COVALENT BOND

 

Background and actual explanation

 

            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 variants of covalent bound theory are 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. The equation that serves as a mathematical model for electrons movement inside atoms is known as the Schrodinger equation:

where: m is the mass of the electron, E is its total energy, V is its potential energy, and h is Planck’s constant. The solution of Schrodinger equation, which gives the electron density distribution are called orbital.

The simplest types of orbital s and p are presented in fig. 1.

Figure 1. s and p orbital shapes

 

The s orbital has a spherical symmetry and p orbital has a bilobar form with a node in the middle.

In the simplest case, a covalent bound should be formed by superposition of two atomic orbital as in fig. 2

Figure 2. Hypothetical covalent bound between s and p orbital

 

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.

            We will describe a simple hybridization for s and p orbital. In this case we can have three basic types of hybridization: sp3, sp2 and sp. These terms specifically refer to the hybridization of the atom and indicate the number of p orbital used to form hybrids.

            In sp3 hybridization all three p orbital are mixed with the s orbital to generate four new hybrids (all will form σ type bonds or hold lone electron pairs).

            Figure 3 sp3 hybridization

 

            If two p orbital are utilized in making hybrids with the s orbital, we get three new hybrid orbital that will form σ type bonds (or hold lone electron pairs), and the "unused" p may participate in π type bonding. We call such arrangement sp2 hybridization.

            If only one p orbital is mixed with the s orbital, in sp hybridization, we produce two hybrids that will participate in σ type bonding (or hold a lone electron pair). In this case, the remaining two p orbital may be a part of two perpendicular π systems.

            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:

Hydrogen 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.

            In order to explain the form of a molecules quantum mechanic propose a new theory called ,,electron pair repulsion theory”. According to this, the shape of a molecule or ion is governed by the arrangement of the electron pairs on the last shell around the central atom; this arrangement is made in such manner to produce the minimum amount of repulsion between them.

             In case of two pairs of electrons (like BeCl2) around central atom the molecule is linear because an angle of 180º insure a minimum interaction between electrons pairs.

            In case of three electron pairs around the central atom (BF3 or BCl3) the molecules adopt a trigonal planar shape with a bond angle of  120º:

 

            In case of four electron pairs around the central atom (CH4) we have a tetrahedral arrangement. A tetrahedron is a regular triangularly-based pyramid. The carbon atom would be at the centre and hydrogen at the four corners. All the bond angles are 109.5°.

            For five pairs around central atom (PF5), the shape is a trigonal bipyramid. Three of the fluorine are in a plane at 120° to each other; the other two are at right angles to this plane. The trigonal bipyramid therefore has two different bond angles - 120° and 90°.

            In case of six electron pairs around the central atom (SF6)  the structure is an octahedral.

 

            Molecular orbital (MO) theory is an alternative way of describing molecular structure and electron density. The fundamental premise of MO theory is that the orbitals used to describe the molecule are not necessarily associated with particular bonds between the atoms but can encompass all the atoms of the molecule. Molecular orbitals consist of combinations of atomic orbitals. In simple molecular orbital (MO) theory, a number of atomic orbitals will combine to form the same number of molecular orbitals. For example, "n" atomic orbitals will combine to form "n" molecular orbitals.

The properties of the molecule are described by the sum of the contributions of all orbitals having electrons.

In localized bonding the number of atomic orbitals that overlap is two (each containing one electron), so that two molecular orbitals are generated. One of these, called a bonding orbital, has a lower energy than the original atomic orbital, and the other, called an antibonding orbital, has a higher energy. As orbital of lower energy fill first, in case of one electron sharing between atoms, both electrons go into the new molecular bonding orbital, since any orbital can hold two electrons. In this case the antibonding orbital remains empty in the ground state.

Let’s consider the simplest molecule - H2. Each H atom has an electron in a 1s orbital. When they come together, these two 1s orbitals overlap as in fig. 4 and form the bound orbital.

In the same time a higher electron density between atoms is counted.

The other anti-bonding orbital is empty and has a shape that would lead to electrons spending more time away from the region between the two atoms. Because of this, this orbital is considered an.

Figure 4. Bonding and antibonding molecular orbital for hydrogen molecule

 

 

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.

            According to new interpretation, every atom of hydrogen possesses an electron magnetic moment due to the electron movement. 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. 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 fig 5. The magnetic moments are pointed parallel but with opposite directions.

            Every atom has own electron and the electron orbit only around his nucleus and the orbits of electrons are situated in parallel planes (fig. 5). 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 regulate the distance between atoms, because when distance becomes lower due to the attractive magnetic interaction, the electrostatic repulsion increase and the equilibrium is maintained.

 

Figure 5 Hydrogen covalent bond formations

 

            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:

 (1.1)

where  and  are electronic magnetic moments due to the different atom’s bound participant;

            B1 represent the intensity of magnetic field created by m1 at level of secondary atom orbit (r2) and B2 represent the intensity of magnetic field created by m2 at level of first atom orbit (r1).

            cos q1 and cos q2 represent the angle between m1 and B2, respectively m2 and B1 and due to the symmetry of hydrogen molecule  q1=q2.

            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 B1 and B2 is antiparallel with orientation of m1, respective m2. This is due to the orientation of B tangent to the line of magnetic field created by m1, respective m2. In fig 6 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.

Due to the orientation of electrons orbits, in case of covalent bound, the same antiparallel orientation is valid also for the m1 and B2, respectively B1 and m2.

            The energy of magnetic interaction between two electrons became:

 (1.2)

q1 = q2 = 0 that means cos q1 = cos q2 =1

            The value of B created by a magnetic moment at distance r is given, according to electrodynamics, by:

 

 (1.3)

where:

            B is the strength of the field;

            r is the distance from the center

            λ is the magnetic latitude (90°-θ) where θ = magnetic colatitudes, measured in radians or degrees from the dipole axis (Magnetic colatitudes is 0 along the dipole's axis and 90° in the plane perpendicular to its axis.);

            M is the dipole moment, measured in ampere square-meters, which equals joules per tesla;

            μ0 is the permeability of free space, measured in henrys per meter.

            For our case, l= 0, M = m, so the field created by first electron at second electron level is

(1.4)

Figure 6 Antiparallel orientations of B and m for the same magnetic moment at xy plane of electron orbit

 

And for second electron at first electron orbit we have:

 (1.5)

            The magnetic interaction became:

 (1.6)

where  and and μ0 is the permeability of free space, measured in henrys per meter.

            For hydrogen electrons due to the symmetry of atom arrangement we have  as value, so we can write:

 (3.7)

            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. 7 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. 7, 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.

Figure 7 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. 8) 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.

FFigure 8 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 orientations 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.