The first rule to describe the organization of electrons in atoms belonging to a compound was the octet rule in the 1920s [1] [2] [3] . This rule imposes that chemically bonded elements should at all time be surrounded by eight electrons. It perfectly suited molecules like methane, ammonia, water and hydrogen fluoride. To render this rule compatible with other compounds like dioxygen, dinitrogen or benzene, multi-bonded connections were imagined [4] [5] . In the 2000s however, R. J. Gillespie already noticed that this rule remains mainly applicable to the few elements composing these specific molecules [6] [7] .

In an attempt to have a unified rule applicable to a wider number of mole- cules, a new rule named the even-odd rule was recently proposed [8] . Following articles have investigated additional ions and molecules and confirmed the applicability of the even-odd rule to a great number of compounds [9] [10] [11] . A side effect was that this rule predicted the existence of molecules that were neither referenced by Greenwood [12] nor by other scientific data references [13] [14] [15] . A pattern was identified showing that these inexistent compounds would more often occur at the top right of the periodic table [15] [16] .

Starting with this observation, the present paper proposes an explicit definition of what makes an element organic or inorganic. Building on the electrons configuration around the nucleus specific to the even-odd rule, it associates an organic state to a surplus of electrons pairs in the inner shell. It also introduces the concept of semi-organic elements.

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] .

On notation and terminology, the reader should also take good notice that ions or molecules bearing an overall charge will be written after these examples: H2O for neutral water, H3O(+) for positive water ions and OH(−) for negative water ions [8] [9] [10] [11] .

The software used to draw ions and molecules is Chemsketch [19] .

There are two different ways to represent the arrangement of electrons around the nucleus of an atom. The first one, as seen in the periodic table, considers the atom as a stand-alone atom isolated from any other atoms. It identifies the total number of electrons and the number of electrons available for bonding. By contrast, the alternative method presented in this article is to consider elements as part of a compound, i.e. connected to other atoms. Here, the electronic structure is composed of three electrons shells including electrons involved in chemical bonds.

Both electronic representations are described below in greater details.

The periodic table follows specific codes, still used by modern chemists. Each element of the periodic table is represented by one or two letters, the acronym of the element name. Two numbers complete the name of each element. The greatest number is the total number of electrons of the element. The smallest number is the valence number, indicating the number of electrons that may be involved in chemical bonds. With this description, only two electrons shells are defined: the inner shell and the valence shell. The number of electrons in the inner shell is equal to the difference between the total number of electrons and the valence number of the element. The inner shell is filled with an even number of electrons.

In most rows of the main group in the periodic table, the inner shell is constant all along the row. In this main group, elements are ordered in 8 columns and valence numbers range from 1 to 8. The column number of the element is equal to the number of electrons in the valence shell: Boron, element of column 3, has for instance three electrons in the valence shell.

While the periodic table considers atoms in a mostly virtual state, unconnected to any other atom, the approach of the even-odd rule is to consider the element in situ, connected to other elements in the context of a chemical compound. The representation of an electronic structure must then take chemical bonds into account [11] .

In the even-odd model, the electronic structure is composed of three shells: an inner shell, an inactive shell and a covalent shell:

The covalent shell is composed of electrons involved in covalent bonds. In dihydrogen, for instance, one covalent bond interconnects two hydrogen atoms and each has one electron in its own covalent shell [11] .

The inactive shell, located inside the covalent shell, contains electrons pairs that are not currently involved in any covalent bonds but are available if needed.

The inner shell contains the remaining electrons that cannot participate in any bonds. Composed of an even number of electrons, it is mostly equal to the inner shell calculated from the periodic table. The exceptions are the subject of the present article and are detailed in Chapter 4.

To keep track of the electronic structure of an element in a compound, a specific notation is used in the following and illustrated below. From left to right: the number of electrons in the inner shell, the number of electrons in the inactive shell and the number of electrons in the covalent shell.

Boron

Element in boron monofluoride

BF in the gas phase [15]

This example illustrates the electronic structure of Boron in a BF compound. The first two numbers are even, i.e. these shells contain electrons pairs. The third number gives the number of electrons located in the covalent shell. In BF, one electron belongs to the boron covalent shell and one electron belongs to the fluorine covalent shell. Together, they form one covalent bond between B and F.

The three numbers of the series inevitably add up to the total number of electrons of the element (here equal to 5 for boron in BF molecules).

In this chapter, the main characteristics of the even-odd rule are summarized and illustrated with a charged boron atom.

In the following, we will use the term “state” to designate the electrical state of an element. Since the even-odd rule limits elements to bearing a single charge or none [10] , elements can only have three states: positive, neutral or negative. The state directly relates to the number of electrons of the element.

Derived from the known valence number from the periodic table, the Effective Valence Number (Ef.V.N.) depends on the state, i.e. the presence or the absence of one electron, as follows:

- In a neutral state, an element has an Ef.V.N. equal to the valence number: no electrons are added or removed.

- In a positive state, an electron is missing and the Ef.V.N. is the valence number decreased by one.

- In a negative state, an electron is added and the Ef.V.N. is the valence number increased by one.

It is important here to recall that the even-odd rule also imposes that two neighbor atoms in a compound can only be interconnected by a single covalent bond [10] .

The even-odd rule is characterized by a representation of elements sur- rounded with several features: 1) three numbers, 2) a state (positive, neutral or negative), and 3) the number of covalent bonds illustrated by line segments.

For example, one would represent a boron atom with two bonds in a positive state as shown below:

The upper left number is as defined by the valence number of the element. The upper right symbol indicates the state (positive (+), neutral or negative (−)). The lower left number is the effective valence number (Ef.V.N.) calculated ear- lier.

The number of possible bonds is derived from the parity of the valence number and the state:

For an atom with an even number of electrons, the number of bonds is:

-In neutral state, even ranging from 0 up to the calculated Ef.V.N.

-In a charged state, odd ranging from 1 up to the Ef.V.N.

For an atom with an odd number of electrons, the number of bonds is:

-In neutral state, odd ranging from 1 up to the Ef.V.N.

-In a charged state, even ranging from 0 up to the Ef.V.N.

In other words, an element always erects number of bonds that has the same parity than its Ef.V.N.

The lower right number is the even number of electrons in the inactive shell; these are electrons that stand ready to be involved in covalent bonds. It is even and calculated by subtracting the number of bonds from the Ef.V.N. (lower left) of the element.

Another example: hydrogen has, in the periodic table, a valence number of 1. For ion H(−), in a negative state, the Ef.V.N. is 2. It can therefore erect 0 or 2 bonds.

The present article proposes that elements of the main group can be classified into 3 sub-groups. The first sub-group is composed of 20 elements, for which the number of electrons in the inner shell is calculated as usual from the periodic table. Elements in this sub-group are defined as inorganic. The second sub-group is composed of elements with an inner shell containing more electrons than expected from the periodic table. Elements in this sub-group are designated as organic. The third sub-group is composed of elements whose organic or inorganic condition is state dependent.

The sub-groups composition is:

- Organic: Oxygen and Fluorine are the only elements fully organic

- Semi-organic: 7 elements compose this sub-group―C, N, S, Cl, Se, Br and I.

- Inorganic: the 20 elements composing this sub-group are neither organic nor semi-organic. In this paper, Hydrogen and Antimony will illustrate this sub- group.

Note that since noble gases do not bound with other elements, they do not belong to any of these sub-groups.

The eleven elements named above will be studied in the present paper, illustrating all 3 sub-groups. Their electronic structures are carefully described in Chapter 5.

As opposed to earlier definitions of on the even-odd rule, in which the valence number is directly issued from the periodic table, the present paper states that the valence number now depends on the sub-group the element belongs to:

- In an inorganic element, the valence number does not depend on the state and is equal to the valence number obtained from the periodic table.

- In an organic element, the number of electrons that could be involved in bonding is not equal to the valence number from the periodic table but always smaller. We could name it the organic valence number. In that case, pairs of electrons have moved into the inner shell. The number of pairs in the inner shell is consequently higher than from the periodic table.

- A semi-organic element is organic in its negative state and inorganic in its positive state. The neutral state can be either and depends on the element location in the periodic table.

Since the valence number is influenced by the sub-group it belongs to, the effective valence number obviously also. This makes the Ef.V.N. of an element dependent on two parameters: the state and the subgroup of the considered element.

Chapter 5 describes applications of the even-odd rule depending on both criteria.

Inorganic elements have a valence number directly obtained from the periodic table. The following example shows an aluminium atom in a negative state and with two bonds (not a double bond). It possesses 13 electrons when neutral, here 14. They are distributed in the electrons shells: 10 electrons in the inner shell, 2 in the inactive shell and 2 in the covalent shell. Each electron of the covalent shell is engaged in a separate covalent bond with an electron from another atom.

20 elements of the main group are inorganic. For the sake of illustration, only two of these are considered. Hydrogen (H) has the least number of electrons of the main group and a valence number of 1, whereas antimony (Sb) has a higher number of electrons and a valence number of 5.

For all states of these two elements, the even-odd rule is strictly applied in Table 1 and Table 2 to calculate the different figures needed and the number of electrons in the different shells. In Table 1 and Table 2, the first row illustrates the positive state, the second row is the neutral state and the third is the negative state. Note that in both Table 1 and Table 2, the upper left number, the number of valence electrons, remains in all states equal to that from the periodic table.

As shown in Table 1, the hydrogen atom has no electron in the inner shell, i.e. the first number 0 (in 0,0,X) is applicable to every state (all three rows) of hydrogen. The second number, the number of electrons in the inactive shell, equals 2 (in 0,2,0) only when hydrogen in a negative state is not bonded (third row).