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Inorganic Chemistry

Bonding and Coordination Chemistry

C. R. RajC-110, Department of Chemistry

Books to follow

Inorganic Chemistry by Shriver & AtkinsPhysical Chemistry: Atkins

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Bonding in s,p,d systems: Molecular orbitals of diatomics,

d-orbital splitting in crystal field (Oh, T

d).

Oxidation reduction: Metal Oxidation states, redox

potential, diagrammatic presentation of potential data.

Chemistry of Metals: Coordination compounds (Ligands &

Chelate effect), Metal carbonylspreparation stability and

application.

Wilkinsons catalyst alkene hydrogenationHemoglobin, myoglobin & oxygen transport

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CHEMICAL BONDING:

A QUANTUM LOOK

H2 // Na+Cl- // C60

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PHOTOELECTRIC EFFECT

When UV light is shone on a metal plate in a vacuum, it emits

charged particles (Hertz 1887), which were later shown to beelectrons by J.J. Thomson (1899).

As intensity of light increases, force

increases, so KE of ejected electrons

should increase.

Electrons should be emitted whatever

the frequency of the light.

Classical expectations

Hertz J.J. Thomson

I

Vacuum

chamber

Metalplate

Collecting

plate

Ammeter

Potentiostat

Light, frequency

Maximum KE of ejected electrons is

independent of intensity, but dependent on

For

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Photoelectric Effect.

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(i) No electrons are ejected, regardless of the intensity of the

radiation, unless its frequency exceeds a threshold value

characteristic of the metal.

(ii) The kinetic energy of the electron increases linearly withthe frequency of the incident radiation but is independent

of the intensity of the radiation.

(iii) Even at low intensities, electrons are ejected immediatelyif the frequency is above the threshold.

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Major objections to the

Rutherford-Bohr model We are able to define the

position and velocity of eachelectron precisely.

In principle we can follow the

motion of each individualelectron precisely like planet.

Neither is valid.

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Werner HeisenbergHeisenberg's name will always be associated with

his theory of quantum mechanics, published in

1925, when he was only 23 years.

It is impossible to specify the exact

position and momentum of a particle

simultaneously.

Uncertainty Principle.

x p h/4 where h is PlanksConstant, a fundamental constant with

the value 6.62610-34 J s.

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Einstein

KE 1/2mv2 = h- is the work function h is the energy of the incident light. Light can be thought of as a bunch ofparticles which have energy E = h. The

light particles are called photons.

h = mv2 +

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If light can behave as

particles,why not particles

behave as wave?

Louis de Broglie

The Nobel Prize in Physics 1929French physicist (1892-1987)

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Louis de Broglie

Particles can behave as wave.

Relation between wavelength and themass and velocity of the particles.

E = h and also E = mc2, E is the energy

m is the mass of the particle

c is the velocity.

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E = mc2 = h mc2 = h p = h / { since = c/} = h/p = h/mv This is known aswave particle duality

Wave Particle Duality

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Light and matter exhibit wave-particle duality

Relation between wave and particle properties

given by the de Broglie relations

Photoelectric effect

Flaws of classical mechanics

Heisenberg uncertainty principle limits

simultaneous knowledge of conjugate variables

The state of a system in classical mechanics is defined by

specifying all the forces acting and all the position and

velocity of the particles.

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Wave equation?

Schrdinger Equation. Energy Levels

Most significant feature of the Quantum

Mechanics: Limits the energies todiscrete values.

Quantization.

1887-1961

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For every dynamical system, there exists a wave function

that is a continuous, square-integrable, single-valued function

of the coordinates of all the particles and of time, and from

which all possible predictions about the physical properties of

the system can be obtained.

The wave function

If we know the wavefunction we know everything it is possible to know.

Square-integrable means that the normalization integral is finite

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Applying Boundary conditions: = 0 at x = 0 C = 0 = D sin kx

d2/dx2 + 82 m/h2 (E-V) = 0Assume V=0 between x=0 & x=a

Also = 0 at x = 0 & ad2/dx2 + [82mE/h2] = 0

V=0

a

x =0 x =a

d2/dx2 + k2 = 0 where k2 = 82mE/h2Solution is: = C cos kx + D sin kx

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An Electron in One Dimensional Box

n

= D sin (n/a)x En =n

2 h2/ 8ma2

n = 1, 2, 3, . . .

E = h2

/8ma2

, n=1 E = 4h2/8ma2 , n=2

E = 9h2/8ma2 , n=3

Energy is quantized

V = V = a

x = 0 x = a

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Characteristics of Wave Function

He has been describedas a moody and impulsive

person. He would tell his

student, "You must not mindmy being rude. I have a

resistance against accepting

something new. I get angry and

swear but always accept after a

time if it is right."

MAX BORN

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Characteristics of Wave Function:

What Prof. Born Said

Heisenbergs Uncertainty principle: We cannever know exactly where the particle is.

Our knowledge of the position of a particle

can never be absolute.

In Classical mechanics, square of wave

amplitude is a measure of radiation intensity

In a similar way, 2 or * may be relatedto density or appropriately the probability of

finding the electron in the space.

Th f ti i th b bilit lit d

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The wave function is the probability amplitude

*2

Probability density

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The sign of the wave function has not direct physical significance: the

positive and negative regions of this wave function both corresponds

to the same probability distribution. Positive and negative regions of

the wave function may corresponds to a high probability of finding a

particle in a region.

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Let (x, y, z) be the probability function, d = 1

Let (x, y, z) be the solution of the wave equationfor the wave function of an electron. Then we may

anticipate that (x, y, z) 2 (x, y, z) choosing a constant in such a way that is

converted to =

(x, y, z) = 2 (x, y, z) 2 d = 1

Characteristics of Wave Function:

What Prof. Born Said

The total probability of finding the particle is 1. Forcing this condition on

the wave function is called normalization.

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2 d = 1 Normalized wave function If is complex then replace 2 by * If the function is not normalized, it can be done

by multiplication of the wave function by aconstant N such that

N22 d = 1 N is termed as Normalization Constant

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Eigen values

The permissible values that a dynamical variable

may have are those given by = a- eigen function of the operator thatcorresponds to the observable whose permissiblevalues area -operator

- wave functiona - eigen value

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If performing the operation on the wave function yields

original function multiplied by a constant, then is an eigenfunctionof the operator

= a

= e2x and the operator = d/dxOperating on the function with the operator

d /dx = 2e2x = constant.e2xe2x is an eigen function of the operator

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For a given system, there may be various possible

values.

As most of the properties may vary, we desire todetermine theaverageor expectationvalue.

We know

= aMultiply both side of the equation by ** = *aTo get the sum of the probability over all space* d = *adaconstant, not affected by the order of operation

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Removing a from the integral and solving for a

a = * d/* dcannot be removed from the integral.a = /

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Chemical Bonding

Two existing theories,

Molecular Orbital Theory (MOT)

Valence Bond Theory (VBT)

Molecular Orbital Theory

MOT starts with the idea that the quantum

mechanical principles applied to atomsmay be applied equally well to the

molecules.

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H-CC-H

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Simplest possible molecule:

H2+ : 2 nuclei and 1 electron.

Let the two nuclei be labeled as A and B &

wave functions as A & B. Since the complete MO has characteristics

separately possessed by A and B, = CAA + CBB

or = N(A +B) = CB/CA, and N - normalization constant

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This method is known as Linear Combinationof Atomic Orbitals or LCAO

A and B are same atomic orbitals exceptfor their different origin.

By symmetry A and B must appear withequal weight and we can therefore write 2 = 1, or =1

Therefore, the two allowed MOs are

= AB

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For A+Bwe can now calculate the energy

From Variation Theorem we can write the

energy function as

E = A+B H A+B/A+B A+B

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A+BH A+B = A H A + B H B + A H B + B H A = A H A + B H B +2AHB

Looking at the numerator:


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= A H A + B H B + 2AHB

Numerator = 2EA + 2

ground state energy of a hydrogen

atom. let us call this as EAAHB = BHA = = resonance integral

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A+BA+B = AA + B B + A B + B A = AA + BB + 2AB

Looking at the denominator:


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= AA + BB + 2AB

A and B are normalized,so A A = BB = 1

AB = BA = S,S = Overlap integral.

Denominator = 2(1 + S)

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E+ = (EA + )/ (1 + S)AlsoE- = (EA - )/ (1S)

Summing Up . . .

E = A+B H A+B/A+B A+BNumerator = 2EA + 2

Denominator = 2(1 + S)

S is very small Neglect SE = EA

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Energy level diagram

EA -

EA + BA

Li bi ti f t i bit l

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Rules for linear combination

1. Atomic orbitals must be roughly of the same energy.

2. The orbital must overlap one another as much as

possible- atoms must be close enough for effectiveoverlap.

3. In order to produce bonding and antibonding MOs,

either the symmetry of two atomic orbital must remainunchanged when rotated about the internuclear line or

both atomic orbitals must change symmetry in identical

manner.

Linear combination of atomic orbitals

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Rules for the use of MOs

* When twoAOs mix, twoMOs will be produced

* Each orbital can have a total of twoelectrons(Pauli principle)

* Lowest energy orbitals are filled first (Aufbauprinciple)

* Unpaired electrons have parallel spin (Hunds rule)

Bond order = (bonding electronsantibonding

electrons)

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A B

A BAB = N(cAA + cBB)

Linear Combination of Atomic Orbitals (LCAO)

2AB = (cA2A2 + 2cAcBAB + cB2B 2)Overlap integral

The wave function for the molecular orbitals can be

approximated by taking linear combinations of atomicorbitals.

Probability density

cextent to which each AO

contributes to the MO

Constructive interference

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cA = cB = 1

+. +.. .+

bondingg

Amplitudes of wavefunctions added

g = N [A + B]

Constructive interference

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2AB = (cA2A2 + 2cAcBAB + cB2B 2)

electron density on original atoms,

density between atoms

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The accumulation of electron density between the nuclei put the

electron in a position where it interacts strongly with both nuclei.

The energy of the molecule is lower

Nuclei are shielded from each other

node

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Amplitudes of wave

functionssubtracted.

Destructive interferenceNodal plane perpendicular to the

H-H bond axis (en density = 0)

Energy of the en in this orbital is

higher.

+. -. ..

antibondingu = N [A - B]

cA = +1, cB = -1 u

+ -

A-B

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The electron is excluded from internuclear region destabilizing

Antibonding

Wh 2 t iWh 2 t i bit lbit l bi th 2bi th 2

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When 2 atomicWhen 2 atomic orbitalsorbitals combine there are 2combine there are 2

resultantresultant orbitalsorbitals..

low energy bonding orbitallow energy bonding orbital

high energyhigh energy antibondingantibonding orbitalorbital1sb 1sa

s1s

s*E

1s

MolecularMolecular

orbitalsorbitals

EgEg. s. s orbitalsorbitals

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Molecular potential energy curve shows the variation

of the molecular energy with internuclear separation.

Looking at the Energy Profile

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Looking at the Energy Profile

Bonding orbital

called 1s orbital s electron

The energy of 1s orbital

decreases as R decreases

However at small separation,

repulsion becomes large

There is a minimum in potentialenergy curve

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11.4 eV

109 nm

H2

Location of

Bonding orbita

4.5 eV

LCAO of n A.O n M.O.

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The overlap integral

dS BA*

The extent to which two atomic orbitals on different atomoverlaps : the overlap integral

S > 0 Bonding S < 0 anti

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S = 0 nonbonding

Bond strength depends on the

degree of overlap

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Homonuclear Diatomics

MOs may be classified according to:

(i) Their symmetry around the molecular axis.

(ii) Their bonding and antibonding character.

s1ss1s*s2ss2s*s2py(2p) = z(2p)y*(2p) z*(2p)s2p*.

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dx

2

-dy

2

and dxy

Cl4Re ReCl4

2-

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A

Bg- identical

under inversion

u- not identical

Place labels g or u in this diagram

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Place labelsgor u in this diagram

sg

*g

s*u

u

First period diatomic molecules

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s1s2H

Energy

HH2

1s 1s

sg

su*

Bond order =

(bonding electronsantibonding electrons)

Bond order: 1

Di t i l l Th b di i H

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s1s2, s*1s2He

Energy

HeHe2

1s 1s

sg

su*

Molecular Orbital theory is powerful because it allows us to predict whethermolecules should exist or not and it gives us a clear picture of the of theelectronic structure of any hypothetical molecule that we can imagine.

Diatomic molecules: The bonding in He2

Bond order: 0

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Second period diatomic molecules

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p

s1s2, s*1s2, s2s2Bond order: 1

Li

Energy

LiLi2

1s 1s

1sg

1su*

2s 2s

2sg

2su*

Diatomic molec les Homon clear Molec les of the Second Period

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s1s2, s*1s2, s2s2, s*2s2Bond order: 0

Be

Energy

BeBe2

1s 1s

1sg

1su*

2s 2s2sg

2su*

Diatomic molecules: Homonuclear Molecules of the Second Period

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Simplified

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Simplified

MO diagram for B2

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Diamagnetic??

2sg

2su*

3sg1u

1g*3su*

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Li : 200 kJ/mol

F: 2500 kJ/mol

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Same symmetry, energy mix-

the one with higher energy moves higher and the one with lower energy moves lower

MO diagram for B2

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2sg

2su*

3sg1u

1g*3su*

B BB2

2s 2s

2sg

2su*

2p

2p3sg

3su*

1u

1g*

(px,py)

HOMO

LUMO

Paramagnetic

C2

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1sg

1u

1g

1sg

1u

1g2

DiamagneticParamagnetic ?X

General MO diagrams

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1sg

1u

1g

1sg

1u

1g

Li2 to N2 O2 and F2

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Orbital mixing Li2 to N2

Bond lengths in diatomic molecules

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Bond lengths in diatomic molecules

Filling bonding orbitals

Filling antibonding orbitals

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Summary

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SummaryFrom a basis set of N atomic orbitals, N molecular orbitals are

constructed. In Period 2, N=8.

The eight orbitals can be classified by symmetry into two sets: 4 sand 4 orbitals.The four orbitals from one doubly degenerate pair of bondingorbitals and one doubly degenerate pair of antibonding orbitals.

The four s orbitals span a range of energies, one being stronglybonding and another strongly antibonding, with the remaining

two s orbitals lying between these extremes.To establish the actual location of the energy levels, it is necessary

to use absorption spectroscopy or photoelectron spectroscopy.

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Distance between b-MO and AO

Heteronuclear Diatomics.

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The energy level diagram is not symmetrical.

The bonding MOs arecloser to the atomicorbitals which are

lower in energy.The antibonding MOs

are closer to thosehigher in energy.

cextent to which each atomic

orbitals contribute to MO

If cAc

Bthe MO is composed principally of

A

HF

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1s 1

2s, 2p 7

=c1 H1s + c2 F2s + c3 F2pzLargely

nonbonding2px and 2py

Polar

1s2 2s214

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