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Home  / GENERAL CHEMISTRY Textbook / Chapter 8. Three-dimensional structures of chemical compounds

Chapter 8. Three-dimensional structures of chemical compounds

The question of spatial arrangement of molecules arises, when one atom is connected with 2, 3 or 4 other atoms. If the atoms, connected to the central atom, have almost identical FIEs, we should expect the placement of the axis (connecting the outermost atoms with the inner ones) to be 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, comprises 180o. In the case of 3 straight lines (interchangeable) this angle comprises 120o; in the case of 4 sraight lines—109 o. Here the experimental data quantitatively corresponds to the calculations.

According to this experiment, the angle between the atoms when connecting 2, 3 or 4 identical atoms to the central one is equal to the theoretically calculated angle. The angle is hardly changed when the connected atoms differ in their FIEs. In the above-cited cases, all the outermost electrons of the central atom take part in bond formation.

Now let's take a case where not all of the atoms' outermost electrons form bonds. Our theory allows calculating the spatial placement of these nonbonding electrons, where 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 = -0.0166x + 1.16    (FIEB = 14)
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, 1.16  units of  the Bohr radius  (0.529 Å) respectively, when 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 is equal to 10, 5, 0 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 the 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 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 (i.e., angle values between the bonds) according to this bonding model, which can be represented thus: 

(:) m B (A) n,   

where  n  is a number of atoms A bonded to atom B;  m  is a 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 orbit's radius of the nonbonding electron pairs is bigger than the radius of the orbit in 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), offered in 1940 by N.Sidgewick and H.Powell, and later modernized by R.J.Gillespie and R.S.Nyholm.

According to the model, the 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 rows NH3, PH3, AsH3, SbH3, the angle between the bonds comprises respectively: 107.3; 93; 91.5o ; and 91.3o

The FIE of these elements decreases in the same sequence: 14.5 ; 10.5 ; 9.8 ; 8.6 eV. Likewise, in row H2O, H2S, H2Se, H2Te, the angle between the bonds comprises: 104.5o, 92.2o,; 91o, 88o. The FIE of the central atom of these molecules comprises 13.6, 10.4, 9.75,  9.01  eV respectively.

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

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 about 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 cited 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 8 electrons in the molecule (i.e., 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 as electronic isomers, among which there is a possibility of the existence of an electronic isomer, where the placement of electrons is identical to that of molecules formed out of these atoms.  If the atom has 2 electrons in the outermost shell, we can presuppose the existence of 2 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 in 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.

The first ionization energy (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 rotates, can exist even in hydrogen-like atoms (atoms with one electron). Experimental confirmation of the existence of atomic isomers is the atomic spectra, in part, the radiation of a helium atom and the splitting of the spectral lines in alkaline metals.

The correlation of the isomers and their FIEs can even depend on the nuclear charge. Indeed, 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 the nuclear charge. If the nuclear charge is equal to 20, the calculated energy coincides with that of the experiment with a precision of 0.1%. 

Such a coincidence of calculated and experimental results confirms the fact that a common Coulomb interaction well describes the electrons' energies of both hydrogen and helium-like atoms. The quantitative evaluation of the atomic and bonding energies, and their theoretical and experimental discrepancies, are given in greater detail in our chemistry book entitled: 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.

Chapter 6. Molecule structure >> 
Chapter 7.** Chemical Bonds in Solid Bodies >>
Chapter 8. Three-dimensional structures of chemical compounds
Chapter 9.** Chemical Reactions   >>
Chapter 10.** Catalysis  >>
Chapter 11. Physical and chemical properties of substances  >>