Volume 130, Issue 16, 28 April 2009

A density functional theory is used to investigate adsorption of colloids on the surfaces grafted by polymers of different architectures, including linear, star, branched, and dendritic structures. In order to calculate the direct bonding connectivity integral, a new numerical algorithm is proposed for polymers with complex architecture. A good agreement of the calculated results and the simulation and experimental data in studying grafted hard chain brushes confirm that our approach does lead a correct prediction. Accordingly, adsorption of colloids in the negative exponential attractive surface was studied. The effects of grafting density, attractive strength, molecular concentration, and size on adsorption were considered. The contour maps of excluded rate show that a complex architecture of polymer chains is much more effective in preventing adsorption than linear polymer brush. The results also show that the grafting density and complex architecture are two key factors to prevent colloidaladsorption, while the surface attractive strength only exhibits slight effect on colloidaladsorption. For polymer brushes with complex architecture, the height of potential of mean force is strongly dependent on the colloidal size. The larger the size, the higher is the potential of mean force, which means that the larger colloidal molecules are harder to penetrate the brush. In short, to prevent colloidaladsorption, it is more suitable to use the polymer brushes with complex architecture.
 ARTICLES

 Theoretical Methods and Algorithms

Net transport due to noiseinduced internal reciprocating motion
View Description Hide DescriptionWe consider a system of two coupled Brownian particles fluctuating between two states. The fluctuations are produced by both equilibrium thermal and external nonthermal noise, the transition rates depending on the interparticle distance. An externally induced modulation of the transition rates acts on the internal degree of freedom (the interparticle distance) and generates reciprocating motion along this coordinate. The system moves unidirectionally due to rectification of the internal motion by asymmetric frictionfluctuations and thus operates as a dimeric motor that converts input energy into net movement. The properties of the motor are primarily determined by the properties of the reciprocating engine, represented by the interparticle distance dynamics. Two main mechanisms are recognized by which the engine operates: energetic and informational. In the physically important cases where only one of the motioninducing mechanisms is operative, exact solutions can be found for the model with linearly coupled particles. We focus on the informational mechanism, in which thermal noise is involved as a vital component and the reciprocating velocity exhibits a rich behavior as a function of the model parameters. An efficient rectification method for the reciprocating motion is also discussed.

Coverage of dynamic correlation effects by density functional theory functionals: Densitybased analysis for neon
View Description Hide DescriptionThe problem of linking the dynamic electron correlation effects defined in traditional ab initio methods [or wave function theories (WFTs)] with the structure of the individual density functional theory(DFT) exchange and correlation functionals has been analyzed for the Ne atom, for which nondynamic correlation effects play a negligible role. A densitybased approach directly hinged on difference radialdensity (DRD) distributions defined with respect the Hartree–Fock radial density has been employed for analyzing the impact of dynamic correlation effects on the density. Attention has been paid to the elimination of basisset incompleteness errors. The DRD distributions calculated by several ab initio methods have been compared to their DFT counterparts generated for representatives of several generations of broadly used exchangecorrelation functionals and for the recently developed orbitaldependent OEP2 exchangecorrelation functional [Bartlett et al., J. Chem. Phys.122, 034104 (2005)]. For the local, generalizedgradient, and hybrid functionals it has been found that the dynamic correlation effects are to a large extend accounted for by densities resulting from exchangeonly calculations. Additional calculations with selfinteraction corrected exchange potentials indicate that this finding cannot be explained as an artifact caused by the selfinteraction error. It has been demonstrated that the VWN5 and LYP correlation functionals do not represent any substantial dynamical correlation effects on the electron density, whereas these effects are well represented by the orbitaldependent OEP2 correlation functional. Critical comparison of the present results with their counterparts reported in literature has been made. Some attention has been paid to demonstrating the differences between the energy and densitybased perspectives. They indicate the usefulness of densitybased criteria for developing new exchangecorrelation functionals.

An efficient generalized polyelectron population analysis in orbital spaces: The holeexpansion methodology
View Description Hide DescriptionWe present relations leading to an efficient generalized population analysis in orbital spaces of usual delocalized molecular orbital wave functions. Besides the calculation of the diagonal elements of the reduced density matrices of any order, one can also calculate efficiently the probabilities (or, in general, the weights) of various occupation schemes of local electronic structures, by using generalized density operators referring to both electrons and electron holes. Within this population analysis, correlated molecular orbital wave functions can be used, and there are no restrictions to the number of the analyzedelectrons and electron holes. It is based on the holeexpansion methodology, according to which a given electronic population is expanded in terms involving only electron holes, which as shown, can be calculated very efficiently; usual difficulties arising from the necessity to handle extremely large local determinantal basis sets are avoided, without introducing approximations. Although an emphasis is given for populations in the basis of orthogonal orbital spaces (providing probabilities), the case of nonorthogonal ones is also considered in order to show the connection of the generalized populations and the traditional weights obtained from valencebond wave functions. Physically meaningful populations can be obtained by using natural orbitals, such as the natural atomic orbitals (NAOs) (orthogonal orbitals) or the preNAO’s (nonorthogonal orbitals); numerical applications for pyrrole molecule are presented in the basis of these natural orbitals.

Optimal sampling efficiency in Monte Carlo simulation with an approximate potential
View Description Hide DescriptionBuilding on the work of Iftimie et al. [J. Chem. Phys.113, 4852 (2000)] and Gelb [J. Chem. Phys.118, 7747 (2003)], Boltzmann sampling of an approximate potential (the “reference” system) is used to build a Markov chain in the isothermalisobaric ensemble. At the end points of the chain, the energy is evaluated at a more accurate level (the “full” system) and a composite move encompassing all of the intervening steps is accepted on the basis of a modified Metropolis criterion. For reference system chains of sufficient length, consecutive full energies are statistically decorrelated and thus far fewer are required to build ensemble averages with a given variance. Without modifying the original algorithm, however, the maximum reference chain length is too short to decorrelate full configurations without dramatically lowering the acceptance probability of the composite move. This difficulty stems from the fact that the reference and full potentials sample different statistical distributions. By manipulating the thermodynamic variables characterizing the reference system (pressure and temperature, in this case), we maximize the average acceptance probability of composite moves, lengthening significantly the random walk between consecutive full energy evaluations. In this manner, the number of full energy evaluations needed to precisely characterize equilibrium properties is dramatically reduced. The method is applied to a model fluid, but implications for sampling highdimensional systems with ab initio or density functional theory potentials are discussed.

Bottlenecks to vibrational energy flow in carbonyl sulfide: Structures and mechanisms
View Description Hide DescriptionFinding the causes for the nonstatistical vibrational energy relaxation in the planar carbonyl sulfide (OCS) molecule is a longstanding problem in chemical physics: Not only is the relaxation incomplete long past the predicted statistical relaxation time but it also consists of a sequence of abrupt transitions between longlived regions of localized energy modes. We report on the phase space bottlenecks responsible for this slow and uneven vibrational energy flow in this Hamiltonian system with three degrees of freedom. They belong to a particular class of twodimensional invariant tori which are organized around elliptic periodic orbits. We relate the trapping and transition mechanisms with the linear stability of these structures.

Approximated electron repulsion integrals: Cholesky decomposition versus resolution of the identity methods
View Description Hide DescriptionWe compare two procedures to gain efficiency by approximating twoelectron integrals in molecular electronic structure calculations. The first one is based on a Cholesky decomposition (CD) of twoelectron integrals, the second one on the use of preoptimized auxiliary or fitting basis sets employed in a “resolution of the identity” (RI) technique. We present and test auxiliary bases for approximating the Coulomb term, which further improves accuracy over previously proposed fitting bases. It is shown that RI methods lead to insignificant errors only, which are partly comparable to or even better than that of CD treatments; but RI procedures are superior in speed. CD methods have certain advantages, however, particularly for extended basis sets.

Dissociation aided and side chain sampling enhanced Hamiltonian replica exchange
View Description Hide DescriptionA new application of Hamiltonian replica exchange method is suggested: The potential energy function is adjusted in such a way that repulsive forces between atoms of solute are reinforced. This dissociation action helps the system to escape from the local minima on the free energy landscape. Compared with other Hamiltonian replica exchange methods in which the potential energy between solute atoms and between solute and solvent atoms was reduced, and compared with the temperature replica exchange method, the new scheme displays superior ability to overcome large free energy barrier in a model system. For protein simulation, the side chain conformation sampling turns out to be an issue and an enhancement method is introduced. Combining the dissociation aided method with the specific side chain sampling technique is proven to be a help to explore the complex energy landscape of protein, which is demonstrated by three independent ab initio folding simulations on the trpzip2 peptide.

Energyconsistent pseudopotentials and correlation consistent basis sets for the elements Hf–Pt
View Description Hide DescriptionNew relativistic energyconsistent pseudopotentials have been generated for the transition metals Hf–Pt. The adjustment was done in numerical twocomponent multiconfiguration Hartree–Fock calculations, using atomic valenceenergy spectra from fourcomponent multiconfiguration Dirac–Hartree–Fock calculations as reference data. The resulting twocomponent pseudopotentials replace the cores of the transition metals and can easily be split into a scalarrelativistic and a spinorbit part. They reproduce the allelectron reference energy data with deviations of for configurational averages and for individual relativistic states. Full series of correlation consistent basis sets from double to quintuplezeta have also been developed in this work for use with the new pseudopotentials. In addition, allelectron triplezeta quality correlation consistent basis sets are also reported in order to provide calibration for the pseudopotential treatment. The accuracy of both the pseudopotentials and basis sets are assessed in extensive coupled cluster benchmark calculations of atomic ionization potentials, electron affinities, and selected excitation energies of all the 5d metal atoms, including the effects of spinorbit coupling.

Openshell molecular electronic states from the parametric twoelectron reduceddensitymatrix method
View Description Hide DescriptionThe parametric variational twoelectron reduceddensitymatrix (2RDM) method, developed from an analysis of positivity (representability) constraints on the 2RDM, is extended to treat both closed and openshell molecules in singlet, doublet, and triplet spin states. The parametric 2RDM method can be viewed as using representability conditions to modify the 2RDM from a configuration interaction singlesdoubles wave function to make the energy size extensive while keeping the 2RDM approximately representable [J. Kollmar, Chem. Phys.125, 084108 (2006); A. E. DePrince and D. A. Mazziotti, Phys. Rev. A76, 049903 (2007)]. Vertical excitation energies between triplet and singlet states are computed in a polarized valence triplezeta basis set. In comparison to traditional singlereference wave function methods, the parametric 2RDM method recovers a larger percentage of the multireference correlation in the singlet excited states, which improves the accuracy of the vertical excitation energies. Furthermore, we show that molecular geometry optimization within the parametric 2RDM method can be efficiently performed through a Hellmann–Feynmanlike relation for the energy gradient with respect to nuclear coordinates. Both the openshell extension and the energygradient relation are applied to computing relative energies and barrier heights for the isomerization reaction . The computed 2RDMs very nearly satisfy well known, necessary representability conditions.

Intracule functional models. IV. Basis set effects
View Description Hide DescriptionWe have calculated position and dot intracules for a series of atomic and molecular systems, starting from an unrestricted Hartree–Fock wave function, expanded using the STO3G, 6–31G, 6–311G, , , , and basis sets as well as the nonpolarized part of Dunning’s ccpV5Z basis. We find that the basis set effects on the intracules are small and that correlation energies from the dot intracule ansatz are remarkably insensitive to the basis set quality. Mean absolute errors in correlation energies across the G1 data set agree to within for all basis sets tested.

Calculating solution redox free energies with ab initio quantum mechanical/molecular mechanical minimum free energy path method
View Description Hide DescriptionA quantum mechanical/molecular mechanical minimum free energy path (QM/MMMFEP) method was developed to calculate the redoxfree energies of large systems in solution with greatly enhanced efficiency for conformation sampling. The QM/MMMFEP method describes the thermodynamics of a system on the potential of mean force surface of the solute degrees of freedom. The molecular dynamics (MD) sampling is only carried out with the QM subsystem fixed. It thus avoids “onthefly” QM calculations and thus overcomes the high computational cost in the direct QM/MM MD sampling. In the applications to two metal complexes in aqueous solution, the new QM/MMMFEP method yielded redoxfree energies in good agreement with those calculated from the direct QM/MM MD method. Two larger biologically important redox molecules, lumichrome and riboflavin, were further investigated to demonstrate the efficiency of the method. The enhanced efficiency and uncompromised accuracy are especially significant for biochemical systems. The QM/MMMFEP method thus provides an efficient approach to free energy simulation of complex electron transferreactions.

Exploring the capabilities of quantum optimal dynamic discrimination
View Description Hide DescriptionOptimal dynamic discrimination (ODD) uses closedloop learning control techniques to discriminate between similar quantum systems. ODD achieves discrimination by employing a shaped control (laser) pulse to simultaneously exploit the unique quantum dynamics particular to each system, even when they are quite similar. In this work, ODD is viewed in the context of multiobjective optimization, where the competing objectives are the degree of similarity of the quantum systems and the level of controlled discrimination that can be achieved. To facilitate this study, the DMORPH gradient algorithm is extended to handle multiple quantum systems and multiple objectives. This work explores the tradeoff between laser resources (e.g., the length of the pulse, fluence, etc.) and ODD’s ability to discriminate between similar systems. A mechanism analysis is performed to identify the dominant pathways utilized to achieve discrimination between similar systems.

Nonadiabatic corrections to rovibrational levels of
View Description Hide DescriptionThe leading nonadiabatic corrections to rovibrational levels of a diatomic molecule are expressed in terms of three functions of internuclear distance: corrections to the adiabatic potential, the effective nuclear mass, and the effective moment of inertia. The resulting radial Schrödinger equation for nuclear motion is solved numerically yielding accurate nonadiabatic energies for all rovibrational levels of the molecule. Results for states with are in excellent agreement with previous calculations by Wolniewicz, and for states with are new.

Recovering fourcomponent solutions by the inverse transformation of the infiniteorder twocomponent wave functions
View Description Hide DescriptionThe twocomponent Hamiltonian of the infiniteorder twocomponent (IOTC) theory is obtained by a unitary blockdiagonalizing transformation of the Dirac–Hamiltonian. Once the IOTC spin orbitals are calculated, they can be back transformed into fourcomponent solutions. The transformed four component solutions are then used to evaluate different moments of the electron density distribution. This formally exact method may, however, suffer from certain approximations involved in its numerical implementation. As shown by the present study, with sufficiently large basis set of Gaussian functions, the Dirac values of these moments are fully recovered in spite of using the approximate identity resolution into eigenvectors of the operator.

Approximating quantum manybody intermolecular interactions in molecular clusters using classical polarizable force fields
View Description Hide DescriptionManybody intermolecular interaction expansions provide a promising avenue for the efficient quantum mechanical treatment of molecular clusters and condensedphase systems, but the computationally expensive threebody and higher terms are often nontrivial. When polar molecules are involved, these manybody terms are typically dominated by electrostatic induction effects, which can be approximated relatively easily. We demonstrate an accurate and inexpensive hybrid quantum/classical model in which one and twobody interactions are computed quantum mechanically, while the manybody induction effects are approximated with a simple classical polarizable force field. Whereas typical hybrid quantum/classical models partition a systemspatially into distinct quantum and classical regions, the model demonstrated here partitions based on the order in the manybody interaction series. This enables a spatially homogeneous treatment of the entire system, which could prove advantageous in studying a wide range of condensedphase molecular systems.

Analysis and classification of symmetry breaking in linear type triatomics
View Description Hide DescriptionThe symmetry of the nuclear framework of polyatomic molecules is qualitatively lowered by small changes in their geometry. This may lead to a dramatic change in the nature of their Hartree–Fock (HF) solutions and to a singular behavior of the corresponding potential energy surfaces (PESs), which may persist even at the correlated level if based on these HF references. We examine a general shape of the restricted HF (RHF) and openshell RHF PESs for the linear triatomic molecules of the type in the vicinity of the symmetric geometries and the role played by the spinrestricted (singlet or doublet) stability of the corresponding HF solutions. This enabled us to classify the character of these surfaces into three basic types depending on the nature of the cut of the PES along the asymmetric stretching mode coordinate. We also examine the implications of the type of these nodes on the PES obtained at the postHF correlated CCSD(T) level as well as on the determination of the vibrational frequencies for both the symmetric and asymmetric stretching modes. When using either the numerical differentiation of the PES or the solution of the Schrödinger equation for the nuclear motion for this purpose, it is shown that either method yields very good results for the symmetric mode frequencies, while the former approach may yield highly erroneous values for the asymmetric mode frequencies depending on the type of the HF PES at the equilibrium geometry in which case the latter approach still provides us with reasonably good results.

Bubble merging in breathing DNA as a vicious walker problem in opposite potentials
View Description Hide DescriptionWe investigate the coalescence of two DNA bubbles initially located at weak domains and separated by a more stable barrier region in a designed construct of doublestranded DNA. In a continuum Fokker–Planck approach, the characteristic time for bubble coalescence and the corresponding distribution are derived, as well as the distribution of coalescence positions along the barrier. Below the melting temperature, we find a Kramerstype barrier crossing behavior, while at high temperatures, the bubble corners perform drift diffusion toward coalescence. In the calculations, we map the bubble dynamics on the problem of two vicious walkers in opposite potentials. We also present a discrete master equation approach to the bubble coalescence problem. Numerical evaluation and stochastic simulation of the master equation show excellent agreement with the results from the continuum approach. Given that the coalesced state is thermodynamically stabilized against a state where only one or a few of the base pairs of the barrier region are reestablished, it appears likely that this type of setup could be useful for the quantitative investigation of thermodynamic DNA stability data as well as the rate constants involved in the unzipping and zipping dynamics of DNA in single molecule fluorescence experiments.

Microcanonical rates, gap times, and phase space dividing surfaces
View Description Hide DescriptionThe general approach to classical unimolecular reaction rates due to Thiele is revisited in light of recent advances in the phase space formulation of transition state theory for multidimensional systems. Key concepts, such as the phase space dividing surface separating reactants from products, the average gap time, and the volume of phase space associated with reactive trajectories, are both rigorously defined and readily computed within the phase space approach. We analyze in detail the gap time distribution and associated reactant lifetime distribution for the isomerizationreaction, previously studied using the methods of phase space transition state theory. Both algebraic (power law) and exponential decay regimes have been identified. Statistical estimates of the isomerization rate are compared with the numerically determined decay rate. Correcting the RRKM estimate to account for the measure of the reactant phase space region occupied by trapped trajectories results in a drastic overestimate of the isomerization rate. Compensating but as yet not fully understood trapping mechanisms in the reactant region serve to slow the escape rate sufficiently that the uncorrected RRKM estimate turns out to be reasonably accurate, at least at the particular energy studied. Examination of the decay properties of subensembles of trajectories that exit the HCN well through either of two available symmetry related product channels shows that the complete trajectory ensemble effectively attains the full symmetry of the system phase space on a short time scale , after which the product branching ratio is 1:1, the “statistical” value. At intermediate times, this statistical product ratio is accompanied by nonexponential (nonstatistical) decay. We point out close parallels between the dynamical behavior inferred from the gap time distribution for HCN and nonstatistical behavior recently identified in reactions of some organic molecules.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Fine structure and hyperfine perturbations in the pure rotational spectrum of the VCl radical in its state
View Description Hide DescriptionThe pure rotational spectrum of the VCl radical in its ground state has been recorded in the range 236–417 GHz using millimeter/submillimeter direct absorption techniques. This species was created in an ac discharge of and argon. Ten rotational transitions of were measured in all five ladders; an additional nine transitions of the spin state were recorded in order to evaluate the hyperfine structure.Hyperfine interactions associated with the nucleus were not resolved, consistent with the ionic structure of the molecule. Because of extensive perturbations caused by the lowlying excited state, the rotational spectrum of the ground state has been found to be quite irregular. The four lowest ladders exhibit unusually large lambdadoubling interactions, with the component showing the largest splitting, over 2 GHz in magnitude. The transitions are also shifted to higher frequency relative to the other spin components. In addition, the hyperfine structure varies widely between the ladders, and an avoided crossing is observed in two transitions of both the and components. The data have been analyzed with a case Hamiltonian, and effective rotational, lambdadoubling, and hyperfine constants have been determined for . Higherorder paritydependent magnetic hyperfine terms and were required in the analysis, derived from perturbation theory, in addition to the usual parameter. The local perturbations evident in these spectra indicate that the excited state lies within the spinorbit manifold of the ground state, well below the predicted value of . Mixing of the and states apparently causes both local and global perturbations in the ground statespectrum.

isotopic system at low temperatures: Microcanonical model and experimental study
View Description Hide DescriptionStatetostate thermal rate coefficients for reactions of all isotopic variants are derived and compared to new experimental data. The theoretical data are also sought for astrochemical modeling of cold environments . The rates are calculated on the basis of a microcanonical approach using the Langevin model and the conservation laws of mass, energy, angular momentum, and nuclear spin. Full scrambling of all five nuclei during the collision is assumed for the calculations and alternatively partial dynamical restrictions are considered. The ergodic principle of the collision is employed in two limiting cases, neglecting (weak ergodic limit) or accounting for explicit degeneracies of the reaction mechanisms (strong ergodic limit). The resulting sets of rate coefficients are shown to be consistent with the detailed balance and thermodynamical equilibrium constants. Rate coefficients, , for the deuteration chain of with HD as well as equilibrium ratios have been measured in a variable temperature 22pole ion trap. In particular, the rate coefficient indicates a change in reaction mechanism when going to higher temperatures. The good overall agreement between experiment and theory encourages the use of the theoretical predictions for astrophysical modeling.