Chemical Bonds between Charged Atoms in the Even-Odd Rule and a Limitation to Eight Covalent Bonds per Atom in Centered-Cubic and Single Face-Centered-Cubic Crystals

Abstract

A crystal is a highly organized arrangement of atoms in a solid, wherein a unit cell is periodically repeated to form the crystal pattern. A unit cell is composed of atoms that are connected to some of their first neighbors by chemical bonds. A recent rule, entitled the even-odd rule, introduced a new way to calculate the number of covalent bonds around an atom. It states that around an uncharged atom, the number of bonds and the number of electrons have the same parity. In the case of a charged atom on the contrary, both numbers have different parity. The aim of the present paper is to challenge the even-odd rule on chemical bonds in well-known crystal structures. According to the rule, atoms are supposed to be bonded exclusively through single-covalent bonds. A distinctive criterion, only applicable to crystals, states that atoms cannot build more than 8 chemical bonds, as opposed to the classical model, where each atom in a crystal is connected to every first neighbor without limitation. Electrical charges can be assigned to specific atoms in order to compensate for extra or missing bonds. More specifically the article considers di-atomic body-centeredcubic, tetra-atomic and dodeca-atomic single-face-centered-cubic crystals. In body-centered crystals, atoms are interconnected by 8 covalent bonds. In face-centered crystal, the unit cell contains 4 or 12 atoms. For di-element crystals, the total number of bonds for both elements is found to be identical. The neutrality of the unit cell is obtained with an opposite charge on the nearest or second-nearest neighbor. To conclude, the even-odd rule is applicable to a wide number of compounds in known cubic structures and the number of chemical bonds per atom is not related to the valence of the elements in the periodic table.G. Auvert, M. Auvert 94

Covalent Bonds Creation between Gas and Liquid Phase Change: Compatibility with Covalent and Even-Odd Rules Based on a “Specific Periodic Table for Liquids”

“…This occurs whatever the electrical charge of the compound and whatever the current phase (solid, liquid or gaseous) [12]. Such electronic structures have been tested on well-known crystals [13] [14].…”

The Even-Odd and the Isoelectronicity Rules Applied to Single Covalent Bonds in Ionic, Double-Face-Centered Cubic and Diamond-Like Crystals

“…A procedure has been recently proposed to draw bonds and to position charges in ions and molecules [5]. This procedure has been tested on crystals [6]. This comparison was successful for a large number of crystals with 8 covalent bonds per atoms.…”

“…The validity of the even-odd rule was recently tested on single-face-centered crystals [6]. For the authors, the previous article reports a valid test to extend the even-odd rule from molecules to crystals with 4 atoms per unit cell.…”

“…In recent papers, the even-odd and the isoelectronicity rules were introduced as a systematic method to precisely predict positions of bonds and charges of atoms in chemical compounds. The rules were successively proven to be effective on ions and molecules [1]- [5], as well as on specific crystal structures [6]. The objective pursued here is to study the possibility to extend the field of application of these rules to other crystal structures.…”

Difference in Number of Electrons in Inner Shells of Charged or Uncharged Elements in Organic and Inorganic Chemistry: Compatibility with the Even-Odd Rule

“…Four important constrains should be remembered throughout the following: 1) Studied elements belong to the main group of the periodic table; 2) Chemical compounds are ions and molecules in gaseous or liquid phases; 3) Two neighbor elements in a compound are never connected through more than one single covalent bond [10]; 4) Elements cannot bear more than a single charge [17] [18].…”