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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5852_Библиотеки_им_академика_М_И_Перельмана.pdf
C H A P T E R 1 Structure and Properties
e
2
e
1
H
A
Forces of
attraction
e
1
Forces of
repulsion
H
B
H
A
H
B
e
2
and energy of the system by
E = EA + E
If a system can be represented by a number of wave functions such as 2.
B
ψ
,
ψ
,
ψ
1
, ..., then the true
2
3
wave function ψ is obtained by taking a liner combination of all these wave functions.
where C
ψ
= N(C
, C2, C3 ,…,arethecoefcientswhicharesoadjustedthattheygiveastateofthelowestenergy.In
1
1ψ1
+ C
2 ψ2
+ C
3 ψ3
…
order to normalize wave function we multiply RHS by a normalizing constant.
ψ
= X (C
1 ψ1
+ C
2 ψ1
+ C
3 ψ3
+ …)
The weights of these coefcients C1, C2, C3, …, can be measured by taking their squares into
consideration.
1.8.2 Application of VB Theory: Formation of Hydrogen Molecule
Let HA and HB represent the nucleus and e1 and e2 the electrons of the two hydrogen atoms, respectively. In
therstinstance,whentheyareseparatedapart,thereisnointeractionbetweenthem.Ifthewavefunctions
for individual atoms are
ψ
=
ψ
ψ
A
ψ
and
ψ
A
B
, respectively, then the function of the system is
B
When the two hydrogen atoms are brought closer, new forces of attraction and repulsion come into play.
The total wave function of the system can be represented as
ψ
=
ψ
(1)
ψ
1
(2)
B
A
where 1 and 2 represent the electrons.
Consider, the formation of a molecule of hydrogen from two hydrogen atoms H
and HB. When the atoms
A
are separated by large distances, there is essentially no attraction between them and, therefore, the energy of
isolated system is taken to be zero. But as they approach each other, they experience new attractive forces
between the nucleus of HA and the electron of H
and vice versa. repulsive forces operate between their
B
electrons. These attractive and repulsive forces are shown in Fig. 1.10.
31
Figure 1.10 Attractive–repulsive forces between two approaching H atoms.
32
d
0
O
+ve–ve
d ൺ
8
Increasing energy
Increasing stability
Internuclear distance (d)
Maximum decrease
in energy (E)
PHARMACEuTICAL ORgAnIC CHEMISTRy
Figure 1.11 Variation of energy during H2 molecule formation.
While the attractive forces tend to decrease the potential energy of the system, the repulsive forces tend to
increase it. Since the attractive forces dominate over the repulsive forces, the potential energy of the system
begins to decrease (Fig. 1.11). This decrease in energy of the system continues up to a certain equilibrium
distance (d0 =74pm)betweenthetwohydrogenatoms,whentheattractiveandrepulsiveforcesjustbalance
each other and the potential energy of the system becomes minimum. A chemical bond is said to have been
formed between the hydrogen atoms at this distance. This equilibrium distance between the nuclei of two
atomsatwhichattractiveandrepulsiveforcesjustbalanceeachotherandthepotentialenergyofthesystem
is minimum is referred to as bond length.
However, if the two hydrogen atoms are pushed further closer than the equilibrium distance (d0), the
repulsive forces overpower the attractive forces and hence the energy of the system begins to increase, as
shown in Fig. 1.11.
Thus, it may be concluded that the formation of a chemical bond between atoms is always accompanied
by decrease in energy of the system. Obviously, the greater the decrease in energy, the lower will be the
energy of the system and stronger will be the bond formed. On the other hand, if the same amount of
energy is supplied to a molecule, the bonded atoms will tend to separate, i.e. bond will break. Evidently the
stronger the bond, the greater will be the amount of energy required to break it. This is commonly expressed
in terms of bond energy andmaybedenedastheenergyrequiredtobreakonemoleofbondsofthesame
kind. For example, the bond energy for H–H bond is 433 kJ mole–1.
1.8.3 Limitations of Valence Bond Theory
In an ionic solid, the ions are held together by electrostatic attraction between positively and negatively
charged ions. But according to valence bond theory, a covalent bond is formed by the sharing of electrons
between the two atoms. Thus, this theory assumes that one of the electrons from the outer shell of one of
the atoms spends a part of the time in the outer shell of the other atom and vice versa.
C H A P T E R 1 Structure and Properties
In this theory, we assume the following:
1. Electrons in molecules are located as if they are present in separate atoms.
2. Electrons maintain their characteristics even in the presence of other atoms.
3. The wave function of a molecule is the product of the atomic wave function of the individual atoms.
Wendthefollowinglimitationsintheseassumptions:
1. If we consider the last assumption, we see that the presence of the other nuclei should affect the
electronic arrangement of all the atoms in the molecule.
2. Except for H
+
,themathematicalcalculationsinmostofthesystemsareverydifcultandforthatwe
2
have to use approximate methods.
3. It is not possible to write a single structure to explain the various features of an ion/molecule and
for that we have to write various resonance forms. Thus we can say that the true structure is only a
resonance hybrid of these structures.
4. It does not explain the paramagnetic character of oxygen.
In spite of the limitations, valence bond theory nds extensive applications in determination of the
geometry of the molecule and ions qualitatively.
An alternate theory to describe the formation of chemical bond is known as molecular orbital theory.
33
1.9 MOLECULAR ORBITAL (MO) THEORY
There is another approach to chemical bonding known as molecular orbital (MO) theory, developed mainly
by Mulliken (1932), which explains the bonding characteristics in a better way.
The molecular orbital theory considers the entire molecule as a unit with all the electrons moving under
theinuenceofallthenucleipresentinthemolecule.Thisapproachrecognizesthateach electron belongs
to the molecule as a whole and may move within the entire molecule.
Molecular Orbitals
When the atoms to be bonded come close together, the orbitals of the bonded atoms lose their individual
character and fuse (overlap) to form larger orbitals called molecular orbitals. Thus, like atomic orbitals,
there are molecular orbitals in a molecule. The only difference is that in atomic orbitals, electrons move
undertheinuenceofonlyone nucleus (i.e. AOs are monocentric), while in molecular orbitals, electrons
moveundertheinuenceofmanynuclei(i.e.MOsarepolycentric).
Molecularorbitalsmay,therefore,be denedas theregions inspace associatedwith allthenuclei of
themoleculewheretheprobabilityofndingaparticularelectronismaximum.Asinthecaseofatomic
orbitals, each molecular orbital can accommodate at the most two electrons with opposite spins.
Itmaybenotedthatelectronsinmolecularorbitalsarenotconnedtoanindividualatom,buttheybelong
to the entire molecule and are said to be delocalized with respect to the individual atoms.
Some important features of molecular orbital theory are as follows:
1. Like an atomic orbital which is around the nucleus of an atom, there are molecular orbitals which are
around the nuclei of a molecule.
34
No new orbital is formed
Valence bond
approach
Molecular
orbital
approach
New molecular orbital is formed
Half-filled atomic orbitals
PHARMACEuTICAL ORgAnIC CHEMISTRy
2. The molecular orbitals are entirely different from the atomic orbitals from which they are formed.
3. Thevalence electronsoftheconstituentatomsareconsideredtobemoving undertheinuenceof
nuclei of participating atoms in the molecular orbital.
4. The molecular orbitals possess different energy levels like atomic orbitals in an isolated atom.
5. The shapes of molecular orbitals are dependent on the shapes of atomic orbitals from which they are
formed.
6. Molecularorbitalsarearrangedinorderofincreasingenergyjustlikeatomicorbitals.
7. The number of molecular orbitals formed is equal to the number of atomic orbitals combining in bond
formation.
8. Likeatomicorbitals,thellingofelectronsinmolecularorbitalsisgovernedbythethreeprinciples
such Aufbau principle, Hund’s rule and Pauli’s exclusion principle.
The shape of molecular orbital formed in case of valence bond approach depicts that the identity of
atomic orbitals is not lost, whereas in case of molecular orbital approach the original identity of atomic
orbitals is completely lost.
The main difference between VBT and MOT is that the molecular orbitals formed in a compound are
quite different from the constituent atomic orbitals. When the atomic orbitals combine to form molecular
orbitals, they lose their identity and merge into each other completely.
Figure 1.12 Comparison of valence bond approach and molecular orbital approach.
C H A P T E R 1 Structure and Properties
+
–
+
–
p
y
p
y
Y
X
+
–
+
–
p
x
p
y
X
Y
1.9.1 Conditions of Formation of Molecular Orbitals
1. For the atomic orbitals to combine and form molecular orbitals, the following conditions must be
satised:
a. The combining atomic orbitals should be of a comparable energy. For example, 1s atomic orbitals
of two atoms can combine but 1s orbital of one atom cannot combine with 2s orbital of the other.
Similarly 2s orbitals cannot combine with 2p orbital. Such combinations are possible only for the
heteronuclear diatomic molecular of the type AB.
35
b. The combining atomic orbitals must overlap to a
large extent: greater the overlap, stable is the
molecule formed. The combining atomic orbitals
must have proper orientation so that they are able
to overlap to a considerable extent.
For instance, overlapping is not possible if s and p
orbitals with orientations shown in Fig. 1.13 (a) approach
each other.
REMEMBER
Symmetry of σ and π electron clouds
Always remember that, in case of σ bond, the electron
density around the internuclear axis is symmetrical
while in case of π electron density is more concentrated
above and below the internuclear axis and hence has
unsymmetrical distribution.
Figure 1.13 (a) py and py orbitals will combine as they have same symmetry about x axis. (b) px and
py orbitals will not combine as they do not have symmetry about x axis.
It may be mentioned here that orbitals that do not have the correct symmetry for combination (e.g. px
and py) are called nonbonding as there is no overall change in energy. Any stabilization that occurs from
overlapping + with + is neutralized by an equal amount of overlapping of + with –.
2. Thus on the basis of symmetry, the allowed and forbidden combinations of various atomic orbitals are
shown in Tables 1.1 and 1.2, assuming x axis as the internuclear axis. Some combinations have been
shown in Figs. 1.14 (a), (b), (c) and (d).
36
s
sp
Z
y
y
y
p–p
p
y
p
y
+
+
y
Sideways overlap
y
y
x
x
y
x
z
z
s s–s overlap
s–p overlap
p–p overlap
along the orbital axis
p Orbitalp Orbital
(a)
(b)
(c)
(d)
PHARMACEuTICAL ORgAnIC CHEMISTRy
Figure 1.14 (a) The s–s overlap. (b) The s–p overlap. (c) The p–p overlap along the orbital axis.
(d) The p–p sideways overlap.
First
orbital
Table 1.2 Allowed and forbidden combinations of atomic orbitals
Table 1.1 Allowed and forbidden atomic orbitals
orbital
Second orbital
(Allowed)
s s or p
p
x
p
z
p
y
First
s or p
p
p
Allowed
combinations
s p - s; s - p
p
x
p
y
p
z
px - p
py - p
s - pz, pz - pzpx - pz; py - p
x
x
z
y
z
x
y
Second orbital
(Forbidden)
py , p
z
py , p
z
s, py , p
x
s, py , p
x
Forbidden
combinations
s - px; s - p
px - py; px - p
px - py; px - p
Type of molecular
orbital formed
Type of molecular
orbital formed
z
z
z
z
σ, σ*
σ, σ*
π, π*
π, π*
σ, σ*
π, π*
π, π*
σ, σ*
C H A P T E R 1 Structure and Properties
MEMORY FOCUS
Valence bond theory was proposed by Heitler and London (1927) and modified by Pauling and Slater.1.
The postulates of valence bond theory are as follows: 2.
a. A covalent bond is formed by the overlapping of orbitals with unpaired electrons having opposite
spins.
b. The greater the extent of overlapping, greater is the strength of the bond.
c. Overlapping takes place only in the direction of maximum electron density of the orbital.
d. The overlapping of orbitals depends on the sizes and shapes of the orbitals.
e. The relative strength of overlapping of orbitals follows the order p–p > s–p > s–s.
The 3. s–s overlapping in H
The two 4. p orbitals can overlap along their axis leading to sigma bonds and lateral overlap leading to the
formation of π bonds. The overlapping along the axis is also known as
Lateral overlapping is also known as 5.
overlapping
.
molecule is much stronger because of small size of 1s orbitals.
2
axial overlapping
parallel overlapping, sideways overlapping
.
or
1.9.2 Differences Between Atomic and Molecular Orbitals
The main differences in atomic and molecular orbitals are given below:
37
conjugate
S. no. Atomic orbitals Molecular orbitals
1. An electron in an atomic orbital is under the
inuenceofonlyonenucleus.
2. Their existence is because of inherent property of
the atoms.
3. They are less stable than bonding molecular orbitals,
which are more stable than antibonding molecular
orbitals.
4. They have simple shapes. They have complex shapes.
5.
They are represented by s, p, d, f, etc. They are represented by σ, σ
Anelectroninamolecularorbitalisundertheinuence
of nuclei of two or more atoms of a molecule.
They are formed by the combination of atomic orbitals
of comparable energies.
They are less or more stable than atomic orbitals.
*,
π, π*.
1.10 FORMATION OF BONDING AND ANTIBONDING MOLECULAR
ORBITALS (LCAO METHOD)
An electron in an atom is described by a wave function, ψ, called an atomic orbital. Similarly, the behaviour
of an electron in a molecule is described by a molecular wave function called the molecular orbital. The
most convenient way of working out the wave functions for molecular orbitals is to adopt the method of
linear combination of atomic orbital (LCAO).
Quantum mechanics show that linear combination of two functions gives not one but two combinations
and hence two molecular orbitals, a bonding orbital and an antibonding orbital.
38
+
Wave AWave B
Wave AWave B
Resultant wave
Resultant wave
Ψ
Ψ
Ψ
Ψ
Ψ
Ψ
Ψ
Ψ
PHARMACEuTICAL ORgAnIC CHEMISTRy
1. Addition when two waves are in phase: If
ψ
and
A
ψ
are the atomic wave functions of the combining
B
atoms A and B, then the wave functions of orbitals can be obtained by the addition or subtraction of
the wave functions of the two atomic orbitals. The additive effect of the electron waves as a result of
the addition combination of atomic orbital wave functions when the two waves are in phase is shown in
Fig. 1.15(a).
2. Subtraction when two waves are not in phase: Similarly, the subtractive effect of the electron waves
as a result of the subtraction combination of atomic orbital wave functions when the two waves are out of
phase is shown in Fig. 1.15(b).
Thus the wave function of bonding orbital is given as:
ψ
=
ψ
+
ψ
b
(Bonding orbital stabilizes molecule) (1.1)
A
B
The wave function of antibonding orbital is given as:
ψ
=
ψ
-
ψ
a
(Antibonding orbital destabilizes molecule) (1.2)
A
B
Figure 1.15 (a) Additive combination of waves. (b) Subtractive combination of waves.
ψ
is called bonding molecular orbital and
b
Squaring Equation 1.1, we get the expression for the electron density (probability) of the bonding
ψ
is called antibonding molecular orbital.
a
molecular orbital:
ψ
It is evident that probability
2
ψAψ
, i.e. in the molecular orbital, there is greater electron density in the region between the nuclei than
B
2
= (
ψ
+
b
2
ψ
is greater than the sum of the probabilities
b
ψ
A
the two isolated atoms. In this molecular orbital, both the nuclei for the electrons is increased. As a result,
the energy of the molecule is lowered and this accounts for the stability of bond A-B. The orbital
therefore termed as bonding molecular orbital.
)2 =
B
2
ψ
2
+
ψ
+ 2
A
ψA ψ
B
B
ψ
2
2
+
ψ
A
by an amount
B
(1.3)
ψ
is
b
C H A P T E R 1 Structure and Properties
+
Crest
Nodal point
Trough
+
−
On the other hand, squaring Equation 1.2 gives the expression for the probability of the antibonding
molecular orbital:
ψ
Evidently, probability is
ψ
2
b
2
less than
b
= (
ψ
+
ψ
A
2
ψ
+
A
2
)2 =
ψ
+
A
B
2
ψ
by an amount 2
B
2
ψ
+ 2
ψA ψ
B
B
ψAψ
i.e. in this molecular orbital, there
B,
(1.4)
is less electron density in the region between the nuclei than the two isolated atoms. This results in greater
repulsion between the nuclei and hence the orbital
ψ
represents the state of higher energy as compared to
a
the energy of the individual atoms. Such an orbital obviously cannot lead to the formation of a chemical
bond and is, therefore, termed as an antibonding molecular orbital.
We have seen above that the combination of the two atomic orbitals forms two molecular orbitals, one
bonding (
ψ
) and the other antibonding (
b
ψ
). The bonding molecular orbital has lower energy than that of
a
atomic orbitals where as the antibonding molecular orbital has higher energy than that of atomic orbitals
from which it is formed as shown in Fig. 1.16.
ψ
a
39
ψ
b
Figure 1.16 Molecular orbitals formed by the combinations of two 1s atomic orbitals.
1.10.1 Bonding and Antibonding Molecular Orbitals in Terms of Wave Functions
We can interpret bonding and antibonding molecular orbitals by considering the interacting AOs as each
being a stationary wave, having a crest (+ sign) and a trough (– sign) as shown in Fig. 1.17. It may be
mentioned here that signs (+) and (–) simply determine the symmetry of the wave functions and have
nothing to do with the electrical charges.
Figure 1.17 Stationary wave showing crest (+) and trough (-).
40
PHARMACEuTICAL ORgAnIC CHEMISTRy
When the two functions interact in such a way that crest (+ sign) of one coincides with the crest (+ sign)
of the other, i.e. when the wave functions of the combining atomic orbitals are in phase and reinforce each
other, we got a resultant wave corresponding to a bonding molecular orbital. In other words, bonding
molecular orbitals is formed by the overlap of atomic orbitals with the same sign.
On the other hand, when the two wave functions interact so that the crest (+ sign) of one coincides with
the trough (– sign) of the other, i.e. when the wave functions of the combining atomic orbitals are out of
phase and cancel each other, we get a resultant wave corresponding to an antibonding molecular orbital is
formed by the combination of atomic orbitals with opposite signs.
1.10.2 Differences between Bonding and Antibonding Molecular Orbitals
The main characteristics and difference between bonding and antibonding molecular orbitals are as
follows:
S. no. Bonding molecular orbital Antibonding molecular orbitals
1. It is formed by the addition overlap of wave functions
of atomic orbitals:
2
ψ
= (
ψ
b
2. It has high electron density in the region between the
two nuclei and this accounts for the stability of the
bond.
3. It possesses lower energy than the atomic orbitals
from which it is formed.
4. It is formed when the lobes of combining atomic
orbitals have the same sign.
5. Electron presents in bonding MO contributes to
attraction and bonding MO is represented by σ or π.
2
+
ψ
)
A
B
It is formed by the subtraction overlap of wave functions
of atomic orbitals:
2
ψ
= (
ψ
a
The electron density is concentrated away from the
internuclearregion,i.e.theprobabilityofndingthe
electron in between the nuclei is negligible.
It possesses higher energy than the atomic orbitals from
which it is formed.
It is formed when the lobes of combining atomic orbitals
have opposite sign.
Electron present in antibonding MO contributes to
repulsion and antibonding MO is represented by σ* or π*.
2
–
ψ
)
A
A
1.11 COMBINATION OF ATOMIC ORBITALS—SIGMA (s) AND PI (p) MOLECULAR ORBITALS
IntheMOtheory,orbitalsareidentiedσ or π depending on the type of the symmetry of the molecular
orbital. A sigma (σ) molecular orbital is one that has cylindrical symmetry around the internuclear axis, i.e.
it does not show any change of sign on rotation through 180º about the axis (Fig. 1.18). Alternatively, it can
be said that a sigma molecular orbital has no nodal plane (in which the electron density is zero) along the
internuclear axis.
The bonding orbital is designated simply as σ orbital and antibonding as σ*.
Such a sigma (σ) orbital is also formed when any two p-atomic orbitals overlap in end-on (along their
axis) position (Fig. 1.19).
When atomic orbitals overlap laterally (side-to-side), the resulting molecular orbital is called a pi (p)
orbital. A π-type orbital does not possess cylindrical symmetry about the internuclear axis, i.e. if we rotate
this molecular orbitals through 180º, it will change sign. In contrast to σ-orbital, π-MO has a nodal plane
(zero electron density) along the internuclear axis as shown in Fig. 1.20.