Volume 132, Issue 3, 21 January 2010

A global potential energy surface is obtained for the ground state of the endoergic reaction. The global potential is obtained by fitting highly correlated ab initio calculations on the system, using relativistic pseudopotential for the gold atom. Several electronic states are calculated correlating with , , and , asymptotes. These states show several conical intersections and curve crossings along the minimum energy reaction path which are analyzed in detail. One of them gives rise to an insertion well in which there are important contributions from the and states of gold, which is interesting because it is analog to the deep chemisorption well appearing in larger goldclusters. Quantum wave packet and quasiclassical trajectory dynamical calculations performed for the reaction at zero total angular momentum are in good agreement, provided that a Gaussian binning method is used to account for the zeropoint energy of products. Finally, integral and differential cross sections are calculated for the reaction with quasiclassical trajectories. Two different reaction mechanisms are found, one direct and the second indirect, in which the Au atom inserts in between the two hydrogen atoms because of the existence of the insertion well discussed above.
 COMMUNICATIONS


Communications: On artificial frequency shifts in infrared spectra obtained from centroid molecular dynamics: Quantum liquid water
View Description Hide DescriptionCentroid molecular dynamics (CMD) is a popular method to extract approximate quantum dynamics from path integral simulations. Very recently we have shown that CMD gas phase infrared spectra exhibit significant artificial redshifts of stretching peaks, due to the socalled “curvature problem” imprinted by the effective centroid potential. Here we provide evidence that for condensed phases, and in particular for liquid water, CMD produces pronounced artificial redshifts for highfrequency vibrations such as the OH stretching band. This peculiar behavior intrinsic to the CMD method explains part of the unexpectedly large quantum redshifts of the stretching band of liquid water compared to classical frequencies, which is improved after applying a simple and rough “harmonic curvature correction.”

Communications: Selfenergy and corresponding virial contribution of electrostatic interactions in dissipative particle dynamics: Simulations of cationic lipid bilayers
View Description Hide DescriptionGeneral expressions of selfenergy and corresponding virial terms for electrostatic interactions in dissipative particle dynamics simulations are derived in this article. In the latticesum electrostatics, we found the essential process is to solve the electric field equation of each individual point charge. Strong inward pressure caused by the selfenergy is eliminated by subtracting the corresponding virial from the total virial. The resulting method is tested by simulating cationic lipid bilayers in constant pressure ensemble.

Communications: Accurate description of atoms and molecules by natural orbital functional theory
View Description Hide DescriptionThe spinconserving density matrix functionaltheory is used to propose an improved natural orbital functional. The Piris reconstruction functional, PNOF, which is based on an explicit form of the twoparticle cumulant satisfying necessary positivity conditions for the twoparticle reduced density matrix, is used to reconstruct the latter. A new approach , as well as an extension of the known to spinuncompensated systems lead to PNOF3. The theory is applied to the calculation of the total energies of the first and secondrow atoms (H–Ne) and a number of selected small molecules. The energy differences between the ground state and the lowestlying excited state with different spin for these atoms, and the atomization energies of the considered molecules are also presented. The obtained values agree remarkably well with their corresponding both CCSD(T, full) and experimental values.
 Top

 ARTICLES

 Theoretical Methods and Algorithms

A divide and conquer real space finiteelement Hartree–Fock method
View Description Hide DescriptionSince the seminal contribution of Roothaan, quantum chemistry methods are traditionally expressed using finite basis sets comprised of smooth and continuous functions (atomcentered Gaussians) to describe the electronic degrees of freedom. Although this approach proved quite powerful, it is not well suited for large basis sets because of linear dependence problems and ill conditioning of the required matrices. The finite element method(FEM), on the other hand, is a powerful numerical method whose convergence is also guaranteed by variational principles and can be achieved systematically by increasing the number of degrees of freedom and/or the polynomial order of the shape functions. Here we apply the realspace FEM to Hartree–Fock calculations in three dimensions. The method produces sparse, banded Hermitian matrices while allowing for variable spatial resolution. This localbasis approach to electronic structure theory allows for systematic convergence and promises to provide an accurate and efficient way toward the full ab initio analysis of materials at larger scales. We introduce a new acceleration technique for evaluating the exchange contribution within FEM and explore the accuracy and robustness of the method for some selected test atoms and molecules. Furthermore, we applied a divideandconquer (DC) method to the finiteelement Hartree–Fock ab initio electronicstructure calculations in three dimensions. This DC approach leads to facile parallelization and should enable reduced scaling for large systems.

Error and efficiency of simulated tempering simulations
View Description Hide DescriptionWe derive simple analytical expressions for the error and computational efficiency of simulated tempering (ST) simulations. The theory applies to the important case of systems whose dynamics at long times is dominated by the slow interconversion between two metastable states. An extension to the multistate case is described. We show that the relative gain in efficiency of ST simulations over regular molecular dynamics (MD) or Monte Carlo(MC) simulations is given by the ratio of their reactive fluxes, i.e., the number of transitions between the two states summed over all ST temperatures divided by the number of transitions at the single temperature of the MD or MC simulation. This relation for the efficiency is derived for the limit in which changes in the ST temperature are fast compared to the twostate transitions. In this limit, ST is most efficient. Our expression for the maximum efficiency gain of ST simulations is essentially identical to the corresponding expression derived by us for replica exchange MD and MC simulations [E. Rosta and G. Hummer, J. Chem. Phys.131, 165102 (2009)] on a different route. We find quantitative agreement between predicted and observed efficiency gains in a test against ST and replica exchange MC simulations of a twodimensional Ising model. Based on the efficiency formula, we provide recommendations for the optimal choice of ST simulation parameters, in particular, the range and number of temperatures, and the frequency of attempted temperature changes.

Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks
View Description Hide DescriptionParametric sensitivity of biochemical networks is an indispensable tool for studying system robustness properties, estimating network parameters, and identifying targets for drug therapy. For discrete stochastic representations of biochemical networks where Monte Carlo methods are commonly used, sensitivity analysis can be particularly challenging, as accurate finite difference computations of sensitivity require a large number of simulations for both nominal and perturbed values of the parameters. In this paper we introduce the common random number (CRN) method in conjunction with Gillespie’s stochastic simulation algorithm, which exploits positive correlations obtained by using CRNs for nominal and perturbed parameters. We also propose a new method called the common reaction path (CRP) method, which uses CRNs together with the random time change representation of discrete state Markov processes due to Kurtz to estimate the sensitivity via a finite difference approximation applied to coupled reaction paths that emerge naturally in this representation. While both methods reduce the variance of the estimator significantly compared to independent random number finite difference implementations, numerical evidence suggests that the CRP method achieves a greater variance reduction. We also provide some theoretical basis for the superior performance of CRP. The improved accuracy of these methods allows for much more efficient sensitivity estimation. In two example systems reported in this work, speedup factors greater than 300 and 10 000 are demonstrated.

Searching for partially reactive sites: Analytical results for spherical targets
View Description Hide DescriptionHow do single or multiple (sub)diffusing particles search for a target with a partially reactive boundary? A finite reaction rate which is typical for many chemical or biochemical reactions is introduced as the possibility for a particle to find a target but not to “recognize” it. The search is not finished until the target is found and recognized. For a single searching particle, the short and longtime regimes are investigated, with a special focus on comparison between perfectly and partially reactive boundaries. For multiple searching particles, explicit formulas for the probability density of the search time are given for subdiffusion in one and three dimensions. The dependence of the mean search time on the density of particles and the reaction rate is analyzed. Unexpectedly, in the high density limit, the particles undergoing slower subdiffusive motion find a target faster.

Molecular applications of analytical gradient approach for the improved virtual orbitalcomplete active space configuration interaction method
View Description Hide DescriptionThe improved virtual orbitalcomplete active space configuration interaction (IVOCASCI) method is extended to determine the geometry and vibrational frequencies for ground and excited electronic states using an analytical total energy gradient scheme involving both first and second order analytical derivatives. Illustrative applications consider the ground state geometries of the benzene , biphenyl , and alanine dipeptide molecules. In addition, the IVOCASCI geometry optimization has been performed for the first excited singlet and triplet states of benzene to assess its applicability for excited and openshell systems. The symmetry benzene triplet optimization produces a saddle point, and a descent along the unstable mode produces the stable minimum. Comparisons with Hartree–Fock, second order Möller–Plesset perturbation theory, complete active space selfconsistent field (CASSCF), and density functional theory demonstrate that the IVOCASCI approach generally fares comparable to or better for all systems studied. The vibrational frequencies of the benzene and biphenyl molecules computed with the analytical gradient based IVOCASCI method agree with the experiment and with other accurate theoretical estimates. Satisfactory agreement between our results, other benchmark calculations, and available experiment demonstrates the efficacy and potential of the method. The close similarity between CASSCF and IVOCASCI optimized geometries and the greater computational efficiency of the IVOCASCI method suggests the replacement of CASSCF treatments by the IVOCASCI approach, which is free from the convergence problems that often plague CASSCF treatments.

Ring polymer molecular dynamics beyond the linear response regime: Excess electron injection and trapping in liquids
View Description Hide DescriptionRing polymermolecular dynamics (RPMD) is used to directly simulate the injection and relaxation of excess electrons into supercritical helium fluid and ambient liquid water. A method for modulating the initial energy of the excess electron in the RPMD model is presented and used to study both lowenergy (cold) and highenergy (hot) electron injections. For cold injection into both solvents, the RPMD model recovers electronically adiabatic dynamics with the excess electron in its ground state, whereas for hot electron injection, the model predicts slower relaxation dynamics associated with electronic transitions between solventcavities. The analysis of solventdynamics during electron localization reveals the formation of an outgoing solvent compression wave in helium that travels for over 2 nm and the delayed formation of water solvation shells on the timescale of 300 fs. Various systemsize effects that are intrinsic to the simulation of excess electron injection are discussed. Comparison of the RPMD simulations with previous mixed quantumclassical dynamics simulations finds general agreement for both the mechanisms and timescales for electron localization, although the electron localization dynamics in the RPMD model is essentially completed within 400 fs in helium and 150 fs in water.

Comparison of molecular dynamics and moment based methods as tools in the computation of time dependent correlation functions
View Description Hide DescriptionMethods, such as the continued fractions that are based on the exact moments (Taylor coefficients) provide powerful analytic techniques for calculating approximate dynamic correlation functions of physical properties. Owing to the practical difficulties associated with obtaining higher order exact moments these methods have been largely eclipsed by molecular dynamics. In this paper we develop the formalism for extracting trajectory moments from a molecular dynamics trajectory and compare the performance of the two methods. We begin by using the classical phase space analogs of quantum wave functions to obtain matrix representations (transition matrices) of the Lie group of time displacement operators. The group elements for small time displacements, which correspond to a step of the trajectory, are approximated by using Trotter’s theorem. The method is applied to the linear harmonic oscillator, the Morse oscillator and the LennardJones potential and the resulting moments compared to those obtained by the Taylor expansion of a truncated continued fraction. We find that in the case of the harmonic oscillator the results from the continued fraction are much better than those from molecular dynamics. In the latter two cases, while the truncated fraction performs better than molecular dynamics both methods produce poor quality higher order moments. However, we are able to show the criterion whereby the overall error introduced by the truncated continued fraction is smaller than that introduced by molecular dynamics. From this work we conclude that the moment based methods produce good results, they are analytic in nature rather than numerical and should not be rejected but can be used to complement molecular dynamics.

Improved version of a local contracted configuration interaction of singles and doubles with partial inclusion of triples and quadruples
View Description Hide DescriptionA local contracted single and double configuration interaction (LCCISD) method, which introduces contracted singly and doubly excited vectors within the framework of bond functions, has been recently proposed [P. Reinhardt et al., J. Chem. Phys.129, 164106 (2008)]. The present work improves this method by introducing a coupledelectron pair approximation (CEPA3) dressing and by incorporating the leading part of linked effects of triples (T) and quadruples (Q) through a series of local fourelectron full CI calculations. Two different ways have been adopted to incorporate this linked TQ effect. One consists of dressing the first column/line of the whole LCCISD matrix. The other one introduces an additional contracted wave function responsible for the linked effect for each bond pair. The present treatments have been applied to the evaluation of equilibrium bond lengths and harmonic frequencies of diatomic molecules (HF, BF, CuH, , , and ) and single bond breaking in HF, , , , butane, and molecules, symmetrical stretching of the two OH bonds in a water molecule, and symmetrical expansion of a triangular cluster. The results show that the performance of the compares favorably with coupledcluster singles and doubles (CCSD) and CCSD(T) methods, presenting similar behaviors around equilibrium and better ones for stretched geometries. The LCCEPA3 method is strictly separable, and the size consistency error of our treatment of triples and quadruples is extremely small. The strict separability can be further achieved by dressing the doubly excited bond functions with the linked TQ effect. The efficiency of truncations on the bielectronic integrals has also been tested.

Numerical coarsegraining of fluid field theories
View Description Hide DescriptionWe present a formalism for the systematic numerical coarsegraining of fieldtheoretic models of fluids that draws upon techniques from both the Monte Carlorenormalization group and particlebased coarsegraining literature. A forcematching technique initially developed for coarsegraining particlebased interaction potentials is adapted to calculate renormalized fieldtheoretic coupling coefficients in a complexvalued field theory, and a related method is introduced for coarsegraining fieldtheoretic operators. The viability of this methodology is demonstrated by coarsegraining a fieldtheoretic model of a Gaussiancore fluid and thereby reducing lattice discretization errors.

Exploiting the spatial locality of electron correlation within the parametric twoelectron reduceddensitymatrix method
View Description Hide DescriptionThe parametric variational twoelectron reduceddensitymatrix (2RDM) method is applied to computing electronic correlationenergies of mediumtolarge molecular systems by exploiting the spatial locality of electron correlation within the framework of the clusterinmolecule (CIM) approximation [S. Li et al., J. Comput. Chem.23, 238 (2002); J. Chem. Phys.125, 074109 (2006)]. The 2RDMs of individual molecular fragments within a molecule are determined, and selected portions of these 2RDMs are recombined to yield an accurate approximation to the correlationenergy of the entire molecule. In addition to extending CIM to the parametric 2RDM method, we (i) suggest a more systematic selection of atomicorbital domains than that presented in previous CIM studies and (ii) generalize the CIM method for openshell quantum systems. The resulting method is tested with a series of polyacetylene molecules, water clusters, and diazobenzene derivatives in minimal and nonminimal basis sets. Calculations show that the computational cost of the method scales linearly with system size. We also compute hydrogenabstraction energies for a series of hydroxyurea derivatives. Abstraction of hydrogen from hydroxyurea is thought to be a key step in its treatment of sickle cell anemia; the design of hydroxyurea derivatives that oxidize more rapidly is one approach to devising more effective treatments.

Benchmark allelectron ab initio quantum Monte Carlo calculations for small molecules
View Description Hide DescriptionWe study the efficiency, precision and accuracy of allelectron variational and diffusionquantum Monte Carlo calculations using Slater basis sets. Starting from wave functionsgenerated by Hartree–Fock and density functional theory, we describe an algorithm to enforce the electronnucleus cusp condition by linear projection. For the 55 molecules in the G2 set, the diffusionquantum Monte Carlo calculations recovers an average of 95% of the correlation energy and reproduces bond energies to a mean absolute deviation of 3.2 kcal/mol. Comparing the individual total energies with essentially exact values, we investigate the error cancellation in atomization and chemical reaction path energies, giving additional insight into the sizes of nodal surface errors.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Potential energy surface and reactive collisions for the system
View Description Hide DescriptionA global potential energy surface is obtained for the ground state of the endoergic reaction. The global potential is obtained by fitting highly correlated ab initio calculations on the system, using relativistic pseudopotential for the gold atom. Several electronic states are calculated correlating with , , and , asymptotes. These states show several conical intersections and curve crossings along the minimum energy reaction path which are analyzed in detail. One of them gives rise to an insertion well in which there are important contributions from the and states of gold, which is interesting because it is analog to the deep chemisorption well appearing in larger goldclusters. Quantum wave packet and quasiclassical trajectory dynamical calculations performed for the reaction at zero total angular momentum are in good agreement, provided that a Gaussian binning method is used to account for the zeropoint energy of products. Finally, integral and differential cross sections are calculated for the reaction with quasiclassical trajectories. Two different reaction mechanisms are found, one direct and the second indirect, in which the Au atom inserts in between the two hydrogen atoms because of the existence of the insertion well discussed above.

Melting of sizeselected aluminum nanoclusters with 84–128 atoms
View Description Hide DescriptionHeat capacities have been measured as a function of temperature for isolated aluminum nanoclusters with 84–128 atoms. Most clusters show a single sharp peak in the heat capacity which is attributed to a melting transition. However, there are several size regimes where additional features are observed; for clusters with 84–89 atoms the peak in the heat capacity is either broad or bimodal. For , , and there are two welldefined peaks, and for , , and there is a dip in the heat capacity at lower temperature than the peak. The broad or bimodal peaks for clusters with 84–89 atoms are not significantly changed by annealing to 823 K (above the melting temperature), but the dips for , , and disappear when these clusters are annealed to 523 K (above the temperature of the dip but below the melting temperature). Both the melting temperatures and the latent heats change fairly smoothly with the cluster size in the size regime examined here. There are steps in the melting temperatures for clusters with around 100 and 117 atoms. The step at is correlated with a substantial peak in the latent heats but the step at correlates with a minimum. Since the latent heats are correlated with the cluster cohesive energies, the substantial peak in the latent heats at indicates this cluster is particularly strongly bound.

Spacetime contours to treat intense fielddressed molecular states
View Description Hide DescriptionIn this article we consider a molecular system exposed to an intense shortpulsed external field. It is a continuation of a previous publication [A. K. Paul, S. Adhikari, D. Mukhopadhyay et al., J. Phys. Chem. A113, 7331 (2009)] in which a theory is presented that treats quantum effects due to nonclassical photon states (known also as Fock states). Since these states became recently a subject of intense experimental efforts we thought that they can be treated properly within the existing quantum formulation of dynamical processes. This was achieved by incorporating them in the Born–Oppenheimer (BO) treatment with timedependent coefficients. The extension of the BO treatment to include the Fock states results in a formidable enhancement in numerical efforts expressed, in particular, in a significant increase in CPU time. In the present article we discuss an approach that yields an efficient and reliable approximation with only negligible losses in accuracy. The approximation is tested in detail for the dissociation process of as caused by a laser field.

Chemiluminescence from the reaction: Collision energy effects on the product rotational alignment and energy release
View Description Hide DescriptionBoth fully dispersed unpolarized and polarized chemiluminescencespectra from the reaction have been recorded under hyperthermal laserablated atomic beamMaxwellian gas conditions at three specific average collision energies in the range of 4.82–7.47 eV. A comprehensive analysis of the whole data series suggests that the band system dominates the chemiluminescence. The polarization results revealed that the product rotational alignment is insensitive to its vibrational state at but develops into an strong negative correlation between product rotational alignment and at 7.47 eV. The results are interpreted in terms of a direct mechanism involving a shortrange, partial electron transfer from to which is constrained by the duration of the collision, so that the reaction has a larger probability to occur when the collision time is larger than the time needed for bending. The latter in turn determines that, at any given , collinear reactive intermediates are preferentially involved when the highest velocity components of the corresponding collision energy distributions are sampled. Moreover, the data at 4.82 eV suggest that a potential barrier to reaction which favors charge transfer to bent at chiefly coplanar geometries is operative for most of the reactive trajectories that sample the lowest velocity components. Such a barrier would arise from the relevant ioniccovalent curve crossings occurring in the repulsive region of the covalent potential ; from this crossing the product may be reached through mixings in the exit channel with potential energy surfaces leading most likely to the spinallowed and products. The variation with increasing of both the magnitude of the average rotational alignment and the rovibrational excitation, as obtained from spectral simulations of the unpolarized chemiluminescencespectra, consistently points to additional dynamic factors, most likely the development of induced repulsive energy release as the major responsible for the angular momentum and energy disposal at the two higher studied. The results of a simplified version of the direct interaction with product repulsiondistributed as in photodissociation model do not agree with the observed average product rotational alignments, showing that a more realistic potential energy surface model will be necessary to explain the present results.

A density functional theory and timedependent density functional theory investigation on the anchor comparison of triarylaminebased dyes
View Description Hide DescriptionTo understand the effects of the anchor part in organic dyes on the energy conversion efficiency of dyesensitized solar cells (DSCs), two different anchor groups used in metalfree triphenylamine (TPA)based organic dyes for DSCs have been theoretically compared. Density functional theory (DFT) and timedependent DFT (TDDFT) study of geometry properties, excitations, and electronic structures of triarylaminebased dyes (TC1 and TPAR1) before and after binding to titanium has been performed under the level of TDPBE1PBE/6311G(d,p)//B3LYP/6311G(d,p). The result shows that cyanoacrylic acid anchor favors better photoelectrochemical properties of DSCs than that of rhodanine3acetic acid anchor via providing more shift of conduction band toward the vacuum energy levels (larger open circuit potentials) and more favorable conjugation with titanium. This study is expected to shed light on the design of metalfree organic dyes for DSCs.

Insights into the mechanistic photodissociation of methyl formate
View Description Hide DescriptionIn this work, we studied the photodissociation dynamics of methyl formate using stateoftheart multireference configuration interaction with single and double excitation and the complete active space selfconsistent field methods. It was found that the direct bond cleavage in the first excited singlet state is the dominant dissociation channel, consistent with the recent experiment [S. H. Lee, J. Chem. Phys.129, 194304 (2008)]. This cleavage mechanism is different from that for aldehydes/ketones where it occurs in the lowest triplet state as a result of the intersystem crossing. On the basis of comparison to the bond fission in the asymmetrically substituted aliphatic carbonyl compounds studied previously, we suggest the photolytic reaction of as a special type of Norrish type I reaction.