosilicon molecules derived from the above should be equally stable. The results may open the way to a substantial field of “argon chemistry.”

Water–silica surface interactions: A combined quantumclassical molecular dynamic study of energetics and reaction pathways
View Description Hide DescriptionWe report studies of water–silica surfaceinteractions using a hybrid firstprinciples–classical molecular dynamics simulation method. The quantum region, which is treated with high accuracy density functional theory, is embedded in a large amorphous matrix described by classical potentials. With this model, both nondissociative and dissociative processes of water molecules at a twomembered ring site, which has been found experimentally on the surface, are studied. Our investigations provide qualitative and quantitative descriptions of the reaction pathways and energy landscape. A barrierfree double hydrogen atom transfer process is observed.
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 ARTICLES

 Theoretical Methods and Algorithms

Brownian dynamics simulations on a hypersphere in 4space
View Description Hide DescriptionWe describe an algorithm for performing Brownian dynamics simulations of particles diffusing on a hypersphere in four dimensions. The system is chosen due to recent interest in doing computer simulations in a closed space where periodic boundary conditions can be avoided. We specifically address the question how to generate a random walk on the 3sphere, starting from the solution of the corresponding diffusion equation, and we also discuss an efficient implementation based on controlled approximations. Since is a closed manifold (space), the average square displacement during a random walk is no longer proportional to the elapsed time, as in Instead, its time rate of change is continuously decreasing, and approaches zero as time becomes large. We show, however, that the effective diffusion coefficient can still be obtained from the time dependence of the square displacement.

Reproducing kernel Hilbert space interpolation methods as a paradigm of high dimensional model representations: Application to multidimensional potential energy surface construction
View Description Hide DescriptionA generic high dimensional model representation (HDMR) method is presented for approximating multivariate functions in terms of functions of fewer variables and for going beyond the tensorproduct formulation. Within the framework of reproducing kernel Hilbert space (RKHS) interpolation techniques, an HDMR is formulated for constructing global potential energy surfaces. The HDMR tools in conjunction with a successive multilevel decomposition technique provide efficient and accurate procedures for reducing a multidimensional interpolation problem to smaller, independent subproblems. It is shown that, when compared to the conventional tensorproduct approach, the RKHS–HDMR methods can accurately produce smooth potential energy surfaces over dynamically relevant, nonrectangular regions using far fewer ab initio data points. Numerical results are given for a reduced twolevel RKHS–HDMR of the reactive system. The proposed RKHS–HDMR is intimately related to Gordon’s blendingfunction methods for multivariate interpolation and approximation. The general findings in the paper and the successful illustration provide a foundation for further applications of the techniques.

Approximate onematrix functionals for the electron–electron repulsion energy from geminal theories
View Description Hide DescriptionA simple extension of the antisymmetrized product of strongly orthogonal geminals theory produces a only” onematrix functional for the electron–electron repulsion energy of a closedshell system that is exact for twoelectron singlet ground states, sizeextensive, and incorporates some intergeminal correlation and thus dispersion effects. The functional is defined only for onematrices with occupation numbers that can be arranged into sets with elements that sum up to two. Its possible generalizations are discussed.

Study of intramolecular electron transfer with a twostate model based on the orbital deletion procedure
View Description Hide DescriptionCarbocations are often used as models for donorbridgeacceptor complexes to study the role of bridges in the electron transport process. In an attempt to delineate the electron delocalization effect from the bridge to the positively charge terminal in the unrestricted Hartree–Fock (UHF) wave functions which are often used for diabatic states to compute the electronic coupling energy, we propose to employ an orbital deletion procedure (ODP) to generate the strictly localized wave functions for the initial (A) and final (B) diabatic states in the electron transfer process in the carbocations of The electronic coupling energy can be subsequently computed with the two diabatic states by solving a secular equation. The comparison of our results with previous theoretical studies based on the widely adopted chargelocalized UHF wave functions and Koopmans’ theorem in the case of positively charged 1,3dimethylenebicyclo[1.1.1]pentane reveals that chargelocalized UHF wave functions overestimates the electronic coupling compared with our method and the Koopmans’ theorem. A further study incorporating four water molecules suggests that the aqueous solution has very limited effect on in the positively charged 1,3dimethylenebicyclo[1.1.1]pentane. To demonstrate the applicability of the current twostate model based on the ODP strategy, we also examined the electron transport across strainfree linear alkyl chains and linear πconjugated bridges

Properties of the exchange hole under an appropriate coordinate transformation
View Description Hide DescriptionUnder a general coordinate transformation, the exchange hole can be made localized, as shown by Springborg [Chem. Phys. Lett. 308, 83 (1999)]. While the conventional or untransformed hole is referenced to the position of an electron, the maximally localized one is referenced to the center of mass of an electron pair. The benefit of a more localized hole is that semilocal density functionals model it and the associated energy density more easily than they model the conventional ones. We show that, out of the class of general coordinate transformations, one can identify a subset (including the maximally localized case) which we call appropriate. Under an appropriate coordinate transformation, while the exchange hole is no longer always normalized, it retains other familiar and useful features such as the conventional ontop value and uniformdensity limit. In particular, its system average remains invariant, retaining the normalization sum rule and the negativity property. Therefore, unlike the exchange energy density the realspace analysis of the exchange energy [into contributions from different electron–electron separations (u)] is uniquely defined. Thus the realspace analysis provides an alternative way to make simple and fair but detailed comparisons of approximate and exact exchange. As a byproduct, we show how to improve the accuracy of the Negele–Vautherin model for the density matrix expansion of the exchange energy by imposing negativity and sum rule constraints on the system average of its maximally localized hole.

Estimating Bohm’s quantum force using Bayesian statistics
View Description Hide DescriptionIn this paper we develop an approximate methodológy for estimating the multidimensional quantum density associated with a statistical bundle of de Broglie–Bohm trajectories. The quantum density is constructed as a discrete sum of nonequivalent Gaussian components. We incorporate the ideas of Bayesianstatistical analysis and an expectationmaximization procedure to compute an approximate quantum force that drives the statistical ensemble quantum trajectories.

Density functional calculations, using Slater basis sets, with exact exchange
View Description Hide DescriptionWe report the extension of our Slatertype orbital (STO) basis code for density functional theory(DFT) calculations to include “exact exchange,” so that Hartree–Fock and hybrid DFT calculations may be performed. Exchange integrals are evaluated through the insertion of a resolution of the identity, using the same auxiliary STO basis set which was used in our original generalized gradient approximationDFT studies. Threecenter twoelectron integrals are evaluated by quadrature. A scheme for introducing diatomic auxiliary STO basis sets is introduced, which enables much larger calculations to be performed. We also report an extension to the evaluation of secondorder molecular properties using these functionals. Calculations for excitation energies to valence and Rydberg states are included.

Hydrodynamic analysis of dynamical tunneling
View Description Hide DescriptionThe process of dynamical tunneling between local mode states is analyzed within the Bohmian approach to quantum mechanics. A number of quantum trajectories are followed for both a coupled Morse potential and the Barbanis potential. The superposition of nearly degenerate eigenstates leads to the formation of numerous permanent nodes concentrated near the potential valley. Around these nodes,vortices are evident on the flux map. Quantum trajectories can be attracted by a vortex and their velocity and kinetic energy will be significantly changed as they spiral around the vortex. However, trajectories starting remotely from vortices reflect more realistically the transition between a pair of localized states. These quantum trajectories can go through one or more regions where the potential energy is higher than the total energy. Hence, barrier tunneling accompanies dynamical tunneling.

Collective probabilities algorithm for surface hopping calculations
View Description Hide DescriptionGeneral equations that transition probabilities of the hopping algorithms in surface hopping calculations must obey to assure the equality between the average quantum and classical populations are derived. These equations are solved for two particular cases. In the first it is assumed that probabilities are the same for all trajectories and that the number of hops is kept to a minimum. These assumptions specify the collective probabilities (CP) algorithm, for which the transition probabilities depend on the average populations for all trajectories. In the second case, the probabilities for each trajectory are supposed to be completely independent of the results from the other trajectories. There is, then, a unique solution of the general equations assuring that the transition probabilities are equal to the quantum population of the target state, which is referred to as the independent probabilities (IP) algorithm. The fewest switches (FS) algorithm developed by Tully is accordingly understood as an approximate hopping algorithm which takes elements from the accurate CP and IP solutions. A numerical test of all these hopping algorithms is carried out for a onedimensional twostate problem with two avoiding crossings which shows the accuracy and computational efficiency of the collective probabilities algorithm proposed, the limitations of the FS algorithm and the similarity between the results offered by the IP algorithm and those obtained with the Ehrenfest method.

Geminal wave functions with Jastrow correlation: A first application to atoms
View Description Hide DescriptionWe introduce a simple generalization of the wellknown geminal wave function already applied in quantum chemistry to atoms and small molecules. The main feature of the proposed wave function is the presence of the antisymmetric geminal part together with a Jastrow factor. Both the geminal and the Jastrow play a crucial role in determining the remarkable accuracy of the manybody state: the former permits the correct treatment of the nondynamic correlation effects; the latter allows the wave function to fulfill the cusp conditions and makes the geminal expansion rapidly converge to the lowest possible variational energies. This ansatz is expected to provide a substantial part of the correlation energy for general complex atomic and molecular systems. The antisymmetric geminal term can be written as a single determinant even in the polarized cases. In general, therefore, the computational effort to sample this correlated wave function is not very demanding, the scaling of the algorithm with the number of atoms being comparable with the simplest Hartree–Fock calculation. We applied this Jastrowgeminal approach to atoms up to always getting good variational energies, by particularly improving those with a strong multiconfigurational nature. Our wave function is very useful for Monte Carlo techniques, such as fixed node. Indeed, the nodal surface obtained within this approach can be substantially improved through the geminal expansion.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

van der Waals states in ozone and their influence on the threshold spectrum of I. Bound states
View Description Hide DescriptionThreshold spectra of several isotopomers of ozone are studied using accurate quantum mechanical calculations and an ab initiopotential energy surface. Shallow van der Waals minima in the dissociation channels, separated from the deep main wells by an high barrier, are shown to accommodate long progressions of assignable states. As a result, dense vibrational spectrum of ozone near dissociation is dominated by van der Waalstype states for all studied isotope compositions.

Ab initio theoretical studies of potential energy surfaces in the photodissociation of the vinyl radical. I. state dissociation
View Description Hide DescriptionThe mechanism of photodissociation of the vinyl radical, starting from the first doublet excited state was studied with highlevel ab initio methods as well as with ab initio direct dynamics. Geometry optimizations of stationary points and surface crossing seams were performed with complete active space selfconsistent field (CASSCF) method, and the energies were reevaluated with singlepoint multireference single and double excitation configuration interaction (MRCISD) calculations. Both internal conversion and intersystem crossing channels, which could bring the excited vinyl radical down to the ground statepotential energy surface leading to dissociation on the ground state, have been identified within planar twisted and symmetry. Direct dynamics calculation indicates that the most feasible reaction channel is the direct internal conversion from to the ground state within planar symmetry, through a minimum of seam of crossing (conical intersection) at an energy of about 80 kcal/mol (with respect to the groundstate equilibrium geometry). The other internal conversions from to through conical intersections within twisted symmetry require energies of about 80 and 75 kcal/mol at the two minima of seam of crossing, respectively, and they are not favored dynamically without initial outofplane vibrational excitation. The intersystem crossing channels between and the lowest quartet state and and within twisted and symmetry are not efficient due to the high energy of the minima of seam of crossing as well as the small spin–orbit coupling.

ZEKE photoelectron spectroscopy of the silver and copperammonia complexes
View Description Hide DescriptionThe singlephoton zero kinetic energy (ZEKE) photoelectron spectra of the silver and copperammonia 1:1 complexes have been observed in order to investigate the vibrational structures of their corresponding ions. The adiabatic ionization potentials (I.P.) of and decrease from those of the free metal atoms by 1.68 and 1.97 eV, respectively. The intermolecular stretching frequencies of the ionized complexes were determined to be 375 cm^{−1} for and 470 cm^{−1} for These observations indicate that the binding is stronger than the binding, consistent with the previous collision induced dissociation experiments. The binding energy of is found to be larger than that of in the neutral state as well from the observed I.P. shifts and the binding energies of the ionized complexes. This is also consistent with the smaller redshift of the origin band of on deuteration and the Franck–Condon intensity patterns observed in the ZEKE spectra. The stronger bonding in the neutral complex is attributed to the more efficient hybridization in the Cu atom.

Femtosecond photon echo measurements of electronic coherence relaxation between the and states of in the presence of He, Ar,
View Description Hide DescriptionPhoton echo and reverse transient gratingmeasurements of the loss of electronic coherence for molecular iodine are presented. Systematic measurements of the coherence decay rate were made as a function of buffer gas. From the dependence of decay rate on numerical density, we calculated experimental cross sections of decoherence. These values range from 135 Å^{2} for helium to 1170 Å^{2} for We find LennardJones parameters for the longrange interactions responsible for decoherence which can be modeled by dispersion forces.

Entrance channel localized states in ozone: Possible application to helium nanodroplet isolation spectroscopy
View Description Hide DescriptionAccurate calculations of the bound rovibrational states of ozone are performed in the region of high vibrational excitation. Two unusual vibrational states localized in the far van der Waals region are discovered. They can be considered as the ground vibrational states of even and odd symmetries bound in the shallow van der Waals well. Properties of these states are presented and discussed, which opens possibilities for experimental realization of the helium nanodroplet isolation rovibrational spectroscopy of ozone.