Volume 124, Issue 22, 14 June 2006
 COMMUNICATIONS


A simple effective potential for exchange
View Description Hide DescriptionThe optimized effective potential (OEP) for exchange was introduced some time ago by Sharp and Horton [Phys. Rev.90, 317 (1953)] and by Talman and Shadwick [Phys. Rev. A14, 36 (1976)]. The integral equation for the OEP is difficult to solve, however, and a variety of approximations have therefore been proposed. These are explicitly orbital dependent and require the same twoelectron integrals as HartreeFock theory. We have found a remarkably simple approximate effective potential that closely resembles the TalmanShadwick potential in atoms. It depends only on total densities and requires no twoelectron integrals.

Noncontinuum effects in nanoparticle dynamics in polymers
View Description Hide DescriptionWe propose a continuum model for the dynamics of particles in polymer matrices which encompasses arbitrary size ratios of the polymer and particle. We present analytical and computer simulation results for the mobility of the particles and the viscosity of the suspension for the case of unentangled polymer melts. Our results indicate strong dependencies of the particle mobility upon the polymerparticle size ratios and much reduced intrinsic viscosities for the suspensions. These predictions rationalize some recent experimental observations on the dynamics of nanoparticles in polymer melts.

An offlattice WangLandau study of the coilglobule and melting transitions of a flexible homopolymer
View Description Hide DescriptionThe WangLandau Monte Carlo approach is applied to the coilglobule and meltingtransitions of offlattice flexible homopolymers. The solidliquidmelting point and coilglobule transition temperatures are identified by their respective peaks in the heat capacity as a function of temperature. The melting and theta points are well separated, indicating that the coilglobule transition occurs separately from melting even in the thermodynamic limit. We also observe a feature in the heat capacity between the coilglobule and meltingtransitions which we attribute to a transformation from a lowdensity liquid globule to a highdensity liquid globule.

Persistent nuclear wave packet oscillation coexistent with incoherent vibrational population at excited centers in
View Description Hide DescriptionWe investigated nuclear wave packet dynamics in the excited state of centers at using timeresolved luminescencespectroscopy. Observed transient spectrum is divided into oscillatory and nonoscillatory components. The former lasts over without appreciable damping and is attributed to the oscillation of the wave packet consisting mainly of the mode around the center. The nonoscillatory part rises quickly after photoexcitation exhibiting a cooling of incoherent vibrational population. This behavior suggests the fast energy dissipation due to the dephasing of the bulk phonon modes.
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 ARTICLES

 Theoretical Methods and Algorithms

Auxiliaryfield quantum Monte Carlo calculations of molecular systems with a Gaussian basis
View Description Hide DescriptionWe extend the recently introduced phaseless auxiliaryfield quantum Monte Carlo (QMC) approach to any singleparticle basis and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with the system size as a low power. A QMC approach with auxiliary fields, in principle, allows an exact solution of the Schrödinger equation in the chosen basis. However, the wellknown sign/phase problem causes the statistical noise to increase exponentially. The phaseless method controls this problem by constraining the paths in the auxiliaryfield path integrals with an approximate phase condition that depends on a trial wave function. In the present calculations, the trial wave function is a single Slater determinant from a HartreeFock calculation. The calculated allelectron total energies show typical systematic errors of no more than a few millihartrees compared to exact results. At equilibrium geometries in the molecules we studied, this accuracy is roughly comparable to that of coupled cluster with single and double excitations and with noniterative triples [CCSD(T)]. For stretched bonds in , our method exhibits a better overall accuracy and a more uniform behavior than CCSD(T).

A combined explicitimplicit method for high accuracy reaction path integration
View Description Hide DescriptionWe present the use of an optimal combined explicitimplicit method for following the reaction path to high accuracy. This is in contrast to most purely implicit reaction path integration algorithms, which are only efficient on stiff ordinary differential equations. The defining equation for the reaction path is considered to be stiff, however, we show here that the reaction path is not uniformly stiff and instead is only stiff near stationary points. The optimal algorithm developed in this work is a combination of explicit and implicit methods with a simple criterion to switch between the two. Using three different chemical reactions, we combine and compare three different integration methods: the implicit trapezoidal method [C. Gonzalez and H. Schlegel, J. Chem. Phys.90, 2154 (1989)], an explicit stabilized third order algorithm [A. A. Medovikov, BIT38, 372 (1998)] implemented in the code DUMKA3 and the traditional explicit fourth order RungeKutta method written in the code RKSUITE. The results for high accuracy show that when the implicit trapezoidal method is combined with either explicit method the number of energy and gradient calculations can potentially be reduced by almost a half compared with integrating either method alone. Finally, to explain the improvements of the combined method we expand on the concepts of stability and stiffness and relate them to the efficiency of integration methods.

Statistical mechanical theory for steady state systems. V. Nonequilibrium probability density
View Description Hide DescriptionThe phase space probability density for steady heat flow is given. This generalizes the Boltzmann distribution to a nonequilibrium system. The expression includes the nonequilibrium partition function, which is a generating function for statistical averages and which can be related to a nonequilibrium free energy. The probability density is shown to give the GreenKubo formula in the linear regime. A Monte Carlo algorithm is developed based upon a Metropolis sampling of the probability distribution using an umbrella weight. The nonequilibrium simulation scheme is shown to be much more efficient for the thermal conductivity of a LennardJones fluid than the GreenKubo equilibrium fluctuation method. The theory for heat flow is generalized to give the generic nonequilibrium probability densities for hydrodynamic transport, for timedependent mechanical work, and for nonequilibrium quantum statistical mechanics.

Quantum Monte Carlo study of the Ne atom and the ion
View Description Hide DescriptionWe report allelectron and pseudopotential calculations of the groundstateenergies of the neutral Ne atom and the ion using the variational and diffusionquantum Monte Carlo (DMC) methods. We investigate different levels of SlaterJastrow trial wave function: (i) using HartreeFock orbitals, (ii) using orbitals optimized within a Monte Carlo procedure in the presence of a Jastrow factor, and (iii) including backflow correlations in the wave function. Small reductions in the total energy are obtained by optimizing the orbitals, while more significant reductions are obtained by incorporating backflow correlations. We study the finitetimestep and fixednode biases in the DMC energy and show that there is a strong tendency for these errors to cancel when the first ionization potential (IP) is calculated. DMC gives highly accurate values for the IP of Ne at all the levels of trial wave function that we have considered.

Comparative assessment of density functional methods for transitionmetal chemistry
View Description Hide DescriptionIn the present study, we comparatively assessed the newly developed M05 functional against a data set of reactionenergies for transitionmetal chemistry. The functionals to which we compare are BLYP, B3LYP, B972, MPWLYP1M, TPSS, and TPSSh. We draw the following conclusions: (1) TPSS gives the best performance for calculating the binding energies of three transitionmetal dimers (, , and ) that have severe multireference character, (2) B972 gives the best performance for calculating the binding energies of the nine metalligand diatomics (three monohydrides, three monoxide, and three monofluorides), and (3) M05 gives the overall best performance for all 18 data in the assessment, and it has a mean unsigned error 55% lower than the popular B3LYP functional. Since the M05 functional also gives good performance for maingroup thermochemistry, for noncovalent chemistry, and for calculating barrier heights, M05 can be applied to a wide range of problems where nonhybrid functionals or functionals designed for kinetics fail.

Relativistic calculation of nuclear magnetic shielding using normalized elimination of the small component
View Description Hide DescriptionThe normalized elimination of the small component (NESC) theory, recently proposed by Filatov and Cremer [J. Chem. Phys.122, 064104 (2005)], is extended to include magnetic interactions and applied to the calculation of the nuclear magnetic shielding in systems. The NESC calculations are performed at the levels of the zerothorder regular approximation (ZORA) and the secondorder regular approximation (SORA). The calculations show that the NESCZORA results are very close to the NESCSORA results, except for the shielding of the I nucleus. Both the NESCZORA and NESCSORA calculations yield very similar results to the previously reported values obtained using the relativistic infiniteorder twocomponent coupled HartreeFock method. The difference between NESCZORA and NESCSORA results is significant for the shieldings of iodine.

Energy gradients with respect to atomic positions and cell parameters for the KohnSham densityfunctional theory at the point
View Description Hide DescriptionThe application of theoretical methods based on densityfunctional theory is known to provide atomic and cell parameters in very good agreement with experimental values. Recently, construction of the exact HartreeFock exchange gradients with respect to atomic positions and cell parameters within the point approximation has been introduced [V. Weber et al., J. Chem. Phys.124, 214105 (2006)]. In this article, the formalism is extended to the evaluation of analytical point densityfunctional atomic and cell gradients. The infinite Coulomb summation is solved with an effective periodic summation of multipole tensors [M. Challacombe et al., J. Chem. Phys.107, 9708 (1997)]. While the evaluation of Coulomb and exchangecorrelation gradients with respect to atomic positions are similar to those in the gas phase limit, the gradients with respect to cell parameters needs to be treated with some care. The derivative of the periodic multipole interaction tensor needs to be carefully handled in both direct and reciprocal space and the exchangecorrelation energy derivative leads to a surface term that has its origin in derivatives of the integration limits that depend on the cell. As an illustration, the analytical gradients have been used in conjunction with the QUICCA algorithm [K. Németh and M. Challacombe, J. Chem. Phys.121, 2877 (2004)] to optimize onedimensional and threedimensional periodic systems at the densityfunctional theory and hybrid HartreeFock/densityfunctional theory levels. We also report the full relaxation of forsterite supercells at the B3LYP level of theory.

Legendretransform functionals for spindensityfunctional theory
View Description Hide DescriptionWe provide a rigorous proof that the HohenbergKohn theorem holds for spin densities by extending Lieb’s Legendretransform formulation to spin densities. The resulting spindensityfunctional theory resolves several troublesome issues. Most importantly, the present paper provides an explicit construction for the spin potentials at any point along the adiabatic connection curve, thus providing a formal basis for the use of exchangecorrelation functionals of the spin density in the KohnSham densityfunctional theory(DFT). The practical implications of this result for unrestricted KohnSham DFT calculations is considered, and the existence of holes below the Fermi level is discussed. We argue that an orbital’s energy tends to increase as its occupation number increases, which provides the basis for a computational algorithm for determining the occupation numbers in KohnSham DFT and helps explain the origin of Hund’s rules and holes below the Fermi level.

Analysis of multiconfigurational wave functions in terms of holeparticle distributions
View Description Hide DescriptionA detailed study of holeparticle distributions in manyelectron molecular systems is presented, based on a representation of the highorder density matrices obtained by an operator technique reminiscent of Bogolyubov’s quantum statistical operator theory. A rigorous definition of density matrices of arbitrary order is given for a composite system of holes and particles. Particular attention is focused on the description of mixed holeparticle distributions. The main results are given as the functionals of excitation operators (generators) that are used in the conventional configuration interaction (CI) and coupled cluster (CC) theories. Local atomic occupation numbers for holes and particles are introduced to provide a measure of the participation of specific atoms in the electron correlation processes. The corresponding total occupations—as well as the holehole, particleparticle, and holeparticle mean distances—provide a useful and physically intuitive description of electron correlation. Suitable computational schemes for numerical evaluation of the above characteristics within full CI and typical CC approaches are presented. The insights one can gain with the developed approach into the peculiarities and nuances of the holeparticle picture in typical electronic processes such as excitation and molecular dissociation are illustrated with specific computations on small molecules and closedshell atoms.

On a new selfconsistentfield theory for the canonical ensemble
View Description Hide DescriptionA significant amount of manybody problems of quantum or classical equilibrium statistical mechanics are conveniently treated at fixed temperature and system size. In this paper, we present a new functional integral approach for solving canonical ensemble problems over the entire coupling range, relying on the method of Gaussian equivalent representation of Efimov and Ganbold [Phys. Status Solidi168, 165 (1991)]. We demonstrate its suitability and competitiveness for performing approximate calculations of thermodynamic and structural quantities on the example of a repulsive potential model, widely used in soft matter theory.

New formulation and implementation for volume polarization in dielectric continuum theory
View Description Hide DescriptionIn the use of dielectric continuum theory to model bulk solvation effects on the electronic structure and properties of a solute, volume polarization contributions due to quantum mechanical penetration of the solute charge density outside the cavity nominally enclosing it are known to be significant. This work provides a new formulation and implementation of methods for solution of the requisite Poisson equation. In previous formulations the determination of the surfacepolarization contribution required evaluation of the difficult to calculate electric field generated by the volume polarization. It is shown that this problematic quantity can be eliminated in favor of other more easily evaluated quantities. That formal advance also opens the way for a more efficient apparatus to be implemented for calculation of the direct contribution of volume polarization to the solvation energy. The new formulation and its practical implementation are described, and illustrative numerical results are given for several neutral and ionic solutes to study the convergence and precision in practice.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Theoretical transition probabilities for the system of AlNC and AlCN isomers based on global potential energy surfaces
View Description Hide DescriptionTransition probabilities were evaluated for the system of AlNC and AlCN isomers to analyze photoabsorption and fluorescence spectra. The global potential energy surfaces (PESs) of the and electronic states were determined by the multireference configuration interaction calculations with the Davidson correction. Einstein’s coefficients were computed by quantum vibrational calculations using the threedimensional PESs of these states and the electronic transition moments for the and systems. Einstein’s coefficients obtained for AlNC or AlCN exhibit that the Al–N or Al–C stretching mode is strongly enhanced in the transition. The absorption and fluorescence spectra calculated for the and systems are discussed comparing with the observed photoexcitation and fluorescence spectra. The lifetimes for the several vibrational levels of the state were calculated to be ca. for AlNC and for AlCN from the fluorescence decay rates of the and emissions.

Is E112 a relatively inert element? Benchmark relativistic correlation study of spectroscopic constants in E112H and its cation
View Description Hide DescriptionWe report the first results of relativistic correlation calculation of the spectroscopic properties for the ground state of E112H and its cation in which spinorbit interaction is taken into account nonperturbatively. Studying the properties of E112 (ekaHg) is required for chemical identification of its longlived isotope, . It is shown that appropriate accounting for spinorbit effects leads to dramatic impact on the properties of E112H whereas they are not so important for . The calculated equilibrium distance, , in E112H is notably smaller than and in HgH, whereas the dissociation energy,, in E112H is close to and in HgH. These data are quite different from and obtained for E112H within the scalarrelativistic DouglasKroll approximation [Nakajima and Hirao, Chem. Phys. Lett.329, 511 (2000)]. Our results indicate that E112 should not be expected to behave like a noble gas in contrast to the results by other authors.

Multireference configuration interaction calculations for the reaction: A correlation scaled ground state potential energy surface
View Description Hide DescriptionThis paper presents a new ground state electronic potential energy surface for the reaction. The ab initio calculations are done at the multireference configuration correction level of theory by complete basis set extrapolation of the augcc energies. Due to lowlying charge transfer states in the transition state region, the molecular orbitals are obtained by sixstate dynamically weighted multichannel selfconsistent field methods. Additional perturbative refinement of the energies is achieved by implementing simple oneparameter correlation energy scaling to reproduce the experimental exothermicity for the reaction.Ab initio points are fitted to an analytical function based on sum of two and threebody contributions, yielding a rms deviation of for all geometries below above the barrier. Of particular relevance to nonadiabaticdynamics, the calculations show significant multireference character in the transition state region, which is located with respect to reactants and features a strongly bent F–H–Cl transition state geometry . Finally, the surface also exhibits two conical intersection seams that are energetically accessible at low collision energies. These seams arise naturally from allowed crossings in the linear configuration that become avoided in bent configurations of both the reactant and product, and should be a hallmark of all atom transfer reactiondynamics between halogen atoms.

The carrier gas pressure effect in a laminar flow diffusion chamber, homogeneous nucleation of butanol in helium
View Description Hide DescriptionHomogeneous nucleation rate isotherms of were measured in a laminar flowdiffusion chamber at total pressures ranging from to investigate the effect of carrier gas pressure on nucleation.Nucleation temperatures ranged from and the measurednucleation rates were between and . The measurednucleation rates decreased as a function of increasing pressure. The pressure effect was strongest at pressures below . This negative carrier gas effect was also temperature dependent. At nucleation temperature of and at the same saturation ratio, the maximum deviation between nucleation rates measured at 50 and was about three orders of magnitude. At nucleation temperature of , the effect was negligible. Qualitatively the results resemble those measured in a thermal diffusion cloud chamber. Also the slopes of the isothermal nucleation rates as a function of saturation ratio were different as a function of total pressure, isotherms yielded the steepest slopes, and isotherms the shallowest slopes. Several sources of inaccuracies were considered in the interpretation of the results: uncertainties in the transport properties, nonideal behavior of the vaporcarrier gas mixture, and shortcomings of the used mathematical model. Operation characteristics of the laminar flowdiffusion chamber at both underand overpressure were determined to verify a correct and stable operation of the device. We conclude that a negative carrier gas pressure effect is seen in the laminar flowdiffusion chamber and it cannot be totally explained with the aforementioned reasons.

Matchingpursuit splitoperator Fouriertransform simulations of excitedstate intramolecular proton transfer in 2(hydroxyphenyl)oxazole
View Description Hide DescriptionThe excitedstate intramolecular protontransfer dynamics associated with the ketoenolic tautomerization reaction in 2(hydroxyphenyl)oxazole is simulated according to a numerically exact quantumdynamics propagation method and a fulldimensional excitedstatepotential energy surface, based on an ab initioreactionsurface Hamiltonian. The reported simulations involve the propagation of 35dimensional wave packets according to the recently developed matchingpursuit/splitoperatorFouriertransform (MP/SOFT) method by Wu and Batista, [J. Chem. Phys.121, 1676 (2004)]. The underlying propagation scheme recursively applies the timeevolution operator as defined by the Trotter expansion to second order accuracy in dynamically adaptive coherentstate expansions. Computations of timedependent survival amplitudes, photoabsorption cross sections, and timedependent reactant(product) populations are compared to the corresponding calculations based on semiclassical approaches, including the HermanKluk semiclassical initial value representation method. The reported results demonstrate the capabilities of the MP/SOFT method as a valuble computational tool to study ultrafast reactiondynamics in polyatomic systems as well as to validate semiclassical simulations of complex (nonintegrable) quantum dynamics in multidimensional model systems.