Volume 135, Issue 13, 07 October 2011

Formation of protein–DNA complex is an important step in regulation of genes in living organisms. One important issue in this problem is the role played by water in mediating the protein–DNAinteractions. In this work, we have carried out atomistic molecular dynamics simulations to explore the heterogeneous dynamics of water molecules present in different regions around a complex formed between the DNA binding domain of human TRF1 protein and a telomeric DNA. It is demonstrated that such heterogeneous water motions around the complex are correlated with the relaxation time scales of hydrogen bonds formed by those water molecules with the protein and DNA. The calculations reveal the existence of a fraction of extraordinarily restricted water molecules forming a highly rigid thin layer in between the binding motifs of the protein and DNA. It is further proved that higher rigidity of water layers around the complex originates from more frequent reformations of broken water–water hydrogen bonds. Importantly, it is found that the formation of the complex affects the transverse and longitudinal degrees of freedom of surrounding water molecules in a nonuniform manner.
 COMMUNICATIONS


Communication: Rigorous calculation of dissociation energies (D _{0}) of the water trimer, (H_{2}O)_{3} and (D_{2}O)_{3}
View Description Hide DescriptionUsing a recent, fulldimensional, ab initiopotential energy surface[Y. Wang, X. Huang, B. C. Shepler, B. J. Braams, and J. M. Bowman, J. Chem. Phys.134, 094509 (2011)]10.1063/1.3554905 together with rigorous diffusion Monte Carlo calculations of the zeropoint energy of the water trimer, we report dissociation energies,D _{0}, to form one monomer plus the water dimer and three monomers. The calculations make use of essentially exact zeropoint energies for the water trimer, dimer, and monomer, and benchmark values of the electronic dissociation energies,D _{e}, of the water trimer [J. A. Anderson, K. Crager, L. Fedoroff, and G. S. Tschumper, J. Chem. Phys.121, 11023 (2004)]10.1063/1.1799931. The D _{0} results are 3855 and 2726 cm^{−1} for the 3H_{2}O and H_{2}O + (H_{2}O)_{2}dissociation channels, respectively, and 4206 and 2947 cm^{−1} for 3D_{2}O and D_{2}O + (D_{2}O)_{2}dissociation channels, respectively. The results have estimated uncertainties of 20 and 30 cm^{−1} for the monomer plus dimer and three monomer of dissociation channels, respectively.

Communication: Brokenergodicity and the emergence of solid behaviour in amorphous materials
View Description Hide DescriptionUsing a combination of theory and molecular dynamics simulations, we show how solid behaviour emerges in amorphousmaterials from microscopic considerations. The effect on the systems response to a sudden change in strain, upon entering the history dependent glass state, is focused on. An important symmetry that is always present in a fluid state, is shown to be broken for a simulated history dependent amorphous solid. Details of how this applies to a single sample and an ensemble of independent samples are discussed, along with the dependence on the time scale the system is monitored on.

Communication: Convergence of anharmonic infrared intensities of hydrogen fluoride in traditional and explicitly correlated coupled cluster calculations
View Description Hide DescriptionIt is shown that the convergence of anharmonic infrared spectral intensities with respect to the basis set size is much enhanced in explicitly correlated calculations as compared to traditional configuration interaction type wave function expansion. Explicitly correlated coupled cluster (CC) calculations using Slatertype geminal correlation factor (CCF12) yield wellconverged dipole derivatives and vibrational intensities for hydrogen fluoride with basis set involving f functions on the heavy atom. Combination of CCF12 with singles, doubles, and noniterative triples (CCSD(T)F12) with small corrections due to quadruple excitations, coreelectron correlation, and relativistic effects yields vibrational line positions, dipole moments, and transition dipole matrix elements in good agreement with the best experimental values.

Communication: Effects of stress on the tube confinement potential and dynamics of topologically entangled rod fluids
View Description Hide DescriptionA microscopic theory for the effect of applied stress on the transverse topological confinement potential and slow dynamics of heavily entangled rigid rods is presented. The confining entanglement force localizing a polymer in a tube is predicted to have a finite strength. As a consequence, three regimes of terminal relaxation behavior are predicted with increasing stress: accelerated reptation due to tube widening (dilation), relaxation via deformationassisted activated transverse barrier hopping, and complete destruction of the lateral tube constraints corresponding to microscopic yielding or a disentanglement transition.
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 ARTICLES

 Theoretical Methods and Algorithms

Polymorph specific RMSD local order parameters for molecular crystals and nuclei: α, β, and γglycine
View Description Hide DescriptionCrystal nucleation is important for many processes including pharmaceutical crystallization, biomineralization, and material synthesis. The progression of structural changes which occur during crystal nucleation are often described using order parameters. Polymorph specific order parameters have been developed for crystallization of spherically symmetric particles; however, polymorph specific order parameters for molecular crystals remain a challenge. We introduce template based polymorph specific order parameters for molecular crystals. For each molecule in a simulation, we compute the root mean squared deviation (RMSD) between the local environment around the molecule and a template of the perfect crystal structure for each polymorph. The RMSD order parameters can clearly distinguish the α, β, and γglycine polymorphcrystal structures in the bulk crystal and also in solvated crystallites. Surface melting of glycine crystallites in supersaturated aqueous solution is explored using the newly developed order parameters. The solvated αglycine crystallite has a thinner surface melted layer than the γglycine crystallite. αglycine forms first out of aqueous solution, so surface melted layer thickness may provide insight into interfacial energy and polymorph selection.

Van der Waals interactions: Evaluations by use of a statistical mechanical method
View Description Hide DescriptionIn this work the induced van der Waals interaction between a pair of neutral atoms or molecules is considered by use of a statistical mechanical method. With use of the Schrödinger equation this interaction can be obtained by standard quantum mechanical perturbation theory to second order. However, the latter is restricted to electrostatic interactions between dipole moments. So with radiating dipoledipole interaction where retardation effects are important for large separations of the particles, other methods are needed, and the resulting induced interaction is the CasimirPolder interaction usually obtained by field theory. It can also be evaluated, however, by a statistical mechanical method that utilizes the path integral representation. We here show explicitly by use of this method the equivalence of the CasimirPolder interaction and the van der Waals interaction based upon the Schrödinger equation. The equivalence is to leading order for short separations where retardation effects can be neglected. In recent works [J. S. Høye, Physica A389, 1380 (2010)10.1016/j.physa.2009.12.003; Phys. Rev. E81, 061114 (2010)]10.1103/PhysRevE.81.061114, the CasimirPolder or Casimir energy was added as a correction to calculations of systems like the electron clouds of molecules. The equivalence to van der Waals interactions indicates that the added Casimir energy will improve the accuracy of calculated molecular energies. Thus, we give numerical estimates of this energy including analysis and estimates for the uniform electron gas.

A discrete interaction model/quantum mechanical method to describe the interaction of metal nanoparticles and molecular absorption
View Description Hide DescriptionA frequencydependent quantum mechanics/molecular mechanics method for the calculation of response properties of molecules adsorbed on metal nanoparticles is presented. This discrete interaction model/quantum mechanics (DIM/QM) method represents the nanoparticle atomistically, thus accounting for the local environment of the nanoparticle surface on the optical properties of the adsorbed molecule. Using the DIM/QM method, we investigate the coupling between the absorption of a silvernanoparticle and of a substituted naphthoquinone. This system is chosen since it shows strong coupling due to a molecular absorption peak that overlaps with the plasmon excitation in the metal nanoparticle. We show that there is a strong dependence not only on the distance of the molecule from the metal nanoparticle but also on its orientation relative to the nanoparticle. We find that when the transitiondipole moment of an excitation is oriented towards the nanoparticle there is a significant increase in the molecular absorption as a result of coupling to the metal nanoparticle. In contrast, we find that the molecular absorption is decreased when the transitiondipole moment is oriented parallel to the metal nanoparticle. The coupling between the molecule and the metal nanoparticle is found to be surprisingly long range and important on a length scale comparable to the size of the metal nanoparticle. A simple analytical model that describes the molecule and the metal nanoparticle as two interacting point objects is found to be in excellent agreement with the full DIM/QM calculations over the entire range studied. The results presented here are important for understanding plasmon–exciton hybridization, plasmon enhanced photochemistry, and singlemolecule surfaceenhanced Raman scattering.

Density functional theory calculations of dynamic first hyperpolarizabilities for organic molecules in organic solvent: Comparison to experiment
View Description Hide DescriptionAgainst experimental values obtained from solutionphase dc electric field induced secondharmonic generation measurements at a fundamental wavelength of 1910 nm, the performance of 20 exchangecorrelation functionals in density functional theory in evaluation of solvent modulated dynamic first hyperpolarizabilities of 82 organic molecules in chloroform, 1,4dioxane, and/or dichloromethane was evaluated. The used exchangecorrelation functionals consisted of generalized gradient approximation (GGA), metaGGA, global hybrids, and rangeseparated hybrids. The PCMX/6311+G(2d,p)//PCMB3LYP/631G(2df,p) level of theory was employed. The calculated results showed functionals with the exact asymptote of the exchange potential gave satisfying linear correlation with R^{2} of 0.95 between experimental data and theoretical values. With a linear correction, these functionals also provided a better accuracy with mean absolute error of 5 × 10^{−30} esu than other functionals. The solvent effect and solvation scheme on the calculated property were also studied.

Polarizability and alignment of dielectric nanoparticles in an external electric field: Bowls, dumbbells, and cuboids
View Description Hide DescriptionWe employ the coupled dipole method to calculate the polarizabilitytensor of various anisotropic dielectricclusters of polarizable atoms, such as cuboid, bowl, and dumbbellshaped nanoparticles. Starting from a Hamiltonian of a manyatom system, we investigate how this tensor depends on the size and shape of the cluster. We use the polarizabilitytensor to calculate the energy difference associated with turning a nanocluster from its least to its most favorable orientation in a homogeneous static electric field, and we determine the cluster dimension for which this energy difference exceeds the thermal energy such that particle alignment by the field is possible. Finally, we study in detail the (local) polarizability of a cubicshaped cluster and present results indicating that, when retardation is ignored, a bulk polarizability cannot be reached by scaling up the system.

Monte Carlo simulation of osmotic equilibria
View Description Hide DescriptionWe present a Metropolis Monte Carlo simulation algorithm for the Tpπensemble, where T is the temperature, p is the overall external pressure, and π is the osmotic pressure across the membrane. The algorithm, which can be applied to small molecules or sorption of small molecules in polymer networks, is tested for the case of LennardJones interactions.

An efficient linear scaling procedure for constructing localized orbitals of large molecules based on the oneparticle density matrix
View Description Hide DescriptionWe have developed a linearscaling algorithm for obtaining the Boys localized molecular orbitals from the oneparticle density matrix. The algorithm is made up of two steps: the Cholesky decomposition of the density matrix to obtain Cholesky molecular orbitals and the subsequent Boys localization process. Linearscaling algorithms have been proposed to achieve linearscaling calculations of these two steps, based on the sparse matrix technique and the locality of the Cholesky molecular orbitals. The present algorithm has been applied to compute the Boys localized orbitals in a number of systems including αhelix peptides, water clusters, and protein molecules. Illustrative calculations demonstrate that the computational time of obtaining Boys localized orbitals with the present algorithm is asymptotically linear with increasing the system size.

Sizeextensive vibrational selfconsistent field method
View Description Hide DescriptionThe vibrational selfconsistent field (VSCF) method is a meanfield approach to solve the vibrational Schrödinger equation and serves as a basis of vibrational perturbation and coupledcluster methods. Together they account for anharmonic effects on vibrational transition frequencies and vibrationally averaged properties. This article reports the definition, programmable equations, and corresponding initial implementation of a diagrammatically sizeextensive modification of VSCF, from which numerous terms with nonphysical size dependence in the original VSCF equations have been eliminated. When combined with a quartic force field (QFF), this compact and strictly sizeextensive VSCF (XVSCF) method requires only quartic force constants of the type, where V is the electronic energy and Q _{ i } is the ith normal coordinate. Consequently, the cost of a XVSCF calculation with a QFF increases only quadratically with the number of modes, while that of a VSCF calculation grows quartically. The effective (meanfield) potential of XVSCF felt by each mode is shown to be harmonic, making the XVSCF equations subject to a selfconsistent analytical solution without matrix diagonalization or a basisset expansion, which are necessary in VSCF. Even when the same set of force constants is used, XVSCF is nearly three orders of magnitude faster than VSCF implemented similarly. Yet, the results of XVSCF and VSCF are shown to approach each other as the molecular size is increased, implicating the inclusion of unnecessary, nonphysical terms in VSCF. The diagrams of the XVSCF energy expression and their evaluation rules are also proposed, underscoring their connected structures.

Correction factors for boundary diffusion in reactiondiffusion master equations
View Description Hide DescriptionThe reactiondiffusion master equation (RDME) has been widely used to model stochastic chemical kinetics in space and time. In recent years, RDMEbased trajectorial approaches have become increasingly popular. They have been shown to capture spatial detail at moderate computational costs, as compared to fully resolved particlebased methods. However, finding an appropriate choice for the discretization length scale is essential for building a reasonable RDME model. Moreover, it has been recently shown [R. Erban and S. J. Chapman, Phys. Biol.4, 16 (2007)10.1088/14783975/4/1/003; R. Erban and S. J. Chapman, Phys. Biol.6, 46001 (2009)10.1088/14783975/6/4/046001; D. Fange, O. G. Berg, P. Sjöberg, and J. Elf, Proc. Natl. Acad. Sci. U.S.A.107, 46 (2010)] that the reaction rates commonly used in RDMEs have to be carefully reassessed when considering reactive boundary conditions or binary reactions, in order to avoid inaccurate – and possibly unphysical – results. In this paper, we present an alternative approach for deriving correction factors in RDME models with reactive or semipermeable boundaries. Such a correction factor is obtained by solving a closed set of equations based on the moments at steady state, as opposed to modifying probabilities for absorption or reflection. Lastly, we briefly discuss existing correction mechanisms for bimolecular reaction rates both in the limit of fast and slow diffusion, and argue why our method could also be applied for such purpose.

Charge carrier dynamics in phononinduced fluctuation systems from timedependent wavepacket diffusion approach
View Description Hide DescriptionA timedependent wavepacket diffusion method is proposed to deal with chargetransport in organic crystals. The electronphonon interactions in both site energies and electronic couplings are incorporated by the timedependent fluctuations which are generated from the corresponding spectral density functions. The numerical demonstrations reveal that the present approach predicts the consistent charge carrier dynamics with the rigorous quantum approaches. In addition, the diffusion coefficients obtained from the Marcus formula are well reproduced at the weak electronic coupling and high temperature limits. It is also found that the chargemobility feature of the crossover from the bandlike to the hoppingtype cannot be predicted from the fluctuations induced by the linear electronphonon interactions with an Ohmic spectral density; however, it indeed appears as the electronic coupling fluctuation exponentially depends on the nuclear coordinates. Finally, it should be noted that although the present approach neglects the imaginary fluctuation, it essentially incorporates the coherent motion of the charge carrier and quantum effect of the phonon motion with a broad regime of the fluctuations for symmetric systems. Besides, the approach can easily be applied to systems having thousands of sites, which allows one to investigate chargetransport in nanoscale organic crystals.

An infinite swapping approach to the rareevent sampling problem
View Description Hide DescriptionWe describe a new approach to the rareevent Monte Carlo sampling problem. This technique utilizes a symmetrization strategy to create probability distributions that are more highly connected and, thus, more easily sampled than their original, potentially sparse counterparts. After discussing the formal outline of the approach and devising techniques for its practical implementation, we illustrate the utility of the technique with a series of numerical applications to LennardJones clusters of varying complexity and rareevent character.

Zerovariance zerobias quantum Monte Carlo estimators for the electron density at a nucleus
View Description Hide DescriptionWe derive new quantum Monte Carlo (QMC) estimators for the electronic density at the position of a point nucleus using the zerovariance and zerobias principles. The resulting estimators are highly efficient, and are significantly simpler to implement and use than alternative methods, as they contain no adjustable parameters. In addition, they can be used in both variational and diffusion QMC calculations. Our best estimator is used to calculate the most accurate available estimates of the total electron density at the nucleus for the firstrow atoms LiNe, the Ar atom, and the diatomic molecules B_{2}, N_{2}, and F_{2}.

Linking the historical and chemical definitions of diabatic states for charge and excitation energy transfer reactions in condensed phase
View Description Hide DescriptionMarcus theory of electron transfer(ET) and Förster theory of excitation energy transfer (EET) rely on the Condon approximation and the theoretical availability of initial and final states of ET and EET reactions, often called diabatic states. Recently [Subotnik et al., J. Chem. Phys.130, 234102 (2009)10.1063/1.3148777], diabatic states for practical calculations of ET and EET reactions were defined in terms of their interactions with the surrounding environment. However, from a purely theoretical standpoint, the definition of diabatic states must arise from the minimization of the dynamic couplings between the trial diabatic states. In this work, we show that if the Condon approximation is valid, then a minimization of the derived dynamic couplings leads to corresponding diabatic states for ETreactions taking place in solution by diagonalization of the dipole moment matrix, which is equivalent to a Boys localization algorithm; while for EET reactions in solution, diabatic states are found through the Edmiston–Ruedenberg localization algorithm. In the derivation, we find interesting expressions for the environmental contribution to the dynamic coupling of the adiabatic states in condensedphase processes. In one of the cases considered, we find that such a contribution is trivially evaluable as a scalar product of the transition dipole moment with a quantity directly derivable from the geometry arrangement of the nuclei in the molecular environment. Possibly, this has applications in the evaluation of dynamic couplings for large scale simulations.

Gaugeorigin independent calculations of Jones birefringence
View Description Hide DescriptionWe present the first gaugeorigin independent formulation of Jones birefringence at the Hartree–Fock level of theory. Gaugeorigin independence is achieved through the use of London atomic orbitals. The implementation is based on a recently proposed atomic orbitalbased response theory formulation that allows for the use of both time and perturbationdependent basis sets [Thorvaldsen, Ruud, Kristensen, Jørgensen, and Coriani, J. Chem. Phys.129, 214108 (2008)]. We present the detailed expressions for the response functions entering the Jones birefringence when London atomic orbitals are used. The implementation is tested on a set of polar and dipolar molecules at the Hartree–Fock level of theory. It is demonstrated that London orbitals lead to much improved basisset convergence, and that the use of small, conventional basis sets may lead to the wrong sign for the calculated birefringence. For large basis sets, London orbitals and conventional basis sets converge to the same results.

Doubled heterogeneous crystal nucleation in sediments of hard sphere binarymass mixtures
View Description Hide DescriptionCrystallization during the sedimentation process of a binary colloidal hard spheres mixture is explored by Brownian dynamicscomputer simulations. The two species are different in buoyant mass but have the same interaction diameter. Starting from a completely mixed system in a finite container, gravity is suddenly turned on, and the crystallization process in the sample is monitored. If the Peclet numbers of the two species are both not too large, crystalline layers are formed at the bottom of the cell. The composition of lighter particles in the sedimented crystal is nonmonotonic in the altitude: it is first increasing, then decreasing, and then increasing again. If one Peclet number is large and the other is small, we observe the occurrence of a doubled heterogeneous crystal nucleation process. First, crystalline layers are formed at the bottom container wall which are separated from an amorphous sediment. At the amorphousfluid interface, a secondary crystal nucleation of layers is identified. This doubled heterogeneous nucleation can be verified in realspace experiments on colloidal mixtures.

Mesoscale hydrodynamic modeling of a colloid in shearthinning viscoelastic fluids under shear flow
View Description Hide DescriptionIn order to study the dynamics of colloidal suspensions with viscoelasticsolvents, a simple mesoscopic model of the solvent is required. We propose to extend the multiparticle collision dynamics (MPC) technique—a particlebased simulation method, which has been successfully applied to study the hydrodynamic behavior of many complex fluids with Newtonian solvent—to shearthinningviscoelasticsolvents. Here, the normal MPC particles are replaced by dumbbells with finiteextensible nonlinear elastic (FENE) springs. We have studied the properties of FENEdumbbell fluids under simple shear flow with shear rate. The stress tensor is calculated, and the viscosity η and the first normalstress coefficient Ψ_{1} are obtained. Shearthinning behavior is found for reduced shear rates, where τ is a characteristic dumbbell relaxation time. Here, both η and Ψ_{1} display powerlaw behavior in the shearthinning regime. Thus, the FENEdumbbell fluid with MPC collisions provides a good description of viscoelastic fluids. As a first application, we study the flow behavior of a colloid in a shearthinningviscoelastic fluid in two dimensions. A slowing down of the colloid rotation in a viscoelastic fluid compared to a Newtonian fluid is obtained, in agreement with recent numerical calculations and experimental results.