Divagations about the periodic table: Boolean hypercube and quantum similarity connections

In this study, several simple aspects associated with the periodic table (PT) of the elements are commented. First, the connection of the PT with the structure of a seven-dimensional Boolean hypercube leads afterward to discuss the nature of those PT elements bearing prime atomic numbers. Second, the use of quantum similarity (QS) to obtain an alternative insight on the PT element relations will be also developed. The foundation of the second part starts admitting that any element of the PT can be attached to a schematic electronic density function, constructed with a single Gaussian function: a Gaussian atomic density function, allowing to consider the PT elements as a set of quantum objects, and permits a straightforward construction of a QS matrix. Such QS scheme can be applied to the whole PT or to any subset of it. Manipulation of the QS matrices attached to any quantum object set allows the evaluation of statistical-like values, acting as coordinates to numerically or graphically represent the chosen PT atomic element sets. © 2019 Wiley Periodicals, Inc.     

From the Mendeleev periodic table to particle physics and back to the periodic table

We briefly describe in this paper the passage from Mendeleev’s chemistry (1869) to atomic physics (in the 1900’s), nuclear physics (in 1932) and particle physics (from 1953 to 2006). We show how the consideration of symmetries, largely used in physics since the end of the 1920’s, gave rise to a new format of the periodic table in the 1970’s. More specifically, this paper is concerned with the application of the group SO(4,2)⊗SU(2) to the periodic table of chemical elements. It is shown how the Madelung rule of the atomic shell model can be used to set up a periodic table that can be further rationalized via the group SO(4,2)⊗SU(2) and some of its sub-groups. Qualitative results are obtained from this nonstandard table.     

Affinity of the elements in group VI of the periodic table to tumors and organs]

In order to investigate the tumor affinity radioisotopes, chromium (51Cr), molybdenum (99Mo), tungsten (181W), selenium (75Se) and tellurium (127mTe)--the elements of group VI in the periodic table--were examined, using the rats which were subcutaneously transplanted with Yoshida sarcoma. Seven preprarations, sodium chromate (Na251CrO4), chromium chloride (51CrCl3), normal ammonium molybdate ((NH4)299MoO7), sodium tungstate (Na2181WO4), sodium selenate (Na275SeO4), sodium selenite (Na275SeO3) and tellurous acid (H2127mTeO3) were injected intravenously to each group of tumor bearing rats. These rats were sacrificed at various periods after injection of each preparation: 3 hours, 24 hours and 48 hours in all preparations. The radioactivities of the tumor, blood, muscle, liver, kidney and spleen were measured by a well-type scintillation counter, and retention values (in every tissue including the tumor) were calculated in percent of administered dose per g-tissue weight. All of seven preparations did not have any affinity for malignant tumor. Na251CrO4 and H2127mTeO3 had some affinity for the kidneys, and Na275SeO3 had some affinity for the liver. Na2181WO4 and (NH4)299MoO4 disappeared very rapidly from the blood and soft tissue, and about seventy-five percent of radioactivity was excreted in urine within first 3 hours.     

On the planar periodic table

We reconsider, in this work, the construction of the two‐dimensional (2‐D) periodic table. The two‐dimensional logarithmic Coulomb system is used to generate atomic shells for the 2‐D atoms. A q‐deformed model is developed to explain the ordering of the shells predicted by the 2‐D Madelung rule. Our model, with the value q=1.26 for the deformation parameter, reproduce very well the above rule. We also compute the key function and the address function which, together with our model for the Madelung rule, permit us to give a new format of the 2‐D periodic table. It is shown that this table is different from the one existing in the literature, and we have a new family of elements, the g family. The question of the existence of 2‐D “ions” is briefly discussed. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 206–211, 2000     

Isodiagonality in the periodic table

Diagonal relationships in the periodic table were recognized by both Mendeléev and Newlands. More appropriately called isodiagonal relationships, the same three examples of lithium with magnesium, beryllium with aluminum, and boron with silicon, are commonly cited. Here, these three pairs of elements are discussed in detail, together with evidence of isodiagonal linkages elsewhere in the periodic table. General criteria for defining isodiagonality are proposed.     

Relation between the location of elements in the Thomsen-Bohr periodic table and the binding substance in soft tissues

Trivalent hard acids (Ga³⁺, In³⁺, Yb³⁺, Tm³⁺), which have complete d-shells, were bound to the acid mucopolysaccharide with a molecular mass of about 10,000 Daltons in soft tissue. Tri-, tetra-, and pentavalent hard acids and some borderline acids which have incomplete d-shells were bound to the acid mucopolysaccharides, whose molecular masses exceed 40,000 Daltons in soft tissues. Based on these results and the facts reported previously a very interesting relationship was recognized between the location of elements in the Thomsen-Bohr periodic table and the substances to which they bind.     

Relations between location of elements in periodic table and affinity for the kidneys (author's transl)

The distribution of many inorganic compounds in rats was investigated in order to evaluate kidney affinity of inorganic compounds. In these experiments, 30%, 10-20% and 4-10% of administered dose was localized in the kidneys in 203Hg-acetate and 203 Bi-acetate, in H198AuCl4, 103PdCl2, 201TlCl, 210Pd(NO3)2 and H2(127M)TeO3, and in Na2(51)CrO4, 54MnCl2, (114m)InCl3 and 7BeCl2, respectively. Some bipositive ions and anions was hardly taken up into the kidneys. And in many hard acids according to classification of Lewis acids, the uptake rate into the kidneys was usually small. On the other hand, Hg, Au and Bi, which have strong binding power to the protein, showed high uptake rate in the kidneys. As Hg++, Au+ and Bi+++ was soft acids according to classification of Lewis acids, it was thought that these elements would bind strongly to soft base (RSH, RS-) present in the kidney.     

Simple method for the precise calculation of atomic energy levels of IB elements in the periodic table

Due to the complicated and typical electronic structure of atoms and ions of the IB group in the periodic table, theoretical calculation of their atomic energy levels has important theoretical and practical significance. In this article, the theoretical calculation of atomic energy levels of the atoms of IB group in the periodic table was completed for the first time within the scheme of the weakest bound electron potential model theory. The results were compared with experimental values and the deviations are about 0.1–1 cm^?1. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Relation between location of elements in periodic table and affinity for the malignant tumor (author's transl)

Affinity of many inorganic compounds for the malignant tumor was examined, using the rats which were subcutaneously transplanted with Yoshida sarcoma. And the relations between the uptake rate into the malignant tumor and in vitro binding power to the protein were investigated in these compounds. In these experiments, the bipositive ions and anions had not affinity for the tumor tissue with a few exceptions. On the other hand, Hg, Au and Bi, which have strong binding power to the protein, showed high uptake rate into the malignant tumor. As Hg++, Au+ and Bi+++ are soft acids according to classification of Lewis acids, it was thought that these elements would bind strongly to soft base (R-SH, R-S-) present in the tumor tissue. In many hard acids (according to classification of Lewis acids), the uptake rate into the tumor was shown as a function of ionic potentials (valency/ionic radii) of the metal ions. It is presumed that the chemical bond of these hard acids in the tumor tissue is ionic bond to hard base (R-COO-, R-PO3(2-), R-SO3-, R-NH2).     

The continuation of the periodic table up to Z = 172. The chemistry of superheavy elements

The chemical elements up toZ = 172 are calculated with a relativistic Hartree-Fock-Slater program taking into account the effect of the extended nucleus. Predictions of the binding energies, the X-ray spectra and the number of electrons inside the nuclei are given for the inner electron shells. The predicted chemical behaviour will be discussed for all elements betweenZ = 104-120 and compared with previous known extrapolations. For the elementsZ = 121–172 predictions of their chemistry and a proposal for the continuation of the Periodic Table are given. The eighth chemical period ends withZ = 164 located below Mercury. The ninth period starts with an alkaline and alkaline earth metal and ends immediately similarly to the second and third period with a noble gas atZ = 172.

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Zusammenfassung Mit einem relativistischen Hartree-Fock-Slater Rechenprogramm werden die chemischen Elemente bis zur Ordnungszahl 172 berechnet, wobei der Einfluß des ausgedehnten Kernes berücksichtigt wurde. Für die innersten Elektronenschalen werden Voraussagen über deren Bindungsenergie, das Röntgenspektrum und die Zahl der Elektronen im Kern gemacht. Die voraussichtliche Chemie der Elemente zwischenZ = 104 und 120 wird diskutiert und mit bereits vorhandenen Extrapolationen verglichen. Für die ElementeZ =121–172 wird eine Voraussage über das chemische Verhalten gegeben, sowie ein Vorschlag für die Fortsetzung des Periodensystems gemacht. Die achte chemische Periode endet mit dem Element 164 im Periodensystem unter Quecksilber gelegen. Die neunte Periode beginnt mit einem Alkali- und Erdalkalimetall und endet sofort wieder wie in der zweiten und dritten Periode mit einem Edelgas beiZ = 172.

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Resumé Les éléments chimiques jusqu'áZ = 172 sont calculés à l'aide d'un programme Hartree-Fock-Slater relativiste en tenant compte de l'extension du noyau. On fournit des prédictions quant aux énergies de liaison, aux spectres X et au nombre d'électrons dans les noyaux pour les couches électroniques internes. Le comportement chimique prévu est discuté pour tous les éléments entreZ = 104–120 et comparé aux extrapolations connues auparavant. Pour les éléments Z =121–172 on effectue des prévisions de propriétés chimiques et l'on propose un prolongement du Tableau Périodique. La huitième période chimique se termine àZ = 164 sous le mercure. La neuviéme période débute avec un métal alcalin et alcalino-terreux et se termine comme la seconde et la troisième période avec un gaz rare àZ = 172.

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This work has been supported by the Bundesministerium für Wissenschaft und Bildung and by the Deutsche Forschungsgemeinschaft.     

The periodic table and the model of emerging truth

The periodic table may be seen as the most successful example of inquiry in the history of science, both in terms of practical application and theoretic understanding. As such, it serves as a model for truth as it emerges from inquiry. This paper offers a sketch of a central moment in the history of chemistry that illustrates an intuitive metamathematical construction, a model of emerging truth (MET). The MET, reflecting the structure the surrounds the periodic table, attempts to capture the salient epistemological elements that warrant truth claims based on sets of models that are progressive in light of both empirical and theoretical advance seen over time.     

Year of the periodic table: Mendeleev and the others

Structural Chemistry - On the occasion of the Year of the Periodic Table of the Elements, the authors look back at the original discovery, its simultaneity and the difficulties of the discoverers...     

Periodic table of elements and nanotechnology

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