Philosophy of Chemistry

We review the early works which were precursors of the Conceptual Density Functional Theory. Starting from Thomas–Fermi approximation and from the exact formulation of Density Functional Theory by Hohenberg and Kohn’s theorem, we will introduce electronegativity and the theory of hard and soft acids and bases. We will also present a general introduction to the Fukui functions, and their relation with nucleophilicity and electrophilicity, with an emphasis towards the importance of these concepts for chemical reactivity.

After the birth of thermodynamics’ second principle—outlined in Carnot's Réflexions sur la puissance motrice du feu —several studies provided new arguments in the field. Mainly, they concerned the thermodynamics’ first principle—including energy conceptualisation—, the analytical aspects of the heat propagation, the statistical aspects of the mechanical theory of heat. In other words, the second half of nineteenth century was marked by an intense interdisciplinary research activity between physics and chemistry: new disciplines applied to the heat developed in the form of (...) analytical, mechanical and statistical theories. Inside all these theories, entropy—the brand-new function that Clausius coined in his Mechanical theory of heat—started to play a central epistemic role. In the present paper, we analyse some steps of the historical process of conceptualisation of such function from 1850 to 1902. Particularly, we retrace the historical–foundational path that—starting from Clausius’ Second Law—lead Boltzmann and Gibbs to their distinguished formulations of statistical entropy. As usual, our research has been unrolled through the analyses of primary sources and by leaning on critical readings of the secondary literature. As for the methodological approach, text analysis of historical documents constituted our privileged modus operandi. This paper is the expression of a collaborative historical research program focused on the thermodynamic foundations of physics–chemistry relationship; early results have already been published by the same authors upon the concepts of reversibility––and––thermal equilibrium. (shrink)

In a recent article entitled “The problem of molecular structure just is the measurement problem”, Alexander Franklin and Vanessa Seifert argue that insofar as the quantum measurement problem is solved, the problems of molecular structure are resolved as well. The purpose of the present article is to show that such a claim is too optimistic. Although the solution of the quantum measurement problem is relevant to how the problem of molecular structure is faced, such a solution is not sufficient to (...) account for the structure of molecules as understood in the field of chemistry. (shrink)

No exact definition of an “organic” substance has been agreed upon by the chemical community and textbook definitions vary substantially. The question of what exactly constitutes an “organic” substance is explored in this paper. Various carbon-containing substances that have been by some considered to be “inorganic” are examined in an attempt to ascertain whether carbon in these compounds display different chemical behavior than what is expected of carbon in an “organic” substance. Types of substances considered are carbon allotropes, carbides, carbonates (...) and bicarbonates, cyanide and cyanate ions, carbido clusters, carbon oxides, and compounds without hydrogen.Graphic abstract. (shrink)

A simple treatment of chemical equilibrium is given, based on Boltzmann’s distribution law. The results are compared with those obtained by using thermodynamics.

The objective of the present review on the evolution of Green Chemistry, since its emergence until 2016, aimed an integrated vision of its progress along the three phases of its development: emergence, divulgation and consolidation. The methodology involved the analysis of a selection of bibliography on the evolution of GC collected from issues of the ACS symposia series; editorials in specialized GC journals; and commemorative birthday papers/editorials of these journals and of the GC itself. The analysis allowed to identify and (...) discuss the characteristics and conceptions of GC agents about fundamental concepts and procedures, in order to visualize and better understand the state of knowledge and the subject areas that make up the field. The main alterations identified in the evolution of GC were: it acquired a better defined identity, with more participation of academy and increased scope; was progressively framed in sustainability; has been aspiring to a holistic frame and to a change on the nature of the innovation for its implementation, from incremental to transformative. The analysis suggests that for supporting expansion and consolidation of GC the following aspects deserve attention: full validation of chemical greenness by metrics; better characterization of the frontiers of GC research areas/themes; increased integration between academy and industry; and penetration in chemistry curricula. Its basic philosophy being the practice of a chemistry more focused on the environment preservation, GC means a new stage in nature and in the history of Chemistry. (shrink)

The periodic table is one of the best-known systems of classification in science. Because of the information it contains, it raises explanation-seeking questions. Quantum mechanical models of the behaviour of electrons may be seen as providing explanations in response to these questions. In this paper we first address the question ‘Do quantum mechanical models of atoms provide legitimate explanations?’ Because our answer is positive, our next question is ‘Are the explanations provided by quantum mechanical models of atoms mechanistic explanations?’. This (...) question is motivated by the fact that in many scientific disciplines, mechanistic explanations are abundant. Because our answer to the second question is negative, our last question is ‘What kind of explanation do quantum mechanical models of atom provide?’ By addressing these questions, we shed light on the nature of an important type of chemical explanation. (shrink)

We re-examine the history of the element “nipponium” discovered by a Japanese chemist Masataka Ogawa in 1908. Since 1996 H.K. Yoshihara has made extensive research into Ogawa’s work and revealed evidence that nipponium proposed for the place of the atomic number of 43 was actually rhenium. In this paper, we provide critical re-interpretations of the existing information and confirmed that Ogawa left indisputable evidence that nipponium was in fact rhenium. We further discuss the reasons for the existing doubts and criticism (...) against Ogawa’s discovery and Yoshihara’s interpretation, and attempt to resolve them. (shrink)

A new way of understanding entropy as a macroscopic property is presented. This is based on the fact that heat flows from a hot body to a cold one even when the hot one is smaller and has less energy. A quantity that determines the direction of flow is shown to be the increment of heat gained divided by the absolute temperature. The same quantity is shown to determine the direction of other processes taking place in isolated systems provided that (...) q is determined by the state of the system. Entropy emerges as the potent energy of a system [Σ], the potency being determined by 1/T. This is shown to tie in with the statistical mechanical interpretation of entropy. The treatment is shorter than the traditional one based on heat engines. (shrink)

This paper aims to highlight how the philosophy of chemistry could be of help for rethinking Nature today. To do so, we will point out: the co-definition of chemical relations and chemical relata within chemical activities; the constitutive role of the modes of intervention in the definition, always open and provisional, of “active” chemical bodies; and the mutual dependence of the levels of organization in chemistry. We will insist on the way chemists tailor networks of interdependencies within which chemical bodies (...) and properties are context-sensitive and mutually determined by means of particular chemical operations or transformations. To conclude, we will show how the specific action of bodies upon the Earth at different scales of space and time, and how the relational definition of a chemical body, pave the way for a new understanding of Nature. (shrink)

This paper comments on a recent article “Revolutionary poetry and liquid crystal chemistry: Herman Gorter, Ada Prins and the interface between literature and science” by Hub Zwart, in which the author explores the influence of the liquid crystal research of Ada Prins on the epic poem Pan written by her long-time lover Herman Gorter. The present paper reviews the basic science of liquid crystals and explains the connections between the work of Prins and its influence on the poem. Other examples (...) of the use of “liquid crystal” as a literary device are identified from renaissance poetry, and the uses of the metaphor in these poems are analysed from a scientific perspective. From these examples it is suggested that creative concepts from poetry may contain elements of substance that appear in hitherto unrecognised scientific realities. (shrink)

Group 3 as Sc–Y–La, rather than Sc–Y–Lu, dominates the literature. The history of this situation, including involvement by the IUPAC, is summarised. I step back from the minutiae of physical, chemical, and electronic properties and explore considerations of regularity and symmetry, natural kinds, and quantum mechanics, finding these to be inconclusive. Continuing the theme, a series of ten interlocking arguments, in the context of a chemistry-based periodic table, are presented in support of lanthanum in Group 3. In so doing, I (...) seek to demonstrate a new way of thinking about this matter. The last of my ten arguments is recast as a twenty-word categorical philosophical statement. (shrink)

There are inherent difficulties in a subject like chemistry particularly the notion of a chemical reaction. In this paper the difficulties are discussed from a teaching and learning perspective and from a history of chemistry perspective. Three teaching/learning studies of the incompleteness of the iron thiocyanate reaction in chemical equilibrium are reviewed and it is shown that a recent historical study of the iron thiocyanate reaction has the potential to challenge the interpretation of the incompleteness of the reaction. This establishes (...) a controversial context where students can be introduced to epistemic thinking, that is, how to interrogate chemistry data and form a conclusion which resonates with what we know about the nature of science. A curriculum suggestion for pre-service chemistry teachers is provided. (shrink)

Despite the periodic table having been discovered by chemists half a century before the discovery of electronic structure, modern designs are invariably based on physicists’ definition of periods. This table is a chemists’ table, reverting to the phenomenal periods that led to the table’s discovery. In doing so, the position of hydrogen is clarified.

The statements and arguments based on experimental evidence used to support the claim that the 3d sub-level is below the 4s sub-level in scandium are examined. The flaw in all the arguments is that they assume the order in which the 3d and 4s sub-levels arrange remains the same in both the neutral atom and in its ions. Analysis of the ground and excited states of atomic spectra shows that as the number of electrons relative to the nuclear charge increases, (...) the 3d level moves higher in energy relative to the 4s level. It is perfectly possible that in a neutral scandium atom the 3d sub-level is above the 4s sub-level and that when it ionizes the energy levels simultaneously rearrange during the process. (shrink)

In the original publication of the article, the author has identified four belated corrections which are listed below.

A large variety of periodic tables of the chemical elements have been proposed. It was Mendeleev who proposed a periodic table based on the extensive periodic law and predicted a number of unknown elements at that time. The periodic table currently used worldwide is of a long form pioneered by Werner in 1905. As the first topic, we describe the work of Pfeiffer, who refined Werner’s work and rearranged the rare-earth elements in a separate table below the main table for (...) convenience. Today’s widely used periodic table essentially inherits Pfeiffer’s arrangements. Although long-form tables more precisely represent electron orbitals around a nucleus, they lose some of the features of Mendeleev’s short-form table to express similarities of chemical properties of elements when forming compounds. As the second topic, we compare various three-dimensional helical periodic tables that resolve some of the shortcomings of the long-form periodic tables in this respect. In particular, we explain how the 3D periodic table “Elementouch”, which combines the s- and p-blocks into one tube, can recover features of Mendeleev’s periodic law. Finally we introduce a topic on the recently proposed nuclear periodic table based on the proton magic numbers. Here, the nuclear shell structure leads to a new arrangement of the elements with the proton magic-number nuclei treated like noble-gas atoms. We show that the resulting alignments of the elements in both the atomic and nuclear periodic tables are common over about two thirds of the tables because of a fortuitous coincidence in their magic numbers. (shrink)

Chemistry and dynamics are closely related in G.W. Leibniz's thinking, from the corpuscularism of his youth to the theory of conspiracy movements that he proposes in his later years. Despite the importance of chemistry and chemical thought in Leibniz's philosophy, interpreters have not paid enough attention to this subject, especially in the recent decades. This work aims to contribute to filling this gap in Leibnizian studies. In this first part of the work I will expose the theory of matter that (...) the young Leibniz conceives under the influence of chemical corpuscularism. Leibniz uses R. Boyle's interpretation of the Aristotelian idea of form in order to give an explanation of the unity and cohesion of bodies. As opposed to the Cartesians, Leibniz puts forth the idea of a dependence between the variables of extension, movement and figure, without losing analytical clarity and with the aim of extending the explanatory power of physics to natural phenomena difficult to approach by Cartesian mechanics. (shrink)

Algorithmic chemistries are often based on a fixed formalism which limits the fragment of chemistry expressible in the domain of the models. This results in limited applicability of the models in contemporary mathematical chemistry and is due to the poor fit between the logic used for model construction and the system being modeled. In this paper, I propose a system-oriented methodology which selects a formalism through a mapping of chemical transformation rules to proof-theoretic structural rules. Using a formal specification framework (...) from the field of artificial chemistry, expressive adequacy is ensured by the choice of logic being based on the system properties to be modeled. To illustrate the methodology, a case study is provided that shows how the proposed approach selects linear logic for modeling resource sensitivity and the proof-theoretic interpretation facilitates translation to a programming language. Since the method results in a plurality of models, I conclude with a discussion on how the proposal contributes to multi-model paradigms in computational pharmacology. (shrink)

In the accompanying article in this issue Neuss challenges the explanation that was first suggested by Schwarz for how to teach the relative occupation and ionization of atomic orbitals in the atoms of metals in the first transition series. The present article is a response to Neuss’ critique which includes a detailed examination of his claim that there is no conclusive evidence for the view that the scandium and other first transition metal atoms lose 4s electrons in preference to those (...) located in 3d orbitals. (shrink)

In the Netherlands, the poet Herman Gorter is mostly known as the author of the neo-romantic poem May and the “sensitivistic” Poems, but internationally he became famous as a propagandist of radical Marxism: the author of influential brochures and of an “open letter” to comrade W.I. Lenin in 1920. During the 1890s, Gorter became increasingly dissatisfied with his poetry, considering it as ego-centric, disinterested and “bourgeois”, unconnected with what was happening in the real world. He wanted to put his poetry (...) on a scientific footing, notably by endorsing a dialectical materialist worldview. In the communist society he envisioned, science would become poetry and poetry would become science. In his opus magnum Pan, two terms are rather prominent, namely heelal and kristal. These signifiers not only reflect important themes, but also two friendships which began around 1900, namely with prominent astronomer and marxist Anton Pannekoek and with Ada Prins, the first woman in the Netherlands who acquired a PhD in chemistry, specialised in liquid crystal research. Whereas Ada Prins is mostly remembered as one of Gorter’s secret lovers, she was first and foremost his educated guide into the complex and enigmatic world of twentieth-century chemistry research. Liquid crystal chemistry became an important source of inspiration for Gorter’s work and the main objective of this paper is to demonstrate her influence on Gorter’s Pan as a scientific poem After presenting the two heroes of this paper, and their work in poetry and chemistry respectively, I will analyse the role of liquid crystals in Herman Gorter’s Pan, highlighting important connections with Ada Prins’ research into liquid crystal chemistry. (shrink)

Synthetic biology aims to synthesize novel biological systems or redesign existing ones. The field has raised numerous philosophical questions, but most especially what is novel to this field. In this article I argue for a novel take, since the dominant ways to understand synthetic biology’s specificity each face problems. Inspired by the examination of the work of a number of chemists, I argue that synthetic biology differentiates itself by a new regime of articulation, i.e. a new way of articulating the (...) questions and phenomena it wants to address. Instead of describing actual existing biological systems, the field aims to describe biological possibilities. In the second part I corroborate this hypothesis through a comparison between early research in the field of the origins of life and contemporary synthetic biologists, who are not so much interested in the historical origin of life on Earth, but rather in a universal biology of the possible origins of any life whatsoever. (shrink)

Classical atoms—“part-less, ontologically irreducible simples” as the conference flyer puts it—are not the atoms of modern chemistry and analogies with the latter can be construed in various ways. They have figured in the historical development of concepts of chemical affinity but without, as Alan Chalmers and I have independently argued, making any significant contribution to empirically justified theories. A purely combinatorial conception of the formation of compounds by juxtaposing atoms is associated with Daltonian atomism. I review the merits of this (...) idea as a solution to problems posed by developments in early nineteenth century chemistry and go on to suggest that subsequent developments in chemistry are as much in agreement with ideas associated with Aristotle as with the ancient atomists, if not more so. The basic issues can be understood without getting involved in detailed chemistry and I hope what I have to say will be of interest to philosophers concerned with the metaphysics of matter but with no special knowledge of chemistry. (shrink)

This undergraduate textbook introduces some fundamental issues in philosophy of science for students of philosophy and science students. The book is divided into two parts. Part 1 deals with knowledge and values. Chap. 1 presents the classical conception of knowledge as initiated by the ancient Greeks and elaborated during the development of science, introducing the central concepts of truth, belief and justification. Aspects of the quest for objectivity are taken up in the following two chapters. Moral issues are broached in (...) Chap. 4, which discusses some aspects of the use and abuse of science, taking up the responsibilities of scientists in properly conducting their business and decision-makers in their concerns with the import of science for society. Part 2 contrasts the view of scientific progress as the rejecting of old hypotheses and theories and replacing them with new ones, represented by Karl Popper, with the conception of progress as accumulating knowledge, saving as much as possible from older theories, represented by Pierre Duhem. A concluding chapter defends the natural attitude of taking the theories of modern science to be literally true, i.e. realism, in the face of arguments drawn partly from the history of scientific progress in criticism of this stance. (shrink)

How do we refer to chemical substances, and in particular to chemical elements? This question relates to many philosophical questions, including whether or not theories are incommensurable, the extent to which past theories are later discarded, and issues about scientific realism. This chapter considers the first explicit reference to types of colorless air in late-eighteenth-century chemical practice. Reference to a gas by one chemist was generally intended to give others epistemological, methodological, and practical access to the gas. This chapter proposes (...) a causal-descriptive theory of reference for chemical substances. Implications for debates about incommensurability and realism are also briefly noted. (shrink)

All suggested notions of reduction of two scientific theories are critically reviewed and analyzed. In particular those applied to the case of the alleged reduction of Chemistry to Quantum mechanics are examined. Since it is recognized that the weakness of this field of research is the lack of a definition of a scientific theory, it is suggested that a scientific theory is characterized by two choices regarding two dichotomies, that is, the kind of mathematics and the kind of logic. According (...) to this view a reduction is only possible between two theories in which the same choices are shared. As a consequence, only one case of reduction in the history of physics is recognized: physical optics to electromagnetism, a case that is commonly accepted. The other cases of claimed reductions are recognized as impossible, owing to the different choices of the two theories at issue and hence the radical variations in meaning of their shared basic notions. In particular, the claimed reduction of Chemistry to Quantum mechanics is disproved in detail. (shrink)

Generally, an object is vague when its properties cannot precisely defined. The ontic view of vagueness is the idea that vagueness is a fundamental property of Nature. This simply means that everything is vague: animals, plants, molecules, atoms, etc. Furthermore, if atoms and molecules are vague, then the subject matter of chemistry is vague. However, we first need to understand why molecules and atoms are vague.

Structure–activity relationship and quantitative SAR are modeling methods largely used in assessing biological properties of chemical substances. QSAR is based on the hypothesis that the chemical structure is responsible for the activity; it follows that similar molecules are expected to have similar properties. Similarity plays an important role in read across, which categorizes molecules primarily on the basis of similarity. Similarity, and chemical similarity too, is a property differently perceived by humans. The various proposed metrics often disagree with human judgment, (...) and no a unique metric for chemical similarity is universally adopted. Researchers argued that categorization is not only explained by similarity but depends as well on abstract knowledge and the task to accomplish. Moreover, similarity cannot be the unique explanation of a categorization, as different perceptual processes take place in category formation. Assuming that similarity judgments are deeply rooted in human knowledge and perception, cognitive sciences contributions are as important as the mathematical considerations of the classical theories. After an excursus in the many views of similarity in philosophy, mathematics, and cognitive science, the paper explores how connectionist systems, which loosely mimic the human cognitive system, could improve similarity-based choices. A case study on building SARs using connectionism and deep neural networks shows the role of similarity in building and explaining those models. A discussion about deep learning for QSAR and as a modeling tool for science concludes the presentation. (shrink)

After briefly presenting the first formulation of the equilibrium constant stated by Guldberg and Waage, this study examines the early thermodynamic and kinetic deductions of the equilibrium law. Firstly, it is discussed how Horstmann applied the concept of entropy to chemical equilibrium reactions, which meant the first thermodynamic explanation of the Guldberg-Waage law of mass action proposed in 1864. A different theoretical derivation of the equilibrium constant came from the works of van’t Hoff. This study analyses the first accurate kinetic (...) treatment of equilibrium reactions as well as van’t Hoff’s imaginative thermodynamic foundation of the constant ratios in chemical equilibrium systems. (shrink)

In the Netherlands, the poet Herman Gorter is mostly known as the author of the neo-romantic poem May and the “sensitivistic” Poems, but internationally he became famous as a propagandist of radical Marxism: the author of influential brochures and of an “open letter” to comrade W.I. Lenin in 1920. During the 1890s, Gorter became increasingly dissatisfied with his poetry, considering it as ego-centric, disinterested and “bourgeois”, unconnected with what was happening in the real world. He wanted to put his poetry (...) on a scientific footing, notably by endorsing a dialectical materialist worldview. In the communist society he envisioned, science would become poetry and poetry would become science. In his opus magnum Pan, two terms are rather prominent, namely heelal and kristal. These signifiers not only reflect important themes, but also two friendships which began around 1900, namely with prominent astronomer and marxist Anton Pannekoek and with Ada Prins, the first woman in the Netherlands who acquired a PhD in chemistry, specialised in liquid crystal research. Whereas Ada Prins is mostly remembered as one of Gorter’s secret lovers, she was first and foremost his educated guide into the complex and enigmatic world of twentieth-century chemistry research. Liquid crystal chemistry became an important source of inspiration for Gorter’s work and the main objective of this paper is to demonstrate her influence on Gorter’s Pan as a scientific poem After presenting the two heroes of this paper, and their work in poetry and chemistry respectively, I will analyse the role of liquid crystals in Herman Gorter’s Pan, highlighting important connections with Ada Prins’ research into liquid crystal chemistry. (shrink)

Is Leibnizian dynamics the New Physics sought in his youth to provide a solution to the problem of body unity/composition? This question can only be answered tentatively. The thesis that I will develop in this second part is that chemical-combinatoria project is not complete without some ideas of dynamics. The idea of form, which since the early Leibniz’s philosophy is projected to give a foundation to the corpuscular theory, only reaches this objective with the theory of conspiring movements that Leibniz (...) develops as the last phase of his dynamics. Within this general objective, this second part develops three secondary issues of importance: Leibniz’s emergent and realistic position, his theory of compounds and the interpretation of the Combinatoria or Characteristica project as a science of forms. (shrink)

Recently, philosophers have come forth with approaches to chemistry based on its actual practice, imparting to it a proper aim and character of its own. These approaches add to the currently growing movement of pluralist philosophies of science. We draw on recent pluralist accounts from chemistry and analyse three notions from modern chemical practice and theory in terms of these accounts, in order to complement the so far more general pluralist approaches with specific evidence. Our survey reveals that the concept (...) of element indicates conceptual pluralisms in chemistry. that electronegativity illustrates methodological pluralism in determining one and the same concept, and that acidity is an instance of plurality hidden behind ‘one notion’. (shrink)

Electron redistribution is the cornerstone of our understanding of chemical reactivity. For the vast majority of organic reactions electrons are assumed to move in pairs providing explanatory mechanisms through the generation of intermediate structures. But for many transformations these discrete steps are idealized constructs, involving intermediates assumed but not empirically justified. This unitary perspective predicated on the curved arrow formalism has resulted in the scenario where for many organic transformations our supposed understanding far surpasses our growing knowledge. Reformulating organic mechanisms (...) to include single electron transfer as a component of, or an alternative to, the prevailing iconic descriptions can provide for a more empirically adequate mechanistic description. In addition using the language of SET presents an opportunity to unify mechanistic concepts under a common donor/acceptor framework. (shrink)

Much has been said about the accuracy of the famous predictions of the Russian chemist Dmitrii Ivanovich Mendeleev, but far less has been written on how he made his predictions. Here we offer an explanation on how Mendeleev used his periodic system to predict both physical and chemical properties of little-known and entirely unknown chemical elements. We argue that there seems to be compelling evidence in favour of Mendeleev genuinely relying on his periodic system in the course of issuing his (...) predictions—a point recently contested by Woody Science after the practice turn in the philosophy, history, and social studies of science, Routledge, Abington, 2014). In particular, by using the known properties of a number of near neighbours of the three entirely unknown elements, we seek to show how the very format of his table enabled it to function as a powerful tool for Mendeleev in arriving at his predicted values. We suggest that Mendeleev’s use of the periodic system in making his prediction gives an illuminative example of what Woody calls “theoretical practices” in science. (shrink)

There has been plenty of empirical evidence which shows that the single-particle picture holds to a good approximation in atomic nuclei. In this picture, protons and neutrons move independently inside a mean-field potential generated by an interaction among the nucleons. This leads to the concept of nuclear shells, similar to the electronic shells in atoms. In particular, the magic numbers due to closures of the nucleonic shells, corresponding to noble gases in elements, have been known to play an important role (...) in nuclear physics. Here we propose a periodic table for atomic nuclei, in which the elements are arranged according to the known nucleonic shells. The nuclear periodic table clearly indicates that nuclei in the vicinity of the magic numbers can be understood in terms of a shell closure with one or two additional nucleons or nucleon holes, while nuclei far from the magic numbers are characterized by nuclear deformation. (shrink)

This article discusses the mathematizing of the chemical periodic system as a grid, which leads to a quadratic function or “binódica function” formed by pairs of periods or binodos. We describe the periodic law as an increasing function of the principal quantum number. It works subject to the dialectical laws that generate; first: gradual quantitative changes:, with “duplication” of periods:. Second: radical quantitative changes:, with the emergence of new quantum transitions, growth and a change in the format of the binodos. (...) We use analytical and graphic methods to mathematize Mendeleev’s law, making the size of the binodos and the continuous series depend on the number of the binode, which is the same quantum number. Likewise, we show a graphic representation, in 2D, of a continuous and self-similar spiral function of the elements, in a geometric growth pattern. (shrink)

The periodic table can be simply demarcated into four classes of metal and four classes of nonmetal. Such a treatment has been obstructed by the traditional view of metalloids as in-between elements; understandable but needless boundary squabbles; and a group-by-group view of the reactive nonmetals. Setting aside these limiting notions reveals some interesting patterns and facilitates teaching and learning the periodic table.

In the original publication of the article under the Acknowledgements section, a contributor name was missed out. The corrected statement should read as follows.