Calculation Of Radial Distribution Function Research Articles

Fast analysis of molecular dynamics trajectories with graphics processing units—Radial distribution function histogramming

The calculation of radial distribution functions (RDFs) from molecular dynamics trajectory data is a common and computationally expensive analysis task. The rate limiting step in the calculation of the RDF is building a histogram of the distance between atom pairs in each trajectory frame. Here we present an implementation of this histogramming scheme for multiple graphics processing units (GPUs). The algorithm features a tiling scheme to maximize the reuse of data at the fastest levels of the GPU’s memory hierarchy and dynamic load balancing to allow high performance on heterogeneous configurations of GPUs. Several versions of the RDF algorithm are presented, utilizing the specific hardware features found on different generations of GPUs. We take advantage of larger shared memory and atomic memory operations available on state-of-the-art GPUs to accelerate the code significantly. The use of atomic memory operations allows the fast, limited-capacity on-chip memory to be used much more efficiently, resulting in a fivefold increase in performance compared to the version of the algorithm without atomic operations. The ultimate version of the algorithm running in parallel on four NVIDIA GeForce GTX 480 (Fermi) GPUs was found to be 92 times faster than a multithreaded implementation running on an Intel Xeon 5550 CPU. On this multi-GPU hardware, the RDF between two selections of 1,000,000 atoms each can be calculated in 26.9 s per frame. The multi-GPU RDF algorithms described here are implemented in VMD, a widely used and freely available software package for molecular dynamics visualization and analysis.

Short Order and Hydrogen Transport in Amorphous Palladium Materials

Molecular dynamics simulation was used for investigating hydrogen migration in Pd-Si alloy at a temperature Т = 300 K. The strong affect of hydrogen dynamics and its defects creation to structure of palladium matrix is stated. The partial radial distribution function calculation for silicon specifies a preferable arrangement of silicon atoms relative to each other in the second coordination sphere. Model calculations have shown that not only silicon atoms can affect hydrogen mobility. Hydrogen itself also can significantly change the diffusion of the other components in the alloy.

New method for calculation of radial distribution function

A method for calculation of radial distribution function for amorphous alloys was developed. It is based on smoothing of each peak of the experimental structure factor (interference function) with the sets of basic functions in the form of wave packages with the subsequent Fourier transformation of the smoothed structure factor. The developed method enables one to analyze the influence of the separate components of the form of structure factor on peculiarities of the radial distribution function.

Structural study of highly dispersed cerium dioxides

Cerium dioxide samples of different dispersivity, obtained by different methods, have been investigated by X-ray diffraction (XRD) analysis, full-profile analysis of diffraction patterns, calculation of radial distribution function (RDF) of electron density, and extended X-ray absorption fine-structure (EXAFS) spectroscopy. According to the XRD data, the samples studied can be identified in the fluorite structure with conventional unit-cell parameters. However, the local structure of highly dispersed samples, determined by the RDF and EXAFS methods, changes: the coordination spheres for the Ce-O distances are represented by two distances.

Structural investigations of the Se–Ag–I system

Glasses from the Se–Ag–I system have been investigated. Structural information is gathered based on results collected by a combination of several types of diffraction measurements. First coordination sphere at r=2.3–2.5 Å determined by radial distribution function calculations can be assumed to be composed by Se–Ag and Ag–I correlations in the network units and Se–Se correlation in the Se cluster units. The interatomic distances and average bond angles decrease with the introduction of additives to selenium. The Raman spectra reveal that the introduction of silver and iodine, in particular, brings about a shift of the Se chain stretching mode towards lower wave numbers (251–236 cm−1). Apparently, the newly formed structure after the introduction of additives into selenium is pretty compact and is becoming more covalent with a stronger interchain interaction. Depending on the concentration of additives the breathing modes of Ag–Se and Ag–I bonds also can be seen.

Characterization of Domain Ordering in Polymer and Dendrimer Thin Films Using Photoluminescence and Third Harmonic Generation (THG) Near-field Scanning Optical Microscopy (NSOM)

We have utilized the high spatial resolution of near-field scanning optical microscopy (NSOM) to characterize nanoscopic electronic inhomogeneity in as-cast thin films of a light-harvesting dendrimer consisting of coumarin-343 (core) and coumarin-2 (peripheral) chromophores and in thermally annealed thin films of the semiconductive polymer poly(2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylene vinylene) (MEH-PPV). Using photoluminescence (PL) and third harmonic generation (THG) NSOM techniques, we have observed nanoscopic domains in these films that exhibit increased delocalization in the excited (using PL) and ground states (using THG). In addition, we have developed a procedure for examining NSOM images via calculation of radial distribution functions (RDFs). RDF analysis of the PL and THG NSOM images indicates that the domains exhibit correlated structure in annealed MEH-PPV films while the light-harvesting dendrimeric material does not. The existence or absence of such nanoscopic amorphous structure can be understood in terms of the molecular structure of each material.

Calculation of binary hard-sphere mixture radial distribution functions at contact from an equation of state

A new method for calculation of the radial distribution functions (RDFs) at contact from a specified hard-sphere mixture equation of state (EOS) is proposed. The method is applied to two available accurate EOS expressions and new analytical formulas for the RDFs are obtained for binary additive hard-sphere mixtures. The results of the new formulas are compared with available computer simulation data and with those of other RDF expressions from the literature. The evidence to date suggests that the new formula is more accurate than alternative formulas currently available.

Application of Kihara potential model to real non-spherical fluids

The calculation of radial distribution function (RDF) of Kihara rigid core fluids is performed using the sequential–analytic (S–A) method and the effect of reduced rigid core diameter on the shape of RDF is demonstrated. A theoretical equation of state for Kihara fluid is presented and used to calculate its reduced critical properties. It has been shown that the critical compressibility factor of a Kihara fluid is solely determined by its reduced rigid core diameter, and hence the critical compressibility factor of any real fluids can be reproduced through adjusting the value of reduced rigid core diameter. Instead of regression of virial coefficient or viscosity data of dilute gases, it is suggested to determine the parameters of Kihara potential model by matching the critical properties of corresponding substances. It has been shown that the Kihara parameters determined by matching critical properties can be used to predict the properties of both dilute and dense fluids while those determined by fitting dilute gas properties cannot.

Calculation of radial distribution function from incomplete experimental diffraction data

A method for calculating atomic radial distribution functions for amorphous materials has been suggested. The method is based on the principle of the maximum informational entropy. Under the condition of a limited amount of the experimental diffraction data, the method allows one to obtain the unique solution and considerably reduces the errors caused by series termination, which are inherent in traditional computational methods based on the Fourier transform. A criterion of using the method of optimum information is formulated, and the reliability of the data obtained are quantitatively estimated. The advantages of the method are demonstrated on the computation of the short-range order in hydrogenated amorphous silicon.

Hard-sphere radii for the generalized Lindemann criterion

Abstract We suggest a simple ad hoc, criterion for hard-sphere radius determination. The set of alkali halide radii calculated is compared with that obtained from a fitting procedure described elsewhere. The deviation does not exceed 10% for the most of elements. The method makes use of a radial distribution function (RDF) for alkali halide crystals. For the first time, we present a simple analytic expression for the RDF of such a system. The RDF calculation employs semiempirical potentials to describe effective ionic interactions.

Structure and Dynamics of a Peptidoglycan Monomer in Aqueous Solution Using NMR Spectroscopy and Simulated Annealing Calculations

The conformation of the peptidoglycan monomer (PGM) from Brevibacterium divaricatum was determined in aqueous solution using a combined approach by 2D NMR spectroscopy, restrained simulated annealing, and molecular dynamics (MD) calculations. MD simulations in water without experimental constraints provided insights into the structure and dynamics of this glycopeptide. Hierarchical cluster analyses for conformer classifications were performed using a global molecular shape descriptor (CoMFA steric fields). Principal component analysis was subsequently employed to extract orthogonal principal conformational properties. Correlated dihedral angle mobilities were identified using a dynamic cross correlation map. The calculation of radial distribution functions for all polar protons of the molecule leads to additional information about the solvation of PGM in a protic solvent, while autocorrelation functions for dihedral angle fluctuations were used to monitor dynamic processes in different regions. From simulated annealing, a set of 11 conformers was obtained, all characterized by a well-defined extended N-terminal peptide part additionally stabilized by the bound disaccharide; the C-terminal part, on the other hand, exhibits more conformational flexibility in agreement with experimental data and MD simulations. The disaccharide conformation is in agreement with the conformational minimum computed for the model disaccharide 3-O-Me-4-O-βGlcNAc-αMurNAc using various force fields. Not only the interglycosidic bond but also the glycopeptide linkage exists in a single, well-defined conformation, for which no conformational changes can be detected during the MD simulations. In contrast, conflicting experimental data for the N-acetyl group of GlcNAc could be explained using a conformer population analysis based on ROE intensities and coupling constants accounting for a conformational equilibrium with one dominantly populated rotamer.

Direct calculation of radial distribution function for hard-sphere chains

The Laplace transform of the average radial distribution function of hard-sphere chains is obtained following the approximation suggested by Chiew [Mol. Phys. 73, 359 (1991)]. The transform expression is of a simple analytical form. The inverse Laplace transform is made analytically. The resulting expression is capable of calculating directly the radial distribution function of hard-sphere chains for any value of r.

Axial oxygen-centered lattice instabilities in YBa2Cu3O7: An application of the analysis of extended x-ray-absorption fine structure in anharmonic systems.

Analysis of polarized copper K-edge extended x-ray-absorption fine-structure (EXAFS) measurements on ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ for temperatures 10\ensuremath{\le}${\mathit{T}}_{\mathrm{nom}}$\ensuremath{\le}105 K indicates that the axial oxygen moves in a double-well potential which softens within a fluctuation region associated with the onset of superconductivity in this material. This fluctuation follows from the coupling between the phonons derived from this double-well potential and the superconducting order parameter. The advantages of EXAFS compared to crystallographic measurements in discerning these aspects of the local structure are discussed. Metrical parameters and the characteristics of the potential are determined by curve fits of the EXAFS. This method is based on the calculation of radial distribution functions from selected model potentials, the forms of which are determined along with the absorber-scatterer distance, scatterer type, and number, by optimization of fits of the experimental data with the EXAFS calculated from these parameters. Unlike perturbative treatments, this approach is ideally suited for highly anharmonic systems because the putative potential can be a very close approximation to the real one and it also offers the advantage of providing dynamical information not available through perturbative treatments.

Calculation of radial distribution functions for molecules in excited vibrational states

It is shown how to reduce N-dimensional probability densities calculated from vibrational wave functions of polyatomic molecules to one-dimensional radial distribution functions. Such distributions are, in principle, derivable from diffraction experiments. In this initial treatment, anharmonicity and nonlinearities in transformations between normal coordinates and internuclear distances are neglected. Illustrative calculations are given for H2O, CF3Cl, and SF6 in various vibrational states or thermal distributions among vibrational states. Possible applications are briefly discussed.

Statistical mechanics of linear molecules. VII. Application of ``blip function'' theory to dense fluids

The ``blip function'' theory proposed by Andersen, Weeks, and Chandler for the calculation of radial distribution functions and thermodynamic properties of dense fluids is written in a form which yields explicit expressions for both the angular and the radial correlations of a dense fluid of linear molecules. This approximation is compared with a variety of correlation functions obtained by numerically solving the extended Percus-Yevick equation for nonspherical molecules. It is found that agreement is generally good at high densities, but worsens at lower densities because of the omission of the effects of attractive interactions in the blip function theory. It is noted that the H.T.A. approximation has certain implications concerning an extension of the theorem of corresponding states which should be applicable to nonspherical as well as spherical molecules. Tests of the extended theorem indicate that it will be necessary to include attractive interactions if this approach is to be useful in a quantitative way.