Volume 140, Issue 3, 21 January 2014

The static and dynamic properties of striped colloidal particles are obtained using molecular dynamics computer simulations. Striped particles with n = 2 to n = 7 stripes of alternating electric charge are modeled at a high level of detail through a pointwise (PW) representation of the particle surface. We also consider the extent to which striped particles are similar to comparable isotropically attractive particles—such as depletion attracting colloids—by modeling striped particles with an isotropic pair interaction computed by coarsegraining (CG) over orientations at a pair level. Surprisingly, the CG models reproduce the static structure of the PW models for a range of volume fractions and interaction strengths consistent with the fluid region of the phase diagram for all n. As a corollary, different nstriped particle systems with comparable pair affinities (e.g., dimer equilibrium constant) have similar static structure. Stronger pair interactions lead to a collapsed structure in simulation as consistent with a glasslike phase. Different nstriped particle systems are found to have different phase boundaries and for certain n's no glasslike state is observed in any of our simulations. The CG model is found to have accelerated dynamics relative to the PW model for the same range of fluid conditions for which the models have identical static structure. This suggests striped electrostatic particles have slower dynamics than comparable isotropically attractive colloids. The slower dynamics result from a larger number of longduration reversible bonds between pairs of striped particles than seen in isotropically attractive systems. We also found that higher nstriped particles systems generally have slower dynamics than lower nstriped systems with comparable pair affinities.
 COMMUNICATIONS


Communication: Stochastic evaluation of explicitly correlated secondorder manybody perturbation energy
View Description Hide DescriptionA stochastic algorithm is proposed that can compute the basissetincompleteness correction to the secondorder manybody perturbation (MP2) energy of a polyatomic molecule. It evaluates the sum of two, three, and fourelectron integrals over an explicit function of electronelectron distances by a Monte Carlo (MC) integration at an operation cost per MC step increasing only quadratically with size. The method can reproduce the corrections to the MP2/ccpVTZ energies of H2O, CH4, and C6H6 within a few mE h after several million MC steps. It circumvents the resolutionoftheidentity approximation to the nonfactorable threeelectron integrals usually necessary in the conventional explicitly correlated (R12 or F12) methods.

Communication: Fully alignmentspecified O_{2} chemisorption on vicinal Si(100)
View Description Hide DescriptionA fully alignmentresolved O2 sticking experiment on a single domain Si(100)(2×1) surface is presented. This provides the first experimental evidence that the reactivity of O2 depends on both the polar and azimuthal angles of the molecular axis relative to a surface. It has been found that, in case of sideon collision, an O2 molecule perpendicular to the dimer on Si(100) is about 40% more reactive than that parallel to the dimer. Comparison of the O2 sticking on flat and vicinal Si(100) surfaces indicates that barrierless dissociation channels exist at the double layer step.
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 ARTICLES

 Theoretical Methods and Algorithms

Nonperturbative calculation of molecular magnetic properties within currentdensity functional theory
View Description Hide DescriptionWe present a novel implementation of Kohn–Sham densityfunctional theory utilizing London atomic orbitals as basis functions. External magnetic fields are treated nonperturbatively, which enable the study of both magnetic response properties and the effects of strong fields, using either standard density functionals or currentdensity functionals—the implementation is the first fully selfconsistent implementation of the latter for molecules. Pilot applications are presented for the finitefield calculation of molecular magnetizabilities, hypermagnetizabilities, and nuclear magnetic resonance shielding constants, focusing on the impact of currentdensity functionals on the accuracy of the results. Existing currentdensity functionals based on the gaugeinvariant vorticity are tested and found to be sensitive to numerical details of their implementation. Furthermore, when appropriately regularized, the resulting magnetic properties show no improvement over standard densityfunctional results. An advantage of the present implementation is the ability to apply densityfunctional theory to molecules in very strong magnetic fields, where the perturbative approach breaks down. Comparison with high accuracy fullconfigurationinteraction results show that the inadequacies of currentdensity approximations are exacerbated with increasing magnetic field strength. Standard densityfunctionals remain well behaved but fail to deliver high accuracy. The need for improved currentdependent densityfunctionals, and how they may be tested using the presented implementation, is discussed in light of our findings.

Definition and determination of the triplettriplet energy transfer reaction coordinate
View Description Hide DescriptionA definition of the triplettriplet energy transfer reaction coordinate within the very weak electronic coupling limit is proposed, and a novel theoretical formalism is developed for its quantitative determination in terms of internal coordinates The present formalism permits (i) the separation of donor and acceptor contributions to the reaction coordinate, (ii) the identification of the intrinsic role of donor and acceptor in the triplet energy transfer process, and (iii) the quantification of the effect of every internal coordinate on the transfer process. This formalism is general and can be applied to classical as well as to nonvertical triplet energy transfer processes. The utility of the novel formalism is demonstrated here by its application to the paradigm of nonvertical triplettriplet energy transfer involving cisstilbene as acceptor molecule. In this way the effect of each internal molecular coordinate in promoting the transfer rate, from triplet donors in the low and highenergy limit, could be analyzed in detail.

Analytic cubic and quartic force fields using densityfunctional theory
View Description Hide DescriptionWe present the first analytic implementation of cubic and quartic force constants at the level of Kohn–Sham densityfunctional theory. The implementation is based on an openended formalism for the evaluation of energy derivatives in an atomicorbital basis. The implementation relies on the availability of openended codes for evaluation of one and twoelectron integrals differentiated with respect to nuclear displacements as well as automatic differentiation of the exchange–correlation kernels. We use generalized secondorder vibrational perturbation theory to calculate the fundamental frequencies of methane, ethane, benzene, and aniline, comparing B3LYP, BLYP, and Hartree–Fock results. The Hartree–Fock anharmonic corrections agree well with the B3LYP corrections when calculated at the B3LYP geometry and from B3LYP normal coordinates, suggesting that the inclusion of electron correlation is not essential for the reliable calculation of cubic and quartic force constants.

Dynamic correlations in Brownian manybody systems
View Description Hide DescriptionFor classical Brownian systems driven out of equilibrium, we derive inhomogeneous twotime correlation functions from functional differentiation of the onebody density and current with respect to external fields. In order to allow for appropriate freedom upon building the derivatives, we formally supplement the Smoluchowski dynamics by a source term, which vanishes at the physical solution. These techniques are applied to obtain a complete set of dynamic OrnsteinZernike equations, which serve for the development of approximation schemes. The rules of functional calculus lead naturally to nonMarkovian equations of motion for the twotime correlators. Memory functions are identified as functional derivatives of a unique space and timenonlocal dissipation power functional.

Mapping continuous potentials to discrete forms
View Description Hide DescriptionThe optimal conversion of a continuous interparticle potential to a discrete equivalent is considered here. Existing and novel algorithms are evaluated to determine the best technique for creating accurate discrete forms using the minimum number of discontinuities. This allows the eventdriven molecular dynamics technique to be efficiently applied to the wide range of continuous force models available in the literature, and facilitates a direct comparison of eventdriven and timedriven molecular dynamics. The performance of the proposed conversion techniques are evaluated through application to the LennardJones model. A surprising linear dependence of the computational cost on the number of discontinuities is found, allowing accuracy to be traded for speed in a controlled manner. Excellent agreement is found for static and dynamic properties using a relatively low number of discontinuities. For the LennardJones potential, the optimized discrete form outperforms the original continuous form at gas densities but is significantly slower at higher densities.

An efficient approach to ab initio Monte Carlo simulation
View Description Hide DescriptionWe present a Nested Markov chain Monte Carlo (NMC) scheme for building equilibrium averages based on accurate potentials such as density functional theory. Metropolis sampling of a reference system, defined by an inexpensive but approximate potential, was used to substantially decorrelate configurations at which the potential of interest was evaluated, thereby dramatically reducing the number needed to build ensemble averages at a given level of precision. The efficiency of this procedure was maximized onthefly through variation of the reference system thermodynamic state (characterized here by its inverse temperature β^{0}), which was otherwise unconstrained. Local density approximation results are presented for shocked states of argon at pressures from 4 to 60 GPa, where—depending on the quality of the reference system potential—acceptance probabilities were enhanced by factors of 1.2–28 relative to unoptimized NMC. The optimization procedure compensated strongly for reference potential shortcomings, as evidenced by significantly higher speedups when using a reference potential of lower quality. The efficiency of optimized NMC is shown to be competitive with that of standard ab initio molecular dynamics in the canonical ensemble.

Finite temperature effects on the Xray absorption spectra of lithium compounds: Firstprinciples interpretation of Xray Raman measurements
View Description Hide DescriptionWe elucidate the role of roomtemperatureinduced instantaneous structural distortions in the Li Kedge Xray absorption spectra (XAS) of crystalline LiF, Li2SO4, Li2O, Li3N, and Li2CO3 using high resolution Xray Raman spectroscopy (XRS) measurements and firstprinciples density functional theory calculations within the eXcited electron and Core Hole approach. Based on thermodynamic sampling via ab initio molecular dynamics simulations, we find calculated XAS in much better agreement with experiment than those computed using the rigid crystal structure alone. We show that local instantaneous distortion of the atomic lattice perturbs the symmetry of the Li 1s coreexcitedstate electronic structure, broadening spectral lineshapes and, in some cases, producing additional spectral features. The excellent agreement with highresolution XRS measurements validates the accuracy of our firstprinciples approach to simulating XAS, and provides both accurate benchmarks for model compounds and a predictive theoretical capability for identification and characterization of multicomponent systems, such as lithiumion batteries, under working conditions.

Unified view on linear response of interacting identical and distinguishable particles from multiconfigurational timedependent Hartree methods
View Description Hide DescriptionA unified view on linear response of interacting systems utilizing multiconfigurational timedependent Hartree methods is presented. The cases of oneparticle and twoparticle response operators for identical particles and up to allsystem response operators for distinguishable degreesoffreedom are considered. The working equations for systems of identical bosons and identical fermions, as well for systems of distinguishable particles are explicitly derived. These linearresponse theories – applicable for discrete excitation spectra – provide numerically exact excitation energies and system's properties, when numerical convergence is achieved in the calculations.

Electronic excitations in a dielectric continuum solvent with quantum Monte Carlo: Acrolein in water
View Description Hide DescriptionWe investigate here the vertical n → π^{*} and π → π^{*} transitions of stransacrolein in aqueous solution by means of a polarizable continuum model (PCM) we have developed for the treatment of the solute at the quantum Monte Carlo (QMC) level of the theory. We employ the QMC approach which allows us to work with highly correlated electronic wave functions for both the solute ground and excited states and, to study the vertical transitions in the solvent, adopt the commonly used scheme of considering fast and slow dielectric polarization. To perform calculations in a nonequilibrium solvation regime for the solute excited state, we add a correction to the global dielectric polarization charge density, obtained self consistently with the solute groundstate wave function by assuming a linearresponse scheme. For the solvent polarization in the field of the solute in the ground state, we use the static dielectric constant while, for the electronic dielectric polarization, we employ the solvent refractive index evaluated at the same frequency of the photon absorbed by the solute for the transition. This choice is shown to be better than adopting the most commonly used value of refractive index measured in the region of visible radiation. Our QMC calculations show that, for standard cavities, the solvatochromic shifts obtained with the PCM are underestimated, even though of the correct sign, for both transitions of acrolein in water. Only by reducing the size of the cavity to values where more than one electron is escaped to the solvent region, we regain the experimental shift for the n → π^{*} case and also improve considerably the shift for the π → π^{*} transition.

Surface tension of spherical drops from surface of tension
View Description Hide DescriptionThe determination of surface tension of curved interfaces is a topic that raised many controversies during the last century. Explicit liquidvapor interface modelling (ELVI) was unable up to now to reproduce interfacial behaviors in drops due to ambiguities in the mechanical definition of the surface tension. In this work, we propose a thermodynamic approach based on the location of surface of tension and its use in the Laplace equation to extract the surface tension of spherical interfaces from ELVI modelling.

Nonlinear response theory in chemical kinetics
View Description Hide DescriptionA theory of nonlinear response of chemical kinetics, in which multiple perturbations are used to probe the time evolution of nonlinear chemical systems, is developed. Expressions for nonlinear chemical response functions and susceptibilities, which can serve as multidimensional measures of the kinetic pathways and rates, are derived. A new class of multidimensional measures that combine multiple perturbations and measurements is also introduced. Nonlinear fluctuationdissipation relations for steadystate chemical systems, which replace operations of concentration measurement and perturbations, are proposed. Several applications to the analysis of complex reaction mechanisms are provided.

Effects of reactant rotational excitation on reactivity: Perspectives from the sudden limit
View Description Hide DescriptionExcitation of reactant rotational degrees of freedom is known to influence reactivity in bimolecular reactions. In this work, this effect is examined for several prototypical activated atomdiatom and atomtriatom reactions through exact quantum scattering calculations on accurate ab initio potential energy surfaces. To rationalize these modespecific effects, the recently proposed sudden vector overlap model is extended to include rotational motions of reactants. Specifically, the enhancement of reactivity is attributed to their coupling with the reaction coordinate at the transition state, as quantified by the alignment between the corresponding normal mode vectors. In addition, a FranckCondon model is introduced to predict the effect of reactant rotational excitation for reactions in which the reactant rotations are decoupled from the reaction coordinate.

Nonadiabatic dynamics of electron transfer in solution: Explicit and implicit solvent treatments that include multiple relaxation time scales
View Description Hide DescriptionThe development of efficient theoretical methods for describing electron transfer (ET) reactions in condensed phases is important for a variety of chemical and biological applications. Previously, dynamical dielectric continuum theory was used to derive Langevin equations for a single collective solvent coordinate describing ET in a polar solvent. In this theory, the parameters are directly related to the physical properties of the system and can be determined from experimental data or explicit molecular dynamics simulations. Herein, we combine these Langevin equations with surface hopping nonadiabatic dynamics methods to calculate the rate constants for thermal ET reactions in polar solvents for a wide range of electronic couplings and reaction free energies. Comparison of explicit and implicit solvent calculations illustrates that the mapping from explicit to implicit solvent models is valid even for solvents exhibiting complex relaxation behavior with multiple relaxation time scales and a shorttime inertial response. The rate constants calculated for implicit solvent models with a single solvent relaxation time scale corresponding to water, acetonitrile, and methanol agree well with analytical theories in the Golden rule and solventcontrolled regimes, as well as in the intermediate regime. The implicit solvent models with two relaxation time scales are in qualitative agreement with the analytical theories but quantitatively overestimate the rate constants compared to these theories. Analysis of these simulations elucidates the importance of multiple relaxation time scales and the inertial component of the solvent response, as well as potential shortcomings of the analytical theories based on single time scale solvent relaxation models. This implicit solvent approach will enable the simulation of a wide range of ET reactions via the stochastic dynamics of a single collective solvent coordinate with parameters that are relevant to experimentally accessible systems.

Investigating rare events with nonequilibrium work measurements. I. Nonequilibrium transition path probabilities
View Description Hide DescriptionWe have developed a formalism for investigating transition pathways and transition probabilities for rare events in biomolecular systems. In this paper, we set the theoretical framework for employing nonequilibrium work relations to estimate the relative reaction rates associated with different classes of transition pathways. Particularly, we derive an extension of Crook's transient fluctuation theorem, which relates the relative transition rates of driven systems in the forward and reverse directions, and allows for the calculation of these relative rates using work measurements (e.g., in Steered Molecular Dynamics). The formalism presented here can be combined with Transition Path Theory to relate the equilibrium and driven transition rates. The usefulness of this framework is illustrated by means of a Gaussian model and a driven proline dimer.

Investigating rare events with nonequilibrium work measurements. II. Transition and reaction rates
View Description Hide DescriptionWe present a formalism for investigating transition pathways and transition probabilities for rare events in biomolecular systems. The formalism is based on combining Transition Path Theory with the results of nonequilibrium work relations, and shows that the equilibrium and nonequilibrium transition rates are in fact related. Aside from its fundamental importance, this allows for the calculation of relative equilibrium reaction rates with driven nonequilibrium simulations such as Steered Molecular Dynamics. The workings of the formalism are illustrated with a few typical numerical examples.
 Advanced Experimental Techniques

Suppression of unimolecular decay of laser desorbed peptide and protein ions by entrainment in rarefied supersonic gas jets under weak electric fields
View Description Hide DescriptionUnimolecular decay of sample ions imposes a limit on the usable laser fluence in matrixassisted laser desorption/ionization (MALDI) ion sources. Traditionally, some modest degree of collisional sample ion cooling has been achieved by connecting MALDI ion sources directly to gasfilled radio frequency (RF) multipoles. It was also discovered in the early 1990s that gasfilled RF multipoles exhibit increased ion transmission efficiency due to collisional ion focusing effects. This unexpected experimental finding was later supported by elementary Monte Carlo simulations. Both experiments and simulations assumed a resting background gas with typical pressures of the order of 1 Pa. However, considerable additional improvements can be achieved if laser desorbed sample ions are introduced immediately after desorption, still within the ion source, in an axisymmetric rarefied supersonic gas jet with peak pressure of the order of 100 Pa and flow velocities >300 m/s, and under weak electric fields. We describe here the design principle and report performance data of an ion source coined “MALDI2,” which incorporates elements of both rarefied aerodynamics and particle optics. Such a design allows superb suppression of metastable fragmentation due to rapid collisional cooling in <10 μs and nearly perfect injection efficiency into the attached RF ion guide, as numerous experiments have confirmed.
 Atoms, Molecules, and Clusters

A density functional tight binding/force field approach to the interaction of molecules with rare gas clusters: Application to (C_{6}H_{6})^{+/0}Ar_{ n } clusters
View Description Hide DescriptionWe propose in the present paper a SCCDFTB/FF (SelfConsistentCharge Density Functional based Tight Binding/ForceField) scheme adapted to the investigation of molecules trapped in rare gas environments. With respect to usual FF descriptions, the model involves the interaction of quantum electrons in a molecule with rare gas atoms in an anisotropic scheme. It includes polarization and dispersion contributions and can be used for both neutral and charged species. Parameters for this model are determined for hydrocarbonargon complexes and the model is validated for small hydrocarbons. With the future aim of studying polycyclic aromatic hydrocarbons in Ar matrices, extensive benchmark calculations are performed on (C6H6)^{+/0}Ar n clusters against DFT and CCSD(T) calculations for the smaller sizes, and more generally against other experimental and theoretical data. Results on the structures and energetics (isomer ordering and energy separation, cohesion energy per Ar atom) are presented in detail for n = 1–8, 13, 20, 27, and 30, for both neutrals and cations. We confirm that the clustering of Ar atoms leads to a monotonous decrease of the ionization potential of benzene for n ⩽ 20, in line with previous experimental and FF data.

Complexation of n SO_{2} molecules (n = 1, 2, 3) with formaldehyde and thioformaldehyde
View Description Hide DescriptionAb initio and density functional theory calculations are used to examine complexes formed between H2CO and H2CS with 1, 2, and 3 molecules of SO2. The nature of the interactions is probed by a variety of means, including electrostatic potentials, natural bond orbital, atoms in molecules, energy decomposition, and electron density redistribution maps. The dimers are relatively strongly bound, with interaction energies exceeding 5 kcal/mol. The structures are cyclic, containing both a O/S⋯S chalcogen bond and a CH⋯O Hbond. Addition of a second SO2 molecule leads to a variety of heterotrimer structures, most of which resemble the original dimer, where the second SO2 molecule engages in a chalcogen bond with the first SO2, and a C⋯O attraction with the H2CX. Some cooperativity is apparent in the trimers and tetramers, with an attractive threebody interaction energy and shortened intermolecular distances.