2. Assignment 2
Submitted By:-
khalid mehmod
Roll No:-
9316
Submitted To:-
Dr.Prof Jawed Saif Sab
Department:-
Applied chemistry
Class:-
M.Sc.
Semester:-
2nd
GOVERNMENT COLLEGE UNIVERSITY FAISLABAD
3. 3Molecular orbital theory:-
Wave function of the electron in H atom at dissimilar energies
levels.
Quantum mechanics cannot tell the accurate orientation of
electron, only the possibility of finding of electron at many
points.
Where the place is shiner the place indicate a higher
probability of finding of electron and the area is less shine the
probability of finding electron is lesser.
Quantum mechanics in molecular bonding theory explain
many ways.
It explains the VBT and molecular MOT.
4. 4According the molecular orbital theory all the valance
electron in molecules are lying with all the nuclei concerned.
In other words, all the valance electrons have an influence on
the stability of the molecule.
Furthermore, MO theory considers that valance shall atomic
orbitals cease to exist when a molecule is formed.
They are replaced by a new set of energy level are with
corresponding new charge cloud division.
These new energy levels are a property of the molecule as
whole and are called consequently molecular orbital.
And electronic energy level in a molecule and the
corresponding charge cloud distribution in a space is called
molecular orbital.
5. 5Molecular orbital may be obtained by the linear combination
of atomic orbital to each atom in the molecule.
The wave function of the atomic orbital is combined
mathematically to produce wave function for their resulting
molecular orbital.
The molecular orbital is poly-centric and not mono-centric as
in the case of an atom.
The number of molecular orbital produced is equal to the
number original atomic orbitals combined.
The rules for filling the electron in these molecular orbitals
are the same as for filling the atomic orbitals.
6. 6Let us consider the formation simple homo-nuclear diatomic
molecule such as hydrogen molecule in which two identical
atoms are linked by an electron pair.
Although the atoms are identical but it will be convenient to
distinguish the two atoms by writing HA and HB. Each
hydrogen atom has a one electron is 1S energy levels. Let the
wave function for explaining the two 1S atomic orbital be ΨA
and ΨB for hydrogen atoms HA and HB.
The effective overlapping of the wave function ΨA and ΨB
will take place only if
(1) the orbitals have similar energy state
(2) the orbitals overlap to a considerable extent
(3) orbitals have the same arrangement.
7. 7All these conditions are fulfilled by atomic orbitals of both the H
atom.
The molecular orbital wave function Ψ will be obtained by the
linear combination the atomic orbital wave function ΨA and ΨB.
Ψ=CAΨA (1s) CBΨB(1s).....................4
Where CA and CB are mixing coefficients, which may be
replaced by single coefficient , thus
Ψ= ΨA (1s) ΨB(1s) ………………………………7
⋏ lambda gives the relative proportions of ΨA (1s) and ΨB (1s)
in the molecular orbital in the ratio of 12: ⋏ 2. Since both HA
and HB are identical thus atomic orbital must make equal
contribution to the molecular orbitals so that ⋏ 2 = 1.
8. 8
Thus, by substituting the value of ⋏ in equation 7 two possible
molecular orbitals wave functions are obtained one from the
addition and other from subtraction.
Ψ bonding = ΨA (1s) +ΨB(1s)
………………………………………….8
Ψ anti-bonding = ΨA(1s) -ΨB(1s)
…………………………………….9
Since the possibility of finding an electron in a specific space
is expressed by, Ψ2 squaring of equation 8 and 9 and will
give the expression for the probability of finding and electron
of any position with in the molecular orbitals and from this
expression the corresponding boundary surfaces and also
energy levels
ΨB2 = ΨA2 (1s)2 +ΨB2 (1s)2 +2Ψa (1s) ΨB (1s)
…………………10
ΨA2 = ΨA2 (1s)2 +ΨB2(1s)2 - 2ΨA (1s) ΨB (1s)
………………….11
9. 9
The boundary surfaces and the relative energies of two MO
which are formed by combining two 1S and AO.
ΨB molecular orbital is formed by the addition of the two 1S
orbitals when atomic orbitals of the same symbol overlap
along the inter-nuclear axis.
Such overlap leads to support of the wave function in the
region between the two nuclei and ΨB2 the possibility of
presence the electron is large between the nuclei, as a result
a strong bond between the atoms.
The bonding molecular orbital is in a lower energy state then
the average energies of the combining atomic orbitals.
The bonding molecular orbitals of the type which are formed
from 1s atomic orbitals are donated as sigma 1S.
10. 10
Ψa is formed by the subtraction of the two 1S orbitals when
orbitals of opposite symbol overlap the wave function
interfere with each other in the region between the two
nuclei and a node is produced.
At the node Ψ= 0 and on either side of the node is small
therefore, Ψa is also small in the region between the nuclei.
The attractive forces will be lesser than the repulsive forces
and the therefore anti-bonding molecular energy level is at a
state of higher energy then the average energies of the
component atomic orbitals.
The anti-bonding molecular orbitals of this type is donated
by sigma star (1s). both bonding and anti-bonding molecular
orbitals have cylindrical symmetry about inter-nuclear axis
therefore these orbitals are called sigma orbitals and the
bonds are called sigma b
11. 11
HOMO-NUCLEAR DIATOMIC
MOLECULES:-
In the second period diatomic we also have to allow for the
overlap of 2p orbitals. The combination of two p orbitals
produces different results depending on which p orbital are
used.
If the x axis is the inter-nuclear axis then two 2px orbitals
which overlap properly is they approach each other end to
end to form two orbitals one sigma 2p bonding orbitals with
electronic charge build up between the nuclei.
The bonding and anti-bonding MO can be described in terms
of wave functions ΨB and ΨA respectively,
ΨB = ΨA (2px) + ΨB (2px) termed as sigma 2px.
ΨA = ΨA (2px) – ΨB (2px) termed as sigma star 2px.
Thus, ΨB is a bonding MO and ΨA is anti-bonding MO.
12. 12
Hetero-nuclear diatomic molecules:-
Diatomic molecules have different atoms are called hetero-
nuclear. The difference in electronegativity in these molecules
causes the MO energy spacing to be different from those in
homo nuclear diatomic.
The general conditions for the most effective combination of
atomic orbitals in a molecule or The AO involved should (1)
have similar energies (2) overlap as much as possible and have
the same symmetry with respect to the x axis.
In a hetero nuclear molecule AB, the choice AO for combination
is guided by information from atomic spectroscopy.
The molecular wave function Ψ by the linear combination of 1s
orbitals on two different atoms can be written as
Ψ = CA 1Sa + CB 1Sb.
13. 13Where the weighting coefficient are unequal. The electron
divisions is given by the square of this wave function is .........
Ψ2 = C2 (1sa)2 + C2B (1sb)2 + 2CACB(1sa) (1sb)
If C2B is greater than C2A there is greater probability of
finding the electron in the orbital of atom B then in that of
atom A.
Let us now apply the MO theory to explain the bonding in
hetero-nuclear diatomic molecules such as HF.
The electronic configuration of hydrogen and fluorine atoms
is. H = 1s1 F = 1s2,2s2,2p5 The combination of H 1s orbitals
with the inner shell orbital 1s or even 2s orbitals of F can be
ruled out because the energies of these orbitals of F are
much too low.
14. 14
The energies of atomic orbitals combining together must be
same in magnitude or the atomic orbital should have
comparable energies.
Thus, in case of the formation of a homo-nuclear diatomic
molecules A2 type the 1sa the atomic orbitals of the atoms
Aa will not combine with the 2Sa atomic orbital of another
atom Ab of the same element. Where Aa add A|B are the
two atoms of molecules A2.
Since their energies are not equal.
Similarly, since the energy difference between 2s and 2p
atomic orbitals is too great, there will also not combine.
But in case of the formation of hetero-nuclear diatomic
molecule of AB type such combination may be expected.
15. 15The charge clouds of the atomic orbitals must overlap one and
other as much as possible if there are combine together to
form the molecular orbital this condition is referred to as the
principle of maximum overlap.
The atomic orbitals should have same symmetry about the
molecular axis. This condition is known as symmetry condition
of atomic orbital.
On the basis of this symmetry condition it is noted that some
of the atomic orbitals which have comparable energies do
overlap but cannot combine to give molecular orbitals thus
molecular orbital cannot be to give molecular orbitals thus
molecular orbital cannot be formed by the overlap of S atomic
orbitals of atom A and 1p atomic orbital of atom B
perpendicular to the molecular axis since the molecular axis is
the z axis.
16. 16
FOR POLY ATOMIC MOLECULES:-
Molecular orbital theory can also be used to develop bonding
scheme for poly-atomic molecules.
However, energy diagrams and the orbital shapes become
more and more complex.
In general, molecular orbital in a poly-atomic system extends
overall the nuclei in a molecule. Indeed, MOT forms the basis
for most of the quantitative investigations of the properties of
large molecules.
Note that only sigma molecular orbital can be found because
H atom have only their 1s orbitals to use in bonding.
These orbitals are themselves of sigma character with
respect to any axis that passes through the nucleus, and
therefore, they can contribute only to sigma molecular
orbitals.
17. 17
In each bonding molecular orbital electron density is large
and continues between adjacent atoms, while in the anti-
bonding molecular orbitals there is anode between each
adjacent pair of nuclei.
Electrons in molecular orbital are de-localized over the
whole extent of the molecular orbital.
The molecular orbital treatment of the bonding in BeH2 can
be expressed in terms of energy level diagram.
The assumptions of the two theories are quite different. VBT
consider that atoms exist with in molecules, and that the
structure of a molecule can be interpreted in terms of its
constituent atoms and the bonds between them.
18. 18Whereas, MOT assumes that the atomic orbital of original
unbounded atoms become replace by a new set of energy
levels called molecular orbital and these orbitals determine
the property of the resulting molecule.
Excited states in molecule can be easily described by MOT.
MOT accounts for the observed para-magnetic character of
O2 molecule but VBT cannot explain the para-magnetic
behavior of O2.
MOT accounts quite nicely for one electron bonds, which are
known to exist. anywhere in the molecule quantum physical
state permit electron to move down the predominance of an
changeable large number of nuclei, as long as there are in
Eigen states allowed by many quantum rules.
19. 19
Thus, when high energy electron with the essential quantity
of energy mean frequency light or other means, electrons
can transition to higher molecular orbitals.
For example, in the simple H diatomic molecule, promotion
of a one electron from a bonding orbital to an anti-bonding
orbital can take place, under Ultra violet radiations.
This promotion weakens the bond between the two H atoms
and can lead to light dissociation the splitting of a chemical
bond due absorption of light.
However in molecular orbital theory some molecular
orbitals may keep electrons that are more localized between
particular pairs of molecular atom, other orbitals may hold
electrons that are disperse more uniformly over the
molecule.
20. 20
IMPORTANCE OF MOT:-
For simple di-atomic molecules, we can make rough estimates of
relatives energies of molecular orbitals by following a few
rules.
However, for triatomic molecules and above, we can only
calculate the energies and shapes of molecular orbitals by solving
the Schrodinger equation for the whole molecule.
This is extremely complicated so we have to rely on computers
and experimental data.
For now, it is enough to understand thebasics of molecular
orbital theory.
Though it is quite complex, MO theory explains many phenomena
that valence bond theory cannot explain.
21. 21Molecular Modeling:-
Using a mixture of VB theory,MO theory and classical
Newtonian mechanics chemists often make computaDonal models
of molecules.
These models areused for calculations that help chemists to
designnew molecules and understand interesting properties of
molecules alrea synthesised.
Molecular mechanics calculations use valence bond theory to fix
thepossible shapes of a moleculeand then use classical
Newtonian mechanics to see how the molecule can twist
and vibrate.
They are very fast and easy to set upso they are best for simple
conformation modeling, where we simply want to know what
shapes a molecule is most likely to take.
22. 22
Ab initio calculations calculate everything beginning from the
Schrodinger Equation.
They take a lot of computational time and are a little more difficult to
set.
Chemists usually use this kind of calculation when they want to
know details of molecular orbitals.
Semi-empirical calculations use some data from experiments and
calculate other parts using the Schrodinger equation.
They are more accurate than molecular mechanics but don’t take
as long as ab initio calculations.
23. 23
Metals, Insulators and Semi-Conductors:-
Band theory helps us understand thedifferences between electrical
conductors, semi conductors and insulators.
For electrons to move through a lattice, there must be a
convenient empty orbital for them to move into.
Ifa band is only partially filled, an electron at the to of the filled band
can move into an empty orbital at an energy level immediately above
and travel through the lattice for a tiny amount of extra energy.
Ifan empty band overlaps with a full band, electrons will transfer into
the empty band and create spacefor electrons to travel.
Insulators, on the other hand, have a large energy gap between the
top of a full band and the bottom of an empty band. It therefore takes a
lot of energy move electrons into empty orbitals and insulators do not
normally conduct electricity.
24. 24
Semi-conductors have a
smaller energy gap between
thetopof thefull band and
thebottom of the empty band,
meaning electrons can enter
an empty orbital with a little
extra energy.
This explains why semi-conductors conduct
electricity better when energy
(asheat, light or electricity) is
added to thelauce.
