The Earth Scientist’s Periodic Table of the Elements and Their Ions: A New Periodic Table Founded on Non-Traditional Concepts

The Earth Scientist’s Periodic Table of the Elements and Their Ions is a fundamentally new table that was first published in 2003 in the Geological Society of America’s (GSA) prominent journal Geology (Railsback 2003). The new table was reported in Nature, it was featured in a cover article by Science News, it was included among Discover magazine’s 100 Top Science Stories of 2003, and its publication was noted in many other magazines and online outlets. GSA sold a large number of reprints of the 2003 paper and then, in 2004, published a revised version of the table in GSA’s Map and Chart Series (Railsback 2004). When GSA’s printed stock ran low, the Society published a further revised version of the table in its Map and Chart Series in 2011 (Railsback 2011). The table has been translated into Chinese (Jin 2006), Spanish (Bernal and Railsback 2008), Portuguese (Franco de Souza Lima and Railsback 2012), and German. The original 2003 paper has been cited in journals ranging from Journal of Mathematical Chemistry to Carbohydrate Research to Geomicrobiology Journal to Journal of Arid Environments to Resource Geology to Reviews in Geophysics, and it has proven useful in understanding the topology of the periodic table (Restrepo et al. 2006). The success of the new Earth Scientist’s Periodic Table of the Elements and Their Ions across the past decade suggests that the periodic table, as a general concept, is not a static document but instead is still subject to evolution, especially as scientific fields beyond traditional chemistry increasingly use chemical perspectives. It further suggests that volumes like this one are not simply retrospective ruminations on a nineteenth-century invention, but instead they can be part of an ongoing process to find new meaning in the periodic concept and to make it more applicable in broader contexts in the twenty-first century. Despite the diversity of periodic tables produced over the last 140 years (e.g., Mazurs 1974), the Earth Scientist’s Periodic Table of the Elements and Their Ions differs both in conceptual origin and in form from almost all previous versions.

The Grand Periodic Function

The discovery of material periodicity must rank as one of the major achievements of mankind. It reveals an ordered reality despite the gloomy pronouncements of quantum philosophers. Periodicity only appears in closed systems with well-defined boundary conditions. This condition excludes an infinite Euclidean universe and all forms of a chaotic multiverse. Manifestations of cosmic order were observed and misinterpreted by the ancients as divine regulation of terrestrial events, dictated by celestial intervention. Analysis of observed patterns developed into the ancient sciences of astrology, alchemy and numerology, which appeared to magically predict the effects of the macrocosm on the microcosm. The sciences of astronomy and chemistry have by now managed to outgrow the magic connotation, but number theory remains suspect as a scientific pursuit. The relationship between Fibonacci numbers and cosmic self-similarity is constantly being confused with spurious claims of religious and mystic codes, imagined to be revealed through the golden ratio in the architecture of the Great Pyramid and other structures such as the Temple of Luxor. The terminology which is shared by number theory and numerology, such as perfect number, magic number, tetrahedral number and many more, contributes to the confusion. It is not immediately obvious that number theory does not treat 3 as a sacred number, 13 as unlucky and 666 as an apocalyptic threat. The relationship of physical systems to numbers is no more mysterious nor less potent than to differential calculus. Like a differential equation, number theory does not dictate, but only describes physical behavior. The way in which number theory describes the periodicity of matter, atomic structure, superconductivity, electronegativity, bond order, and covalent interaction was summarized in a recent volume. The following brief summary of these results is augmented here by a discussion of atomic and molecular polarizabilities, as derived by number theory, and in all cases specified in relation to the grand periodic function that embodies self-similarity over all space-time.

Nuclear Lattice Model and the Electronic Configuration of the Chemical Elements

In the earliest days of science researchers were arguing philosophically what might be the reasonable explanation for an observed phenomenon. The majority of the contemporary scientific community claims that these arguments are useless because they do not add anything to our understanding of nature. The current consensus on the aim of science is that science collects facts (data) and discerns the order that exists between and among the various facts (e.g., Feynman 1985). According to this approach the mission of science is over when the phenomenon under investigation has been described. It is left to the philosophers to answer the question what is the governing physical process behind the observed physical phenomenon. Quantum mechanics is a good example of this approach, “It works, so we just have to accept it.” The consequence is that nearly 90 years after the development of quantum theory, there is still no consensus in the scientific community regarding the interpretation of the theory’s foundational building blocks (Schlosshauer et al. 2013). I believe that identifying the physical process governing a natural phenomenon is the responsibility of science. Dutailly (2013) expressed this quite well: A “black box” in the “cloud” which answers our questions correctly is not a scientific theory, if we have no knowledge of the basis upon which it has been designed. A scientific theory should provide a set of concepts and a formalism which can be easily and indisputably understood and used by the workers in the field. In this study the main unifying principle in chemistry, the periodic system of the chemical elements (PSCE) is investigated. The aim of the study is not only the description of the periodicity but also the understanding of the underlying physics resulting in the PSCE. By 1860 about 60 elements had been identified, and this initiated a quest to find their systematic arrangement. Based on similarities, Dobereiner (1829) in Germany suggested grouping the elements into triads.

The Philosophical Importance of the Periodic Table

The Centrality of the periodic table to chemistry is beyond dispute. What seems just as obvious to me is that the table should be seen to play an equally central role in the philosophical understanding of scientific inquiry. This may be a minority opinion; if we look at philosophical discussions of scientific issues broadly, such a view seems unsupported by philosophical practice. Philosophers have been exercised by the problematic aspects of science: revolutions rather than normal scientific practice; aspects of science that are conceptually problematic, for example, quantum mechanics; areas of science that include explanatory accounts that deviate from standard models, for example, evolutionary theory; or aspects of science that raise moral or social issues, such as the biomedical sciences. Chemistry, with a long track record of unsurprising growth, with myriad of applications taken for granted, and with a strongly supported and unifying theory may seem to be just too boring to exercise philosophers interested in resolving puzzles, developing surprising theories, and engendering novel insights. But as I will attempt to show, the most normal of normal sciences, physical chemistry with the periodic table at its core, offers a view of science relevant to central philosophical concerns. In what follows I will offer an overview of three philosophical areas for which the periodic table is salient, while indicating a logical image of a scientific structure of the sort that the table exemplifies. I look first at methodology, and in particular the role of counterevidence in evaluating generalizations. Second I look at how the table permits a reinterpretation of foundational epistemological notions of truth. Finally, I will look at ontology, how the table supports our commitment to the fundamental nature of reality. The basis of my analysis is a model of emerging truth (MET). This metamathematical model is available in a number of publications and I will include only its most basic elements in a technical appendix. In place of the formal construction I will offer the philosophical intuitions it encodes, intuitions that draw upon the structure of chemistry with the periodic table at its core.

The Chemist as Philosopher: D. I. Mendeleev’s “The Unit” and “Worldview”

The Periodic System of chemical elements is almost certainly the most widely recognized scientific object in the world today, even though extensive debates persist about what it exactly is. Is it a theory, a collection of empirical data, a tabular arrangement of that data, a particular (best) tabular arrangement, a “paper tool,” or something else besides? Precisely because the periodic system has over close to 150 years remained so significant to the training and practice of scientists, the broader field of science studies has devoted considerable attention to it, most prominently in the philosophy of science. Among the many different approaches to articulating a philosophical foundation for the periodic system, one central strand is historicist, which places great emphasis on the individual (or individuals) to whom one attributes its discovery (Gordin 2012). Almost universally, credit for the formulation of the periodic system is assigned to St. Petersburg chemist Dmitrii Ivanovich Mendeleev (1834–1907) for his 1869 table of elements, which he later used to predict the properties of three yet-undiscovered elements. Although the philosophical justification of the periodic system by no means requires engagement with Mendeleev’s own views about the periodic system—or, as argued in Gordin (2004, 182–189), how those views changed over the course of his lifetime as periodicity became more central to chemical practice—nonetheless it remains of interest to understand precisely what Mendeleev thought he was about in constructing his system, as well as his post hoc justifications of it. There is, however, an obstacle to the full development of this line of inquiry: the Russian language itself. There is a substantial body of Imperial Russian, Soviet, and post-Soviet scholarship that would be of interest to the international community of philosophers and historians of chemistry, but it remains locked in a language not widely read by Western scholars. Even more problematic, only a very slender selection of primary sources are accessible in Western European languages (most widely cited are those available in English, although the corpus is larger if one includes French and German).

What Elements Belong in Group 3 of the Periodic Table?

The question of precisely which elements should be placed in group 3 of the periodic table has been debated from time to time with apparently no resolution. This question has also received a recent impetus from several science news articles following an article in Nature Magazine in which the measurement of the ionization energy of the element lawrencium was reported for the first time. We believe that this question is of considerable importance for chemists and physicists as well as students of these subjects. It is our experience that students are typically puzzled by the fact that published periodic tables show variation in the way that group 3 is displayed. Instructors typically cannot answer questions that students may have on this matter. The aim of this chapter is to make a clear-cut recommendation regarding the membership of group 3, which we believe should consist of the elements scandium, yttrium, lutetium, and lawrencium. Although the arguments in favor of replacing lanthanum and actinium by lutetium and lawrencium are rather persuasive there is a popular and mistaken belief that IUPAC supports the traditional periodic table with lanthanum and actinium in group 3. This view has been disputed by Jeffrey Leigh in an interesting article in which he made it clear that IUPAC has not traditionally taken a view as to the correctness of any version of the periodic table and that there is no such thing as an officially approved IUPAC periodic table. We will briefly review the previous arguments that have been provided in favor of moving lutetium and lawrencium into group 3 of the periodic table in place of lanthanum and actinium. We will then reiterate what we take to be a categorical argument in favor of this placement and will discuss any remaining issues. When added to other arguments made over more than 50 years it becomes clear that the time may have arrived for IUPAC to make a ruling on this question.

Heavy, Superheavy . . . Quo Vadis?

Uranium was Discovered in 1789 by the German chemist Martin Heinrich Klaproth in pitchblende ore from Joachimsthal, a town now in the Czech Republic. Nearly a century later, the Russian chemist Dmitri Mendeleev placed uranium at the end of his periodic table of the chemical elements. A century ago, Moseley used x-ray spectroscopy to set the atomic number of uranium at 92, making it the heaviest element known at the time. This chapter will deal with the quest to explore that limit and heavy and superheavy elements, and provide an update on where continuation of the periodic table is headed and some of the significant changes in its appearance and interpretation that may be necessary. Our use of the term “heavy elements” differs from that of astrophysicists who refer to elements above helium as heavy elements. The meaning of the term “superheavy” element is still not exactly agreed upon and has changed over the past several decades. “Ultraheavy” is occasionally used. Interestingly, there is no formal definition of “periodic table” by the International Union of Pure and Applied Chemistry (IUPAC) in their glossary of definitions: the “Gold Book.” But there are plenty of definitions in the general literature—including Wikipedia, the collaborative, free, internet encyclopedia which calls the “periodic table” a “tabular arrangement of the chemical elements, organized on the basis of their atomic numbers, electron configurations (electron shell model), and recurring chemical properties. Elements are presented in order of increasing atomic number (the number of protons in the nucleus).” IUPAC’s first definition of a “chemical element” is: “A species of atoms; all atoms with the same number of protons in the atomic nucleus.” Their definition of atom: “the smallest particle still characterizing a chemical element. It consists of a nucleus of positive charge (Z is the proton number and e the elementary charge) carrying almost all its mass (more than 99.9%) and Z electrons determining its size.”

The “Chemical Mechanics” of the Periodic Table

In 1969, the centennial of Mendeleev’s discovery of the periodic table was commemorated by an international conference devoted to the periodicity and symmetry of the elementary structure of matter. The conference was held in the Vatican and brought together a selected audience of first-rate atomic and nuclear scientists. In 1971, the proceedings were published in a joint publication [1] of the Academy of Sciences of Torino and the National Academy in Rome. Among the many interesting contributions, the American cosmologist John Archibald Wheeler described a mind-boggling journey from “Mendeleev’s atom to the collapsing star.” According to Wheeler [2], Mendeleev was convinced that the atom is not “deathlike inactivity” but a dynamic reality and Mendeleev expressed his hope that the discovery of an orderly pattern would “hasten the advent of a true chemical mechanics.” This hope has certainly been met by Schrödinger’s wave mechanics, which provides an accurate tool to simulate the properties of the elements. However, the overall structure and symmetry of the periodic table continues to defy understanding. The quest for an effective universal force law at the basis of the mechanics of multi-electron atoms forms the topic of this contribution. The search for central force laws should start with Bertrand’s theorem in classical mechanics. In 1873, the French mathematician Joseph Louis Bertrand presented to the Paris Academy a short note [3, 4] on central force laws that give rise to stable orbits. For a proper understanding of the research question which Bertrand was addressing, we start from an everyday experiment. A mass attached to a string can easily be swept around in a perfectly circular orbit by simply pulling on the string. The only requirement is that the force should be fixed and directed toward the center of the orbit. If we want the mass to go faster, we simply have to pull harder.

The Periodic Table Retrieved from Density Functional Theory Based Concepts: The Electron Density, the Shape Function and the Linear Response Function

“The periodic table of the elements is one of the most powerful icons in science: a single document that captures the essence of chemistry in an elegant pattern.” This statement taken from Eric Scerri’s marvelous book The Periodic Table: Its Story and Its Significance (Scerri 2007) grasps in one simple sentence the status that the periodic table has acquired in chemistry, but not only in chemistry: every person all over the world who took high school chemistry remembers for the rest of his/her life at least one thing from it (and from science courses in general): this mysterious table of the elements omnipresent in all books and documents, often decorating the classroom. Why? Although the answer is not easy it is probably because a whole discipline of science is condensed in a simple table or scheme offering at one glimpse the essence (and the beauty) of a part of science which for the rest of the lives of many students will remain unexplored—and even for which these students will create an aversion among others in view of the “polluting role” of chemistry. Nevertheless at some moment in their lives these students felt “something” that was remarkable and which they always remember, as witnessed by their comments when visiting their old school of university with their children. In the hierarchy of the sciences chemistry is often considered, mainly by physicists, as the “physics of the outer shell.” It is sometimes said that chemistry, as also quoted by Scerri (2007), has no deep ideas, not a few fundamental laws like in physics or biology (such as those governing quantum mechanics, relativity and evolution), but the not-so-distant observer will disagree: chemical periodicity as precisely reflected in the periodic table is in my view not only the most fundamental law of chemistry, but is a law or if you want an “organizing principle” with the same status as these famous laws in adjacent disciplines! Chemical periodicity is at the heart of reducing an astonishing amount of experimental data (and nowadays theoretical data as well) to a limited number of patterns often with common origin, enabling one to understand and interpret the properties of the now more-than 50 million compounds registered in the databases of the Chemical Abstracts Services (Toussant, 2009).

The Periodic System: A Mathematical Approach

The Periodic Table, Despite its near 150 years, is still a vital scientific construct. Two instances of this vitality are the recent formulation of a periodic table of protein complexes (Ahnert et al. 2015) and the announcement of four new chemical elements (Van Noorden 2016). “Interestingly, there is no formal definition of ‘Periodic Table’,” claims Karol (2017) in his chapter of the current volume. And even worse, the related concepts that come into play when referring to the periodic table (such as periodic law, chemical element, periodic system, and some others) overlap, leading to confusion. In this chapter we explore the meaning of the periodic table and of some of its related terms. In so doing we highlight a few common mistakes that arise from confusion of those terms and from misinterpretation of others. By exploring the periodic table, we analyze its mathematics and discuss a recent comment by Hoffmann (2015): “No one in my experience tries to prove [the periodic table] wrong, they just want to find some underlying reason why it is right.” We claim that if the periodic table were “wrong,” its structure would be variable; however the test of the time, including similarity studies, show that it is rather invariable. An approach to the structure of the periodic system we follow in this chapter is through similarity. In so doing we review seven works addressing the similarity of chemical elements accounting for different number of elements and using different properties, either chemical or physical ones. The concept of “chemical element” has raised the interest of several scholars such as Paneth (1962) and is still a matter of discussion given the double meaning it has (see, e.g., Scerri 2007, Earley 2009, Ruthenberg 2009, Ghibaudi et al. 2013, van Brakel 2014, Restrepo & Harré 2015), which is confusing, leading to misconceptions. The two meanings of the concept of chemical element are basic and simple substance. According to Paneth (1962), a basic substance belongs to the transcendental world and it is devoid of qualities, and therefore is not perceptible to our senses.