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surface, which belong to the observed equilibrium structure of
molecules, possess certain symmetry properties with respect to the
bond orbitals, whose origin is the mutual repulsion between adjacent
orbitals. We shall now see how these trends affect the bond angles
and the torsional angles.

The BendinggPotential

 

The angles between bonds connected to a given atom are essen-
tially determined by the tendency of the bonds to be as far apart
as possible. Thus, if only two bond orbitals are connected to a
single atom, as in BeHZ, they will be colinear. Similarly, three
orbitals connected to an atom are always coplanar, with bond angles
of around 120°. Each bond angle separately would tend to increase,
but since it is impossible for one of the three bond angles in the
plane to increase without decreasing the others, the minimum of the
total bending potential energy is reached when the three bond angles
are about equal. (The angles would be exactly equal for idential
bonds, as one would expect to observe in CH?). Similarly, four
bonds connected to an atom form a tetrahedral structure*, with all
six angles between the four bonds equal to the tetrahedral angle
109,47° when the four bonds are identical, as is the case in C34.
Deviations from the tetrahedral angle occur when the four bonds are
not equal, as is the case in most tetrahedral carbon atoms. (The
deviations_are usually small, 2 to 3°, unless.the molecule is
strained by other forces, as is the case in a number of ring mole—
cules, like cyclobutane, cyclodecane and other cycloalkanes, where
the closure of the ring imposes significant deviations from the
tetrahedral angles, or in overcrowded molecules like tri-tertiary
butyl—methane. In the same way, when five bonds are connected to
an atom, as in pentavalent phosphorus compounds, three bonds are
coplanar (equatorial) and two are perpendicular to the plane of the
others (axial). This is the highest symmetry available for such a
structure, and the fact that it is an energy minimum point can be
derived from symmetry considerations.

Deviations from these rules occur when lone pairs of electrons
form bond-like orbitals. For example, the two 0H bonds in the water
molecule form an angle of 105°, but there are two lone pairs of
electrons which are connected to the oxygen atom and form lobes
which behave like chemical bonds in the sense that they repel each
other and the adjacent 0H bonds. Thus, the two 0H bonds and the
two lone pairs form a tetrahedral structure around the oxygen atom.
Similarly, the three NH bonds and the one lone pair of NH3 form a
tetrahedral structure, so that NHgis pyramidal, not planar.

 

*Tetrahedral structure means that the central atom is considered to
be at the centre of a tetrahedron while the 4 atoms bonded to it
are located at the vertices.

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