Modern charge density studies: the entanglement of experiment and theory

This tutorial review article is intended to provide a general guidance to a reader interested to learn about the methodologies to obtain accurate electron density mapping in molecules and crystalline solids, from theory or from experiment, and to carry out a sensible interpretation of the results, for chemical, biochemical or materials science applications. The review mainly focuses on X-ray diffraction techniques and refinement of experimental models, in particular multipolar models. Neutron diffraction, which was widely used in the past to fix accurate positions of atoms, is now used for more specific purposes. The review illustrates three principal analyses of the experimental or theoretical electron density, based on quantum chemical, semi-empirical or empirical interpretation schemes, such as the quantum theory of atoms in molecules, the semi-classical evaluation of interaction energies and the Hirshfeld analysis. In particular, it is shown that a simple topological analysis based on a partition of the electron density cannot alone reveal the whole nature of chemical bonding. More information based on the pair density is necessary. A connection between quantum mechanics and observable quantities is given in order to provide the physical grounds to explain the observations and to justify the interpretations.

Materials properties from electron density distributions: Molecular magnetism and linear optical properties

The general goal of this thesis is correlating observable properties of organic and metal-organic materials with their ground-state electron density distribution. In a long-term view, we expect to develop empirical or semi-empirical approaches to predict materials properties from the electron density of their building blocks, thus allowing to rationally engineering molecular materials from their constituent subunits, such as their functional groups. In particular, we have focused on linear optical properties of naturally occurring amino acids and their organic and metal-organic derivatives, and on magnetic properties of metal-organic frameworks. For analysing the optical properties and the magnetic behaviour of the molecular or sub-molecular building blocks in materials, we mostly used the more traditional QTAIM partitioning scheme of the molecular or crystalline electron densities, however, we have also investigated a new approach, namely, X-ray Constrained Extremely Localized Molecular Orbitals (XC-ELMO), that can be used in future to extracted the electron densities of crystal subunits. With the purpose of rationally engineering linear optical materials, we have calculated atomic and functional group polarizabilities of amino acid molecules, their hydrogen-bonded aggregates and their metal-organic frameworks. This has enabled the identification of the most efficient functional groups, able to build-up larger electric susceptibilities in crystals, as well as the quantification of the role played by intermolecular interactions and coordinative bonds on modifying the polarizability of the isolated building blocks. Furthermore, we analysed the dependence of the polarizabilities on the one-electron basis set and the many-electron Hamiltonian. This is useful for selecting the most efficient level of theory to estimate susceptibilities of molecular-based materials. With the purpose of rationally design molecular magnetic materials, we have investigated the electron density distributions and the magnetism of two copper(II) pyrazine nitrate metal-organic polymers. High-resolution X-ray diffraction and DFT calculations were used to characterize the magnetic exchange pathways and to establish relationships between the electron densities and the exchange-coupling constants. Moreover, molecular orbital and spin-density analyses were employed to understand the role of different magnetic exchange mechanisms in determining the bulk magnetic behaviour of these materials. As anticipated, we have finally investigated a modified version of the X-ray constrained wavefunction technique, XC-ELMOs, that is not only a useful tool for determination and analysis of experimental electron densities, but also enables one to derive transferable molecular orbitals strictly localized on atoms, bonds or functional groups. In future, we expect to use XC-ELMOs to predict materials properties of large systems, currently challenging to calculate from first-principles, such as macromolecules or polymers. Here, we point out advantages, needs and pitfalls of the technique. This work fulfils, at least partially, the prerequisites to understand materials properties of organic and metal-organic materials from the perspective of the electron density distribution of their building blocks. Empirical or semi-empirical evaluation of optical or magnetic properties from a preconceived assembling of building blocks could be extremely important for rationally design new materials, a field where accurate but expensive first-principles calculations are generally not used. This research could impact the community in the fields of crystal engineering, supramolecular chemistry and, of course, electron density analysis.

A Global Trend towards Democratic Convergence? A Lijphartian Analysis of Advanced Democracies.

The article offers a systematic analysis of the comparative trajectory of international democratic change. In particular, it focuses on the resulting convergence or divergence of political systems, borrowing from the literatures on institutional change and policy convergence. To this end, political-institutional data in line with Arend Lijphart’s (1999, 2012) empirical theory of democracy for 24 developed democracies between 1945 and 2010 are analyzed. Heteroscedastic multilevel models allow for directly modeling the development of the variance of types of democracy over time, revealing information about convergence, and adding substantial explanations. The findings indicate that there has been a trend away from extreme types of democracy in single cases, but no unconditional trend of convergence can be observed. However, there are conditional processes of convergence. In particular, economic globalization and the domestic veto structure interactively influence democratic convergence.

XMapTools: a MATLAB©-based program for electron microprobe X-ray image processing and geothermobarometry

XMapTools is a MATLAB©-based graphical user interface program for electron microprobe X-ray image processing, which can be used to estimate the pressure–temperature conditions of crystallization of minerals in metamorphic rocks. This program (available online at http://www.xmaptools.com) provides a method to standardize raw electron microprobe data and includes functions to calculate the oxide weight percent compositions for various minerals. A set of external functions is provided to calculate structural formulae from the standardized analyses as well as to estimate pressure–temperature conditions of crystallization, using empirical and semi-empirical thermobarometers from the literature. Two graphical user interface modules, Chem2D and Triplot3D, are used to plot mineral compositions into binary and ternary diagrams. As an example, the software is used to study a high-pressure Himalayan eclogite sample from the Stak massif in Pakistan. The high-pressure paragenesis consisting of omphacite and garnet has been retrogressed to a symplectitic assemblage of amphibole, plagioclase and clinopyroxene. Mineral compositions corresponding to ~165,000 analyses yield estimates for the eclogitic pressure–temperature retrograde path from 25 kbar to 9 kbar. Corresponding pressure–temperature maps were plotted and used to interpret the link between the equilibrium conditions of crystallization and the symplectitic microstructures. This example illustrates the usefulness of XMapTools for studying variations of the chemical composition of minerals and for retrieving information on metamorphic conditions on a microscale, towards computation of continuous pressure–temperature-and relative time path in zoned metamorphic minerals not affected by post-crystallization diffusion.

A thermodynamic model for di-trioctahedral chlorite from experimental and natural data in the system MgO-FeO-Al2O3-SiO2-H2O. Applications to P-T sections and geothermometry

We present a new thermodynamic activity-composition model for di-trioctahedral chlorite in the system FeO–MgO–Al2O3–SiO2–H2O that is based on the Holland–Powell internally consistent thermodynamic data set. The model is formulated in terms of four linearly independent end-members, which are amesite, clinochlore, daphnite and sudoite. These account for the most important crystal-chemical substitutions in chlorite, the Fe–Mg, Tschermak and di-trioctahedral substitution. The ideal part of end-member activities is modeled with a mixing-on-site formalism, and non-ideality is described by a macroscopic symmetric (regular) formalism. The symmetric interaction parameters were calibrated using a set of 271 published chlorite analyses for which robust independent temperature estimates are available. In addition, adjustment of the standard state thermodynamic properties of sudoite was required to accurately reproduce experimental brackets involving sudoite. This new model was tested by calculating representative P–T sections for metasediments at low temperatures (<400 °C), in particular sudoite and chlorite bearing metapelites from Crete. Comparison between the calculated mineral assemblages and field data shows that the new model is able to predict the coexistence of chlorite and sudoite at low metamorphic temperatures. The predicted lower limit of the chloritoid stability field is also in better agreement with petrological observations. For practical applications to metamorphic and hydrothermal environments, two new semi-empirical chlorite geothermometers named Chl(1) and Chl(2) were calibrated based on the chlorite + quartz + water equilibrium (2 clinochlore + 3 sudoite = 4 amesite + 4 H2O + 7 quartz). The Chl(1) thermometer requires knowledge of the (Fe3+/ΣFe) ratio in chlorite and predicts correct temperatures for a range of redox conditions. The Chl(2) geothermometer which assumes that all iron in chlorite is ferrous has been applied to partially recrystallized detrital chlorite from the Zone houillère in the French Western Alps.

The Role of Hydrogen Bond in Designing Molecular Optical Materials

In this perspective article, we revise some of the empirical and semi-empirical strategies for predicting how hydrogen bonding affects molecular and atomic polarizabilities in aggregates. We use p-nitroaniline and hydrated oxalic acid as working examples to illustrate the enhancement of donor and acceptor functional-group polarizabilities and their anisotropy. This is significant for the evaluation of electrical susceptibilities in crystals; and the properties derived from them like the refractive indices.

Voter Participation in the 1998 Bundestag Elections: A Theoretical Modification and Empirical Application of Downs’ Theory of Voter Participation

This article seeks to contribute to the illumination of the so-called 'paradox of voting' using the German Bundestag elections of 1998 as an empirical case. Downs' model of voter participation will be extended to include elements of the theory of subjective expected utility (SEU). This will allow a theoretical and empirical exploration of the crucial mechanisms of individual voters' decisions to participate, or abstain from voting, in the German general election of 1998. It will be argued that the infinitely low probability of an individual citizen's vote to decide the election outcome will not necessarily reduce the probability of electoral participation. The empirical analysis is largely based on data from the ALLBUS 1998. It confirms the predictions derived from SEU theory. The voters' expected benefits and their subjective expectation to be able to influence government policy by voting are the crucial mechanisms to explain participation. By contrast, the explanatory contribution of perceived information and opportunity costs is low.