Covalent bound

Actual interpretation

Covalent bonds are formed as a result of the sharing of one or more electrons. In classical covalent bond, each atom donates half of the electrons to be shared. According to actual theories, this sharing of electrons is as a result of the electronegativity (electron attracting ability) of the bonded atoms. As long as the electronegativity difference is no greater than 1.7 the atoms can only share the bonding electrons.

Being in impossibility to explain coordinative complex and also the structure of a lot of common compounds, new theories about covalent bound were proposed. In the Valence Bond (VB) theory – one of must representative in quantum mechanic - an atom rearranges its atomic orbital prior to the bond formation. Instead of using the atomic orbital directly, mixtures of them (hybrids) are formed. This mixing process is termed hybridization and as result are obtained spatially-directed hybrid orbital.

An atom will adjust its hybridization in such a way as to form the strongest possible bonds and keep all its bonding and lone-pair electrons in as low-energy hybrids as possible, and as far from each other as possible (to minimize electron-electron repulsions).

In the simplest example hydrogen molecule formation, hdrogen atoms need two electrons in their outer level to reach the noble gas structure of helium. The covalent bond, formed by sharing one electron from every hydrogen atom, holds the two atoms together because the pair of electrons is attracted to both nuclei.

**Proposed model of covalent bound**

In proposed theory a covalent bound implies only a coupling of magnetic moments of individual atoms in order to obtain a greater stability. The electrons remain and orbit around proper nucleus, and consequently there is no sharing of electrons between atoms. When a covalent bound is broken the coupling between these magnetic moments is lost and of course every atom remains with his electrons. The situation is quite different in quantum theories, because when a covalent bond is broken the electrons are probabilistically distributed back to atoms so an electron form one atom can arrive to the other atom participating at bound. In proposed theory the electrostatic interaction between atoms participating at covalent bound formation is less important.

According to new interpretation, every atom of hydrogen possesses an electron magnetic moment due to the electron movement arround nucleus. The magnetic moment of nucleus is lower so it is not important in this case. The electron magnetic moment is formed by combination of orbital and spin magnetic moment using known rules of vectors and the orbital moment is greater then spin moment. The covalent bond means that both atoms attract reciprocally due to the magnetic interaction between their magnetic moments. The simplest interaction between two magnetic moments of different electron from different atoms is showed in down picture. The magnetic moments are pointed parallel but with opposite directions.

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Every atom has own electron and the electron orbit only around his nucleus and the orbits of electrons are situated in parallel planes . There is a dynamical equilibrium regarding a minimum distance between atoms, when the electrostatic repulsion force became stronger and a maximum distance between atoms when the coupling between magnetic moments force the atoms to move one to another. There is also an electrostatic push due to the electron reciprocal interaction and a nuclear push due to the nucleus reciprocal interaction. These interactions are smaller than magnetic interaction so the molecule is stable in normal condition.

The hydrogen molecules formed due to the opposite orientation of electrons magnetic moments has a lower energy comparative with the state of single atoms of hydrogen. The energy interaction between hydrogen atoms is given by:

W = -μ_{1}B_{2}cosθ_{1} -μ_{2}B_{1}cosθ_{2}(1.1)

where μ_{1} and μ_{2} are electronic magnetic moments due to the different atom’s bound participant;

B_{1} represent the intensity of magnetic field created by μ_{1} at level of secondary atom orbit (r2) and B_{2} represent the intensity of magnetic field created by μ_{2} at level of first atom orbit (r1).

cos θ_{1} and cos θ_{2} represent the angle between μ_{1} and B2, respectively μ_{2} and B1 and due to the symmetry of hydrogen molecule θ_{1}=θ_{2}.

So in a first approximation, one electron is moving in the magnetic field created by the other electron from the other atom and reciprocally.

The orientation of B_{1} and B_{2} is antiparallel with orientation of μ_{1}, respective μ_{2}. This is due to the orientation of B tangent to the line of magnetic field created by μ_{1}, respective μ_{2}. In fig 3.2 is presented, as example, the magnetic moment produced by electron moving in the x-y plane with nucleus in the origin of system. The magnetic moment is along the z axis, the line of magnetic field go from North Pole and enter into the South Pole. The vector B is tangent to the magnetic line field, and at orbit electron plane and in other direction then N and S poles, B is antiparallel with m.

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Due to the orientation of electrons orbits, in case of covalent bound, the same antiparallel orientation is valid also for the μ_{1} and B_{2}, respectively B_{1} and μ_{2}.

The energy of magnetic interaction between two electrons gain a simpler expresion using a well known relation between the value of B created by a magnetic moment at distance r -see wikipedia:

The major and fundamental difference between quantum theory and proposed theory is that after forming of hydrogen molecules, every atom of hydrogen has only one electron around nucleus. The hydrogen atom doesn’t have a doublet structure according to new theory. There is no difference in atomic structure between atom of alone hydrogen atom and hydrogen atom in molecule. The only difference is the coupling of magnetic moment of hydrogen with another magnetic moment and this coupling insure a lower energy in case of molecule.

As comparison, quantum mechanic is incapable to explain why two opposite spin are lowering the energy of system. In the same time there is a contradiction in actual theory when the electrons are filled on subshell in atomic structure and when a covalent bound is formed. More precisely, the electrons fill a subshell first with one electron in every orbital with parallel spins and after that the existing electrons complete the orbital occupation with opposite electron spin. So if the coupled spin state is more stable, at occupation of subshell should be occupied complete an orbital and after hat another orbital.

For other elements, when we have a single electron in the last shell the situation is simple because for the inner shells, magnetic moments suffer an internal compensation. What’s happened when we have more electrons on the last shell?

Normally in the ground state electrons form pairs with opposite spin in order to maintain a low level of energy. But at interaction with other reactants a process of decoupling of pairs of electrons can happened. Depending on the condition of reaction, on the structure of element, on the stability of formed compound it is possible to have a partial decoupling or a total decoupling of electrons from last shell. As example: chloride having 7 electrons on the last shell, can participate:

• with one electron in chemical combination like in ground state,

• with 3 electrons, that means a decoupling of one pair of electrons plus the initial decoupled electron;

• with 5 electrons, that means a decoupling of two pairs of electrons plus the initial decoupled electron;

• with 7 electrons, that means a decoupling of three pairs of electrons plus the initial decoupled electron.

When a single electron on the last shell is presented and we have a single element bound, the orientation of electron magnetic moment is not so important. Of course the molecule formed is linear. When the number of electron magnetic moments is greater, the situation it is a little bit complicated but solvable and easy to understand. The magnetic moments of electrons are treated classical this means, the energy is minimum when the spread of magnetic moment is maximum. As consequence the magnetic moments, and of course the formed bounds, will have such orientation in order to insure a minimum interaction.

In case of two electrons on the last shell, this means two magnetic moments, and consequently two covalent bounds, the molecule is linear, the angle between bounds is 180º in case of two simple bound.

In case of three magnetic moments (three covalent simple bounds) a trigonal planar arrangement is preferred or a pyramidal trigonal structure in case of central atom with one lonely electron pair.

In case of four magnetic moments (four covalent simple bounds) the molecule will have a tetrahedral arrangement.

For five and six magnetic moment (five or six simple covalent bounds), a trigonal bipyramid and an octahedral structure are preferred.

In case of seven magnetic moments, due to the sterical interaction, it is imperative that minimum one covalent bound to be double due to the geometry of molecules.

Chloride with his electron structure can form up to seven covalent bounds. Don’t be scared with counting of number of electrons around chloride nucleus. Even we have seven covalent bound we will have only seven electrons on the last shell. But, sometimes the structure forms needs the necessity of an eighth bound, and in this case chloride catches another electron, and will form eight covalent bounds. We will see this situation for example at anion perchlorat structure.

This is the situation when only simple bounds are formed between atoms. But what is possible to predict using our model when a double or triple bond is formed?

In order to have a single bound between atoms we have seen that magnetic moments are opposite and situated on the line which unify both nucleus. A double bound have to respect the same condition: magnetic moment need be opposite in order to insure a lower energy for system.

Let’s take carbon as example with four magnetic moments. In order to form a first bound we must have fulfilled the condition that every atom comes with two electrons magnetic moments opposite orientated. For a simpler visual representation the first bound will be represented along the line which passes through both nuclei, even in reality the magnetic moments are a little bit shifted from this perfect alignment. In fig. 10 the simple bound is represented by magnetic moments noted with μ1x. For the second bound (called pi bound in quantum mechanic) in order to have an opposite orientation of magnetic moments, these must be orientated after z or y axes (in fig. 3.3 μ2z is after z axis). The minimum energy is attaint when the two magnetic moments participating at the second bound are in the same plane, so the first and second bound between carbon atoms delimitate a plane in our case x-z plane.

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Figure 3.3 Double bound formations

In order to have minimum energy perturbations the other two magnetic moments of every atoms of carbon, which will form other sigma bounds must be situated in x-z plane but directed to exterior. Practically, the magnetic moments of every atoms of carbon design a regulated triangular pyramid, one top orientated and another down orientated. Consequently three magnetic moments are in the same plane and the angle between them is 120º. This observation will help in designing the shape of molecules.

The double covalent bound formation suppose an alignments of four magnetic moments, and this fact force the molecule to preserve a certain geometry; the rotation around double bound is impossible. The other magnetic moments (m3 and m4) in our example can form other two simple covalent bound and they are orientated in another plane perpendicular on the plane of formed bounds.

Some energy is spent for the alignments of second or third magnetic moments in case of double and triple covalent bound; it’s normally that energy of secondary bound is smaller in comparison with energy of first bond. And also the coupling is not so strong in case of two magnetic moments aligned on two parallel lines (case of pi bound) like in case of alignment on the same line (case of sigma bound).

The formation of triple covalent bond between two atoms implies that we have minimum three magnetic moments available; we will discuss for carbon which present four magnetic moments. The first two magnetic moments from every atoms form double bound as up described (μ1x form sigma bound and μ2z a pi bound). The third magnetic moment orbital found in plane x-y in case of double covalent bound, must be aligned after z axe (fig. 3.4) and will form a second pi bound. The fourth remaining orbital will be align in opposite with μ1x. Practically in case of a triple bond the distribution of magnetic moment is crossed, similar to ground state. The only difference is that in this case we have a coupling between electron magnetic moment from different atoms and not from the same atom like in ground state. If in ground state in case of carbon for the same atom μ1 is coupled with μ4 and μ2 with μ3 from the same atoms, in case of triple bound every of these magnetic moments are coupling with other magnetic moments form another atoms.

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Figure 3.4 Triple bound formation

For chosen example the magnetic moments μ4 remain free and can form another simple bound with other two atoms. In the case of a triple bound the molecule is linear due to the alignment of magnetic moments.

As we can see the difference between energetic of double bond or triple bond and energetic of similar number of single bonds is given by the orientation of magnetic moments during interaction and is not a different interaction. Consequently the energy of second bond (pi bound) interaction will differ as value regarding the first bound (sigma bound).

In case of different atoms which form a covalent bond, we will have the same coupling between magnetic moments of electrons participating at bond building. The magnetic moments of two electrons from two different elements will differ a little bit as absolute value. Consequently the opposite orientation of magnetic moments during bound formation leave the bound with a small magnetic moment uncompensated. In case of identical atoms the compensation is complete. Therefore some molecules possess a small remanent magnetic moment.