Molecular crystal global phase diagrams. II. Reference lattices

In the first part of this series [Keith et al. (2004). Cryst. Growth Des. 4, 1009-1012; Mettes et al. (2004). Acta Cryst. A60, 621-636], a method was developed for constructing global phase diagrams (GPDs) for molecular crystals in which crystal structure is presented as a function of intermolecular potential parameters. In that work, a face-centered-cubic center-of-mass lattice was arbitrarily adopted as a reference state. In part two of the series, experimental crystal structures composed of tetrahedral point group molecules are classified to determine what fraction of structures are amenable to inclusion in the GPDs and the number of reference lattices necessary to span the observed structures. It is found that 60% of crystal structures composed of molecules with T_d point-group symmetry are amenable and that eight reference lattices are sufficient to span the observed structures. Similar results are expected for other cubic point groups

Free energy and surface tension of arbitrarily large Mackay icosahedral clusters

We present a model for predicting the free energy of arbitrarily large Mackay icosahedral clusters. van der Waals clusters are experimentally observed to be particularly stable at magic numbers corresponding to these structures. Explicit calculations on the vibrational states were used to determine the spectrum of fundamental frequencies for smaller (~561 atoms). Combining these predictions with correlations for the moment of inertia and for the minimum potential energy of large clusters leads to free energies of arbitrary large clusters. The free energies are used to predict the chemical potential and surface tension as a function of size and temperature. This connects macroscopic properties to the microscopic atomic parameters

Thermodynamic properties and homogeneous nucleation rates for surface-melted physical clusters

We predict the free energy of van der Waals clusters (Fn) in the surface-melted temperature regime. These free energies are used to predict the bulk chemical potential, surface tension, Tolman length, and vapor pressure of noble gas crystals. Together, these estimates allow us to make definitive tests of the capillarity approximation in classical homogeneous nucleation theory. We find that the capillarity approximation underestimates the nucleation rate by thirty orders of magnitude for argon. The best available experiments are consistent with our calculation of nucleation rate as a function of temperature and pressure. We suggest experimental conditions appropriate for determining quantitative nucleation rates which would be invaluable in guiding further development of the theory. To make the predictions of Fn, we develop the Shellwise Lattice Search (SLS) algorithm to identify isomer fragments and the Linear Group Contribution (LGC) method to estimate the energy of isomers composed of those fragments. Together, SLS/LGC approximates the distribution of isomers which contribute to the configurational partition function (for up to 147-atom clusters). Estimates of the remaining free energy contributions come from a previous paper in this series

The hindered rotor density-of-states interpolation function

We construct an approximation to the partition function for hindered rotors based entirely on their asymptotic behavior and no fitting parameters. The approximant is shown to be quite accurate in all temperature ranges. Explicit auxiliary functions are derived for the Helmholtz free energy, internal energy, heat capacity, and entropy. We apply this function to estimating the heat capacity and unimolecular dissociation rate for ethane

Molecular crystal global phase diagrams. III. Sufficient parameter space determination

In previous parts of this series [Mettes et al. (2004). Acta Cryst. A60, 621-636; McClurg & Keith (2010). Acta Cryst. A66, 38-49] a method for constructing global phase diagrams (GPDs) for molecular crystals was developed and the method was applied to single-component ordered crystal structures of tetrahedral molecules. GPDs are useful for visualizing what types of crystal structures a given molecule may assume depending on molecular form/interaction. Their construction uses group-theoretical methods which enumerate all possible symmetry breakings during a statistical mechanical high-to-low temperature search. In this work these results are expanded upon by outlining a method to determine a sufficiently rich parameter space to represent the experimentally observed crystal structures in a data set derived from the Cambridge Structural Database. This is significant because previous work (Mettes et al., 2004) did not specify the number of parameters needed for GPDs. Although there are suggestions in the literature that thousands of parameters are required to adequately describe tetrahedral molecule intermolecular potentials, it is found that 15 parameters are sufficient to represent the structures of the test data. The origin of this difference and its implications for determining GPD parameter values from a more detailed intermolecular potential and for interpreting GPD parameter values are discussed

Gene Set Enrichment in eQTL Data Identifies Novel Annotations and Pathway Regulators

Genome-wide gene expression profiling has been extensively used to generate biological hypotheses based on differential expression. Recently, many studies have used microarrays to measure gene expression levels across genetic mapping populations. These gene expression phenotypes have been used for genome-wide association analyses, an analysis referred to as expression QTL (eQTL) mapping. Here, eQTL analysis was performed in adipose tissue from 28 inbred strains of mice. We focused our analysis on “trans-eQTL bands”, defined as instances in which the expression patterns of many genes were all associated to a common genetic locus. Genes comprising trans-eQTL bands were screened for enrichments in functional gene sets representing known biological pathways, and genes located at associated trans-eQTL band loci were considered candidate transcriptional modulators. We demonstrate that these patterns were enriched for previously characterized relationships between known upstream transcriptional regulators and their downstream target genes. Moreover, we used this strategy to identify both novel regulators and novel members of known pathways. Finally, based on a putative regulatory relationship identified in our analysis, we identified and validated a previously uncharacterized role for cyclin H in the regulation of oxidative phosphorylation. We believe that the specific molecular hypotheses generated in this study will reveal many additional pathway members and regulators, and that the analysis approaches described herein will be broadly applicable to other eQTL data sets

The James Webb Space Telescope Mission

Twenty-six years ago a small committee report, building on earlier studies, expounded a compelling and poetic vision for the future of astronomy, calling for an infrared-optimized space telescope with an aperture of at least $4m$. With the support of their governments in the US, Europe, and Canada, 20,000 people realized that vision as the $6.5m$ James Webb Space Telescope. A generation of astronomers will celebrate their accomplishments for the life of the mission, potentially as long as 20 years, and beyond. This report and the scientific discoveries that follow are extended thank-you notes to the 20,000 team members. The telescope is working perfectly, with much better image quality than expected. In this and accompanying papers, we give a brief history, describe the observatory, outline its objectives and current observing program, and discuss the inventions and people who made it possible. We cite detailed reports on the design and the measured performance on orbit.Comment: Accepted by PASP for the special issue on The James Webb Space Telescope Overview, 29 pages, 4 figure

Critical Comparison of Droplet Models in Homogeneous Nucleation Theory

We review the droplet models commonly used in calculations of the rate of homogeneous nucleation from the vapor. A statistical mechanical framework is used to form a common basis for comparison of the models. The asymptotic models (Capillarity, Tolman, and higher order models) and the semiphenomenological models introduced by A. Dillmann and G. E. A. Meier (1991) (J. Chem. Phys.94, 3872) are shown to be consistent with the statistical mechanical approach. The Lothe/Pound (J. Lothe and G. M. Pound (1962), J. Chem. Phys.36, 2080) formalism overcounts the degrees of freedom for a cluster and is therefore inconsistent. The self-consistency correction is shown to be an arbitrary method for handling a truncation error

Taxonomy of Cocrystal Ternary Phase Diagrams

A taxonomy of cocrystal ternary phase diagrams is presented. It is based upon an enumeration of distinct ternary phase diagrams as functions of the free energy of formation for each of a selected set of crystalline phases. In addition to topologically distinct diagrams, phase diagrams are distinguished as to the congruent or incongruent dissolution of the cocrystalline phase. The diagrams are organized according to the set of solid phases and the number of three-phase regions. Phase diagrams and free energy surfaces are provided for representative examples of each illustrated case