Hydrogenic atoms exhibit the familiar 2n^2 shell degeneracy, whereas the observed periods of the periodic system follow the distinct shell-capacity sequence (2, 8, 8, 18, 18,… ) . We present an Algebraic Quantum Shell Construction Framework (AQSCF) that interprets this sequence through the sequential admission of angular-momentum manifolds under a central potential. A compact algebraic expression, formulated as a stepwise function of the period number, reproduces the observed shell capacities and the sequence of noble-gas shell closures ( Z=2,10,18,36,54,86, and 118), while predicting the next algebraic shell closure beyond oganesson. The underlying physical interpretation is provided by centrifugal barriers, which delay the energetic stabilization and sustained population of higher-angular-momentum orbitals (d, f, g, ...). The proposed framework describes shell evolution through three complementary stages: geometric admission of angular-momentum manifolds, penetration-governed chronological population, and energetic reorganization of the populated atom. This distinction provides a structural interpretation of the experimentally observed difference between electron filling order and ionization order. A Symmetry Completion Index is further introduced to characterize the occupation of finite angular-momentum manifolds, identifying half-filled and fully filled subshells as symmetry extrema associated with enhanced stability. When considered collectively, the nineteen experimentally established deviations from the Madelung filling rule are shown to cluster into three recurring structural phenomena associated with delayed higher- ℓ population, symmetry completion, and persistent frontier-electron occupation. The resulting framework provides a structural interpretation that connects quantum angular-momentum symmetry with shell capacities, shell closure, subshell ordering, and the large-scale organization of the periodic system
The problem of unconceived alternatives represents one of the most profound epistemological challenges in the confirmation of chemical reaction mechanisms. Chemists rely on experimental and computational evidence density functional theory (DFT), kinetic analyses, isotopic labeling, and increasingly machine learning to rule out alternative mechanistic pathways. Yet the possibility of entirely unconceived mechanisms remains an enduring epistemic concern. This paper provides a systematic philosophical analysis of this problem, drawing on recent work in the philosophy of chemistry and general philosophy of science, and applies the resulting insights to a detailed case study from organometallic catalysis (palladium-catalyzed oxidative addition) and to the emerging field of sustainable chemistry. Building on the analysis, the paper proposes a novel five-step epistemological framework the Polysystemic Meta-Empirical Framework for Mechanism Confirmation (PME-MC) that integrates polysystemic epistemology, meta-empirical theory assessment, and the principle of “knowing-through-making.” The framework is grounded in a moderate epistemic pluralist realist position, which holds that while multiple theoretical systems can yield partial but convergent knowledge of mechanisms, such knowledge remains provisional and historically situated. Unlike previous accounts that treat unconceived alternatives as a purely theoretical threat to realism (Stanford 2006), this paper develops a practice-oriented framework anchored in chemical methodology and material engagement. The paper also addresses philosophical objections to the framework and provides a concrete decision matrix for assessing mechanistic confidence in practice. The article concludes by outlining future research directions and implications for chemical education and policy.
The chemical bond is a central organizing concept in chemistry. Yet it is absent from the molecular Hamiltonian and no “bond operator” exists. Bonding is therefore not a primitive term at the quantum level but rather a descriptor arising from the quantum state. The logical consequences of this observation are revisited. Statements such as “bonding stabilizes structure” are often useful effective explanations; however, when interpreted as fundamental causal claims, they risk circular reasoning (petitio principii), whereby bonding is inferred from a stationary structure and subsequently invoked as its primitive cause. The same caution applies to concepts such as steric repulsion. Bonding accompanies stationary structures and correlates strongly with their properties but should not be regarded as their microscopic cause. Particular attention is devoted to QTAIM bond and virial paths. Bond paths are observable electron-density-based topological features while remaining derived from an underlying quantum state. Illustrative examples are drawn from hydrogen–hydrogen bonding, REG/IQA analyses, non-covalent interaction (NCI) approaches, molecular mechanics force fields, AI-based molecular modelling, AlphaFold, and protein stability in condensed phases. Molecular mechanics provides an instructive counterpoint because bonds are introduced explicitly as spring-like interaction terms, whereas modern AI approaches predict accurate structures and energetics without encoding bonds as primitive mechanistic causes. Causation, explanatory direction, language, and the autonomy of chemistry are also briefly discussed. The aim is not to diminish the central role of the concepts related to bonding in chemistry, but rather to place these concepts at the correct logical level as powerful, state-dependent descriptors that organize, classify, predict, and often effectively explain chemical behavior without necessarily constituting causes in any conceptual sense. Finally, the paper suggests that explaining why bonding descriptors possess such extraordinary predictive and explanatory power despite their derived status may constitute one of the next major conceptual challenges for the foundations of chemistry.
In recent years, about two hundred papers per year are published on the use of the solutions of the ferrate(VI) ion, FeO42−. For the past 180 years, it was believed that these red-violet solutions were first obtained by the founder of the phlogiston theory, Georg Ernst Stahl (1659–1734) at the beginning of the 18th century. However, the analysis of primary sources suggests that these solutions were already known to the apothecary, Johannes Zwelfer (Zwölfer, 1618–1668) in the mid-17th century. In the Pharmacopoeia regia of 1668, Zwelfer gave a recipe for crocus martis cachecticus, a remedy for anemia, in which a red-violet solution of iron appeared to be an intermediate product. To obtain this solution, he first heated iron filings with saltpeter until ignition, and then dissolved the resulting sintered mass in hot water. The decomposition of the red-violet solution resulted in the precipitation of ultrafine powder of iron(III) oxide, which was the medicinal product. Thus, Zwelfer’s primacy in the synthesis and application of ferrate ion solutions should be established.
This work presents a geometric model of orbital occupation in the atom. Starting from a small number of geometric assumptions, a periodic structure is obtained in which electrons are represented as equal-sized spheres. The resulting structure provides a consistent representation of the S, P, D and F orbitals and their occupation according to the Aufbau principle and the constraints associated with the periodic table. The very possibility of obtaining, within a single geometric framework, a consistent representation that satisfies these constraints may itself be regarded as a finding worthy of consideration, even before examining the model’s correspondence with additional atomic properties. Once the geometric structure has been established, spatial coordinates are derived for the electrons and used to calculate the atomic covalent radius. The calculated radii are compared with empirical covalent-radius data for elements with even atomic numbers between 2 and 96. The results indicate a systematic correspondence between the model and the empirical data, including the reproduction of the general trends of the covalent radius across the periodic table. The agreement is stronger for low and intermediate atomic numbers and decreases for heavier elements. The covalent radius is not used in the construction of the model but rather serves as a test case for evaluating the resulting structure. Consequently, the existence of a systematic correspondence between the model predictions and covalent-radius data may suggest that the proposed geometric structure captures certain aspects of atomic regularities. These findings do not constitute proof of the physical validity of the model. However, they indicate that simple structural-geometric approaches may have value as an additional tool for examining atomic structure and its properties.
Mary and Michael Laing’s 2006 essay urging that Dulong and Petit’s law not be ignored has gone substantively unanswered for two decades. We argue that the answer requires more than the inclusion of one law in a curriculum that already includes many. The standard chemistry curriculum is built around what we call the cumulative axis—the historical sequence Dalton, Thomson, Rutherford, Bohr, Schrödinger—and the atom that Petit and Dulong introduced in 1819 does not lie on that axis. We develop a four-dimensional argument that the Petit–Dulong atom is generated by a methodologically distinct experimental practice, answers a different question (the identity question rather than the individuation question), refers as a different natural kind term in the sense of Stanford and Kitcher’s Causal Theory of Reference (CTR2), and is penetrated rather than absorbed by Einstein-Debye quantum refinement. We then redeploy Meyer and Land’s notion of the threshold concept in a deliberately inverted form, proposing the Petit–Dulong threshold as a diagnostic threshold concept whose function is not to be traversed by the learner but to render a curricular omission visible. The standard pedagogical reading of student conflict at this threshold as misconception is, on our analysis, a misdiagnosis: the conflict is the symptom of a structural curricular omission, not a learner deficit.
The early history of chromatography presents a philosophically revealing pattern: a major transformation in scientific practice that neither followed nor produced any corresponding crisis in scientific theory. When Mikhail Tswett introduced chromatographic adsorption analysis in the first years of the twentieth century, the technique was rejected despite its practical efficacy. It was revived in the early 1930s by Richard Kuhn and Edgar Lederer, rapidly adopted, and became foundational to modern analytical chemistry. No theoretical transformation separated Tswett’s rejection from chromatography’s later acceptance, and no theoretical revision accompanied its eventual triumph. This paper argues that this episode cannot be adequately explained by theory-centred accounts of scientific change, including the standard Kuhnian model, and proposes a conceptual response: the distinction between the theoretic and praxical dimensions of scientific paradigms. The praxical paradigm designates the discipline-wide constellation of canonical procedures, standards of evidence, and modes of manipulation considered legitimate — a supra-local, historically sedimented practical order that shapes but is not reducible to theoretical commitments. The relationship between the theoretical and praxical dimensions is one of use rather than derivation: practice draws on theoretical vocabulary without being determined by theoretical change. The paper reconstructs the praxical paradigm of early twentieth-century organic and physiological chemistry, shows how it excluded chromatography without theoretical grounds, and analyses its eventual transformation under practical rather than theoretical pressure. The early history of chromatography is thereby situated as an earlier and analytically clearer demonstration of the theory-practice disjunction than the mid-century instrumental revolution with which it is usually associated.
This paper traces the transformation of biology’s self-image through the concept of molecularism: the cultural myth that crystallised around the success of molecular biology in the twentieth century. Beginning with Theodosius Dobzhansky’s 1964 observation that “a good man cannot teach zoology” — a symptom of the internal devaluation of an entire epistemic tradition — the paper argues that molecular biology did not merely adopt chemical methods but internalised chemistry’s constitutive agenda: a purposive orientation in which understanding a material system is inseparable from the capacity to transform it. This chemical agenda, rooted historically in the Rockefeller Foundation’s deliberate investment in the molecular approach and philosophically in the productive, synthesis-oriented dimension of chemistry identified by Bensaude-Vincent and Simon, crystallised over the second half of the twentieth century into a cultural myth in Mary Midgley’s sense — a structuring imaginative framework operative in scientific self-understanding, popular culture, policy, and commercial practice. The paper examines how popular culture stabilises and amplifies molecularism, how it re-enters scientific practice through AI-driven biology, synthetic biology, and the eugenic applications of genomics, and how it has reshaped biology’s institutional architecture through the fusion of biology with medicine. The paper argues that biology has developed a cultural unconscious — assumptions about what it is and what it should be doing that operate below the level of explicit methodological reflection. Recognising molecularism as a historically contingent framework rather than scientific necessity is proposed as a precondition for both a revised biological self-image and an ethics of molecular biology adequate to its subject matter.
The Aufbau principle is used to predict electron configurations and to rationalise the block structure of the periodic table/spiral, yet it suffers from 2 main limitations, the inability to predict 20 “anomalous” configurations and reflect the true order of subshell energies, especially in the “d” and “f” block elements. This work introduces the Construcción principle, a unified framework that simultaneously accounts for both the ordering of differentiating electrons between successive elements and the energy of subshells, thereby predicting the observed electron configurations throughout the periodic table/spiral. This principle also incorporates relativistic stabilisation of s subshells in heavy elements. Moreover, 2 special filling rules are proposed to explain deviations from standard filling: (1) preferential occupation of larger and diffuse subshells by intraorbital repulsion at “d” and “f” block onsets, and (2) stabilisation of half-filled subshells through electron exchange. Prior to formulating these rules, the composition of Group 3 is critically examined using chemical and electronic evidence supporting the inclusion of lutetium and lawrencium in this group, thereby avoiding an artificial interruption of the “d” block against the filling rules. Accordingly, lanthanum and actinium should be regarded as the “anomalous” beginning of the “f” block, filling a d subshell instead of an f one in the formulation of Rule 1. Application of the Construcción principle, including its 2 special filling rules, reduces the number of “anomalous” configurations to only 2, palladium and thorium, yielding correct predictions of electron configurations and consequently, a clear periodic classification.
There is a controversy concerning the role of the Born-Oppenheimer approximation (BOA) in quantum chemistry molecular orbital calculations. Some philosophers argue that because the BOA clamps the position of the nuclei in space the BOA fixes the outcome of the calculation, thus calling into question the calculation’s legitimacy. As a contribution to the debate, we perform a thermochemical analysis to determine the absolute energies of the quantum Hamiltonian operator, Ĥψ, in kJmol–1, with respect to the constitutional isomers ethanol and dimethyl ether and their constituent particles. Our results show that the difference between the quantum Hamiltonian enthalpies, the ΔQHH, is tiny: − 407,023 kJmol–1 vs. − 407,116 kJmol–1, a 0.02
Proteins owe their diverse roles to their dynamic character. Two aspects of protein behavior that depend on dynamism are protein folding and conformational isomerization. While the former describes the process by which an unstructured polypeptide chain spontaneously folds into a protein with a specific three dimensional structure, the latter describes the reversible interconversion of distinct structural states of the protein. Apart from their scientific interest, protein folding and conformational isomerization raise important metaphysical questions concerning causation and identity. In this paper, I argue that protein folding is a dispositional teleological process in which the inherent potentiality of the unstructured polypeptide chain to fold into a specific three-dimensional form is manifested. Here, teleology is seen not as the end dictating the present, but the outworking of an entity’s potential. The conformational isomerization of a protein, and the existence of a protein not as a single structure but as an ensemble of conformational isomers, raises questions concerning identity – how should we conceive identity in the face of continuous change? To understand this, I propose a qualified meaning for ‘identity’ – dynamic identity, according to which change is recognized as an existential element of every actuality. All actualities are characterized by ceaseless activity, where this activity involves both an actuality’s internal, constitutive interactions as well as relationships with actualities in its environment. Combined, these internal and external relations act to maintain the actuality in a quasi-stable state while at the same time propelling the actuality into a future of transformation into other, successive quasi-stable states. An actuality’s activities not only sustain it in the present moment in a quasi-stable state, but also establish the conditions for progression into its future. This paper concludes by examining how the dynamic nature of proteins reveals fundamental metaphysical principles.
The inversion of left and right in the mirror image of a human body is accounted for by the different sensitivity of optics to shape and functionality, and, in the general case, by the elementary properties of vector spaces. The observation that some objects give a mirror image that is not superposable on the object itself is extended to the existence of pairs of real objects, each superposable on the mirror image of the other. The components of such pairs, called enantiomorphs, are distinguished as right- and left-handed. The property that allows this distinction is chirality, which is relevant in both contact and field interactions with chiral counterparts. Chirality may be present both locally and for the whole object, at both macroscopic and microscopic scales; in the latter case, chiral molecules, ions, radicals – distinguished through their representations – are called enantiomers. In both domains, the chirality of an object is related to its use, but it may be vital for pharmaceuticals and phytosanitary products at the molecular scale, because the enzymes, sensors, and receptors of living organisms are, as a rule, chiral, and therefore recognize – and subsequently process for often necessary functions – only one of the possible enantiomers. Chirality is an observable that cannot modify the chemical potentials, which are physical quantities determining the equilibrium constant of chemical reactions. Thus the reactivity of enantiomers can differ only in terms of kinetics.
The many biological processes that define cellular physiology depend on a vast network of biochemical reactions. Each of these reactions is initiated by the formation of a complex between the macromolecules and metabolites that are involved in the reaction. Biochemical studies suggest that these complexes exist and operate as function wholes, not as mere aggregative assemblies of their component molecules. The metaphysical question I ask in this paper is how such unity arises—what are the metaphysical foundations for such unity? To help in this analysis, I enlist the resources of three metaphysical systems: process-relational philosophy, Aristotelian-scholastic substance philosophy, and Ivor Leclerc’s philosophy of nature. While these systems all regard nature as inherently dynamic and relational, they account for the unity of complex entities in different ways. In the end, I advance a proposal for an ontology of biochemical complexes based on a synthesis of metaphysical positions inspired by the Aristotelian substance ontology of Thomas Aquinas and the process-relational ontologies of Nicholas Rescher, John Dupré, and Ivor Leclerc. Two features of this account emerge as critical: (1) The molecular entities comprising a biochemical complex are not actual, but possess virtual being; only the resultant complex is actual, and (2) The ontological unity of a biochemical complex arises from relation, which is defined as the dynamic interactions among the molecules that comprise the complex. Relation maintains the structural integrity of the resultant complex, sets it apart from its environment as an individual, and accounts for its becoming.
The AdNDP model of chemical bonding combines Lewis-type valence bonds with multi-center molecular orbital analysis. The question is addressed to what extent it offers an understanding of the delocalized bonding in the exploding area of pure boron sheets and clusters. It is argued that such understanding cannot be reached without invoking resonance. A vibronic definition of resonance is proposed, and its connection to the Rabi toy model is discussed.
This study constitutes a serious attempt to reshape the epistemological framework for understanding unexpected phenomena in organic chemistry, through a thorough critical analysis of fifteen historically documented cases spanning two centuries of chemical development. The study moves from the traditional model that treats “chance” as accidental luck, to the “material response” model that views these phenomena as manifestations of the intrinsic complexity of matter and its capacity to surprise prevailing theoretical models. This transformation necessitates rethinking fundamental concepts in chemical philosophy. The methodology relies on a precise analytical trilogy comprising critical historical reading of knowledge contexts, philosophical induction of epistemological patterns, and the study of socio-institutional dynamics governing the acceptance or rejection of anomalous phenomena. The integrated application of this methodology reveals new dimensions in understanding chemical discovery. The study concludes that unexpected phenomena represent fertile epistemological moments revealing the dialectical dialogue between abstract reason and material complexity, and proposes a radical shift in understanding the nature of chemical knowledge and its production methods, opening new horizons for future research in the philosophy of chemistry. The analysis distinguishes between serendipity, unexpectedness, and opportunistic observation, drawing on relevant literature to contextualize these concepts.
