ENGINEERING CHEMISTRY DEPARTMENT OF S& · Web viewAtoms form bonds by sharing electrons. Atoms can...

ENGINEERING CHEMISTRY DEPARTMENT OF S&H

UNIT - IMOLECULAR STRUCTURE AND THEORIES OF BONDING

Introduction:Atoms form bonds by sharing electrons. Atoms can share two, four, or six electrons, forming single, double, and triple bonds respectively. Although it is impossible to determine the exact position of an electron, it is possible to calculate the probability that one will find the electron at any point around the nucleus using the Schrödinger Equation. This equation can help predict and determine the energy and spatial distribution of the electron, as well as the shape of each orbital.Orbital: An Orbital is a three dimensional space around nucleus where the probability of finding an electron is high. They represent the probability of finding an electron in any one place. They correspond to different energies. So an electron in an orbital has definite energy. Each orbital is denoted by a number and a letter. The number denotes the energy level of the electron in the orbital. Thus 1 refers to the energy level closest to the nucleus; 2 refers to the next energy level further out, and so on. The letter refers to the shape of the orbital. The letters go in the order s, p, d, f, g, h, i, j, etc.Atomic Orbitals: Atomic orbitals are regions of space around the nucleus of an atom where an electron is likely to be found. Atomic orbitals allow atoms to make covalent bonds. An atomic orbital can have a maximum of two electrons. Atomic orbitals are labelled as s, p, d, and f sublevels.s OrbitalsThe s orbital is spherical and hold a maximum of two electrons. It has one sub-energy level. The order of size is 1s < 2s < 3s < …, as shown below.

p Orbitals:The p orbital is dumbbell shaped and can hold up to six electrons. It has three sub energy levels. These are given the symbols px, py and pz. The p orbitals at the second energy level are called 2px, 2py and 2pz. There are similar orbitals at subsequent levels: 3px, 3py, 3pz, 4px, 4py, 4pz and so on.

ENGINEERING CHEMISTRYDEPARTMENT OF HUMANITIES & SCIENCES ©MRCET (EAMCET CODE: MLRD) d ORBITALSThe d and f orbitals have more complex shapes. The d level has five sub-energy groups and holds up to 10 electrons, The five 3d orbitals are called 3dxy, 3dxz, 3dyz, 3dx² - y², 3dz²Molecular orbital (MO): Atoms join to form molecules. When two atoms move closer together to form a molecule, atomic orbitals overlap and combine to become molecular orbitals.

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Molecular orbital (MO): Atoms join to form molecules. When two atoms move closer together to form a molecule, atomic orbitals overlap and combine to become molecular orbitals. Molecular orbitals are regions around molecules where electrons are most likely to be found. The number of newly formed molecular orbitals is equal to the number of combined atomic orbitals. The molecular orbital surrounds the two nuclei of the atoms, and electrons can move around both nuclei. Similar to atomic orbitals, molecular orbitals maximally contain 2 electrons, which have opposite spins. Molecular orbitals are of two types, bonding molecular orbitals and antibonding molecular orbitals. Bonding molecular orbitals contain electrons in the ground state and antibonding molecular orbitals contain no electrons in the ground state. Electrons may occupy in the antibonding orbitals if the molecule is in the excited state.DIFFERENCES BETWEEN ATOMIC AND MOLECULAR ORBITAL

Atomic orbital Molecular orbitalAtomic orbital is the region having the

highest probability of finding an electron inan atom

Molecular orbital is the region having thehighest probability of finding an electron of a

moleculeAtomic orbitals are inherent property of an

atom.Formed by the electron cloud around the

Atom

Molecular orbitals are formed bycombination of atomic orbitals that have

nearly the same energy

The shape is determined by the type ofatomic orbital(s,p,d or f)

The shape is determined by the shapes ofAtomic orbitals that make the molecule. They

have complex shapes

Schrodinger equation is used Linear combination of atomic orbitals(LCAO) is used

Monocentric as it is found around a singleReaction

Polycentric as it is found around differentnuclei

Molecular Orbital TheoryIntroductionThe Molecular Orbital Theory, initially developed by Robert S. Mullikan, incorporates the wave like characteristics of electrons in describing bonding behavior. In Molecular Orbital Theory, the bonding between atoms is described as a combination of their atomic orbitals. While the Valence Bond Theory and Lewis Structures sufficiently explain simple models, the Molecular Orbital Theory provides answers to more



complex questions. In the Molecular Orbital Theory, the electrons are delocalized. Electrons are considered delocalized when they are not assigned to a particular atom or bond (as in the case with Lewis Structures). Instead, the electrons are “smeared out” across the molecule. The Molecular Orbital Theory allows one to predict the distribution of electrons in a molecule which in turn can help predict molecular properties such as shape, magnetism, and Bond Order.Valence Bond Theory fails to answer certain questions like Why He2 molecule does not exist and why O2 is paramagnetic Therefore in 1932 F. Hood and RS. Mulliken came up with theory known as Molecular Orbital Theory to explain questions like above. According to Molecular Orbital Theory individual atoms combine to form molecular orbitals, as the electrons of an atom are present in various atomic orbitals and are associated with several nuclei.Molecular orbital (MO) theory is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule.ENGINEERING CHEMISTRYDEPARTMENT OF HUMANITIES & SCIENCES ©MRCET (EAMCET CODE: MLRD) Postulates of MOT are:

Two atoms come together, interact and forms a bond. All the atomic orbitals on either nuclei mix together to form a new orbital called molecular orbital.

The molecular orbitals are formed by mixing of the atomic orbitals of same energy level and symmetry.

After formation of molecular orbital, the atomic orbitals lose their identity. Each and every electron in the molecular orbital belongs to all the nuclei of the molecules. Atoms have atomic orbitals with one nuclei and Molecules have molecular orbitals with n nuclei.

Thus, atoms are monocentric while molecules are polycentric. The number of molecular orbitals formed is equal to the atomic orbitals mixing. Molecular orbitals can be bonding, anti-bonding, and non-bonding orbitals. Bonding molecular orbitals are lower in energy than the corresponding anti-bonding orbitals. Each molecular orbital is described by a wave function Ψ, which in turn is associated with a set of

quantum number. Electrons fill up these orbitals in the same way as atomic orbitals in accordance to the 3 principles

(Aufbau, Hunds and Pauli Principle). The Aufbau principle states that orbitals are filled with the lowest energy first. The Pauli Exclusion Principle states that the maximum number of electrons occupying an orbital is

two, with opposite spins. Hund’s rule states that when there are several MOs with equal energy, the electrons occupy the MOs

one at a time before two occupy the same MO.Electrons may be considered either of particle or of wave nature. Therefore, an electron in an atom may be described as occupying an atomic orbital, or by a wave function Ψ, which are solution to the Schrodinger wave equation. Wave function is a mathematical function related to probability of finding the particle in a particular region of space.

Electrons in a molecule are said to occupy molecular orbitals. The wave function of a molecular orbital may be obtained by one of two methods:

1. Linear Combination of Atomic Orbitals (LCAO).2. United Atom Method.Linear Combination of Atomic Orbitals (LCAO)As per this method the formation of orbitals is because of Linear Combination (addition or subtraction) of atomic orbitals which combine to form molecule. Consider two atoms A and B which have atomic orbitals described by the wave functions ΨA and ΨB .If electron cloud of these two atoms overlap, then the wave function for the molecule can be obtained by a linear combination of the atomic orbitals ΨA and ΨB i.e. by subtraction or addition of wave functions of atomic orbitalsΨMO= ΨA + ΨB



The above equation forms two molecular orbitalsENGINEERING CHEMISTRYDEPARTMENT OF HUMANITIES & SCIENCES ©MRCET (EAMCET CODE: MLRD) Bonding Molecular OrbitalsWhen addition of wave function takes place, the type of molecular orbitals formed are called Bonding Molecular orbitals and is represented by ΨMO = ΨA + ΨB.

They have lower energy than atomic orbitals involved. It is similar to constructive interference occurring in phase because of which electron probability density increases resulting in formation of bonding orbital. Molecular orbital formed by addition of overlapping of two s orbitals shown in Figure 1. It is represented by Anti-Bonding Molecular OrbitalsWhen molecular orbital is formed by subtraction of wave function, the type of molecular orbitals formed are called Antibonding Molecular Orbitals and is represented by ΨMO = ΨA -ΨB.They have higher energy than atomic orbitals. It is similar to destructive interference occurring out of phase resulting in formation of antibonding orbitals. Molecular Orbital formed by subtraction of overlapping of two s orbitals are shown in figure no. 2. It is represented by s* [(*) is used to represent antibonding molecular orbital) called Sigma Antibonding.

Therefore, Combination of two atomic orbitals results in formation of two molecular orbitals, bonding molecular orbital (BMO) whereas other is anti-bonding molecular orbital (ABMO). BMO has lower energy and hence greater stability than ABMO. First BMO are filled then ABMO starts filling because BMO has lower energy than that of ABMO.Formation of molecular orbitals occurs by the combination of atomic orbitals of proportional symmetry and comparable energy. Therefore, a molecular orbital is polycentric and atomic orbital is monocentric. Number of molecular orbitals formed is equal to the number of atomic orbitals.

Relative Energies of Molecular OrbitalsBonding Molecular Orbitals (BMO) - Energy of Bonding Molecular Orbitals is less than that of Anti Bonding Molecular Orbitals because the attraction of both the nuclei for both the electron (of the combining atom) is increased.ENGINEERING CHEMISTRYDPARTMENT OF HUMANITIES & SCIENCES ©MRCET (EAMCET CODE: MLRD) Anti-Bonding Molecular Orbitals (ABMO) - Energy of Anti Bonding Molecular Orbitals is higher than Bonding Molecular Orbitals because the electrons move away from the nuclei and are in repulsive state. The Energies of Bonding Molecular Orbitals and Anti-Bonding Molecular Orbitals are shown inFig 2 :



FIG:2Molecular orbitals of diatomic molecules:Molecular Orbitals for diatomic Molecules formed from a Linear Combination of Atomic Orbitals is shown below:

ENGINEERING CHEMISTRYDEPARTMENT OF HUMANITIES & SCIENCES ©MRCET (EAMCET CODE: MLRD)

Filling Electrons in MO DiagramsThe next step in constructing an MO diagram is filling the newly formed molecular orbitalsWith electrons. Three general rules apply:

The Aufbau principle states that orbitals are filled starting with the lowest energy The Pauli Exclusion Principle states that the maximum number of electrons. occupying

an orbital is two, with opposite spins. Hund’s rule states that when there are several MOs with equal energy, and the

Electrons occupy the MOs one at a time before two occupy the same MO.The filled MO that is highest in energy is called the Highest Occupied Molecular Orbital, or HOMO; the empty MO just above it is the Lowest Unoccupied Molecular Orbital, or LUMO. The electrons in the bonding MOs are called bonding electrons, and any electrons in the antibonding orbital are called antibonding electrons. The reduction these electrons’ energy is the driving force for chemical bond formation.Energy Level DiagramThe factors upon which relative energies of molecular orbitals depend are:(i) Energies of the Atomic orbitals combining to form Molecular Orbitals.(ii) The extent of overlapping between the atomic orbitals. The greater the overlap, the more the bonding orbital is lowered and the anti-bonding orbital is raised in energy relative to AOs



1s Atomic Orbitals (AOs) of two atoms form two Molecular Orbitals (MOs) designated as s1s and s *1s.The 2s and 2p orbitals (eight AOs of two atoms) form four bonding MOs and four anti-bonding MOs as:Bonding MOs: σ 2s, σ 2pz, π 2px, π 2pyAnti – Bonding MO: σ *2s, σ *2pz, π *2px, π *2pyThe order of increasing energy of molecular orbitals obtained by combination of 1s, 2s and 2p orbitals of two atoms is →σ1s, σ *1s, σ 2s, σ *2s, σ 2pz, π 2px = π 2py, π *2px= π *2py, σ *2pz(Energy Increases from left to right)Bond order:It may be defined as the half of difference between the number of electrons present in thebonding orbitals and the antibonding orbitals that is,

Bond order (B.O.) = (No. of electrons in BMO - No. of electrons in ABMO)/ 2

Those with positive bonding order are considered stable molecule while those with negativebond order or zero bond order are unstable molecule.ENGINEERING CHEMISTRNT OF HUMANITIES & SCIENCES ©MRCET (EAMCET CODE: MLRD) Magnetic Behavior: If all the molecular orbitals in species are spin paired, the substance isdiamagnetic. But if one or more molecular orbitals are singly occupied it is paramagnetic.

Molecular Orbital Energy Level Diagrams of N2, O2 and F2

Nitrogen Molecule N2: Nitrogen atom has seven electrons. In the formation of N2molecule, a total of 14

electrons are arranged in molecular orbitals as:

π22py

KK σ22s σ*2

2s ,σ22pz .

π22px

Bond order = 12 (10-4) = 3.

Thus nitrogen molecule contains a triple bond and is highly stable therefore nitrogen exist as N2 molecule.

Moreover all the electrons are paired therefore it is diamagnetic.

For N2 and lower molecules →

σ 1s, σ *1s, σ 2s, σ *2s, [π 2px = π 2py], σ 2px [π *2px= π *2py], σ*2pz



Oxygen Molecule O2: Each oxygen atom has 6 valence electrons. Assuming that inner orbitals do not

participate in bonding, altogether 12 electrons have to be accommodated in molecular orbitals. The

molecular electronic configuration will be:

π22py π*1

2py

O2= KK σ22s σ*2

2sσ22pz

π22px π*1

2px

In the case of oxygen, the difference between the energies of 2s and 2pz atomic orbitals is quite large (1430

kJ/mol) and hence interaction between these orbitals and subsequent changes in order of energies of

molecular orbitals do not take place. Thus, the usual order of energies as given in section 4of energies of

molecular orbitals do not take place. Thus, the usual order of energies as given in section 4.3 is followed. As

a evident from the energy level diagram that two unpaired electrons are present, thus the molecule is

paramagnetic. This is one of the great successes of molecular orbital theory, as it could predict the

paramagnetism of oxygen molecule which could not be explained on the basis of valence bond theory.

Bond order = (10-6)/2 = 2. Thus a double bond is present in the molecule.

For O2 and higher molecules →

σ1s, σ *1s, σ 2s, σ *2s, σ 2pz, [π2px = π2py], [π*2px= π*2py], σ *2pz



Flourine Molecule F2: Flourine atom has 7 electrons in the outermost shell and hence 14 electrons are

arranged in the molecular orbital as:

π22py π*2

2py

=KK σ22s σ*2

2sσ22pz

π22px π*2

2px

Bond Order = 12(8 - 6) = 1

The F-F bond is rather weak. Since there are no unpaired electrons, the molecule is diamagnetic.

π Molecular Orbitals of Butadiene and Benzene

Butadiene

Molecular Orbitals of 1,3-Butadiene

1,3-Butadiene contains two double bonds that are conjugated.

It is "built" from 4 sp2 hybridsed C atoms, each contributing a p atomic orbital containing 1 electron.

An alternative way to consider "building" the π molecular orbitals is by combining the π molecular

orbitals of two ethene molecules.

This requires that we make an in-phase and an out-of-phase combination for both the π and π* of

ethene.

Either way, we end up with the same set of 4 π molecular orbitals.



Notice how the number of nodes and the number of anti-bonding interactions increases as you go up

the diagram above.

The diagram to the right shows the relative

energies of the π molecular orbitals of 1,3-

butadiene (derived from ethene) and the

electron configuration.

The horizontal centre line denotes the energy

of a C atomic p orbital. Orbitals below that line

are bonding those above are anti-bonding.

We now have 4 electrons to arrange, 1 from

each of the original atomic p orbitals. These

are all paired in the two stabilised pi bonding

orbitals, π1 and π2. The highest occupied

molecular orbital or HOMO is π2 in 1,3-

butadiene (or any simple conjugated diene).

In contrast, the anti-bonding π* orbitals contain

no electrons. The lowest unoccupied orbital

or LUMO is π3 in 1,3-butadiene (or any

simple conjugated diene).

The relative energies of these orbitals can be accounted for by counting the number of bonding and anti-

bonding interactions in each:

π1 has bonding interactions between C1-C2, C2-C3 and C3-C4



oOverall = 3 bonding interactions

π2 has bonding interactions between C1-C2 and C3-C4 but anti-bonding between C2-C3

oOverall = 1 bonding interaction

π3 has bonding interactions between C2-C3 but anti-bonding between C1-C2 and C3-C4

oOverall = 1 anti-bonding interaction

π4 has anti-bonding interactions between C1-C2, C2-C3 and C3-C4

oOverall = 3 anti-bonding interactions

BenzeneA molecular orbital description of benzene provides a more satisfying and more general treatment of

"aromaticity". We know that benzene has a planar hexagonal structure in which all the carbon atoms are

sp2 hybridized, and all the carbon-carbon bonds are equal in length. As shown below, the remaining cyclic

array of six p-orbitals ( one on each carbon) overlap to generate six molecular orbitals, three bonding and

three antibonding. The plus and minus signs shown in the diagram do not represent electrostatic charge, but

refer to phase signs in the equations that describe these orbitals (in the diagram the phases are also color

coded). When the phases correspond, the orbitals overlap to generate a common region of like phase, with

those orbitals having the greatest overlap (e.g. π1) being lowest in energy. The remaining carbon valence

electrons then occupy these molecular orbitals in pairs, resulting in a fully occupied (6 electrons) set of

bonding molecular orbitals. It is this completely filled set of bonding orbitals, or closed shell that gives the

benzene ring its thermodynamic and chemical stability, just as a filled valence shell octet confers stability on

the inert gases.

The Molecular Orbitals of Benzene

Crystal Field Theory (CFT)



Crystal field theory is very much different from valence bond theory. According to valence bond theory,

bonding between the metal ion and the ligands is purely covalent, while according to crystal field theory, the

interaction between the metal ion and ligands, is purely electrostatic, i.e metal-ligand bonds are 100% ionic.

Crystal field theory (CFT) describes the breaking of orbital degeneracy in transition metal complexes due to

the presence of ligands. CFT qualitatively describes the strength of the metal-ligand bonds. Based on the

strength of the metal-ligand bonds, the energy of the system is altered. This may lead to a change

in magnetic properties as well as color. This theory was developed by Hans Bethe and John Hasbrouck van

Vleck.

Crystal Field Theory was developed to describe important properties of complexes (magnetism, absorption

spectra, oxidation states, coordination,).

Salient features of crystal-field theory are:

1. The transition metal ion is surrounded by the ligands with lone pairs of electrons and the complex is a

combination of central ion surrounded by other ions or molecules or dipoles i.e. ligands.

2. All types of ligands are regarded as point charges.

3. The ionic ligands, like F-, Cl-, CN-, etc., are regarded as negative point charges, or point charges and the

neutral ligands, like H2O, NH3, etc., are regarded as point dipoles or just dipoles. (CFT regards neutral

ligands as dipolar) If the ligand is neutral, the negative end of this ligand dipole is oriented towards the

metal atom.

4. The interactions between the metal ion and the negative ends of anion (or ion dipoles) are purely

electrostatic, i.e. the bond between the metal and ligand is considered 100 percent ionic.

5. The ligands surrounding the metal ion produce electrical field and this electrical field influences the

energies of the orbitals of central metal ion, particularly d-orbitals.

6. In the case of free metal ion, all the five d-orbitals have the same energy. Such orbitals having the same

energies are called degenerate orbitals.

Crystal field splitting of d orbitals:

In a free transition metal or ion, there are five d-orbitals which are dxy, dyz , dzx , dz^2 and d(x2 -y2) . These

are divided into 2 sets based on their orientation in space:

t2g : The 3d-orbitals (dxy, dyz and dzx ) which orient in the regions between the coordinate axes .

These are non-axial orbitals. t2g are three fold degenerate.

eg : the other two orbitals (dz2 and d(x2 -y2) ) which orient along the axis . These are two fold

degenerate and also known as axial orbitals.


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In an isolated gaseous atom, all the five d orbital are degenerate. (They have same energy).

On the approach of the ligands in a complex, the electrons in the d orbital of the central ion are repelled by

the lone pairs of the ligands. This repulsion will raise the energy level of the d orbitals. All the ligands

approaching the energy of each orbital will increase by the same amount.

In other words, they will remain degenerate. Since d-orbitals differ in their orientation, those orbitals lying

in the direction of the ligands is raised to a larger extent than the others. So, five degenerate d-orbitals will

split into two sets, having different amount of energies. This splitting of five degenerate d-orbitals of the

metal ion under the influence of approaching ligands, into two sets of orbitals having different energies is

called as Crystal- field splitting.

This splitting is affected by the following factors:

1. Nature of the ligands. The stronger the ligand, the greater is the splitting.

2. Oxidation state of the central metal ion. A higher oxidation state leads to larger splitting.

3. Size of d orbitals (i.e., transition series).

4. Geometry of the complex.

5. Nature of the metal ion

6. Arrangement of the ligands around the metal ion

Crystal Field Splitting in Octahedral Complexes

The octahedral arrangement of six ligands surrounding the central metal ion is as shown in the figure.

In an octahedral complex, the metal ion is at the centre and the ligands are at the six corners. In the figure,

the directions x, y and z point to the three adjacent corners of the octahedran. The lobes of the eg orbitals

(dx2-y2 and dz2) point along the x, y and z axis while the lobes of the t2g orbitals (dxy, dzx and dyz) point in



between the axes. As a result, the approach of six ligands along the x, y z, -x,-y and –z directions will

increase the energy of dx2-y2 and dz2 orbitals (which point towards the ligands) much more than that it

increases the energy of dxy, dzx and dyz orbitals ( which point in between the metal-ligand bond axis).

The approach of the ligands is considered as a two-step process. In the first step, it is assumed that the

ligands approach the metal ion spherically, i.e. at an equal distance from each of the d-orbitals. At this stage

all the d- orbitals are raised in energy by the same amount (The five d-orbitals remain degenerate0.

In the second step the spherical field changes to octahedral field leading to splitting of orbitals.

The energy difference between t2g and eg orbitals is known as crystal field splitting and it is denoted by the

symbol Δo or 10Dq

Thus, under the influence of an octahedral field, the d orbitals split into triply degenerate orbitals with less

energy and another as doubly degenerate orbitals with higher energy. The main energy level between these

two sets of orbitals is taken as zero, which is called bari centre. The splitting between these two

Fig: Splitting of d-orbitals in an octahedral complex

orbitals is called crystal field splitting. The magnitude of stabilization will be 0.4 Δo and the magnitude of

destabilization will be 0.6 Δo.

Crystal Field Splitting in Tetrahedral Complexes:The tetrahedral arrangement of four ligands surrounding the metal ions is as shown in the figure.

A regular tetrahedron is a cube. One atom is at the centre of the cube and four of the eight corners of the

cube are occupied by ligands. The directions x, y and z point to the face centres. The dx 2-y2 and dz2 orbitals

point along the x, y and z directions and dxy, dzx and dyz orbitals point in between x, y and z directions.



The direction of approach of ligands does not coincide exactly with either the e or t 2 orbitals. The t2 orbitals

are pointing close to the direction in which the e orbitals are lying in between the ligands. As a result, the

energy of t2 orbitals increases compared to the energy of e orbitals. Thus, d orbitals again split into two sets-

triply degenerate t2 of higher energy and doubly degenerate e orbitals of lower energy. That is, t2 orbitals

are raised by 0.4 Δt in energy and the e orbitals are stabilized by 0.6 Δt in energy.

The energy difference between the two sets of orbitals (Δt) will be about half the magnitude of that in an

octahedral complex (Δo).0

Square Planar Complexesd-Orbital Splitting in Square Planar Coordination.

Square planar coordination can be imagined to result when two ligands on the z-axis of an

octahedron are removed from the complex, leaving only the ligands in the x-y plane. As the z-

ligands move away, the ligands in the square plane move a little closer to the metal.

The orbital splitting diagram for square planar coordination can thus be derived from the octahedral

diagram.

As ligands move away along the z-axis, d-orbitals with a z-component will fall in energy.

The dz2 orbital falls the most, as its electrons are concentrated in lobes along the z-axis.

The dxz and dyz orbitals also drop in energy, but not as much.



Conversely, the dx2-y2 and the dxy orbitals increase in energy. The splitting diagram for square

planar complexes is more complex than for octahedral and tetrahedral complexes, and is shown

below with the relative energies of each orbital.

Crystal Field Stabilization Energy:

The crystal field stabilization energy (CFSE) is the stability that results from placing a transition metal ion in

the crystal field generated by a set of ligands. It arises due to the fact that when the d-orbitals are split in a

ligand field (as described above), some of them become lower in energy than before with respect to a

spherical field known as the bari centre in which all five d-orbitals are degenerate. For example, in an

octahedral case, the t2g set becomes lower in energy than the orbitals in the bari centre. Owing to the splitting

of the d orbitals in a complex, the system gains an extra stability due to the rearrangement of the d electrons

filling in the d levels of lower energy. The consequent gain in bonding energy is known as crystal field

stabilization energy (CFSE). For an octahedral complex, CFSE:

CSFE = - 0.4 x n(t2g) + 0.6 x n(eg) Δ0

Where, n(t2g) and n(eg) are the no. of electrons occupying the respective levels.

For a tetrahedral complex, CFSE:

The tetrahedral crystal field stabilization energy is calculated the same way as the octahedral crystal field

stabilization energy. The magnitude of the tetrahedral splitting energy is only 4/9 of the octahedral splitting

energy, or Δ t =4/9 Δ0.

CSFE = 0.4 x n(t2g) -0.6 x n(eg) Δt

Where, n(t2g) and n(eg) are the no. of electrons occupying the respective levels.

Crystal Field Stabilization Energy in Square Planar Complexes.

Square planar coordination is rare except for d8 metal ions. Among the d8 metal ions exhibiting

square planar coordination are nickel(II), palladium(II),platinum(II), rhodium(I), iridium(I),



copper(III), silver(III), and gold(III).Copper(II) and silver(II), both d9 ions, are occasionally found in

square planar coordination.

All known square planar complexes of d8 ions are diamagnetic, because the highest energy orbital

(dx2-y2) is greatly destabilized, and pairing in the dxy orbital is more favourable than placing an

unpaired electron in the dx2-y2 orbital.

The crystal field stabilization energy for a diamagnetic square planar d8metal complex is readily calculated

by the usual method:

The pairing energy correction is included because a free d8 ion has 2unpaired electrons, but a square planar

d8 complex has no unpaired electrons.

Band structure of solids and Effect of doping on conductance

Band Theory of Solids

A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the

available energies for electrons in the materials. Instead of having discrete energies as in the case of free

atoms, the available energy states form bands. Crucial to the conduction process is whether or not there are

electrons in the conduction band. In insulators the electrons in the valence band are separated by a large gap

from the conduction band, in conductors like metals the valence band overlaps the conduction band, and in

semiconductors there is a small enough gap between the valence and conduction bands that thermal or other

excitations can bridge the gap. With such a small gap, the presence of a small percentage of a doping

material can increase conductivity dramatically.

An important parameter in the band theory is the Fermi level, the top of the available electron energy levels

at low temperatures. The position of the Fermi level with the relation to the conduction band is a crucial

factor in determining electrical properties.



Band gap dependence on interatomic spacing



Insulator Energy Bands

Most solid substances are insulators, and in terms of the band theory of solids this implies that there is a large forbidden gap between the energies of the valence electrons and the energy at which the electrons can move freely through the material (the conduction band).

Glass is an insulating material which may be transparent to visible light for reasons closely correlated with its nature as an electrical insulator. The visible light photons do not have enough quantum energy to bridge the band gap and get the electrons up to an available energy level in the conduction band. The visible properties of glass can also give some insight into the effects of "doping" on the properties of solids. A very small percentage of impurity atoms in the glass can give it color by providing specific available energy levels which absorb certain colors of visible light. The ruby mineral (corundum) is aluminum oxide with a small amount (about 0.05%) of chromium which gives it its characteristic pink or red color by absorbing green and blue light.

While the doping of insulators can dramatically change their optical properties, it is not enough to overcome the large band gap to make them good conductors of electricity. However, the doping of semiconductors has a much more dramatic effect on their electrical conductivity and is the basis for solid state electronics.



Semiconductor Energy Bands

For intrinsic semiconductors like siliconand germanium, the Fermi level

is essentially halfway between the valence and conduction bands.

Although no conduction occurs at 0 K, at higher temperatures a finite

number of electrons can reach the conduction band and provide some

current. In doped semiconductors, extra energy levels are added.

The increase in conductivity with temperature can be modeled in terms of the

Fermi function, which allows one to calculate the population of the

conduction band.

Conductor Energy Bands

In terms of the band theory of solids, metals are unique as good

conductors of electricity. This can be seen to be a result of their valence

electrons being essentially free. In the band theory, this is depicted as an

overlap of the valence band and the conduction band so that at least a fraction

of the valence electrons can move through the material.

Effect of doping on conductance

Doping

Doping means the introduction of impurities into a semiconductor crystal to the defined modification of

conductivity. Two of the most important materials silicon can be doped with, are boron (3 valence electrons

= 3-valent) and phosphorus (5 valence electrons = 5-valent). Other materials are aluminum, indium (3-

valent) and arsenic, antimony (5-valent).

The dopant is integrated into the lattice structure of the semiconductor crystal, the number of outer electrons

define the type of doping. Elements with 3 valence electrons are used for p-type doping, 5-valued elements

for n-doping. The conductivity of a deliberately contaminated silicon crystal can be increased by a factor of

106.

n-doping



The 5-valent dopant has an outer electron more than the silicon atoms. Four outer electrons combine with

ever one silicon atom, while the fifth electron is free to move and serves as charge carrier. This free electron

requires much less energy to be lifted from the valence band into the conduction band, than the electrons

which cause the intrinsic conductivity of silicon. The dopant, which emits an electron, is known as an

electron donor (donare, lat. = to give).

The dopants are positively charged by the loss of negative charge carriers and are built into the lattice, only

the negative electrons can move. Doped semimetals whose conductivity is based on free (negative) electrons

are n-type or n-doped. Due to the higher number of free electrons those are also named as majority charge

carriers, while free mobile holes are named as the minority charge carriers.

n-doping with phosphorus

Arsenic is used as an alternative to phosphorus, because its diffusion coefficient is lower. This means that

the dopant diffusion during subsequent processes is less than that of phosphorus and thus the arsenic remains

at the position where it was introduced into the lattice originally.

p-doping

In contrast to the free electron due to doping with phosphorus, the 3-valent dopant effect is exactly the

opposite. The 3-valent dopants can catch an additional outer electron, thus leaving a hole in the valence band

of silicon atoms. Therefore the electrons in the valence band become mobile. The holes move in the opposite

direction to the movement of the electrons. The necessary energy to lift an electron into the energy level of

indium as a dopant, is only 1 % of the energy which is needed to raise a valence electron of silicon into the

conduction band.

With the inclusion of an electron, the dopant is negatively charged, such dopants are called acceptors

(acceptare, lat. = to add). Again, the dopant is fixed in the crystal lattice, only the positive charges can move.

Due to positive holes these semiconductors are called p-conductive or p-doped. Analog to n-doped

semiconductors, the holes are the majority charge carriers, free electrons are the minority charge carriers.

p-doping with boron



Doped semiconductors are electrically neutral. The terms n- and p-type doped do only refer to the majority

charge carriers. Each positive or negative charge carrier belongs to a fixed negative or positive charged

dopant.

N- and p-doped semiconductors behave approximately equal in relation to the current flow. With increasing

amount of dopants, the number of charge carriers increases in the semiconductor crystal. Here it requires

only a very small amount of dopants. Weakly doped silicon crystals contain only 1 impurity per

1,000,000,000 silicon atoms, high doped semiconductors for example contain 1 foreign atom per 1,000

silicon atoms.

Electronic band structure in doped semiconductors

By the introduction of a dopant with five outer electrons, in n-doped semiconductors there is an electron in

the crystal which is not bound and therefore can be moved with relatively little energy into the conduction

band. Thus in n-doped semiconductors the donator energy level is close to the conduction band edge, the

band gap to overcome is very small.

Analog, through introduction of a 3-valent dopant in a semiconductor, a hole is available, which may be

already occupied at low-energy by an electron from the valence band of the silicon. For p-doped

semiconductors the acceptor energy level is close the valence band.

Band model of doped semiconductors

The p-n junction



Short Answer Questions

1. What is LCAO Method?

2. What is meant by bonding and antibonding orbitals?

3. What is meant by Bond Order?

4. What are the conditions of combination of atomic orbitals?

5. Define CFSE.

6. What are the salient features of CFT?

7. Represent the splitting of d-orbitals in octahedral complexes?

8. What is doping? Give examples.

9. What is the effect of doping on conductance?

Long Answer Questions

1. Explain how the atomic orbitals combine to form bonding and antibonding molecular orbitals?

2. Explain the molecular orbital energy level diagrams of F2, N2 and O2?



3. What is the molecular orbitals of diatomic molecules?

4. Draw and explain the Pi molecular orbitals of Benzene and Butadiene?

5. Explain about the band structure of solids?

6. What is the effect of doping on conductance?

7. What are the salient features of CFT?

8. Explain the crystal field splitting of transition metal ion d-orbitals in tetrahedral, octahedral and square planar complexes?

TUTORIAL QUESTIONS:

1. List out the Differences between Bonding and Anti-Bonding molecular orbitals.2. Calculate the bond orders of Nitrogen , Flourine and Oxygen molecules3. Give the crystal field stabilisation energies of Octahedral ,Tetrahedral and Square planar complexes.4. Why is Oxygen molecule paramagnetic while Nitrogen molecule in diamagnetic?5. Define Spectro chemical series .6. Which complexes are spin free complexes?7. Explain why benzene is Aromatic in nature.8. Define Huckel rule.9. Draw the Pi molecular orbitals of Benzene and Butadiene.10. Write the increasing order of the splitting power of ligands.

ASSIGNMENT QUESTIONS:

1) Draw the molecular orbital energy level diagrams of N2, O2, and F2.

2) Define bond order ,bond length and bond dissociation energy.3) Give few examples of Dopants. 4) Sketch the shapes of Molecular orbitals formed by the overlap of 2s and 2p orbitals.5) What is the effect of doping on conductance?6) Define Crystal Field Stabilisation energy.7) What is the maximum number of electrons that can occupy a molecular orbital and why?8) Write the Magnetic properties and Bond order of N2, O2 and F2



9) Represent the electronic configuration of molecular orbitals for N2, O2 and F2

10) Draw the shapes of s, p and d orbitals11) Give the differences between p type and n type semi conductors.12) Why is Flourine molecule very stable?13) How is a Nodal plane produced in molecular orbitals?14) What is the relationship between bond order and Bond length?15) Differentiate the properties of diamagnetic and paramagnetic molecules.16) Define Magnetic moment.17) Give examples of conductors, semiconductors and insulators.18) Sketch the diagrams of square planar, tetrahedral and octahedral complexes.


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