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Chapter 3: Molecular structure Page 57

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 electron-

nucleus 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


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


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


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

number

orientation Angles

2 Linear

180O

3 Triangular

planar

120O

4 Tetrahedral

109.5o


5 Trigonal

Bipyramidal

90o-120

o

6

Octahedral

90o

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

Chapter 3: Molecular structure 2

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.


Table 3-2 Molecular geometry according to the VSER method:


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 valence-

bond (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


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.


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.


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.


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


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


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


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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