3. Molecular structure
1.Molecular structure and covalent bonding
theories
Valance shell electron pair repulsion (VSEPR) Theory
In a molecule composed of a central atom bonded covalently to
several peripheral atoms the bonding and lone pairs are oriented
so that electron-electron repulsions are minimized while electronnucleus attractions are maximized. The method of determining
this orientation is called the valence-shell electron-pair
repulsion or VSEPR method. The assumptions behind the
method are:
1. Electron pairs in the valence shell of an atom tend to orient
themselves so that their total energy is minimized. This means
that they approach the nucleus as closely as possible, while at
the same time staying as far away from each other as possible,
thus minimizing interelectronic repulsions.
2. Because lone pairs are spread out more broadly than are
bonding pairs, repulsions are greatest between two lone pairs,
intermediate between a lone pair and a bonding pair, and
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weakest between two bonding pairs. This order of repulsion is
shown as in figure 3-1
Figure 3-1 Order of repulsion between electron pairs
3. Repulsive forces decrease sharply with increasing interpair
angle. They are strong at 90°, much weaker at 120°, and very
weak at 180°.
Figure 3-2 Steric number 4: Two possible orientation
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Steric number and electron-pair orientation:
The first step in the VSEPR method for determining the shape of
a molecule is to draw its Lewis structure in order to find out how
many electron pairs are located around the central atom.
Consider arsenic trichloride, AsCl3, and sulfur tetrafluoride, SF4, as
examples. Their Lewis structures are, respectively.
The steric number is defined as the total number of electron
pairs (lone and bonding) around the central atom. As can be seen
from the above Lewis structures, arsenic has a steric number of 4
in AsCl3, while in SF4; the steric number of sulfur is 5. (The valence
shell of sulfur has been expanded to 10 electrons.)
The steric number determines the orientation in space of the
valence-shell pairs. Table 3-1 shows the orientations expected for
steric numbers of 2, 3, 4, 5, and 6. Each of the orientations is the
one which minimizes electron-pair repulsion for that steric number.
For example, for a steric number of 4, we might consider a square
planar orientation, as shown in Fig.3-2. But in this orientation the
interpair angle is 90°, which produces a greater interpair repulsion
than the tetrahedral orientation does. (That is, the pairs are closer
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together.) Thus, for a steric number of 4, tetrahedral geometry is
preferred over square-planar geometry.
In AsCl3 the steric number is 4, and so the orientation of
valence-shell electron pairs around the As atom is predicted to be
tetrahedral. In SF4, with steric number of 5, the orientation is trigonal
bipyramidal, as Table 3-1 shows.
Table 3-1 Special orientations of electrons pairs around a central atom
Steric
orientation
Angles
number
2 Linear
3
Triangular
180O
120O
planar
4
Tetrahedral
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5
Trigonal
90o-120o
Bipyramidal
90o
6
Octahedral
Lone pairs and molecular geometry:
The second step is to determine the number and location of
lone pairs. This is really no problem in the case of AsCl3. The
Lewis structure shows that only one pair of electron; is a lone pair.
Since all corners of a regular tetrahedron are equivalent, all we
need to say is that the Ions pair is at a corner. (See Fig. 3-3) The
resulting molecular shape is denned by the location of the four atoms
aria is called a trigonal pyramid.
Figure 3-3 The AsCl4 molecule: Trigonal pyramid
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Example 3-1: Predict the shape of the chloride trifluoride molecule CLF3
Fig 3-4 Possible orientation of ClF3
The steric number is 5, so interpair repulsion is least when the
five pairs occupy the corners of a trigonal bipyranids (Table 3-1).
Because the molecule has two lone pairs, these have three
possible orientations, as is shown in Fig. 3-4. Structure II in the
illustration can be ruled out, because I and III each have fewer lone
pair-lone pair repulsions at 90°. Structure III is favored over I,
because it has fewer lone pair-bonding pair repulsion at 90°.
Therefore, we predict III, a "T-shape," for GIF. Experiments show
that the CIFs, molecule does indeed3 hove This Shape but it is
Slightly distorted the distortion is a accounted for by the repulsion
between the two lone pairs and the axial bonding pairs.
Table 3-2 summarizes the molecule geometries predicted for
steric numbers 2 through 7.
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Table 3-2 Molecular geometry according to the VSER method:
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Valence-Bond Theory and Orbital Overlap
Two approaches have been used for the purpose of
describing the covalent bond and the electronic structures of
molecules. At its most sophisticated level each approach employs
quantum mechanics, but the basic assumptions of the two
methods are quite different. The first approach, called valencebond (VB) theory, considers that when a pair of atoms forms a
bond, the atomic orbitals of each atom remain essentially
unchanged and that a pair of electrons occupies an orbital in.
each of the atoms simultaneously. The second method,
molecular-orbital (MO) " theory, assumes that the atomic orbitals
of the original unbonded atoms become replaced by a new set of
molecular energy levels, called molecular orbitals, and that the
occupancy of these orbitals determines properties of the resulting
molecule. Although the VB and MO methods appear to be quite
different, it turns out that rigorous calculations using each method
yield similar results. With the advent of sophisticated electronic
computers many such calculations have been successfully
completed, and the results support the usefulness of both the VB
and MO models for covalent bonding.
The hydrogen molecule
Let us now reconsider the H2 molecule and once more picture
its formation from two isolated, ground-state H atoms. Each H atom
has at the start a single electron in is atomic orbital. For identification
purposes we will call the two H atoms A and B. After the covalent
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bond has been formed, we find that each electron now exists in the I
s orbitals of both atoms. This can be shown schematically as
It should be emphasized that we are not showing four
electrons here, but only two occupying both orbitals at the same
time.
According to valence-bond theory simultanious occupaucy of
orbitals of two atoms by a pair of electrons is possible if the
orbitals overlap each other to an appreciable extent.
Figure 3-5 Overlap of Is orbitals in H2 (σ bond).
Figure. 3-5 shows the boundary surfaces of the 1s orbitals of
two bonded hydrogen atoms. The orbital overlap produces a
region of enhanced electron probability density located directly
between the nuclei. Note that the bond axis (the line connecting
the two nuclei) passes through the middle of this region.
Furthermore, the overlap region is symmetrical around the bond
axis, because each atomic orbital is spherical.
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At this point we will borrow a term from MO theory. The bond in H2
is a sigma (σ) bond, one in which the charge-cloud of the shared
pair is centered on and is symmetrical around the bond axis. Such
a charge cloud is said to have axial, or cylindrical, symmetry,
The hydrogen fluoride molecule
A sigma bond can also be formed as a result of the overlap of
an s and a p orbital. Consider hydrogen fluoride, HF. Before
bonding, a fluorine atom has the following ground-state electronic
configuration:
F
1s
2s
2p
Two of the three 2p orbitals are filled. Assume that the
unpaired electron is in the 2px of a hydrogen atom overlaps one
of these lobes end-on (Fig. 3-6), then the shared electron pair
spends most of its time in a region which is centered on and
symmetrical around the bond axis. The bond in HF is therefore a
sigma bond.
A σ bond can also be formed as the result of the overlap of
two p orbitals, but the overlap must be end-to-end as in the fluorine
molecule, F2. Here the 2p: orbital of one F atom overlaps the 2p2
orbital of the second as is shown in Fig. 3-7.
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Pi- bonding
When p orbitals overlap sideways, the results are different. If we
assume as before that the bond axis is the x axis and choose the
2p: orbitals for overlap (Fig. 3-8) the resulting sidc-to-side overlap
produces enhanced electron probability density in two regions
which are on opposite sides of the bond axis. This is characteristic of
a pi (Π) bond, another term borrowed from MO theory.
Multiple bonds
In a double or triple bond one bond is always a σ bond, and
the remaining bonds are π bonds. The nitrogen molecule N2 provides
an example of a triple bond. The ground-state electronic
configuration of a nitrogen atom is
N
1s
2s
2p
Here the three unpaired electrons are in the 2p6 2py and 1p-, orbitals.
Respectively. Each of these orbitels overlaps the corresponding
orbital of the other atoms, the two pz orbitals overlap end-to-end to
form a σ bond, the two 2py orbitals, side-to-side to form a π bond,
and the two 2p: orbitals, side-to-side to form a second π bond.
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These three bonds are shown separately as overlapping boundary
surfaces in Fig. 3-9 The three overlaps together constitute the triple
bond. Compare this with the simple Lewis structure
Hybrid orbitals
Carbon forms countless compounds in which its atoms bond
covalently to four other atoms. The simplest of these is methane, CH4.
How can we describe the four covalent bonds in this molecule in
terms of orbital overlap? The ground state electronic, configuration of
C is
C
1s
2s
2p
Carbon thus appears to be able to form only two covalent
bonds by contributing each of its two unpaired electrons to a shared
pair. But the short-lived methylene (CH2) molecule is much less
stable than CH4
In the methane molecule (Fig. 3-10) each H atom is located at
the corner of a regular tetrahedron, shown inscribed in a cube in
the drawing, so that the relationship between these two regular
solids can be seen. In CH4, all bond lengths are the same and the
angle between each C—H bond and any of the other three is the
tetrahedral angle, 109.5°. The observed tetrahedral structure of
methane is what we expect after applying VSEPR
theory to this molecule.
According to the Lewis structure for methane the
carbon evidently uses all four of its valence electrons
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so that four C—H bonds can be formed. It is not too difficult to
see how carbon can form four bonds. Suppose that one of the 2S
electrons is promoted to the vacant, but higher energy, 2p orbital.
C
1s
2s
2p
Now the C atom appears to be ready to form four σ bonds by
overlap of its 2s and 2p orbitals with the 1s orbitals of four H
atoms. The difficulty here is that if the bonding occurred this way,
the CH4 molecule would not be tetrahedral. Instead, its shape would
be like that shown in Fig. 3-11. In Fig 3-11 a through c are shown
the three C—H bonds which would result from overlap of the three
1p orbitals of C with the Is orbitals of three H atoms. The fourth
bond might go almost anywhere, because an s orbital is spherically
symmetrical and good overlap is possible from any direction. If the
last H is located as far away as possible from the other H atoms in
order to minimize inter electronic repulsion, then it goes in the
position indicated in d. The entire proposed CH4 structure is shown
in Fig. 3 - 11. If these orbitals were used in bonding, methane
would evidently have the shape of a trigonal pyramid, but it does
not. In CH4 all bond angles are equal and all H atoms are
equivalent. The experimentally determined structure of methane is
tetrahedral. How can we account for it using the s and p orbitals of
carbon? The answer is that the ground-state set of s and p orbitals
of carbon is replaced by a new set which is suitable for forming
four equivalent bonds, each at the tetrahedral angle from each of
the others. This may sound like a kind of orbital sleight of hand,
and so in order to aid understanding of this replacement we will
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pause to consider first two simpler cases, the bonding of beryllium
and boron.
sp Hybrid orbitals
Beryllium (Z =4) forms a hydrogen compound which at high
temperatures exists as discrete BeH2 molecules. The ground-state
electronic configuration of a Be atom is
B
1s
2s
2p
The two bonds in BeH2 are found to be oriented at 180° from
each other; that is, the molecule is linear. How does this come
about? When a Be atom forms its two bonds, its 2S and one of its
2p orbitals are replaced by a pair of new orbitals, and these new
orbitals, hybrid orbitals, are used for bonding, that each orbital
corresponds to a solution, a wave function, to the Schrodinger
wave equation. Because the wave equation is a differential equation,
any set of its solutions can be combined mathematically to form a
new set of wave functions which are also solutions. These new
wave functions are said to be hybrids of the original ones and
correspond to a set of hybrid orbitals.)
Perhaps some pictures will help. At the left of Fig. 3-12 are
shown an s and a p orbital. In the illustration the plus and minus
signs are not charges. Each is the algebraic sign of the wave
function in the designated lobe of the orbital. Now we will
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combine or mix the orbitals, first (upper-right drawing) by adding
the p to the s.
The result is a hybrid orbital, in which the density of electronic
charge has increased where the original wave functions had the
same sign and has decreased where they had opposite signs.
This hybrid orbital, called an sp orbital, is highly directional;
overlap is favored in the direction of its large major lobe.
Subtraction of the original s and p orbitals (lower-right drawing) yields
the second hybrid orbital. It is equivalent to the first, but points 180°
away. Thus by combining or mixing two nonequivalent orbitals (one is
an s and the other, a p) we have obtained two equivalent sp hybrid
orbitals.
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