Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

The ring opening of cyclobutene is characterized by a competition of the two different pathways: a usual pathway over a saddle of index one (SP1) along the conrotatory behavior of the end groups, as well as a “forbidden” pathway over a saddle point of index two (SP2) along the disrotatory behavior of the end CH2 groups. We use the system of ordinary differential equations for the method of the gentlest ascent dynamics (GAD) to determine saddle points of the potential energy surface (PES) of the ring opening of cyclobutene to cis-butadiene. We apply generalized GAD formulas for the search of a saddle point of index two. To understand the relation of the different regions of the PES (around minimums, around SPs of index one or two) we also calculate valley-ridge inflection (VRI) points on the PES using Newton trajectories (NT). VRIs and the corresponding singular NTs subdivide the regions of “attraction” of the different SPs. We calculate the connections of the SP2 (in its different symmetry versions) with different SPs of index one of the PES by different “reaction pathways.” We compare the possibilities of the tool of the GAD curves for the exploration of PESs with these of NT. The barrier of the disrotatory SP2 is somewhat higher than the barrier of the conrotatory SP1, however, pathways across the slope to the SP2 open additional reaction valleys. © 2015 Wiley Periodicals, Inc.

/pdf/embedding-of-the-saddle-point-of-index-two-on-the-pes-of-the-3boo4537p8.pdf

Embedding of the saddle point of index two on the PES of the ring opening of cyclobutene

It is shown that the path described by the gentlest ascent dynamics to find transition states (Weinan and Zhou in Nonlinearity 24:1831, 2011) is an example of a quickest nautical path for a given stationary wind or current, the so-called Zermelo navigation variational problem. In the present case, the current is the gradient of the potential energy surface. The result opens the possibility to propose new curves based on Zermelo’s theory for two tasks: locate transition states and define reaction paths. The relation between a minimal variational character, which some former reaction pathways possess, and the minimum energy path is discussed.

/pdf/the-variational-nature-of-the-gentlest-ascent-dynamics-and-1pl8hog3nw.pdf

The variational nature of the gentlest ascent dynamics and the relation of a variational minimum of a curve and the minimum energy path

Water-soluble π-conjugated polymers are increasingly considered for DNA biosensing. However, the conformational rearrangement, supramolecular organization and dynamics upon interaction with DNA have been overlooked, which prevents the rational design of such detection tools. To elucidate the binding of a cationic polythiophene (CPT) to DNA with atomistic resolution, we performed molecular simulations of their supramolecular assembly. Comparison of replicated simulations show a multiplicity of CPT binding geometries that contribute to the wrapping of CPT around DNA. The different binding geometries are stabilized by both electrostatic interactions between CPT lateral cations and DNA phosphodiesters and van der Waals interactions between the CPT backbone and the DNA grooves. Simulated circular dichroism (CD) spectra show that the induced CD signal stems from a conserved geometrical feature across the replicated simulations, i. e. the presence of segments of syn configurations between thiophene units along the CPT chain. At the macromolecular scale, we inspected the different shapes related to the CPT binding modes around the DNA through symmetry metrics. Altogether, molecular dynamics (MD) simulations, model Hamiltonian calculations of the CD spectra, and symmetry indices provide insights into the origin of induced chirality from the atomic to the macromolecular scale. Our multidisciplinary approach points out the hierarchical aspect of CPT chiral organization induced by DNA.

Binding Mode Multiplicity and Multiscale Chirality in the Supramolecular Assembly of DNA and a π-Conjugated Polymer

We revisit the so-called gentlest ascent dynamics reaction path model for finding saddle points of any index in multidimensional potential energy surfaces. The variational nature of the method is analyzed in detail, and an algorithm for the integration of its equations of motion is proposed based on the optimization-based shrinking dimer method. By means of three different two-dimensional model potential energy surfaces, we argue that the combination of the proposed method with Newtonian (dissipative) dynamics could lead to a practical scheme for the exhaustive exploration of potential energy landscapes.

/pdf/exploring-potential-energy-surfaces-with-gentlest-ascent-4p31nqhs3p.pdf

Exploring potential energy surfaces with gentlest ascent dynamics in combination with the shrinking dimer method and Newtonian dynamics

Despite its undeniable problems from a philosophical point of view, the concept of molecular structure, with attributes such as shape and symmetry, directly borrowed from the description of macroscopic objects, is nowadays central to most of the chemical sciences. Descriptions such as "the tetrahedral carbon atom" or "octahedral coordination complexes" are widely used as much in elementary textbooks as in the most up-to-date research articles. The definition of molecular shape is, however, not as simple as it might seem at first sight. Molecules don't behave as macroscopic objects do, and the arrangement of atoms within a molecule changes continuously due to the incessant motion of its constituent particles, nuclei, and electrons. How are molecular shape and symmetry affected by this thermal motion? In this Minireview, we introduce the language of continuous symmetry measures as a new tool to quantitatively describe the effects of temperature on molecular shape and symmetry, enriching in this way the set of molecular descriptors that might be used in the establishment of new empirical structure-property relations, of great interest in concomitant areas such as medicinal chemistry or materials science.

Effects of Temperature on the Shape and Symmetry of Molecules and Solids.

The study of molecular systems involves models describing the evolution of the system through barriers separating basins of attraction on a high dimensional potential energy surface. It is a challenge problem inherent to a complex molecular system. Recently Samanta and E (J Chem Phys 136:124104, 2012) have proposed an extended gentlest ascent dynamics where the system should hop from one saddle point on a potential energy surface to a next saddle point. In the present study we do an analysis of this dynamical model using different two-dimensional potential energy surfaces. The extended gentlest ascent dynamics is a model that corresponds in its mathematical formulation to a set of first order ordinary differential equations. Due to this fact the initial conditions and features are also studied to see their effect on the dynamical behavior.

/pdf/some-remarks-on-the-model-of-the-extended-gentlest-ascent-2tzou6lo7z.pdf

Some remarks on the model of the extended gentlest ascent dynamics

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Effects of Temperature on the Shape and Symmetry of Molecules and Solids.

Some remarks on the model of the extended gentlest ascent dynamics