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Physical Origin of Chemical Periodicities in the System of Elements

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Physical Origin of Chemical Periodicities in the System of Elements Pure Appl. Chem. 2019; 91(12): 1969–1999 Conference paper Chang-Su Cao, Han-Shi Hu, Jun Li* and W. H. Eugen Schwarz* Physical origin of chemical periodicities in the system of elements https://doi.org/10.1515/pac-2019-0901 Abstract: The Periodic Law, one of the great discoveries in human history, is magnificent in the art of chemistry. Different arrangements of chemical elements in differently shaped Periodic Tables serve for different purposes. “Can this Periodic Table be derived from quantum chemistry or physics?” can only be answered positively, if the internal structure of the Periodic Table is explicitly connected to facts and data from chemistry. Quantum chemi- cal rationalization of such a Periodic Tables is achieved by explaining the details of energies and radii of atomic core and valence orbitals in the leading electron configurations of chemically bonded atoms. The coarse horizon- tal pseudo-periodicity in seven rows of 2, 8, 8, 18, 18, 32, 32 members is triggered by the low energy of and large gap above the 1s and nsp valence shells (2 ≤ n ≤ 6 !). The pseudo-periodicity, in particular the wavy variation of the elemental properties in the four longer rows, is due to the different behaviors of the s and p vs. d and f pairs of atomic valence shells along the ordered array of elements. The so-called secondary or vertical periodicity is related to pseudo-periodic changes of the atomic core shells. The Periodic Law of the naturally given System of Elements describes the trends of the many chemical properties displayed inside the Chemical Periodic Tables. While the general physical laws of quantum mechanics form a simple network, their application to the unlimited field of chemical materials under ambient ‘human’ conditions results in a complex and somewhat accidental structure inside the Table that fits to some more or less symmetric outer shape. Periodic Tables designed after some creative concept for the overall appearance are of interest in non-chemical fields of wisdom and art. Article note: A collection of invited papers based on presentations at Mendeleev 150: 4th International Conference on the Periodic Table (Mendeleev 150), held at ITMO University in Saint Petersburg, Russian Federation, 26–28 July 2019. *Corresponding authors: Jun Li, Department of Chemistry, Theoretical Chemistry Center, Tsinghua University, Beijing 100084 China; and Department of Chemistry, Southern University of Science and Technology, Shenzhen 518055 China, e-mail: [email protected]; and W. H. Eugen Schwarz, Department of Chemistry, Theoretical Chemistry Center, Tsinghua University, Beijing 100084 China; and Physical Chemistry Lab, S&T Faculty, Siegen University, Siegen 57068 Germany, e-mail: [email protected] Chang-Su Cao and Han-Shi Hu: Department of Chemistry, Theoretical Chemistry Center, Tsinghua University, Beijing 100084 China Open Access. © 2019 Chang-Su Cao et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 Public License. 1970 C.-S. Cao et al.: Physical origin of chemical periodicities in the system of elements Keywords: atomic orbitals; chemical concepts; chemical elements; chemistry under ambient conditions; Mendeleev 150; periodic table for chemical science; periodic table, inner structure; quantum chemistry. Introduction To begin with, we analyze important chemical observations and draw conceptual conclusions on the ‘Natural System’ of ‘Chemical Elements’. Then, we work out what may be meant by ‘Periodicity of Elements’ and by the question “Can the ‘Periodic System’ of Chemical Elements be derived from basic physics”. The actual variations of various general properties of elements in chemical compounds under ambient conditions of temperature and pressure along an appropriately ordered array of elements are displayed in ‘Chemical Peri- odic Tables’. These property variations determine the inner structure of a Chemical Periodic Table, and that has to be derived quantum chemically. We present several examples of how variations of empirically derived properties can be derived quantum theoretically. On this basis we summarize on the Physical Origin of the Periodicities in the Natural System of Chemical Elements and comment in this context on several conceptual issues, brought up in the communities of chemists, educators, philosophers and artists. The latter ones create new outer shapes of Periodic Tables with apparent symmetries that are independent of its inner structure that is coupled to the chemical facts. Historical and conceptual background of the natural system of chemical elements Chemical elements and their similarities With the 118 now known elements, the concept of element has evolved through a long history. During the early period of enlightenment in ancient Greece, various rational, though speculative philosophic concepts of ele- ments were proposed by Demokritos and Lucretius, different ones by Plato, Aristoteles and others [1, 2]. After the beginning of the second period of rational enlightenment, i.e. in early modern Europe, and after the combination with the experimental scientific method, English Robert Boyle [3] formulated an empirically based concept of chemical elements around 1660, where he defined the elements as the conserved entities in chemical transfor- mations, in the laboratory. As scientists, we assume the same nature working inside and outside the laboratory. More than a century later in the 1780s, just before the chaotic political revolution, and by a peaceful evo- lutionary scientific jump, French Antoine Lavoisier with his wife Marie-Anne Paulze and a group of Parisian Fig. 1: System of Elements of Gmelin [6], redrawn by Leach [16]. In addition, we have marked the groups on the left and right sides, which are now called halogens, chalcogens, pnicogens and alkali and alkaline earth metals, forming the empirically given ‘backbone’ of the later Periodic System. The empirically unique H and 2nd row elements (Be–O, baptized типичecкий by Mendeleev) [17–19], are here highlighted by bold boxes. Neither Leopold Gmelin nor Lothar Meyer [20] had found a systematic arrangement for the plenty of chemically more similar transition metals, here at the middle bottom; only Mendeleev achieved it in 1869 [17, 18, 21]. The invention of Periodic Tables focused the view of subsequent generations more on kinships within the groups, and also between adjacent groups, but less so on other relations among similar elements. C.-S. Cao et al.: Physical origin of chemical periodicities in the system of elements 1971 scientists implemented Boyle’s concept into practical reality [4]. The group identified more than 30 elements [5]. In subsequent decades, further elements were discovered. In the early 1840s, German Leopold Gmelin [6] arranged more than 50 elements in a two-dimensional table with groups of chemically similar elements by exploiting common qualitative viewpoints of the practicing chemists (Fig. 1). Basic parts of the structure of the Natural System of Chemical Elements were already found thereby, with the groups of the electropo- sitive metals on one side and of the electronegative non-metallic halogens, chalcogens and pnicogens (in present day parlance) on the other side. While these similarity clusters of elements were based on ‘chemical feeling’, it was only recently (in the 2000s) that several groups of mathematical chemists [7–15] verified and refined those chemical similarity concepts. By applying chemo-metric approaches to big empirical data sets of molecules, the felt similarities between elements could be partially or fully quantified. The meaning of ‘chemical element’ The word element or its synonyms were used in various cultures since antiquity for two different con- cepts. The first meaning was some real, simply composed matter, such as liquid water or yellow sulfur. The second meaning was a principle or an abstract substance that is the dominating component in the real matter, and is conserved in some sense in chemical transformations of real compounds. Mendeleev was one of the first scholars in modern times to stress this difference and systematically distinguished the two meanings [21, 28]. Accordingly, the IUPAC [29] defines an element (i) as the concept of an abstract species in a compound with “all atoms with the same number of protons in the atomic nucleus”, and (ii) also as a real, elementary or simple substance, i.e. as a “pure chemical substance composed of atoms with the same number of protons”. Referring to the definition of the abstract elements, it is sometimes argued that an element has no properties except the given number of nuclear protons. We here hold that the physical nuclear charge number Z specifies (defines) an element, which carries many further ‘secondary’ chemical properties. Some properties have well-defined integer values. Examples are Z itself, but interpreted by the chemists as the number of electrons per neutral atom; the number of core electrons Ncore, determining the number of valence active electrons Nval = Z – Ncore, which are energetically well above the closed, chemically inert core shells; Nval determines the group number g in a Chemical Periodic Table. Some properties of the elements lie within narrow real intervals, such as the averaged atomic masses of the isotopic mixtures common on earth, which are given to us through astrophysical history [30]. There are also properties defined in a more fuzzy manner, namely the averaged properties of atoms in different compounds, such as the electron-attracting
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