Volume 122, Issue 1, 01 January 2005
 ARTICLES

 Theoretical Methods and Algorithms

Coulomb potentials in two and three dimensions under periodic boundary conditions
View Description Hide DescriptionA method to sum over logarithmic potential in twodimensions (2D) and Coulomb potential in three dimensions (3D) with periodic boundary conditions in all directions is given. We consider the most general form of unit cells, the rhombic cell in 2D and the triclinic cell in 3D. For the 3D case, this paper presents a generalization of Sperb’s work [R. Sperb, Mol. Simulation 22, 199 (1999)]. The expressions derived in this work converge extremely fast in all region of the simulation cell. We also obtain results for slab geometry. Furthermore, selfenergies for both 2D as well as 3D cases are derived. Our general formulas can be employed to obtain Madelung constants for periodic structures.

Gaining mechanistic insight from closed loop learning control: The importance of basis in searching the phase space
View Description Hide DescriptionThis paper discusses different routes to gaining insight from closed loop learning control experiments. We focus on the role of the basis in which pulse shapes are encoded and the algorithmic search is performed. We demonstrate that a physically motivated, nonlinear basis change can reduce the dimensionality of the phase space to one or two degrees of freedom. The dependence of the control goal on the most important degrees of freedom can then be mapped out in detail, leading toward a better understanding of the control mechanism. We discuss simulations and experiments in selective molecular fragmentation using shaped ultrafast laser pulses.

Densityfunctional theorysymmetryadapted intermolecular perturbation theory with density fitting: A new efficient method to study intermolecular interaction energies
View Description Hide DescriptionThe previously developed DFTSAPT approach, which combines symmetryadapted intermolecular perturbation theory (SAPT) with a densityfunctional theory(DFT) representation of the monomers, has been implemented by using density fitting of twoelectron objects. This approach, termed DFDFTSAPT, scales with the fifth power of the molecular size and with the third power upon increase of the basis set size for a given dimer, thus drastically reducing the cost of the conventional DFTSAPT method. The accuracy of the density fitting approximation has been tested for the ethyne dimer. It has been found that the errors in the interaction energies due to density fitting are below with suitable auxiliary basis sets and thus one or two orders of magnitude smaller than the errors due to the use of a limited atomic orbital basis set. An investigation of three prominent structures of the benzene dimer, namely, the T shaped, parallel displaced, and sandwich geometries, employing basis sets of up to augmented quadrupleζ quality shows that DFDFTSAPT outperforms secondorder MøllerPlesset theory (MP2) and gives total interaction energies which are close to the best estimates infered from combining the results of MP2 and coupledcluster theory with single, double, and perturbative triple excitations.

Geometry optimization of molecular clusters and complexes using scaled internal coordinates
View Description Hide DescriptionScaled internal coordinates are introduced for use in the geometry optimization of systems composed of multiple fragments, such as solvated molecules, clusters, and biomolecular complexes. The new coordinates are related to bond lengths, bond angles and torsion angles by geometrydependent scaling factors. The scaling factors serve to expedite the optimization of complexes containing outlying fragments, without hindering the optimization of the intramolecular degrees of freedom. Trial calculations indicate that, at asymptotic separations, the scaling factors improve the rate of convergence by a factor of 4 to 5.

An extended hybrid density functional (X3LYP) with improved descriptions of nonbond interactions and thermodynamic properties of molecular systems
View Description Hide DescriptionWe derive here the form for the exact exchange energy density for a density that decays with Gaussiantype behavior at long range. This functional is intermediate between the B88 and the PW91 exchange functionals. Using this modified functional to match the form expected for Gaussian densities, we propose the X3LYP extended functional. We find that X3LYP significantly outperforms Becke three parameter Lee–Yang–Parr (B3LYP) for describing van der Waals and hydrogen bond interactions, while performing slightly better than B3LYP for predicting heats of formation,ionization potentials,electron affinities,proton affinities, and total atomic energies as validated with the extended G2 set of atoms and molecules. Thus X3LYP greatly enlarges the field of applications for density functional theory. In particular the success of X3LYP in describing the water dimer (with and within the error bars of the most accurate determinations) makes it an excellent candidate for predicting accurate ligand–protein and ligand–DNA interactions.

Highlevel ab initio studies of unimolecular dissociation of the groundstate radical
View Description Hide DescriptionA comprehensive study of the unimolecular dissociation of the radical on the ground doublet and excited quartet potential energy surfaces has been carried out with multireference single and double excitation configuration interaction and secondorder multireference perturbation methods. Two forms of the radical have been located in the linear and cyclic region of the lowest doublet potential energy surface with an isomerization barrier of 62.2 kcal/mol above the linear Three equivalent minima of cyclic are connected by low barrier, meaning the molecule is free to undergo pseudorotation. The cyclic is metastable with respect to ground state products, and dissociation must occur via intersystem crossing to a quartet potential energy surface. Minima on the seams of crossing between the doublet and quartet potential surfaces are found to lie substantially higher in energy than the cyclic minima. This strongly suggests that cyclic possesses a long collisionfree lifetime even if formed with substantial internal excitation.

The extrapolation of oneelectron basis sets in electronic structure calculations: How it should work and how it can be made to work
View Description Hide DescriptionWe consider the extrapolation of the oneelectron basis to the basis set limit in the context of coupled cluster calculations. We produce extrapolation coefficients that produce much more accurate results than previous extrapolation forms. These are determined by fitting to accurate benchmark results. For coupled cluster singles doubles energies, we take our benchmark results from the work of Klopper that explicitly includes the interelectronic distance. For the perturbative triples energies, our benchmark results are obtained from large eventempered basis set calculations.

Anharmonic vibrational properties by a fully automated secondorder perturbative approach
View Description Hide DescriptionThis paper describes the implementation of a fully automated code for the building of anharmonic force constants and their use in a secondorder perturbative evaluation of vibrorotational parameters. Next, a number of test applications are discussed, which show the strengths and limits of various computational levels.

The aromatic fluctuation index (FLU): A new aromaticity index based on electron delocalization
View Description Hide DescriptionIn this work, the aromatic fluctuation index (FLU) that describes the fluctuation of electronic charge between adjacent atoms in a given ring is introduced as a new aromaticity measure. This new electronic criterion of aromaticity is based on the fact that aromaticity is related to the cyclic delocalized circulation of π electrons. It is defined not only considering the amount of electron sharing between contiguous atoms, which should be substantial in aromatic molecules, but also taking into account the similarity of electron sharing between adjacent atoms. For a series of rings in 15 planar polycyclic aromatic hydrocarbons, we have found that, in general, FLU is strongly correlated with other widely used indicators of local aromaticity, such as the harmonicoscillator model of aromaticity, the nucleus independent chemical shift, and the paradelocalization index (PDI). In contrast to PDI, the FLU index can be applied to study the aromaticity of rings with any number of members and it can be used to analyze both the local and global aromatic character of rings and molecules.

Shortrange exchange and correlation energy density functionals: Beyond the localdensity approximation
View Description Hide DescriptionWe propose approximations which go beyond the localdensity approximation for the shortrange exchange and correlationdensity functionals appearing in a multideterminantal extension of the Kohn–Sham scheme. A first approximation consists of defining locally the range of the interaction in the correlation functional. Another approximation, more conventional, is based on a gradient expansion of the shortrange exchangecorrelation functional. Finally, we also test a shortrange generalizedgradient approximation by extending the Perdew–Burke–Ernzerhof exchangecorrelation functional to shortrange interactions.

Electron–molecule scattering calculations in a 3D finite element Rmatrix approach
View Description Hide DescriptionWe have implemented a threedimensional finite element approach, based on tricubic polynomials in spherical coordinates, which solves the Schrödinger equation for scattering of a low energy electron from a molecule, approximating the electron exchange as a local potential. The potential is treated as a sum of three terms: electrostatic, exchange, and polarization. The electrostatic term can be extracted directly from ab initio codes (GAUSSIAN 98 in the work described here), while the exchange term is approximated using different local density functionals. A local polarization potential approximately describes the long range attraction to the molecular target induced by the scattering electron.

Normconserving Hartree–Fock pseudopotentials and their asymptotic behavior
View Description Hide DescriptionWe investigate the properties of normconserving pseudopotentials (effective core potentials) generated by inversion of the Hartree–Fock equations. In particular, we investigate the asymptotic behavior as and find that such pseudopotentials are nonlocal over all space, apart from a few special cases such as H and He. Such extreme nonlocality leads to a lack of transferability and, within periodic boundary conditions, an undefined total energy. The extreme nonlocality must therefore be removed, and we argue that the best way to accomplish this is a minor relaxation of the normconservation condition. This is implemented, and pseudopotentials for the atoms H–Ar are constructed and tested.

Variational optimization of effective atom centered potentials for molecular properties
View Description Hide DescriptionIn plane wave based electronic structure calculations the interaction of core and valence electrons is usually represented by atomic effective core potentials. They are constructed in such a way that the shape of the atomic valence orbitals outside a certain core radius is reproduced correctly with respect to the corresponding allelectron calculations. Here we present a method which, in conjunction with density functionalperturbation theory, allows to optimize effective core potentials in order to reproduce groundstate molecular properties from arbitrarily accurate reference calculations within standard density functional calculations. We demonstrate the wide range of possible applications in theoretical chemistry of such optimized effective core potentials (OECPs) by means of two examples. We first use OECPs to tackle the link atom problem in quantum mechanics/molecular mechanics (QM/MM) schemes proposing a fully automatized procedure for the design of link OECPs, which are designed in such a way that they minimally perturb the electronic structure in the QM region. In the second application, we use OECPs in two sample molecules (water and acetic acid) such as to reproduce electronic densities and derived molecular properties of hybrid (B3LYP) quality within general gradient approximated (BLYP) density functional calculations.

Unbiased estimators for spatial distribution functions of classical fluids
View Description Hide DescriptionWe use a statisticalmechanical identity closely related to the familiar virial theorem, to derive unbiased estimators for spatialdistribution functions of classical fluids. In particular, we obtain estimators for both the fluid density in the vicinity of a fixed solute and the pair correlation of a homogeneous classical fluid. We illustrate the utility of our estimators with numerical examples, which reveal advantages over traditional histogrambased methods of computing such distributions.

Toward a robust and general molecular simulation method for computing solidliquid coexistence
View Description Hide DescriptionA rigorous and generally applicable method for computing solidliquid coexistence is presented. The method overcomes some of the technical difficulties associated with other solidliquid simulation procedures and can be implemented within either a molecular dynamics or Monte Carlo framework. The method consists of three steps: First, relative Gibbs free energy curves are created for the solid and liquid phases using histogram reweighting. Next, the free energy difference between the solid and liquid phases is evaluated at a single state point by integrating along a pseudosupercritical transformation path that connects the two phases. Using this result, the solid and liquidfree energy curves are referenced to a common point, allowing a single coexistence point to be determined. Finally, GibbsDuhem integration is used to determine the full coexistence curve. To evaluate its utility, this method is applied to the LennardJones and NaCl systems. Results for solidliquid coexistence agree with previous calculations for these systems. In addition, it is shown that the NaCl model does not correctly describe solidliquid coexistence at high pressures. An analysis of the accuracy of the method indicates that the results are most sensitive to the transformationfree energy calculation.

The slowscale stochastic simulation algorithm
View Description Hide DescriptionReactions in real chemical systems often take place on vastly different time scales, with “fast” reaction channels firing very much more frequently than “slow” ones. These firings will be interdependent if, as is usually the case, the fast and slow reactions involve some of the same species. An exact stochastic simulation of such a system will necessarily spend most of its time simulating the more numerous fast reaction events. This is a frustratingly inefficient allocation of computational effort when dynamical stiffness is present, since in that case a fast reaction event will be of much less importance to the system’s evolution than will a slow reaction event. For such situations, this paper develops a systematic approximate theory that allows one to stochastically advance the system in time by simulating the firings of only the slow reaction events. Developing an effective strategy to implement this theory poses some challenges, but as is illustrated here for two simple systems, when those challenges can be overcome, very substantial increases in simulation speed can be realized.

Critical examination of the supermolecule density functional theory calculations of intermolecular interactions
View Description Hide DescriptionThe results of calculations employing twelve different combinations of exchange and correlation functionals are compared with results of ab initio calculations for two different configurations of the water dimer and three different configurations of the thymineadenine complex. None of the density functional theory(DFT) treatments could properly reproduce the results of coupledcluster calculations for all configurations examined. The DFT approaches perform well when the interaction energy is dominated by the electrostatic component and the dispersion energy is less important. Two mechanisms that compensate for the missing dispersion component were identified. The first one is the decrease of the magnitude of the intermolecular exchangerepulsion and the second one is the increase of the magnitude of the attractive deformation energy. For some functionals both effects are observed together, but for some other ones only the second effect occurs. The three correlation functionals that were examined were found to make only very small contributions to the deformation energy. The examination of angular and distance dependence of the interactions shows that the currently available DFT approaches are not suitable for developing intermolecular potential energy surfaces. They could however be used to find global minima on potential energy surfaces governed by intermolecular electrostaticinteractions. Additional single point ab initio calculations are recommended as the means of validating optimized structures.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Quantum and quasiclassical studies of the reaction using benchmark potential surfaces
View Description Hide DescriptionWe have performed quantum mechanical (QM) dynamics calculations within the independentstate approximation with new benchmark triplet and surfaces [B. Ramachandran et al., J. Chem. Phys. 119, 9590 (2003)] for the rovibronic statetostate measurements of the reaction [Zhang et al., J. Chem. Phys. 94, 2704 (1991)]. The QM and experimental rotational distributions peak at similar levels, but the QM distributions are significantly narrower than the measurements and previous quasiclassical dynamics studies. The OH(low populations observed in the measurements are nearly absent in the QM results. We have also performed quasiclassical trajectory with histogram binning (QCTHB) calculations on these same benchmark surfaces. The QCTHB rotational distributions, which are qualitatively consistent with measurements and classical dynamics studies using other surfaces, are much broader than the QM results. Application of a Gaussian binning correction (QCTGB) dramatically narrows and shifts the QCTHB rotational distributions to be in very good agreement with the QM results. The large QCTGB correction stems from the special shape of the joint distribution of the classical rotational/vibrational action of OH products. We have also performed QM and QCT calculations for the transition, from threshold to ∼130 kcal mol^{−1} collision energy as a guide for possible future hyperthermal Oatom measurements. We find in general a mixed energy release into translation and rotation consistent with a late barrier to reaction.Angular distributions at high collision energy are forward peaked, consistent with a stripping mechanism. Direct collisional excitation channel cross sections, in the same energy range are large, comparable in magnitude to the reactive channel cross sections. Although the state dominates most collision processes, above ∼48 kcal mol^{−1}, the state plays the major role in collisional excitation.

Vibrationally resolved rate coefficients and branching fractions in the dissociative recombination of
View Description Hide DescriptionWe have studied the dissociative recombination of the first three vibrational levels of in its electronic ground state. Absolute rate coefficients, cross sections, quantum yields and branching fractions have been determined in a mergedbeam experiment in the heavyion storage ring, CRYRING, employing fragment imaging for the reaction dynamics. We present the absolute total rate coefficients as function of collision energies up to 0.4 eV for five different vibrational populations of the ion beam, as well as the partial (vibrationally resolved) rate coefficients and the branching fractions near 0 eV collision energy for the vibrational levels 1, and 2. The vibrational populations used were produced in a modified electron impact ion source, which has been calibrated using dissociativecharge transferreactions. The measurements indicate that at low collision energies, the total rate coefficient is weakly dependent on the vibrational excitation. The calculated thermal rate coefficient at 300 K decreases upon vibrational excitation. The partial rate coefficients as well as the partial branching fractions are found to be strongly dependent on the vibrational level. The partial rate coefficient is the fastest for and goes down by a factor of two or more for and 2. The quantum yield, linked to the green airglow, increases strongly upon increasing vibrational level. The effects of the dissociative recombination reactions and super elastic collisions on the vibrational populations are discussed.

Mass spectrometric and computational study of SnPb in the gas phase
View Description Hide DescriptionThe SnPb molecule has been identified in a Knudsen effusion mass spectrometry experiment. The direct dissociationreaction and two isomolecular exchange reactions involving the and molecules have been studied, in the 1426–1705 K range of temperatures, using both second and third law procedures. The has been derived, for the first time, as (122.6±4.0) kJ mol^{−1}. Density functional and ab initio calculations up to the coupled clusters level of theory were also performed. In addition, the anion dissociation energy of (179.2±4.2) kJ mol^{−1} was determined using the mass spectrometric value derived in this investigation and literature data.