# <span class=strong>Reception and Poster Session</span>

Tuesday, July 24, 2007 - 5:00pm - 6:30pm

Lind 400

**Method for determination of Hubbard model phase diagram from**

optical lattice experiments by two parameter scaling

Vivaldo Campo (University of Minnesota, Twin Cities)

We propose[1] an experimental scheme to obtain the phase diagram

of the Hubbard model using cold atoms in optical lattices.[2] The

scheme is based on measuring the total energy for a sequence of

trapping potentials with diﬀerent proﬁle and is independent of di-

mensionality. Its essential ingredient is a two-parameter scaling pro-

cedure that combines a variant of the familiar ﬁnite-size scaling with

a nontrivial additional ’ﬁnite-curvature scaling’ necessary to reach

the homogeneous limit. We illustrate the viability of the scheme

in the one-dimensional case, using simulations based on the Bethe

Ansatz local-density approximation as a substitute for experimental

data, and show that the ﬁlling corresponding to the Mott transition

can be determined with better than 3% accuracy.**Numerical method for solving stochastic differential equations with non-Gaussian noise**

Changho Kim (Korea Advanced Institute of Science and Technology (KAIST))

We propose numerical integration schemes to solve stochastic differential equations driven by two important non-Gaussian noises – dichotomous Markov noise and Poissonian white shot noise. Our formula, which is based on an integral equation, which is equivalent to the stochastic differential equation, utilizes a discrete time approximation with fixed integration time step. We show that our integration formula approaches the Euler formula if these noises approach the Gaussian white noise. We further propose a simplified weak scheme that significantly reduces the computation time, while still satisfying the moment properties up to the required order. Our approach is readily applicable to dynamical systems driven by arbitrary types of noise, provided there exists a way to describe the random increment of the noise accumulated during each integration time step. The accuracy and efficiency of the proposed algorithms are numerically examined.**Molecular modelling the structure and dynamics of alginate**

oligosaccharides

Hoda Abdel-Aal Bettley (University of Manchester)

Joint work with Richard A. Bryce.

Alginate copolymers are a key component of the extracellular polymeric

substances (EPS) matrix of bacterial microorganisms such as P. aeruginosa, and

occur in high abundance in nature. Alginate heteropolysaccharides comprise

alternating blocks of alpha-(1->4)-linked L-guluronate and beta-(1->4)-linked

D-mannuronate. To understand the microscopic behaviour and interactions of

these flexible acidic sugars within the EPS matrix, a suitable molecular-level

model is required. We derive a molecular mechanical force field for the two

uronic acids, with validation against available experimental data. We then

construct a detailed study of the structure and dynamics of alginate chains. We

explore alginate models of increasing complexity, from disaccharides to single-

and double-stranded oligomer helices, employing the techniques of molecular

dynamics and replica-exchange molecular dynamics. The condensed phase behaviour

of these systems is discussed, including the role of counterions and the

implications for interaction with other constituents of the EPS matrix.**Objective structures and their applications**

Kaushik Dayal (University of Minnesota, Twin Cities)

Objective structures [1] are a recent classification of atomic and

molecular structures that includes numerous systems of current

interest. Examples are nanotubes and biological virus components.

While these structures are not crystalline, there are many strong

analogies to crystals. These analogies can be exploited to generalize

computational techniques developed in the context of crystals to these

new systems. Further, they may provide strategies for self-assembly

and structure determination.

Some examples of current work exploiting these ideas will be

presented. These include finding the normal modes of these structures

(in analogy with phonons), Objective Molecular Dynamics in analogy

with conventional MD, and DFT and other first-principles techniques in

the Objective setting. Recent work on finding all possible objective

structures will be described.

[1] R. D. James, Objective Structures, J. Mech. Phys. Solids, 54,

2354-2390 (2006).**Uniqueness of the density-to-potential mapping in excited-state**

density-functional theory

Prasanjit Samal (University of Minnesota, Twin Cities)

Jont work with Manoj K. Harbola (Department of Physics, Indian Institute of Technology, Kanpur 208016, India).

The question of whether there exists a mapping from

an excited-state density to a potential is central to performing density-functional calculation for excited states. The motivation of the present work is to establish a unique way of selecting a system (potential) for a given excited-state density. The issue of density – to – potential mapping has been addressed in a series of work by Sahni et al [1], Harbola [2] and Gaudoin et al [3]. In the work of [1] and [2], it was shown that ground- or excited-state density can be generated by configuration of one’s choice. In the work [3], they have shown that even with a fixed configuration, one could reproduce same excited-state density from more than one potentials as shown in Fig.1. This implies in addition to the excited-state density one requires some extra information to establish such a unique mapping. This has been done by comparison of ground state densities in Levy-Nagy [4] theory. Following the earlier attempts we have further explored the density-to-potential mapping based on the work of Levy-Nagy [4] and Gorling [5] for excited-states [6]. We have proposed a new criterion [7], which uniquely establishes such mapping.

href=/2006-2007/SP7.23-8.3.07/activities/Samal-Prasanjit/samal-full.gif>

src=/2006-2007/SP7.23-8.3.07/activities/Samal-Prasanjit/samal.gif>

Fig.1: Two potentials (middle panel) giving the same excited-state density (upper panel)

along with their corresponding ground-state densities (lower panel) for an excited-state

of the three electron 1D infinitely deep well model system.**References:**

[1] V. Sahni, L. Massa, R. Singh and M. Slamet, Phys. Rev. Lett. 87, 113002 (2001).

[2] M. K. Harbola, Phys. Rev. A 69, 042512 (2004).

[3] R. Gaudoin and K. Burke, Phys. Rev. Lett. 93, 173001 (2004).

[4] M. Levy and A. Nagy, Phys. Rev. Lett. 83, 4361 (1999).

[5] A. Gorling, Phys. Rev. A 59, 3359 (1999).

[6] P. Samal, M. K. Harbola and A. Holas, Chem. Phys. Lett. 419, 217 (2006)

[7] P. Samal and M. K. Harbola, J. Phys. B 39, 4065 (2006).**Particle-Scaling function (P3S) algorithm for electrostatic problems in free**

boundary conditions

Alexey Neelov (Universität Basel)

A simple algorithm for fast calculation of the Coulombic forces and energies of

point particles with free boundary conditions will be presented. Its

calculation time scales as N log N for N particles. This novel method has lower

crossover point with the full O(N^2) direct summation than the Fast Multipole

Method. The forces obtained by our algorithm are analytical derivatives of the

energy which guarantees energy conservation during a molecular dynamics

simulation. Our method is based on the Poisson solver [2] for continuous

charge distribution that uses the Deslaurier-Dubuc (interpolating) wavelets.

[1] L. Genovese, T. Deutsch, A. Neelov, S. Goedecker, and G. Beylkin, Efficient

solution of Poisson's equation with free boundary conditions, J. Chem. Phys.

125, 007415 (2006).

[2] A. Neelov, S. A. Ghasemi, S. Goedecker, Particle-Particle, Particle-Scaling

function (P3S) algorithm for electrostatic problems in free boundary

conditions, J. Chem. Phys., 2007 (to appear)**An ab initio molecular dynamics simulation of solid CL-20:**

mechanism and kinetics of thermal decomposition

Olexandr Isayev (Jackson State University)

Joint work with Leonid Gorb,^{(1and 2)}Mo. Qasim,^{(2)}and

Jerzy Leszczynski.^{(1)}

CL-20

(Octahydro-1,3,4,7,8,10-hexanitro-5,2,6-(iminomethenimino)-1H-imidazo[4,5-b]-pyrazin)

is one of the most important high energetic nitramines which

are used as explosives and propellants. The decomposition of

CL-20 is very complicated and involves hundreds of elementary

reactions. Accurate knowledge of these reactions and

predictions of their kinetic parameters are important for

modeling these complex processes in combustion and explosion.

However, due to the energetic nature of these materials and the

rapid rates of the intermediate reactions, it is difficult to

monitor these individual reactions experimentally. Recent

advances in first principles modeling have led to enormous

progress toward understanding complex condensed phase chemical

phenomena. Theoretical methods, especially accurate ab initio

molecular dynamics method, provide a viable alternative to

study the dynamics of these reactions. Electronic properties

and the dynamics of the initial thermal decomposition step of

gas-, and e-crystal phases of CL-20 are investigated using the

Car-Parrinello molecular dynamics (CPMD) approach. The

difference in the reaction pathways between gas- and crystal

phases has been accounted for the strong intermolecular

interaction into crystal lattice. The thermal rate constants

have been also estimated.^{1)}Computational Center of Molecular Structure and Interactions,

Jackson State University, Jackson, MS 39217^{2)}US Army ERDC, Vicksburg, MS, 39180.**Temperature-regulated microcanonical dynamics**

Emad Noorizadeh (University of Edinburgh)

Joint work with Ben Leimkuhler (School of Mathematics, University of Edinburgh) and Frederic Legoll (LAMI, Ecole Nationale des Ponts et Chaussees, France).

We describe a new dynamical technique for the equilibration of molecular dynamics. Temperature is moderated by a control law and an additional variable, as in Nose dynamics,

but whose influence on the system decreases as the system approaches equilibrium. This device enables approximation of microcanonical averages and autocorrelation functions consistent with given target temperature. Moreover, we demonstrate that the suggested technique is effective for the regulation of heat production in a nonequilibrium setting.**New numerical algorithms and software for minimizing**

biomolecular potential energy functions

Dexuan Xie (University of Wisconsin)

This poster reports some progresses we made recently in developing numerical algorithms and program packages for minimizing large scale biomolecular potential energy functions, which is one of the fundamental tasks in biomolecular simulations.

The new algorithms are designed from a sparse incomplete Hessian matrix constructed by a spherical cutoff strategy according to the problem size and computer capability. They are called the incomplete Hessian Newton method (IHN), the truncated-IHN method (T-IHN), and the refined T-IHN method (RT-IHN), respectively. The program package of RT-IHN for solving the biomolecular potential energy minimization problem is developed based on a widely-used biomolecular simulation packages, CHARMM. This poster will give RT-IHN a detailed description, and present its numerical performances for some large scale protein systems.

In theory, these new algorithms are defined and analyzed for a general unconstrained minimization problem with a target function having a dense Hessian matrix. They are proved to be convergent globally. While IHN and T-IHN are shown to have a linear rate of convergence, RT-IHN is proved to have a super-linear rate of convergence. Hence, these new algorithms can be applied to other large scale scientific and engineering applications. For this purpose, we develop a general program package of RT-IHN in C++ based on the optimization program package TAO (http://www-unix.mcs.anl.gov/tao/index.html), and apply it to solve the chemical database optimal projection mapping problem.

This is the joint work with Mazen G. Zarrouk and Jun Wang.**A Bell-Evans-Polanyi principle for molecular dynamics trajectories and**

its implications for global optimization

Shantanu Roy (Universität Basel)

Joint work with Waldemar Hellmann and Stefan Goedecker (Institute of Physics, University of Basel).

The Bell-Evans-Polanyi principle that is valid for a chemical reaction that

proceeds along the reaction coordinate over the transition state is extended to

molecular dynamics trajectories that in general do not cross the dividing

surface between the initial and the final local minimum at the exact transition

state. Our molecular dynamics Bell-Evans-Polanyi principle states that low

energy molecular dynamics trajectories are more likely to lead into the basin

of attraction of a low energy local minimum than high energy trajectories. In

the context of global optimization schemes based on molecular dynamics our

molecular dynamics Bell-Evans-Polanyi principle implies that using low energy

trajectories one needs to visit a smaller number of distinguishable local

minima before finding the global minimum than when using high energy

trajectories.**Absolute entropy and free energy of free and bound states of a mobile**

loop of alpha-amylase using the

hypothetical scanning method

Srinath Cheluvaraja (University of Pittsburgh)

A new simulation method is studied which is capable of calculating the

absolute entropy and free energy of a microstate. The method is based on

calculating the probability of a member in the statistical ensemble by

growing the configuration in a step-by-step manner and expressing it as

a product of conditional probabilities, each of which is calculated by

performing

simulations at every step. This is a potentially exact method with the errors

arising only from inadequate sampling. The method is applied to a small protein loop in

implicit solvent and the results obtained agree quite well with those

obtained from other (approximate) methods. Unlike other

methods, all long range interactions are taken into account in the

reconstruction procedure.**Precision problems in density functional development**

for better molecular modeling

Michael Teter (Cornell University)

Classical modeling depends upon Density Functional Theory (DFT)

for its potential parameters, and quantum modeling usually uses DFT directly. The only significant

improvement in DFT in the last 40 years has been the gradient corrections by Perdew et al., and they

only improved the gross energy errors without improving molecular geometries or forces. Indeed, many

of the talks in the second week address this problem. If we are to get better modeling, we need DFT

functional development.

The primary problem with DFT functional development is that the total energy errors are quadratic in electron

density errors while the force errors are linear, so that further improvements must get the electron densities

right. The differences between the electron densities predicted by the various theories is at the 1-2% level.

So, in order to get the differences right, one must actually have a numerical method which resolves the

density to 1/10% or the energies to a part per million. Easy-to-use methods which can achieve this accuracy

regularly do not exist, hence my work.**Mesoscopic model for the fluctuating hydrodynamics of binary and ternary mixtures**

Erkan Tüzel (North Dakota State University)

Joint work with Guoai Pan (National Institute for Nanotechnology, Canada),

Thomas Ihle and Daniel M. Kroll (Department of Physics,

North Dakota State University).

A recently introduced particle-based model for fluid dynamics

with continuous velocities is generalized to model

immiscible binary mixtures. Excluded volume interactions

between the two components are modeled by stochastic

multiparticle collisions which depend on the local velocities

and densities. Momentum and energy are conserved

locally, and entropically driven phase separation occurs for

high collision rates. An explicit expression for the equation

of state is derived, and the concentration dependence of the

bulk free energy is shown to be the same as that of the

Widom-Rowlinson model. Analytic results for the phase diagram

are in excellent agreement with simulation data.

Results for the line tension obtained from the analysis of the

capillary wave spectrum of a droplet agree with measurements

based on the Laplace's equation. The dispersion relation for

the capillary waves is derived and compared with the

numerical measurements of the time correlations of the radial

fluctuations in the damped and over-damped limits.

The introduction of amphiphilic dimers makes it possible to

model the phase behavior of ternary surfactant mixtures.**Multilevel summation method for Coulomb interactions**

David Hardy (University of Illinois at Urbana-Champaign)

The multilevel summation method (MSM) computes an approximation to

the pairwise interaction potential and its gradient with an amount of

work that scales linearly as the size of the system. The potential

is smoothly split into a sum of partial potentials of increasing

range and decreasing variability with the longest-range parts

interpolated from grids of increasing coarseness. Multilevel

summation is especially appropriate for dynamical simulations,

because it can produce continuous forces for both nonperiodic and

periodic boundary conditions. A small correction to the grid-based

force approximation can be used to conserve both energy and momentum.**Conformational reinvestigation of two cyclic pentapeptides: to**

a generic approach in drug development

Pieter Hendrickx (University of Ghent (UG))

Joint work with I. Van den Eynde^{2}, J.C. Martins^{1}and D. Tourwé^{2}

As part of a bigger research effort which consists of the

development of a generic approach for drug development, two

cyclic peptides based on the active sequence of somatostatin

were characterized using nuclear magnetic resonance

spectroscopy (NMR). In order to obtain the 3D conformation of

these molecules, conformational relevant parameters (eg. nOe,

scalar couplings and amide temperature coefficients) were

recorded. A simulated annealing protocol using distance

restraints was used to obtain a set of conformations which were

validated by analysis of the hydrogen bridges present and by

recalculating the measured scalar couplings.

Future efforts will consist of generating mathematical

descriptions (templates) of this kind of small peptide chains

as well as creating templates of non-peptidic small molecules.

This must allow for an intelligent choice for drug templates

upon positive screening results of the small peptide molecules.^{1}NMR and Structure Analysis Unit, Department of Organic

Chemistry, Ghent University, Krijgslaan 281 S4 B-9000 Gent,

Belgium^{2}Unit for Organic Studies, Department of Organic

Chemistry, Vrije Universiteit Brussel, Pleinlaan 2 9G616 B-1050

Elsene, Belgium**Modelling of local defects in crystals**

Amélie Deleurence (École Nationale des Ponts-et-Chaussées (ENPC))

Work in collaboration with Eric Cancès (CERMICS-ENPC, France) and Mathieu Lewin (Department of Mathematics, Université de Cergy, France)

We present mathematical results obtained for a new mean-field model

dedicated to the description of interacting electrons in crystals with local

defects. We work with a reduced Hartree-Fock model, obtained from the

usual Hartree-Fock model by neglecting the exchange term. Then we

deduce a new variational model for computing the perturbation in a

basis of precomputed maximally localized Wannier functions of the

reference perfect crystal. Finally we show some numerical results in

which we have applied the variational approximation and used a

one-dimensional model with Yukawa interaction potential.**A comparison of maximum likelihood and weighted**

residual approximations to the potential of mean force

Eric Cyr (University of Illinois at Urbana-Champaign)

The potential of mean force (PMF) describes the change in free energy

along a reaction coordinate and determines the strength and likelihood

of association in molecular systems. Current methods, like Thermodynamic

Integration (TI) and WHAM, use piecewise linear and piecewise constant

approximations of the PMF. We propose two methods that allow the use

of arbitrary basis functions, one based on maximum likelihood

estimation and another on the method of weighted residuals. Numerical

comparisons with TI and WHAM are performed.**A systematic method to explore possible silicon tip structures used in AFM**

Seyed-Alireza Ghasemi (Universität Basel)

We present a systematic way to construct silicon tips by using

the minima hopping method(MHM) with limited temperature.

In Molecular Dynamics part of the MHM we limit the temperature to

some value used in experiments. We used Tight-Binding

scheme to evaluate energy and forces of silicon and hydrogen atoms

in MHM. Structures with lowest energy obtained with this method

are used in AFM simulation and force between tip and surface is

calculated in terms of distance and some of obtained results

are presented in this poster.