The spiral form of the Periodic Law is proposed as its fundamental graphic representation. This idea is based on the fact that the spiral is the most appropriate form in description transitions from simple to complicated. The spiral is easily obtained from the linear succession of the elements when they are ranged by growing nuclear charge. The spiral can be simply transformed into many other graphic representations, including tables. This paper suggests the conception of the autonomy of blocks. This autonomy (...) is clearly seen in the variation of the outer electronic shells, in the width and the height of the blocks, as well as the number and properties of elements included therein. The regularities in the changes of element properties are pronounced in certain blocks but actually absent in others. The blocks can be permuted to obtain full-fledged versions of Periodic Table. The new stage of the verification of the blocks autonomy is the use of the total number of the differentiating electrons as an independent variable in describing the properties of the elements and their compounds. Consideration of individual blocks made it possible to deduce the periodic equations valid for all the elements within each block. Formulation of the Periodic Law is advanced: while describing characteristic determining the properties of the elements, the nuclear charge is replaced by the total number of differentiating electrons. Two modifications of the conventional Periodic Table are obtained by minimal changes. The first one shows the secondary and the additional periodicites. Another table shows the total number of differentiating electrons for each element. (shrink)

In the Periodic Tables the transition from atoms to double-charged cations is accompanied by alterations in the composition of s and p blocks and reciprocal location of blocks, as well as by changes in the composition and length of periods. We have previously described the relationship between the atom properties and the total number of differentiating electrons. This paper demonstrates that, despite the above transition-related alterations, this relationship is also valid for the description of the properties of double-charged cations. This (...) can be exemplified by the dependence of the ionization energy on the total number of p electrons in p block, d electrons in d block, and f electrons in f block. Furthermore, a single periodic equation is sufficient for the description of properties of all of double-charged cations from each block. (shrink)

This work utilizes examples from chemical sciences to present fundamentals of dialectics and synergetics. The laws of dialectics remain appropriate at the level of atoms, at the level of molecules, at the level of the reactions, and at the level of ideas. The law of the unity and conflict of opposites is seen, for instance, in the relationships between the ionization energy and electron affinity of atoms, between the forward and back reactions, as well as in the differentiation and integration (...) between the various areas of chemistry. The law of the passage of quantitative changes into qualitative changes describes the transformation properties of the compounds when the number and arrangement of atoms in the molecule undergoes changes. According to this law, the development is accompanied by breaks and jumps. This paper suggests equations for the description of these relationships. The law of the negation of the negation is manifested in the Periodic Law, in the evolution of ideas about the mutual transformation of chemical elements, in the development the concept of triads of elements, etc. Small changes in the conventional Periodic Table on the basis of previously rejected versions allow reflecting secondary and additional periodicity. Synergetics, similarly to dialectics, is dedicated to the studies of general laws of evolution. Synergetics includes highly advanced and specified ideas of dialectics. The cornerstone of synergetics is the principles of self-organization and nonlinearity. Mathematical development of these concepts was substantially facilitated by considering oscillating chemical reactions as an example. These reactions are quite complex and therefore provide adequate models for self-organization. Oscillations may exist only upon execution of specific thermodynamic, mathematical, and chemical conditions. Mechanisms of several oscillatory reactions are briefly reviewed. The construction of novel biomimetic or smart materials based on oscillating reactions is described. (shrink)

Demarcation of elements for two subsets appears to be the most fundamental approach to their classification. If one draws a vertical straight line through the middle of each block of elements in the Periodic table, all the elements are divided into two subsets: “early” and “later”. For example, in the d-block, the early ones are Sc–Mn, and the late ones, respectively, are Fe–Zn. Later elements partially repeat the properties of the early ones, and this is defined as the internal periodicity. (...) Another criterion for dividing the elements into two subsets is the evenness and oddness of the sum of n + l, where n is the principal quantum number, and l is the orbital quantum number for the outer electron subshells. Properties of the odd elements are closer to each other than to properties of even elements, and vice versa. This regularity is manifested as the secondary periodicity. The history of concepts, which considered the existence of subsets as well as of inner and secondary periodicities, is discussed. The features of the electronic structure, which underlie the existence of subsets, are considered. The existence of subsets was depicted earlier by dividing the periodic table into two tables or by applying a mirror-symmetric table. Small changes are proposed in the conventional Periodic table, allowing to reflect the existence of the considered subsets. (shrink)

Demarcation of elements for two subsets appears to be the most fundamental approach to their classification. If one draws a vertical straight line through the middle of each block of elements in the Periodic table, all the elements are divided into two subsets: “early” and “later”. For example, in the d-block, the early ones are Sc–Mn, and the late ones, respectively, are Fe–Zn. Later elements partially repeat the properties of the early ones, and this is defined as the internal periodicity. (...) Another criterion for dividing the elements into two subsets is the evenness and oddness of the sum of n + l, where n is the principal quantum number, and l is the orbital quantum number for the outer electron subshells. Properties of the odd elements are closer to each other than to properties of even elements, and vice versa. This regularity is manifested as the secondary periodicity. The history of concepts, which considered the existence of subsets as well as of inner and secondary periodicities, is discussed. The features of the electronic structure, which underlie the existence of subsets, are considered. The existence of subsets was depicted earlier by dividing the periodic table into two tables or by applying a mirror-symmetric table. Small changes are proposed in the conventional Periodic table, allowing to reflect the existence of the considered subsets. (shrink)

This manuscript aims to systematically consider the main periodicity and additional (secondary, internal, and tetrad) periodicities using a uniform approach. The main features are summarized in table form. The history of the origin and development of these concepts is discussed. It is described how these periodicities manifest themselves and how they are determined at the experimental and theoretical levels. Areas of manifestation of these periodicities are outlined. As the general approach to explaining internal periodicity, attention is drawn to the symmetry (...) of the quantum number S of atoms and the principle of equivalence of electrons and holes. Arguments are presented in favor of a more correct classification of the tetrad effect as tetrad periodicity, and an overview of this regularity is provided. A small modification of the conventional Periodic table is proposed, which reflects all the mentioned periodicities. (shrink)

This paper describes the construction of the Periodic Tables for cations of all elements with charges + 1, + 2, + 3 and anions with charge − 1. The Table for cations+1 differs significantly from other newly constructed Tables and from known Tables, as the d- and f-blocks are inserted into s-block and split it up for two parts. Importantly, a new type of 3d- and 4f-shell contractions has been discovered. The manifestations of secondary periodicity in case of anions is (...) absent or opposite to the manifestations observed for atoms and cations. For kainosymmetric anions, the ionization energies are lowered, which contradicts the theoretical assumptions and experimental data supporting the classical concept of kainosymmetry. Simple formulas are proposed for quantitative description of the manifestations of internal periodicity and kainosymmetry. The regularities of change in these manifestations depending on the charge and the position of ions or atoms in the Periodic Table are established. In the 6th period, the bifurcation in the properties characteristic of the internal periodicity does not occur at usual position, i.e. in the middle of the row from the block of the Periodic Table, but takes place earlier, along with the transition of the electronic configurations p2–p3. In other words, the place of transition from "early" to "late" elements changes. (shrink)