Challenges for the Periodic Systems of Elements: Chemical,Historical and Mathematical Perspectives

We celebrate 150 years of periodic systems that reached their maturity in the 1860s. They began as pedagogical efforts to project corpuses of substances on the similarity and order relationships of the chemical elements. However, these elements are not the canned substances wrongly displayed in many periodic tables, but rather the abstract preserved entities in compound transformations. We celebrate the systems, rather than their tables or ultimate table. The periodic law, we argue, is not an all-encompassing achievement, as it does not apply to every property of all elements and compounds. Periodic systems have been generalised as ordered hypergraphs, which solves the long-lasting question on the mathematical structure of the systems. In this essay, it is shown that these hypergraphs may solve current issues such as order reversals in super-heavy elements and lack of system predictive power. We discuss research in extending the limits of the systems in the super-heavy-atom region and draw attention to other limits: the antimatter region and the limit arising from compounds under extreme conditions. As systems depend on the known chemical substances (chemical space) and such a space grows exponentially, we wonder whether systems still aim at projecting knowledge of compounds on the relationships among the elements. We claim that systems are not based on compounds anymore, rather on 20th century projections of the 1860s systems of elements on systems of atoms. These projections bring about oversimplifications based on entities far from being related to compounds. A linked oversimplification is the myth of vertical group similarity, which raises questions on the approaches to locate new elements in the system. Finally, we propose bringing back chemistry to the systems by exploring similarity and order relationships of elements using the current information of the chemical space. We ponder whether 19th century periodic systems are still there or whether they have faded away, leaving us with an empty 150^th celebration.     

Microsolvation of small cations and anions

Recent advances in the theoretical treatment of microsolvation of small ions, a problem with practical implications in chemistry, physics, and biology, are exposed. In particular, we discuss sound stochastic approaches to sample complex energy landscapes and delve into the nature of bonding interactions that dictate both structural and energetical preferences. An in-depth analysis of the effect of formal charges in the surrounding network of solvent to solvent hydrogen bonds is also presented. The problem, as expected, is more complicated than simple definitions may forecast.     

How Many Water Molecules Does it Take to Dissociate HCl?

The potential energy surfaces of the HCl(H₂O)_n (n is the number of water molecules) clusters are systematically explored using density functional theory and high‐level ab initio computations. On the basis of electronic energies, the number of water molecules needed for HCl dissociation is four as reported by some experimental groups. However, this number is five owing to the inclusion of entropic factors. Wiberg bond indices are calculated and analyzed, and the results provide a quadratic correlation and classification of clusters according to the nondissociated, partially dissociated, and fully dissociated character of the H?Cl bond. Our computations show that if temperature is not controlled during the experiment, the values obtained for the dipole moment (or for any measurable property) are susceptible to change, providing a different picture of the number of water molecules needed for HCl dissociation in a nanoscopic droplet.     

Structure-fate relationships of organic chemicals derived from the software packages E4CHEM and WHASSE

A risk assessment of chemicals is to be performed on the basis of the model EUSES, developed by the Commission of the European Union. The model package E4CHEM (Exposure Estimation for Potentially Ecotoxic Environmental Chemicals), developed in 1984-1992, is presented and applied in this paper as a model which allows a model-supported evaluation of chemicals. E4CHEM consequently does not have the wide applicability and technical comfort of the more recently developed model EUSES. The simulation models of E4CHEM characterize the chemical behavior in the environment by many aspects. Hence, there is a need to condense all of these aspects to get a clear impression of what will be the fate of the chemicals. Starting with the already published concept of exposure maps, we will discuss how partial orders may be helpful in establishing generalized structure-fate relationships. The software WHASSE is applied.     

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.     

Local structural order in nanostructured hematite

Nanostructured α-Fe₂O₃ powders were prepared by high-energy ball milling. The milling process spans grinding times from 30 min to 24 h. The as-milled samples were characterized by means of ⁵⁷Fe Mössbauer spectrometry, Rietveld analysis of X-ray diffraction data and particle size analysis. The obtained results evidence the presence of disordered hematite characterized by a hyperfine field distribution with a well-behaved dependence on the mean crystallite size for which the mean hyperfine field decreases asymptotically as the grain size decreases. A new relationship is proposed in order to describe such behavior. Finally the presence of superparamagnetic grains, the occurrence of a partial topotactic phase transformation into a spinel phase and tool induced contamination are also presented and discussed.     

Relating β+ radionuclides’ properties by order theory

We studied 27 β⁺ radionuclides taking into account some of their variants encoding information of their production, such as integral yield, threshold energy and energy of projectiles used to generate them; these radionuclides are of current use in clinical diagnostic imaging by positron emission tomography (PET). The study was conducted based on physical, physico-chemical, nuclear, dosimetric and quantum properties, which characterise the β⁺ radionuclides selected, with the aim of finding meaningful relationships among them. In order to accomplish this objective the mathematical methodology known as formal concept analysis was employed. We obtained a set of logical assertions (rules) classified as implications and associations, for the set of β⁺ radionuclides considered. Some of them show that low mass defect is related to high and medium values of maximum β⁺ energy, and with even parity and low mean lives; all these parameters are associated to the dose received by a patient subjected to a PET analysis.