Improvement of the Lewis-Abegg-Octet Rule Using an “Even-Odd” Rule in Chemical Structural Formulas: Application to Hypo and Hyper-Valences of Stable Uncharged Gaseous Single-Bonded Molecules with Main Group Elements

As Lewis proposed his octet rule, itself inspired by Abegg’s rule, that a molecule is stable when all its composing atoms have eight electrons in their valence shell, it perfectly applied to the vast majority of known stable molecules. Only a few stable molecules were known that didn’t fall under this rule, such as PCl5 and SF6, and Lewis chose to leave them aside at the time of his research. With further advances in chemistry, more exceptions to this rule of eight have been found, usually with the central atom of the structure having more or less than eight electrons in its valence shell. Theories have been developed in order to modify the octet rule to suit these molecules, defining these as hyper- or hypo-valent molecules and using other configurations for the electrons. The present paper aims to propose a representation rule for gaseous single-bonded molecules that makes it possible to reconcile both;molecules following the octet theory and those which do not. In this representation rule, each element of the molecule is subscripted with two numbers that follow a set of simple criteria. The first represents the number of valence electrons of the element;while the second is calculated by adding the first number to the number of the element’s covalent bonds within the molecule. The latter is equal to eight for organic molecules following the octet rule. Molecules being exceptions to the octet rule are now encompassed by this new even-odd rule: they have a valid chemical structural formula in which the second number is even but not always equal to eight. Both rules—octet and even-odd—are discussed and compared, using several well-known gaseous molecules having one or several single-bonded elements. A future paper will discuss the application of the even-odd rule to charged molecules.

Chemical Structural Formulas of Single-Bonded Ions Using the “Even-Odd” Rule Encompassing Lewis’s Octet Rule: Application to Position of Single-Charge and Electron-Pairs in Hypo- and Hyper-Valent Ions with Main Group Elements

Lewis developed a 2D-representation of molecules, charged or uncharged, known as structural formula, and stated the criteria to draw it. At the time, the vast majority of known molecules followed the octet-rule, one of Lewis’s criteria. The same method was however rapidly applied to represent compounds that do not follow the octet-rule, i.e. compounds for which some of the composing atoms have greater or less than eight electrons in their valence shell. In a previous paper, an even-odd rule was proposed and shown to apply to both types of uncharged molecules. In the present paper, the even-odd rule is extended with the objective to encompass all single-bonded ions in one group: Lewis’s ions, hypo- and hypervalent ions. The base of the even-odd representation is compatible with Lewis’s diagram. Additionally, each atom is subscripted with an even number calculated by adding the valence number, the number of covalent bonds of the element, and its electrical charge. This paper describes how to calculate the latter number and in doing so, how charge and electron-pairs can actually be precisely localized. Using ions known to be compatible with Lewis’s rule of eight, the even-odd rule is compared with the former. The even-odd rule is then applied to ions known as hypo- or hypervalent. An interesting side effect of the presented rule is that charge and electron-pairs are unambiguously assigned to one of the atoms composing the single-charged ion. Ions that follow the octet rule and ions that do not, are thus reconciled in one group called “electron-paired ions” due to the absence of unpaired electrons. A future paper will focus on the connection between the even-odd rule and molecules or ions having multiple bonds.

The Even-Odd Rule on Single Covalent-Bonded Structural Formulas as a Modification of Classical Structural Formulas of Multiple-Bonded Ions and Molecules

In organic chemistry, as defined by Abegg, Kossel, Lewis and Langmuir, compounds are normally represented using structural formulas called Lewis structures. In these structures, the octet rule is used to define the number of covalent bonds that each atom forms with its neighbors and multiple bonds are frequent. Lewis’ octet rule has unfortunately shown limitations very early when applied to non-organic compounds: most of them remain incompatible with the “rule of eight” and location of charges is uncertain. In an attempt to unify structural formulas of octet and non-octet molecules or single-charge ions, an even-odd rule was recently proposed, together with a procedure to locate charge precisely. This even-odd rule has introduced a charge-dependent effective-valence number calculated for each atom. With this number and the number of covalent bonds of each element, two even numbers are calculated. These numbers are both used to understand and draw structuralformulas of single-covalent-bonded compounds. In the present paper, a procedure is proposed to adjust structural formulas of compounds that are commonly represented with multiple bonds. In order to keep them compatible with the even-odd rule, they will be represented using only single covalent bonds. The procedure will then describe the consequences of bond simplification on charges locations. The newly obtained representations are compared to their conventional structural formulas, i.e. single-bond representation vs. multiple-bond structures. Throughout the comparison process, charges are precisely located and assigned to specific atoms. After discussion of particular cases of compounds, the paper finally concludes that a rule limiting representations of multiplecovalent bonds to single covalent bonds, seems to be suitable for numerous known compounds.

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

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-centered-cubic, 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.

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

The recently introduced even-odd rule has been shown to successfully represent chemical structures of ions and molecules. While comparing available drawings in the scientific literature with the list of compounds predicted by the even-odd rule, it became however obvious that existing compounds are fewer than expected. Several predicted compounds involving many covalent bonds have apparently never been experimentally observed. Neutral oxygen for instance is expected to have 6 valence electrons, whereas oxygen can only build a maximum of two bonds, as in water. This specificity is observed for elements in the top-right corner of the periodic table. For compounds to contain only single covalent bonds, and thus follow the even-odd rule, further explanations are necessary. The present paper proposes that those specific elements experience a transfer of electrons from the valence shell into the inner shell, making them unavailable for further bonding. These elements will be described as organic, hereby providing a clear and hopefully unifying definition of the term. In opposition, inorganic elements have a constant inner shell no matter their electrical state or the number of bonds they maintain. More than 70 compounds involving 11 elements of the main group are studied, revealing a progression from fully inorganic elements at the left of the periodic table to fully organic elements. The transition between inorganic or organic elements is made of few elements that take an organic form when negatively charged;they are labelled semi-organic. The article concludes that the fully organic elements of the main group are Oxygen and Fluorine, whereas semi-organic elements are more numerous: C, N, S, Cl, Se, Br and I. Thus, the even-odd rule becomes fully compatible with scientific knowledge of compounds in liquid or gaseous phase.

How the Even-Odd Rule, by Defining Electrons Pairs and Charge Positions, Can Be Used as a Substitute to the Langmuir-Octet Rule in Understanding Interconnections between Atoms in Ions and Molecules

In the course of time, numerous rules were proposed to predict how atoms connect through covalent bonds. Based on the classification of elements in the periodic table, the rule of eight was first proposed to draw formulas of organic compounds. The later named octet rule exhibited shortcomings when applied to inorganic compounds. Another rule, the rule of two, using covalent bonds between atoms, was proposed as an attempt to unify description of organic and inorganic molecules. This rule unfortunately never managed to expand the field of application of the octet rule to inorganic compounds. In order to conciliate organic and inorganic compounds, the recently put forward even-odd and the isoelectronicity rules suggest the creation of one group of compounds with pairs of electrons. These rules compass the rule of two for covalent bonds as well as the octet rule for organic compounds and suggest transforming bonds of multi-bonded compounds in order to unify representations of both groups of compounds. The aim of the present paper is fourfold: to extend the rule of two to every atom shells;to replace the well-known octet rule by the even-odd rule;to apply the isoelectronicity rule to each atom and to reduce the influence range of the charge of an atom in a compound. According to both rules, the drawing of one atom with its single-covalent bonds is described with electron pairs and charge positions. To illustrate the rules, they are applied to 3D configurations of clusters.

Coherence of the Even-Odd Rule with an Effective-Valence Isoelectronicity Rule for Chemical Structural Formulas: Application to Known and Unknown Single-Covalent-Bonded Compounds

Ions or molecules are said to be isoelectronic if they are composed of different elements but have the same number of electrons, the same number of covalent bonds and the same structure. This criterion is unfortunately not sufficient to ensure that a chemical structure is a valid chemical compound. In a previous article, a procedure has been described to draw 2D valid structural formulas: the even-odd rule. This rule has been applied first to single-bonded molecules then to single-charged single-bonded ions. It covers hypovalent, hypervalent or classic Lewis’ octet compounds. The funding principle of the even-odd rule is that each atom of the compound possesses an outer-shell filled only with pairs of electrons. The application of this rule guarantees validity of any single-covalent-bond chemical structure. In the present paper, this even-odd rule and its electron-pair criterion are checked for coherence with an effective-valence isoelectronic rule using numerous known compounds having single-covalent-bond connections. The test addresses Lewis’ octet ions or molecules as well as hypovalent and hypervalent compounds. The article concludes that the even-odd rule and the effective-valence isoelectronicity rule are coherent for known single-covalent-bond chemical compounds.

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

A decrease in temperature will eventually turn a gas into liquid and then into a solid. Each of these phase change shows a higher degree in cohesion of molecules. While it is usually admitted that molecules in solids form additional connections, the cohesion of molecules in liquids is usually explained by changes in kinetics of molecules. Given that the density of a solid is nearly the same than that of a liquid, the present paper assumes a different stand and considers that connections between molecules must be similar in liquids and in solids. The difference between gas, in which molecules are entirely loose, and liquid, is therefore the presence of an additional connection between gaseous molecules. This paper describes how and where these connections are built with the help of a few rules and a “specific periodic table for liquids”. The coherence of this approach is reinforced by its capacity to explain phase change of forty well-known molecules containing inorganic and organic elements.

A Specific Periodic Table for Chemistry of Organic, Semi-Organic and Inorganic Elements: Compatibility with the Even-Odd Rule,the Number of Electrons and the Isoelectronicity Rule

Following the introduction of the new even-odd and isoelectronic rules and definitions affecting the understanding of electronic structure and bonds, the author has thought necessary to summarize understandings in the form of a table. The classical periodic table, a simple tool used by generations of physicists, is here extended to become a useful tool aimed specifically at chemists. In chemistry, position and number of covalent bonds of each atom are needed, as well as the exact location of charges. The table gives the number of possible bonds for each element and reveals how it is affected by charges. Additionally, the specific table indicates for each atom its isoelectronic elements and highlights the distinction between organic and inorganic elements. Discussion is led on the first two rows of the table by successfully comparing its statement with more than 50 well-known liquid and gaseous compounds.

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

Although atom configuration in crystals is precisely known thanks to imaging techniques, there is no experimental way to know the exact location of bonds or charges. Many different representations have been proposed, yet no theory to unify conceptions. The present paper describes methods to derive bonds and charge location in double-face-centered cubic crystals with 4 and 6 atoms per unit cell using two novel rules introduced in earlier works: the even-odd and the isoelectronicity rules. Both of these rules were previously applied to ions, molecules and some solids, and the even-odd rule was also tested on two covalent crystal structures: centered-cubic and single-face-centered cubic crystals. In the present study, the diamond-like structure was subjected to the isoelectronicity rule in order to derive Zinc-blende structures. Rock-salt-like crystals were derived from each other using both rules. These structures represent together more than 230 different crystals. Findings for these structures are threefold: both rules describe a very sure method to obtain valid single covalent-bonded structures;single covalent structures can be used in every case instead of the classical ionic model;covalent bonds and charges positions do not have any relation with the valence number given in the periodic table.

Introducing an Extended Covalent Bond between Oxygen Atoms with an OXO-Shape in Ions and Molecules: Compatibility with the Even-Odd and the Isoelectronicity Rules

Building on the recent success of the even-odd rule, the present paper explores its implications by studying the very specific case of OXO compounds. These compounds are usually represented with double bonds linking two oxygen atoms to a central atom—as in carbon dioxyde—yet can sometimes be drawn in a triangular structure, such as in calcium dioxyde. Measurement data moreover indicate that most OXO compounds have an angle around 120° between oxygen atoms, although that seems incompatible with triangular representations. The aim here is to unify these commonly admitted representations by linking oxygen atoms through a single bond that is longer than usual covalent bonds: an “elongated bond”. This elongated bond has the interesting effect of suppressing the need for double bonds between oxygen and the central atom. The elongated bond concept is applied to about a hundred of molecules and ions and methodically compared to classical representations. It is shown that this new representation, associated to the even-odd rule, is compatible with all studied compounds and can be used in place of their classical drawings. Its usage greatly simplifies complex concepts like resonance and separated charges in gases. Elongated bonds are also shown to be practicable with the isoelectronic rule as well as isomers, and throughout chemical reactions. This study of an especially long and wide angle bond confirms the versatility of the even-odd rule: it is not limited to compounds with short covalent bonds and can include OO covalent bond lengths of more than 200 pm and with OXO angles above 90°.

Basic Steps in Chemical Dissociation of Gaseous Molecules Using an Even-Odd Rule, a Specifically Adapted Periodic Table and a Covalent Bonding Rule

When writing equations of chemical dissociation, students and scholars are taught two fundamental rules to balance the equation. On both sides of the equation, the types of elements and their quantity are conserved, as well as the global electrical charge. This paper introduces additional methods during dissociation of gaseous compounds, to precisely describe how electrical charges locally move and how bonding structures are modified. Specific rules revolving around electrons pairs displacements are developed and applied to about 150 dissociations of small gaseous molecules using atoms from the three first rows of the periodic table. Results obtained tend to demonstrate the relevance of these tools for chemists.

First Step in Dissociation Process in the Gas Phase for Small Molecules with Neutral Atoms: Application with the Even-Odd Rule and a Specific Periodic Table for Organic and Inorganic Atoms

Dissociations in the gas phase of small molecules have been intensively studied and dissociation energies of various gases are available in reference works. Configurations of compounds before and after the dissociation are usually known, but local charges are not defined. Building on the even-odd rule, the topic of a series of previous articles by the same author, the objective of this paper is to show how it can be used to give electronic rules for dissociations in gases. To this end, a specific periodic table is created and used. The rules are applied to a selection of more than 30 common molecules, showing that the even-odd rule and its consequences are useful in explaining the phenomenon of dissociation in gases.

Observation of an Even-Odd Asymmetric Transport in High Landau Levels

Magnetotransport experiments including tilt fields are performed on ultrahigh mobility L-shaped Hall-bar samples of GaAs/AlGaAs quantum wells. The low-temperature longitudinal resistivity （ρxx） data demonstrate that a striking even-odd asymmetric transport exists along the [110] direction at half filling in N ≥ 2 high Landau levels. Although the origin for the peculiar even-odd asymmetry remains unclear, we propose that the coupling strength between electrons within the same Landau level and between the neighboring two Landau levels should be considered in future studies. The tilt field data show that the in-plane field can suppress the formation of both bubble and stripe phases.

Stability in Liquid Phases of Molecular Compounds Composed of Saturated Atoms: Application with the Even-Odd Rule and a Specific Periodic Table for Liquids

Building on the idea that molecules in liquid phase associate into multi-molecular complexes through covalent bonds, the present article focuses on the possible structures of these complexes. Saturation at atomic level is a key concept to understand where connections occur and how far molecules aggregate. A periodic table for liquids with saturation levels is proposed, in agreement with the even-odd rule, for both organic and inorganic elements. With the aim at reaching the most stable complexes, meaning no other chemical reactions can occur in the liquid phase, the structure of complexes resulting from liquefaction of about 30 molecules is devised. The article concludes that complexes in liquids generally assume rounded shapes of an intermediate size between gas and solid structures. It shows that saturation and covalent bonds alone can explain the specific properties of liquids. While it is generally acknowledged that molecular energy in gases and solids are respectively linear kinetic and vibratory, we suggest that rotatory energy dominates in liquids.

Some Strong Limit Theorems for Even-odd Markov Chain Fields Indexed by Trees

首先，强壮的限制定理的一个班被构造二 nonnegative 鞅证明。然后，他们被用于各种甚至奇怪的 Markov 链地和在纸定义的 Markov 链地的学习。最后，为甚至奇怪的 Markov 链领域和 Markov 的一些强壮的限制定理锁住领域被获得。

奇偶相干态信号场下的量子关联和纠缠

为了实现两原子之间的非经典关联,借助于电磁诱导光透明(electromagnetically induced optical transparency,EIT)机制,利用量子态的映射技术,研究原子系综内两原子的量子关联和纠缠。结果表明:分别通过测量扰动刻画的量子关联和并发度刻画的量子纠缠,发现它们都能够被绝热地生成,但是,随着平均光子数的增加,二者的演变完全不同。随着平均光子数的增加,无论信号场是奇数相干态还是偶数相干态,它们都有利于量子关联的生成。对于奇相干态信号场,量子纠缠随着光子数的增加而逐渐减小;对于偶相干态信号场,量子纠缠却经历了一个先增加后减小的过程。系综内原子个数的增加,使得原子间的退相干加剧,从而导致量子关联和纠缠都被削弱。

Pell方程组x^(2)-40y^(2)=1与y^(2)-Dz^(2)=9的公解

设D=2p_(1)⋯p_(s)(1≤s≤4),其中p_(1),⋯,p_(s)是互不相同的奇素数。主要利用奇偶分析、同余、递归序列以及Pell方程解的性质等初等方法,对Pell方程组x^(2)-40y^(2)=1与y^(2)-Dz^(2)=9的公解进行研究。得出当D≠2×7×103时,该方程组仅有平凡解(x,y,z)=(±19,±3,0);当D=2×7×103时,除了平凡解(x,y,z)=(±19,±3,0)外,还有非平凡解(x,y,z)=(±27379,±4329,±114)。研究结果丰富了这类Pell方程组整数解的研究内容。

基于优化奇偶重构法的光伏阵列自适应重构技术设计

对于光伏阵列而言,阴影遮挡和阵列损坏会导致其输出功率降低。为了提升光伏阵列的输出功率,提出了一种优化的奇偶重构方法(Optimized Odd Even Configuration,OOEC),纠正了奇偶重构法(Odd Even Configuration,OEC)在局部阴影超过4列时,重构效果差的缺点。所提出的方法将光伏阵列分为自由重构模块和固定重构模块,根据不同的阴影情况调整连接方式,确定最佳的连接关系,并与Arrow So Du ku,Zig-zag,OEC三种方法进行仿真实验对比,仿真结果表明,经过OOEC重构后的光伏阵列输出功率明显提高,光伏阵列的PU输出特性曲线更加趋向于单峰,并且从失配损耗,功率提升百分比,性能比,均衡指数上看来,OOEC有着更好的性能。

基于改进型双模分数阶重复控制器的高速磁悬浮电机谐波电流抑制

主动磁悬浮轴承系统的转子不平衡和传感器跳动会使系统产生谐波电流,从而导致谐波振动。重复控制器能同时抑制同频和倍频谐波,但传统重复控制器必须确保控制系统的采样频率与实际转频之比为整数,极大地限制了其适用性。为解决此问题,设计了一种改进型双模分数阶重复控制器。采用拉格朗日插值法将分数阶变为整数,解决了重复控制的非整数延迟问题;通过双支路独立地消除奇偶次谐波,第1次、2次、3次、4次和5次谐波分别降低了87.9%、61.3%、86.9%、36.9%和85.3%。仿真和试验结果验证了改进型重复控制器对谐波电流抑制的精确性和有效性。