Some recent work in mathematical chemistry is discussed. It is claimed that quantum mechanics does not provide a conclusive means of classifying certain elements like hydrogen and helium into their appropriate groups. An alternative approach using atomic number triads is proposed and the validity of this approach is defended in the light of some predictions made via an information theoretic approach that suggests a connection between nuclear structure and electronic structure of atoms.

We review different studies of the Periodic Law and the set of chemical elements from a mathematical point of view. This discussion covers the first attempts made in the 19th century up to the present day. Mathematics employed to study the periodic system includes number theory, information theory, order theory, set theory and topology. Each theory used shows that it is possible to provide the Periodic Law with a mathematical structure. We also show that it is possible to study the (...) chemical elements taking advantage of their phenomenological properties, and that it is not always necessary to reduce the concept of chemical elements to the quantum atomic concept to be able to find interpretations for the Periodic Law. Finally, a connection is noted between the lengths of the periods of the Periodic Law and the philosophical Pythagorean doctrine. (shrink)

Hydrogen is troublesome in any periodic table classification. This being so it may as well be placed in a position that confers desirable attributes to the arrangement of the elements, while notionally recognising its lineage to the group 1 alkali metals and the group 17 halogens. Since the noble gases bridge the halogens and the alkali metals, and hydrogen encompasses the transition from the alkali metals to the halogens, there is more to the idea of hydrogen over helium. (Meyer 1870, (...) p. 357) (Proust 1927, p. 559). (shrink)

Though complex networks have been widely applied in the research of chemistry, there is hardly any introduction about the establishment of networks using chemical bonds. In this paper, we consider chemical elements as a system linked by chemical bonds and create the undirected chemical bond network by abstracting nodes from elements and undirected edges from bonds. Connectivity, heterogeneity, small world and disassortativity of this network show the macro structural rationality of this system. The degree and k-order neighbors of an element, (...) which represent the micro topology of this network, can be used to measure its chemical reactivity and detect how many kinds of compounds it can form. The similarity between two elements is measured by the Jaccard index and the VOS mapping technique, results of which are similar to well-known similarities between elements shown by the periodic table. The establishment and topological analysis of this network provide another way to understand and study elements and bonds, and more chemical properties of elements and bonds can be studied by complex networks. (shrink)

Periodic tables (PTs) are the ‘ultimate paper tools’ of general and inorganic chemistry. There are three fields of open questions concerning the relation between PTs and physics: (i) the relation between the chemical facts and the concept of a periodic system (PS) of chemical elements (CEs) as represented by PTs; (ii) the internal structure of the PS; (iii)␣The relation between the PS and atomistic quantum chemistry. The main open questions refer to (i). The fuzziness of the concepts of chemical properties (...) and of chemical similarities of the CE and their compounds guarantees the autonomy of chemistry. We distinguish between CEs, Elemental Stuffs and Elemental Atoms. We comment on the basic properties of the basic elements. Concerning (ii), two sharp physical numbers (nuclear charge and number of valence electrons) and two coarse fuzzy ranges (ranges of energies and of spatial extensions of the atomic orbitals, AOs) characterize the atoms of the CEs and determine the two-dimensional structure of the PS. Concerning (iii), some relevant ‘facts’ about and from quantum chemistry are reviewed and compared with common ‘textbook facts’. What counts in chemistry is the whole set of nondiffuse orbitals in low-energy average configurations of chemically bonded atoms. Decisive for the periodicity are the energy gaps between the core and valence shells. Diffuse Rydberg orbitals and minute spin–orbit splittings are important in spectroscopy and for philosophers, but less so in chemical science and for the PS. (shrink)

As part of a series of contributions on patterns in the periodic table, the relationships among the transition metals are examined here in a systematic manner. It is concluded that the traditional method of categorizing transition elements by group or by period is not as valid as by using combinations thereof. From chemical similarities, it is proposed that the transition metals be considered as the [V–Cr–Mn] triad; the [Fe–Co–Ni–Cu] tetrad; the [Ti–Zr–Hf–Nb–Ta] pentad; the [Mo–W–Tc–Re] tetrad; and the [Ru–Os–Rh–Ir–Pd–Pt–Au] heptad. Silver (...) does not fit neatly in anywhere and is better linked with thallium. (shrink)

There are many things that philosophy of biology might be. But, given the existence of a professional philosophy of biology that is arguably a progressive research program and, as such, unrivaled, it makes sense to define philosophy of biology more narrowly than the totality of intersecting concerns biologists and philosophers (let alone other scholars) might have. The reasons for the success of the “new” philosophy of biology remain poorly understood. I reflect on what Dutch and Flemish, and, more generally, European (...) philosophers of biology could do to improve the situation of their discipline locally, regionally, and internationally, paying particular attention to the lessons to be learned from the “Science Wars.”. (shrink)