Is a "homogeneous" description of dynamic heterogeneities possible?

We study the simplest model of dynamic heterogeneities in glass forming liquids: one-spin facilitated kinetic Ising model introduced by Fredrickson and Andersen [G. H. Fredrickson and H. C. Andersen, Phys. Rev. Lett. 53, 1244 (1984); J. Chem. Phys. 83, 5822 (1985)]. We show that the low-temperature, long-time behavior of the density autocorrelation function predicted by a scaling approach can be obtained from a self-consistent mode-couplinglike approximation.     

Modeling real dynamics in the coarse-grained representation of condensed phase systems

This work presents a systematic multiscale methodology to provide a more faithful representation of real dynamics in coarse-grained molecular simulation models. The theoretical formalism is based on the recently developed multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B. 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] and relies on the generalized Langevin equation approach and its simpler Langevin equation limit. The friction coefficients are determined in multiscale fashion from the underlying all-atom molecular dynamics simulations using force-velocity and velocity-velocity correlation functions for the coarse-grained sites. The diffusion properties in the resulting CG Brownian dynamics simulations are shown to be quite accurate. The time dependence of the velocity autocorrelation function is also well-reproduced relative to the all-atom model if sufficient resolution of the CG sites is implemented.     

Diffusion in linear porous media with periodic entropy barriers: A tube formed by contacting spheres

The problem of transport in quasi-one-dimensional periodic structures has been studied recently by several groups [D. Reguera et al., Phys. Rev. Lett.96, 130603 (2006); P. S. Burada et al., Phys. Rev. E75, 051111 (2007); B. Q. Ai and L. G. Liu, ibid.74, 051114 (2006); B. Q. Ai et al., ibid.75, 061126 (2007); B. Q. Ai and L. G. Liu, J. Chem. Phys.126, 204706 (2007); 128, 024706 (2008); E. Yariv and K. D. Dorfman, Phys. Fluids19, 037101 (2007); N. Laachi et al., Europhys. Lett.80, 50009 (2007); A. M. Berezhkovskii et al., J. Chem. Phys.118, 7146 (2003); 119, 6991 (2003)]. Using the concept of "entropy barrier" [R. Zwanzig, J. Phys. Chem.96, 3926 (1992)] one can classify such structures based on the height of the entropy barrier. Structures with high barriers are formed by chambers, which are weakly connected with each other because they are connected by small apertures. To escape from such a chamber a diffusing particle has to climb a high entropy barrier to find an exit that takes a lot of time [I. V. Grigoriev et al., J. Chem. Phys.116, 9574 (2002)]. As a consequence, the particle intrachamber lifetime tau(esc) is much larger than its intrachamber equilibration time, tau(rel), tau(esc)>tau(rel). When the aperture is not small enough, the intrachamber escape and relaxation times are of the same order and the hierarchy fails. This is the case of low entropy barriers. Transport in this case is analyzed in the works of Schmid and co-workers, Liu and co-workers, and Dorfman and co-workers, while the work of Berezhkovskii et al. is devoted to diffusion in the case of high entropy barriers.     

Simplified derivation of a one-range addition theorem of the Yukawa potential

The one-range addition theorem [J. Fernández Rico, R. López, and G. Ramírez, Int. J. Quantum Chem. 34 , 121 (1988)] for the Yukawa potential is rederived in a very simple manner using weakly convergent expansions [E. J. Weniger, J. Math. Phys. 26 , 276 (1985)] of plane waves in the Fourier representation. It is discussed in which sense the addition theorem converges. The relation to Sturmian expansions of Coulomb Green functions is pointed out. © 1992 John Wiley & Sons, Inc.     

Excitation energies for a benchmark set of molecules obtained within time-dependent current-density functional theory using the Vignale-Kohn functional

In this article we explain how the existing linear response theory of time-dependent density-functional theory can be extended to obtain excitation energies in the framework of time-dependent current-density-functional theory. We use the Vignale-Kohn current-functional [G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996)] which has proven to be successful for describing ultranonlocal exchange-correlation effects in the case of the axial polarizability of molecular chains [M. van Faassen, P. L. de Boeij, R. van Leeuwen, J. A. Berger, and J. G. Snijders, Phys. Rev. Lett. 88, 186401 (2002); J. Chem. Phys. 118, 1044 (2003)]. We study a variety of singlet excitations for a benchmark set of molecules. The pi(*)<--pi transitions obtained with the Vignale-Kohn functional are in good agreement with experiment and other theoretical results and they are in general an improvement upon the adiabatic local density approximation. In case of the pi(*)<--n transitions the Vignale-Kohn functional fails, giving results that strongly overestimate the experimental and other theoretical results. The benchmark set also contains some other types of excitations for which no clear failures or improvements are observed.     

Computer simulation study of metastable ice VII and amorphous phases obtained by its melting

Molecular dynamics simulations of metastable ice VII and cubic ice Ic are carried out in order to examine (1) the ability of commonly used water interaction potentials to reproduce the properties of ices, and (2) the possibility of generating low-density amorphous (LDA) structures by heating ice VII, which is known to transform to LDA at approximately 135 K at normal pressure [S. Klotz, J. M. Besson, G. Hamel, R. J. Nelmes, J. S. Loveday, and W. G. Marshall, Nature (London) 398, 681 (1999)]. We test four simple empirical interaction potentials of water: TIP4P [W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys. 79, 926 (1983)], SPC/E [H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, J. Phys. Chem. B 91, 6269 (1987)], TIP5P [M. W. Mahoney and W. L. Jorgensen, J. Chem. Phys. 112, 8910 (2000)], and ST2 [F. H. Stillinger and A. Rahman, J. Chem. Phys. 60, 1545 (1974)]. We have found that TIP5P ice VII melts at 210 K, TIP4P at 90 K, and SPC/E at 70 K. Only TIP5P water after transition has a structure similar to that of LDA. TIP4P and SPC/E have almost identical structures, dissimilar to any known water or amorphous phases, but upon heating both slowly evolve towards LDA-like structure. ST2 ice VII is remarkably stable up to 430 K. TIP4P and SPC/E predict correctly the cubic ice collapse into a high-density amorphous ice (HDA) at approximately 1 GPa whereas TIP5P remains stable up to approximately 5 GPa. The densities of the simulated ice phases differ significantly, depending on the potential used, and are generally higher than experimental values. The importance of proper treatment of long-range electrostatic interactions is also discussed.     

Cyclization of Rouse chains at long- and short-time scales

We have investigated cyclization of a Rouse chain at long and short times by a Langevin dynamics simulation method. We measure St, the fraction of nonreacted chains, for polymerizations ranging from Z=5 to Z=800 and capture distances ranging from a=0.1b to a=8b where b is the bond length. Comparison is made with two theoretical approaches. The first is a decoupling approximation used by Wilemski and Fixman to close the relevant master equation [J. Chem. Phys. 58, 4009 (1973); 60, 866 (1974)]. The second approach is the renormalization group arguments of Friedman and O'Shaughnessy [Phys. Rev. Lett 60, 64 (1988); J. Phys. II 1, 471 (1991)]. We find that at long times St decays as a single exponential with rate k(infinity). The scaled decay rate K=k(infinity)tauR appears to approach a constant value independent of the capture distance for very large chains consistent with the predictions of both the renormalization group (RG) and Wilemski-Fixman closure approximation. We extract K*, the long chain limit of K, from the fixed point a=a* where K is independent of Z. K* is larger than both the RG and closure predictions but much closer to the RG result. More convincing evidence for the RG analysis is obtained by comparing the short-time decay of St to long-time results. The RG analysis predicts that dSdt should decay as a power law at early times and that the exponent in the power law is related to K by a simple expression with no free parameters. Our simulations find remarkable agreement with this parameter-free prediction even for relatively short chains. We discuss possible experimental consequences of our result.     

Prospect for characterizing interacting soft colloidal structures using spin-echo small angle neutron scattering

Spin-echo small angle neutron scattering (SESANS) provides a new experimental tool for structural investigation. Due to the action of spin-echo encoding, SESANS measures a spatial correlation function in real space, as opposed to the structure factor S(Q), I(Q), in momentum (Q) space measured by conventional small angle neutron scattering. To establish the usefulness of SESANS in structural characterization, particularly for interacting colloidal suspensions, we have previously conducted a theoretical study of the SESANS correlation functions for model systems consisting of particles with uniform density profiles [X. Li, C.-Y. Shew, Y. Liu, R. Pynn, E. Liu, K. W. Herwig, G. S. Smith, J. L. Robertson, and W.-R. Chen J. Chem. Phys. 132, 174509 (2010)]. Within the same framework, we explore in the present paper the prospect of using SESANS to investigate the structural characteristics of colloidal systems consisting of particles with nonuniform intraparticle mass distribution. As an example, a Gaussian model of interacting soft colloids is used to investigate the manifestation of structural softness in a SESANS measurement. The exploration shows a characteristically different SESANS correlation function for interacting soft colloids, in comparison to that of a uniform hard sphere system. The difference arises from the Abel transform imbedded in the mathematical formalism bridging the SESANS spectra and the spatial autocorrelation function.     

SF-[2]R12: a spin-adapted explicitly correlated method applicable to arbitrary electronic states

The [2](R12) method [M. Torheyden and E. F. Valeev, J. Chem. Phys. 131, 171103 (2009)] is an explicitly correlated perturbative correction that can greatly reduce the basis set error of an arbitrary electronic structure method for which the two-electron density matrix is available. Here we present a spin-adapted variant (denoted as SF-[2](R12)) that is formulated completely in terms of spin-free quantities. A spin-free cumulant decomposition and multi-reference generalized Brillouin condition are used to avoid three-particle reduced density matrix completely. The computational complexity of SF-[2](R12) is proportional to the sixth power of the system size and is comparable to the cost of the single-reference MP2-R12 method. The SF-[2](R12) method is shown to decrease greatly the basis set error of multi-configurational wave functions.     

Pathways of cluster growth and kinetic slowing down in a model of short-range attractive colloids

We present the results of an extensive 3D Brownian dynamics simulation of the self-assembly of colloidal particles for a short-range attractive model that is quenched below its metastable critical point. In particular, results are obtained in the small-volume-fraction, low-temperature region in which we find so-called sticky beads that diffuse around the system, without reaching a final large cluster on the timescale of our simulation. For larger volume fractions in this low-temperature regime, a gel forms as the result of kinetically slowed down spinodal decomposition, as shown earlier for other short-range attractive models (Foffi, G.; De Michele, C.; Sciortino, F.; Tartaglia, P. Phys. Rev. Lett. 2005, 94, 078301. Zaccarelli, E. J. Phys.: Condens. Matter 2007, 19, 323101). We also show that for quenches below the critical point but above the intersection of the binodal with the glass line, two-step crystallization takes place. For sufficiently small volume fractions, the first step is the nucleation of dense fluid drops, followed by the second step of crystallization within these drops, as first proposed for a model of protein crystallization for quenches just above the metastable critical point (ten Wolde, P. R.; Frenkel, D. Science 1997, 277, 1975). For larger values of the volume fraction, the initial step is spinodal decomposition that leads to the formation of an interconnected network of low- and high-density fluids. The second step is crystallization that takes place within the dense fluid phase.     

Utilization of deformations in molecular quantum chemistry and application to density functional theory

The aim of this article is to present in a way accessible to most quantum chemists a general mathematical method which consists in deforming wave functions and density functions (in the spirit of the local scaling transformation). This deformation method allows us to obtain several new results, including a characterization of the set of wave functions that have the same given density function (which gives a new insight on a result of G. Zumbach and K. Maschke, Phys. Rev. A 28 , 544 (1983)) and an N-representability result where symmetry is taken into account. We also propose new theoretical ways to generate approximations of the exact density functional and give a numerical example. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 221–231, 1998     

Many-body calculations of low-energy eigenstates in magnetic and periodic systems with self-healing diffusion Monte Carlo: steps beyond the fixed phase

The self-healing diffusion Monte Carlo algorithm (SHDMC) [F. A. Reboredo, R. Q. Hood, and P. R. C. Kent, Phys. Rev. B 79, 195117 (2009); F. A. Reboredo, ibid. 80, 125110 (2009)] is extended to study the ground and excited states of magnetic and periodic systems. The method converges to exact eigenstates as the statistical data collected increase if the wave function is sufficiently flexible. It is shown that the dimensionality of the nodal surface is dependent on whether phase is a scalar function or not. A recursive optimization algorithm is derived from the time evolution of the mixed probability density, which is given by an ensemble of electronic configurations (walkers) with complex weight. This complex weight allows the phase of the fixed-node wave function to move away from the trial wave function phase. This novel approach is both a generalization of SHDMC and the fixed-phase approximation [G. Ortiz, D. M. Ceperley, and R. M. Martin, Phys Rev. Lett. 71, 2777 (1993)]. When used recursively it simultaneously improves the node and the phase. The algorithm is demonstrated to converge to nearly exact solutions of model systems with periodic boundary conditions or applied magnetic fields. The computational cost is proportional to the number of independent degrees of freedom of the phase. The method is applied to obtain low-energy excitations of Hamiltonians with magnetic field. Periodic boundary conditions are also considered optimizing wave functions with twisted boundary conditions which are included in a many-body Bloch phase. The potential applications of this new method to study periodic, magnetic, and complex Hamiltonians are discussed.     

Modeling collective behavior of molecules in nanoscale direct deposition processes

We present a theoretical model describing the collective behavior of molecules in nanoscale direct deposition processes such as dip-pen nanolithography. We show that strong intermolecular interactions combined with nonuniform substrate-molecule interactions can produce various shapes of molecular patterns including fractal-like structures. Computer simulations reveal circular and starlike patterns at low and intermediate densities of preferentially attractive surface sites, respectively. At large density of such surface sites, the molecules form a two-dimensional invasion percolation cluster. Previous experimental results showing anisotropic patterns of various chemical and biological molecules correspond to the starlike regime [P. Manandhar et al., Phys. Rev. Lett. 90, 115505 (2003); J.-H. Lim and C. A. Mirkin, Adv. Mater. (Weinheim, Ger.) 14, 1474 (2002); D. L. Wilson et al., Proc. Natl. Acad. Sci. U.S.A. 98, 13660 (2001); M. Su et al., Appl. Phys. Lett. 84, 4200 (2004); R. McKendry et al., Nano Lett. 2, 713 (2002); H. Zhou et al., Appl. Surf. Sci. 236, 18 (2004); G. Agarwal et al., J. Am. Chem. Soc. 125, 580 (2003)].     

Local biaxiality in cholesteric liquid crystals from the surface interaction model

The feature of local biaxiality of the orientational order in twisted nematics and cholesteric liquid-crystalline phases is faced by modeling the mean field orientational potential on the basis of the surface interaction model [A. Ferrarini, G. J. Moro, P. L. Nordio, and G. R. Luckhurst, Mol. Phys. 77, 1 (1992)]. Here we present a tool for the complete parameterization of the potential for general molecular structures and recover the long-pitch approximation usually invoked to model the molecular order in these phases. The method is applied to archetype molecular geometries (an ellipsoidal object, a conical object, a lath-shaped molecule, and the shape's enantiomers of a propellerlike molecule) in order to evaluate the dependence of the second-rank orientational order parameters on the pitch of the phase. Special emphasis is given to the so-called biaxiality parameter B [Z. Yaniv, N. A. P. Vaz, G. Chidichimo, and J. W. Doane, Phys. Rev. Lett. 47, 46 (1981)], which can be experimentally determined by the analysis of time-averaged (2)H-NMR spectra of deuterated probes dissolved in the twisted phase. The model calculations show how probes with different geometries are sensitive to the local biaxiality.     

Variationally stable calculations for molecular systems: polarizabilities and two-photon ionization cross section for the hydrogen molecule

The variationally stable method of Gao and Starace [B. Gao and A. F. Starace, Phys. Rev. Lett. 61, 404 (1988); Phys. Rev. A 39, 4550 (1989)] has been applied for the first time to the study of multiphoton processes in molecular systems. The generalization in theory is presented, as well as the calculation of properties such as the static and dynamic polarizabilities of the hydrogen molecule and the generalized two-photon ionization cross section. The Schwinger variational iterative method [R. R. Lucchese and V. McKoy, Phys. Rev. A 21, 112 (1980)] has been applied in the achievement of the photoelectron wave function, while a Hartree-Fock representation has been used for the target. This research has been motivated by the scarceness of ab initio calculations of molecular multiphoton ionization cross sections in the literature.     

On the density scaling of pVT data and transport properties for molecular and ionic liquids

In this work, a general equation of state (EOS) recently derived by Grzybowski et al. [Phys. Rev. E 83, 041505 (2011)] is applied to 51 molecular and ionic liquids in order to perform density scaling of pVT data employing the scaling exponent γ(EOS). It is found that the scaling is excellent in most cases examined. γ(EOS) values range from 6.1 for ammonia to 13.3 for the ionic liquid [C(4)C(1)im][BF(4)]. These γ(EOS) values are compared with results recently reported by us [E. R. López, A. S. Pensado, M. J. P. Comu?as, A. A. H. Pádua, J. Fernández, and K. R. Harris, J. Chem. Phys. 134, 144507 (2011)] for the scaling exponent γ obtained for several different transport properties, namely, the viscosity, self-diffusion coefficient, and electrical conductivity. For the majority of the compounds examined, γ(EOS) > γ, but for hexane, heptane, octane, cyclopentane, cyclohexane, CCl(4), dimethyl carbonate, m-xylene, and decalin, γ(EOS) < γ. In addition, we find that the γ(EOS) values are very much higher than those of γ for alcohols, pentaerythritol esters, and ionic liquids. For viscosities and the self-diffusion coefficient-temperature ratio, we have tested the relation linking EOS and dynamic scaling parameters, proposed by Paluch et al. [J. Phys. Chem. Lett. 1, 987-992 (2010)] and Grzybowski et al. [J. Chem. Phys. 133, 161101 (2010); Phys. Rev. E 82, 013501 (2010)], that is, γ = (γ(EOS)/φ) + γ(G), where φ is the stretching parameter of the modified Avramov relation for the density scaling of a transport property, and γ(G) is the Gru?neisen constant. This relationship is based on data for structural relaxation times near the glass transition temperature for seven molecular liquids, including glass formers, and a single ionic liquid. For all the compounds examined in our much larger database the ratio (γ(EOS)/φ) is actually higher than γ, with the only exceptions of propylene carbonate and 1-methylnaphthalene. Therefore, it seems the relation proposed by Paluch et al. applies only in certain cases, and is really not generally applicable to liquid transport properties such as viscosities, self-diffusion coefficients or electrical conductivities when examined over broad ranges of temperature and pressure.     

A proper approach for nonequilibrium molecular dynamics simulations of planar elongational flow

We present nonequilibrium molecular dynamics simulations of planar elongational flow (PEF) by an algorithm proposed by Tuckerman et al. [J. Chem. Phys. 106, 5615 (1997)] and theoretically elaborated by Edwards and Dressler [J. Non-Newtonian, Fluid Mech. 96, 163 (2001)], which we shall call the proper-SLLOD algorithm, or p-SLLOD for short. [For background on names of algorithms see W. G. Hoover, D. J. Evans, R. B. Hickman, A. J. C. Ladd, W. T. Ashurst, and B. Moran, Phys. Rev. A 22, 1690 (1980) and D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984).] We show that there are two sources for the exponential growth in PEF of the total linear momentum of the system in the contracting direction, which has been previously observed using the so-called SLLOD algorithm. The first comes from the SLLOD algorithm itself, and the second from the implementation of the Kraynik and Reinelt [Int. J. Multiphase Flow 18, 1045 (1992)] boundary conditions. Using the p-SLLOD algorithm (to eliminate the first source) implemented with our simulation strategy (to eliminate the second) in PEF simulations, we no longer observe the exponential growth. By analyzing the equations of motion, we also demonstrate that both the SLLOD and the DOLLS algorithms are intrinsically unsuitable for representing a nonequilibrium system with elongational flow. However, the p-SLLOD algorithm has a rigorously canonical structure in laboratory phase space, and thus can represent a nonequilibrium system not only for elongational flow but also for a general flow.     

"Adiabatic-hindered-rotor" treatment of the parahydrogen-water complex

Inspired by a recent successful adiabatic-hindered-rotor treatment for parahydrogen pH(2) in CO(2)-H(2) complexes [H. Li, P.-N. Roy, and R. J. Le Roy, J. Chem. Phys. 133, 104305 (2010); H. Li, R. J. Le Roy, P.-N. Roy, and A. R. W. McKellar, Phys. Rev. Lett. 105, 133401 (2010)], we apply the same approximation to the more challenging H(2)O-H(2) system. This approximation reduces the dimension of the H(2)O-H(2) potential from 5D to 3D and greatly enhances the computational efficiency. The global minimum of the original 5D potential is missing from the adiabatic 3D potential for reasons based on solution of the hindered-rotor Schro?dinger equation of the pH(2). Energies and wave functions of the discrete rovibrational levels of H(2)O-pH(2) complexes obtained from the adiabatic 3D potential are in good agreement with the results from calculations with the full 5D potential. This comparison validates our approximation, although it is a relatively cruder treatment for pH(2)-H(2)O than it is for pH(2)-CO(2). This adiabatic approximation makes large-scale simulations of H(2)O-pH(2) systems possible via a pairwise additive interaction model in which pH(2) is treated as a point-like particle. The poor performance of the diabatically spherical treatment of pH(2) rotation excludes the possibility of approximating pH(2) as a simple sphere in its interaction with H(2)O.