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The question of the spatial arrangement of molecules arises when one atom is connected with two, three or four other atoms. If the atoms connected to the central atom have near-identical FIEs, we should expect the placement of the axis connecting the outermost atoms with the inner ones to set them as far apart as possible.

This is conditioned by a mutual repulsion of the bonding electrons. The spatial arrangement of molecules is not changed even if some atoms have different FIEs and are connected to the central atoms with another type of bond.

From stereometry, we know that an angle between two straight lines projected from one point and placed at a maximal distance from each other is 180o. In the case of three interchangeable straight lines, this angle is 120o; in the case of four sraight lines, it is 109o. Here, the experimental data quantitatively corresponds to the calculations.

According to this experiment, the angle between the atoms when two, three or four identical atoms are connected to the central atom is equal to the theoretically calculated angle. The angle is barely changed when the connected atoms differ in their FIEs. In the above-mentioned cases, all the outermost electrons of the central atom take part in bond formation.

Now, let's discuss a case where not all of the atoms' outermost electrons form bonds. Our theory allows us to calculate the spatial placement of these nonbonding electrons when one of the atoms bonded by a covalent bond has a very small FIE. In such a case, the atom's FIE is equal to zero (i.e., at the limit) and allows evaluation of the spatial position of the nonbonding electrons. Using equations 6.4-5 to 6.4-7, the value of 'a' was calculated. [Here 'a' is the radius of the circle on which the connected electrons rotate.]

We have determined the changes of a in molecule A-B when the FIE of atom A is changed from 17 eV to 5 eV at two constant B atoms' FIEs (14 eV and 5 eV), which are expressed via the following equations and shown in figures 8-1 and 8-2:

a = -0.016x + 1.7 (FIEB = 5) x = FIEA

Radius of Circle a vs. FIE of Atom A (FIE of Atom B = 14 eV)

Figure 8.1

Radius of Circle a vs. FIE of Atom A (FIE of Atom B = 5 eV)

Figure 8.2

According to these equations, when the FIE of atom A decreases, the radius of the electronic circle increases; when the FIE of atom B decreases, the radius of the orbit increases. When atom B's FIE is 14 eV, the electronic orbits' radii a comprise 1, 1.1 and 1.16 units of the Bohr radius (0.529 Å), respectively, and the FIE of atom A = 10, 5, 0.

Likewise, atom B's FIE is equal to 5 eV, the electronic orbits' radii a are equal to 1.54, 1.62 and 1.7 units of the Bohr radius, respectively, and the FIE for atom A is equal to ten, five and zero, respectively. Thus, according to the model, with the decrease of the FIE in atoms A and B, the radius of the bonding electronic orbit increases. When the FIE of atom A is equal to zero with

the constant FIE of atom B, the radius achieves its maximal value. Then, when the FIE of atom B is decreased, we expect an increase in the radius of the electronic orbit.

If we extrapolate from these results with reference to the question asked above, we can expect the following dependency for the radius of the electronic orbit a of the nonbonding pair of electrons in the atom: the radius of this orbit should increase when the FIE of atom B decreases. Now, let's see what dependencies we should expect in spatial structure (particularly the sizes of the angles between the bonds), according to this bonding model, which can be represented thus:

(:) m B (A) n,

n is the number of atoms A bonded to atom B; m is the number of undivided pairs of electrons (:).

According to the model, the angle between atoms A (angle A B A) is defined by the repulsion between the electronic orbits and by their radii.

In all cases, independent of the FIEs of atoms A and B, the radius of the orbit of the nonbonding electron pairs is bigger than the radius of the orbit of the bonding electron pairs. Therefore, we should expect a decrease in the repulsion between the electron pairs in the following manner: Nonbonding pair of electrons — nonbonding pair of electrons > nonbonding pair of electrons — bonding pair of electrons > bonding pair of electrons — bonding pair of electrons.

This sequence was also observed experimentally and was generalized by the Valence Shell Electron Pair Repulsion Theory (VSEPR) written in 1940 by N.Sidgewick and H.Powell, which was later modernized by R.J.Gillespie and R.S.Nyholm.

According to the model, interelectronic repulsion should increase when the FIE of the central atom decreases. Then, the value of angle ABA should increase when the FIE of atom B decreases.

Experimental data has shown that some groups of compounds in the periodic table reveal a decrease in the angle value between the bonds when the FIE of the central atom decreases. For example, in NH3,PH3, AsH3and SbH3, the angles between the bonds are 107.3o_{, 93}o_{, 91.5}o_and 91.3o_{, respectively.}

The FIEs of these elements decrease in the same sequence: 14.5, 10.5, 9.8, 8.6 eV. Likewise, in H2O, H2S, H2Se and H2Te, the angles between the bonds are 104.5o_{, 92.2}o,_{, 91}o _{and 88}o_, respectively. The FIEs of the central atoms of these molecules are 13.6, 10.4, 9.75 and 9.01 eV, respectively.

In the framework of the VSEPR, these dependencies were regarded as anomalous and required additional explanation.

Thus, our theory of chemical bonding can quantitatively explain the dependencies observed in experiments on the study of spatial structures of chemical compounds without any supplemental suppositions. The explanation of the spatial structure of chemical phenomena in the framework of our theory allows us to specify the model of the atom. In the first approach, we have placed the atom in a single plane.

According to the spatial structure of water, for example, the bonding and nonbonding electrons rotate in circles situated at the top of the tetrahedron. If the placement of the eight electrons in the molecule (their rotation along the circular orbits at the tops of the tetrahedron) greatly differed in energy as compared to their placement in the atom, we would have a much smaller energy gain during bond formation.

That is, we can suppose that the placement of electrons in the atom hardly differs from that in the molecule.

More precisely, this conclusion can be formulated as follows:

Electrons in the atom can be placed on different positions, so some few electronic isomers may exist. There is a possibility of the existence of an electronic isomer, where the placement of electrons is identical to a placement of electrons in molecules formed out of these atoms. If the atom has two electrons in its outermost shell, we can assume the existence of two isomers. In one of the isomers, the electrons rotate in one circle, while in the other they rotate in parallel circles. Another factor that causes an increase in the possibility of such an electron distribution can be the presence of the nuclei's magnetic moment. This phenomenon is present on our Earth. Indeed, we know that electrons, coming from space, gather in circles on the magnetic poles of the Earth. The appearance of an atomic electron isomer in a helium-like atom, where the electrons rotate in parallel planes, can be caused by the fact that, in these circles, the electrons rotate in opposite directions.

FIE of the isomer mixture can be defined by the FIE of an isomer with the smallest value since, in the process of defining the FIE, electronic isomerization of the isomers can take place. The appearance of atomic electron isomers, when the electrons rotate is in opposite directions, can be expected when the number of electrons in the atom's outermost layer is more than two.

Atomic electron isomers, which differ in the direction of the rotation of their electrons relative to the axis, around which the atom's nucleus rotate, can exist even in hydrogen-like atoms (atoms with one electron. The atomic spectra, in part, the spectra of a helium atom and the splitting of the spectral lines in alkaline metals are an experimental confirmation of the existence of atomic isomers.

The correlation of the isomers and their FIEs can even depend on nuclear charge. According to the experimentally defined correlation, the deviation of the calculated energy value of helium- like atoms, as compared to that of the experiment, depends on nuclear charge. If nuclear charge is 20 a.u., the calculated energy coincides with that of the experiment with a precision of 99.9%.

Such a coincidence of calculated and experimental results confirms that the electrons' energies in both hydrogen and helium-like atoms can be described as common Coulomb interactions. The quantitative evaluation of the atomic and bonding energies and their theoretical and experimental discrepancies are given in greater detail in our chemistry book, How Chemical Bonds Form and

Chemical Reactions Proceed, page 300.

The energy deviation between small values in experiments and helium-like atoms with small charges can be caused not only by the presence of an isomer or entropy phenomenon, but also by a change of the electronic orbit from a circular to an elliptical one.