Gyration-radius dynamics in structural transitions of atomic clusters

This paper is concerned with the structural transition dynamics of the six-atom Morse cluster with zero total angular momentum, which serves as an illustrative example of the general reaction dynamics of isolated polyatomic molecules. It develops a methodology that highlights the interplay between the effects of the potential energy topography and those of the intrinsic geometry of the molecular internal space. The method focuses on the dynamics of three coarse variables, the molecular gyration radii. By using the framework of geometric mechanics and hyperspherical coordinates, the internal motions of a molecule are described in terms of these three gyration radii and hyperangular modes. The gyration radii serve as slow collective variables, while the remaining hyperangular modes serve as rapidly oscillating "bath" modes. Internal equations of motion reveal that the gyration radii are subject to two different kinds of forces: One is the ordinary force that originates from the potential energy function of the system, while the other is an internal centrifugal force. The latter originates from the dynamical coupling of the gyration radii with the hyperangular modes. The effects of these two forces often counteract each other: The potential force generally works to keep the internal mass distribution of the system compact and symmetric, while the internal centrifugal force works to inflate and elongate it. Averaged fields of these two forces are calculated numerically along a reaction path for the structural transition of the molecule in the three-dimensional space of gyration radii. By integrating the sum of these two force fields along the reaction path, an effective energy curve is deduced, which quantifies the gross work necessary for the system to change its mass distribution along the reaction path. This effective energy curve elucidates the energy-dependent switching of the structural preference between symmetric and asymmetric conformations. The present methodology should be of wide use for the systematic reduction of dimensionality as well as for the identification of kinematic barriers associated with the rearrangement of mass distribution in a variety of molecular reaction dynamics in vacuum.     

Composition-induced structural transitions in mixed Lennard-Jones clusters: global reparametrization and optimization

As extended benchmarks to global cluster structure optimization methods, we provide a first systematic point of entry into the world of strongly mixed rare gas clusters. A new set of generalized Lennard-Jones pair potentials is generated for this purpose, by fitting them to high-end ab initio reference data. Employing these potentials in our genetic algorithm-based global structure optimization framework, we examined various systems from binary to quinary mixtures of atom types. A central result from this study is that the famous fcc structure for 38 atoms can survive for certain binary mixtures but appears to be prone to collapsing into the dominating icosahedral structure, which we observed upon introduction of one single atom of a ternary type.     

Considerations in the determination of orientational order parameters from X-ray scattering experiments

An assessment of the data processing and analysis methods used to obtain the second- and fourth-rank orientational order parameters of liquid crystals from X-ray scattering experiments has been carried out, using experimental data from four extensively studied alkyl-cyanobiphenyls and calculated data generated from two general types of theoretical orientational distribution function. The application of a background subtraction and two different baseline correction methods to the scattering profiles is assessed, along with three different methods to analyse the processed data. The choice of baseline correction method is shown to have a significant effect: an offset to zero overestimates the order parameters from the experimental and calculated data sets, particularly for lower order parameters arising from broad distributions, whereas an offset to a value estimated from regions of low scattering intensity provides experimental values close to those reported from other experimental techniques. By contrast, the three different analysis methods are shown generally to result in relatively small absolute differences between the order parameters. We outline a straightforward general approach to experimental X-ray scattering data processing and analysis for uniaxial phases that results in order parameters that match well with those reported using other experimental techniques.     

Determination of orientational order parameters in oriented lipid membrane systems by angle-resolved fluorescence depolarization experiments

Angle-resolved fluorescence depolarization experiments have been performed on some lipid membrane systems in order to test the validity of a recently developed theory describing this type of experiments. Good agreement between theory and experiment was found. The experiments yield the order parameters 〈P₂〉 and 〈P₄〉 and a rotational correlation time τ_c. On applying an information-theoretic form of the orientational distribution function. 〈P₂〉 and 〈P₄〉 were used to estimate the degree of order in the systems studied. Knowledge of 〈P₄〉 proved useful to get more detailed information on the orientational order. Another finding was that the angle between the absorption and emission moment of the used fluorescent probe, diphenyl-hexatriene, depends on the membrane system in which it is incorporated. Finally, the experimental results point to the fact that for some membrane systems the molecular motion is inadequately described by the simple strong-collision model.     

Energy barriers and structural transitions of small Al clusters

Energy barriers between low-lying configurational states were calculated for several small Al clusters. Calculations were carried out considering a model potential comprising two- and three-body interactions. Parameters used in this potential energy function were evaluated from fits to high level ab initio calculations for Al clusters. Energy barriers separating low-lying configurations were found to be in varying heights. Results indicate that isomeric transformations between several low-lying high-symmetry forms of small Al clusters are quite likely and may take place at relatively low temperatures.     

Molecular dynamics study of orientational order and rotational melting in clusters of TeF6

Molecular dynamics simulations of the behavior of molecules in crystalline clusters of TeF₆ were carried out on systems of 100, 150, 250, and 350 molecules. Several diagnostic functions were applied to investigate whether rotational melting occurred before translational melting. These functions included the coefficient of rotational diffusionD _θ(T), the “orientational Lindemann index” δ_θ(T), the “orientational angular distribution function”Q(θ,T), and the “orientational pair-correlation function”g _θ(r, T). All indicators implied that rotational melting occurred before translational melting, that it began with the outermost molecules, and that its onset for smaller clusters was at lower temperatures than for larger clusters. Results also showed that the rotational transition coincided with the transition from a lower symmetry phase (monoclinic) to cubic, a phenomenon that had been noted by others to occur with some regularity for systems of globular molecules.     

Determination of order parameters from carbon-fluorine dipolar coupling

A convenient NMR method for the determination of the order parameters for liquid crystals containing a fluorinated phenyl ring is described. The technique consists of measuring the carbon-fluorine dipolar coupling constants in the one-dimensional C-13 spectrum of the molecule. The order parameters may then be calculated for the fluorine-containing ring with a high degree of precision because of the excellent resolution afforded by the 1-D C-13 spectra. The method is used to determine the core order parameters for 4-n-hexyloxybenzilidene-4'-fluoroaniline (FAB-OC6). The results of the carbon-fluorine dipolar coupling method are compared with two established methods for determining the core order parameters of phenyl rings, namely deuterium NMR spectroscopy and SLF/VAS, a two-dimensional C-13 NMR spectroscopy. Some comments about the orientational properties of the fluorinated liquid crystal FAB-OC6 are made.     

Determination of atomic parameters from powder diffraction intensity ratios

The basis for a systematic use of intensity ratios is given in order to determine positional and occupational parameters. Given a series of N powder diffraction intensities, the matrix of intensity ratios is defined. Expressing them as vectors, it is shown that they form a subset of $\text{1}\text{2}\text{(N}{}^2\text{? N)}$ elements in a vectorial space with dimension N ? 1. Since any intensity ratio may be obtained from the product or division of other ratios, their vectorial representation is used to define a criterion for independence for a set of ratios, transforming the product in a sum of the corresponding vectors. Any set of N ? 1 independent ratios may be used in the determination of atomic parameters. In order to find the most suitable set, it is proposed to assign an index to each intensity ratio, which depends upon the difference between observed and calculated values and their derivatives with respect to the parameters to be determined. Then, an independent set of intensity ratios is chosen among those with higher indices, for each point of a convenient grid in the space of the parameters, finding the best set at each point. Finally, the best absolute set is defined as that with the minimum value of an agreement indicator between observed and calculated values. An illustrative example of the procedure indicated above is shown, and the results are compared with those obtained by other powder integrated intensity methods. In this work, comparison with the Rietveld profile refinement method is not considered.     

Relationship of orientational order parameters of impurity molecules in a nematic matrix

Institute of Physics, Siberian Division, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 33, pp. 168–170, January–February, 1992.     

De novo determination of bond orientations and order parameters from residual dipolar couplings with high accuracy

We report the de novo determination of 15N-1H bond orientations and motional order parameters for the protein ubiquitin with high accuracy based solely on NMR residual dipolar coupling measurements made in six distinct alignment media. The resulting bond orientations are in agreement with RDC-refined orientations of either solid or solution state coordinates to within approximately 2 degrees , which is also the estimated precision of the resulting orientations. The squared generalized order parameters, which reflect amplitudes of motion spanning the picosecond to millisecond time scales, exhibit a correlation with picosecond time scale order parameters derived from conventional NMR 15N spin relaxation methods. Provided that RDC measurements can be obtained using many different alignment media, this approach (called direct interpretation of dipolar couplings) may significantly impact the attainable accuracy and the molecular weight range accessible to NMR structure determination in the solution state, as well as provide a route for the study of motions occurring on the nanosecond to microsecond time scales, which have been traditionally difficult to study at atomic resolution.     

Instantaneous normal mode analysis of orientational motions in liquid water: local structural effects

We have investigated the effects of local structures on the orientational motions in liquid water in terms of the instantaneous normal mode (INM) analysis. The local structures of a molecule in liquid water are characterized by two different kinds of index: the asphericity parameter of its Voronoi polyhedron and the numbers of the H bonds donated and accepted by the molecule. According to the two kinds of index, the molecules in the simulated water are classified into subensembles, for which the rotational contributions to the INM spectrum are calculated. Our results indicate that by increasing the asphericity, the rotational contribution has a shift toward the high-frequency end in the real spectrum and a decrease in the fraction of the imaginary modes. Furthermore, we find that this shift essentially relies on the number of the donated H bonds of a molecule, but has almost nothing to do with that of the accepted H bonds. The local structural effects resulting from the geometry of water molecule are also discussed.     

Quantification of global orientational order in organic solids by magic-angle spinning deuterium NMR with rotor synchronization

A new method for the characterization of orientational order in organic solids based on magic-angle spinning NMR spectroscopy is introduced. The method is related to the rotor-synchronized magic-angle spinning experiment proposed by Harbison and Spiess [Chem. Phys. Lett. 124, 128 (1986)], but exploits the anisotropy of the deuterium quadrupolar coupling instead of the carbon-13 chemical shielding anisotropy. Magic-angle spinning provides a sensitivity advantage over pseudostatic techniques; using the deuterium quadrupolar coupling makes the method applicable to systems that do not exhibit large carbon chemical shift anisotropies, such as aliphatic polymers. Due to the magnitude of the deuterium quadrupolar coupling, a large number of spinning sidebands can be reliably observed, allowing for a precise determination of the orientational distribution function. Experimental data are analyzed in terms of Wigner matrix basis functions as well as the conjugate orthogonal functions framework. Unidirectionally cold-drawn poly(ethylene) is used as an example to demonstrate the method.     

Using vibrational modes in the search for global minima of atomic and molecular clusters

The reaction between dimethyl sulfide (CH₃SCH₃) and nitrate radical (NO₃) is studied using density functional theory and ab initio methods. The transition state for this reaction is optimized at different levels of theory and basis sets, and then used for kinetics calculations of the rate constant. The CH₃SCH₃ + NO₃ reaction leading to CH₃SCH₂ and HNO₃ is shown to have a negative activation energy and thus negative temperature dependence. The study confirms that the NO₃ radical is a significant contributor to the oxidation of DMS in the troposphere.     

Determination of exchange interaction parameters in heterospin exchange clusters

An approach to calculation of the intracluster exchange parameters of molecular heterospin systems is proposed. This approach allows one to estimate the model errors of the parameters to be determined. The efficiency of this technique is demonstrated by analyzing the experimental data for the Cu(II), Ni(II), and Co(II) molecular complexes with stable nitroxides.     

Short-range orientational order and thermodynamic properties of polymer solutions

The concept of short-range orientational order was applied to the calculation of thermodynamic characteristics of polymer solutions in terms of the lattice model. It was shown that allowance for short-range order makes it possible to explain negative values of the entropy of mixing and the existence of a lower critical solution temperature in both polymer solutions and solutions of low-molecular-mass compounds. It was found that systems with lower critical solution temperature can exist even when the degree of orientational order in solutions slightly increases as compared with the corresponding values of this parameter in their components.     

Determination of protein structures consistent with NMR order parameters

Order parameters obtained from NMR experiments characterize distributions of bond vector orientations. Their interpretation, however, usually requires the assumption of a particular motional model. We propose a multiple-copy simulation method in which the experimental order parameters are used as restraints in conjunction with a standard molecular force field. The latter effectively acts as a sophisticated motional model, allowing ensembles of structures consistent with the experimental order parameters to be determined.     

Covalent bond orders and atomic anisotropies from iterated stockholder atoms

Iterated stockholder atoms are produced by dividing molecular electron densities into sums of overlapping, near-spherical atomic densities. It is shown that there exists a good correlation between the overlap of the densities of two atoms and the order of the covalent bond between the atoms (as given by simple valence rules). Furthermore, iterated stockholder atoms minimise a functional of the charge density, and this functional can be expressed as a sum of atomic contributions, which are related to the deviation of the atomic densities from spherical symmetry. Since iterated stockholder atoms can be obtained uniquely from the electron density, this work gives an orbital-free method for predicting bond orders and atomic anisotropies from experimental or theoretical charge density data.     

Structural transitions and melting of copper clusters

Molecular dynamics is used to study the melting and structural transitions of small copper clusters. The melting temperature is found to be proportional to the average coordination number. Small icosahedral clusters melt at slightly higher temperatures than the cubic structures. Small cuboctahedral clusters are not stable but transform via a nondiffusive transition to icosahedral structure.     

Calculation of long-range orientational order parameters in impure nematic liquid crystals using an extended van der Waals model

For the atended van der Waals model of a binary nematic system consisting of rigid biaxial molecules, we consider the following properties: the relation between the orientational order parameters of a nematic liquid crystal (NLC) S⁽¹⁾ and a nonmesomckphic impurity S⁽²⁾, the relation between S⁽²⁾ and the biaxiality parameter D⁽²⁾ of the impurity, and the lowered clearing temperature of NLC upon dissolution of the nonmesogen. The dependence of these characteristics on the fom and size of component molecules and the intermolecular attraction potential is analyzed. The model reproduces the experimental dependence of S⁽²⁾ and D⁽²⁾ on temperature and structure of the nematic matrix.Scientific Research Institute of Chemistry, St. Petersburg State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 34, No. 5, pp. 106–115, September–October, 1993.Translated by L. Smolina