Atomic and molecular spectroscopy chm323

l (L) = orbital angular momentum quantum number l (L) = Total orbital angular momentum (vector), lz = Projection of l on z-axis (ml) lz = ± l, ± (l -1), ± (l -2)……..0. s (S) = Spin angular momentum quantum number s (S) = Total spin angular momentum (vector) sz (Sz) = Projection of S on z-axis (ml) sz (Sz) = ± s, ± (s-1), ± (s-2)……..0., for integer values of S OR ± s, ± (s-1), ± (s-2)……..1/2, for half-integer values of S j (J) = Total angular momentum quantum number j (J) = Total angular momentum (vector) jz (Jz) = Projection of J on z-axis (ml) jz (Jz) = ± j, ± (j-1), ± (j-2)……0, for integer values of J OR ± j, ± (j-1), ± (j-2)……..1/2, for half-integer values of J

Common notations and its explanations

Fundamentals of Molecular Spectroscopy

CHM 323

Atomic Spectroscopy

l √2 lz = +1ħ

Orbital angular momentum (l)

√2 lz = -1ħ

l

√2 lz = +1ħ

√2 lz = 0

For H-atom (one e-system)

I = I(I+1) ħ ; l = 1, I = √2

s √3/2 sz = +1/2ħ

Spin angular momentum (s)

s

√3/2 sz = +1/2ħ

√3/2 sz = +1/2ħ

s = s(s+1) ħ ; s = ½ , s = √3/2

l √2 lz = +1ħ

s √3/2 sz = +1/2ħ

Orbital angular momentum (l) Spin angular momentum (s)

Orbital and Spin angular momentum (l, s)

l

s

lz = +1ħ

sz = +1/2ħ

√2

√3/2

l

s

lz = +1ħ

sz = +1/2ħ

√2

√3/2

z-axis projection l

s

lz = +1ħ

sz = +1/2ħ √3/2

√2

l

s lz = +1ħ

sz = +1/2ħ √3/2

√2

l

s

j

l = 1 and s = 1/2

j = [j(j+1)]1/2 ħ = √15/2 ħ

l

s lz = +1ħ

sz = +1/2ħ

jz = +3/2 ħ

lz = +1 and sz = +1/2

√3/2ħ

√2 ħ √15/2 ħ

j = Il + sI = I1 + ½I = 3/2

l

s j

Spin-orbit coupling : total electron angular momentum (j)

S-O coupling

2p orbital

l

s √3/2 ħ

√2 ħ

j = [j(j+1)]1/2 ħ = √3/2 ħ

lz = +1ħ

sz = -1/2ħ

l = 1 and s = 1/2 lz = +1 and sz = -1/2

j = Il - sI = I1 - ½I = 1/2

l

s

√3/2ħ j

j jz = +½ħ √3/2ħ

jz = +½ħ S-O coupling

lz = 0 l s √3/2

ħ

√2 ħ

sz = -1/2ħ

j = [j(j+1)]1/2 ħ = √3/2 ħ

s = 1/2 lz = 0 and sz = -1/2

j √3/2 ħ

jz = -½ħ

S-O coupling

s lz = 0 l

√2 ħ

√3/2 ħ sz = +1/2ħ

s = 1/2 lz = 0 and sz = +1/2

j = [j(j+1)]1/2 ħ = √3/2 ħ

j √3/2 ħ jz = +½ħ S-O coupling

l

s +½ħ

√2 ħ

√3/2ħ

lz = -1ħ

l = 1 and s = 1/2 lz = -1 and sz = +1/2

j = [j(j+1)]1/2 ħ = √3/2 ħ

j = Il - sI = I1 - ½I = 1/2

l

s

jz = -½ħ j √3/2ħ

j jz = -½ħ √3/2ħ

S-O coupling

l

s √2 ħ

√3/2ħ lz = -1ħ sz = -1/2ħ

l = 1 and s = 1/2 lz = -1 and sz = -1/2

j = [j(j+1)]1/2 ħ = √15/2 ħ

j = Il + sI = I1 + ½I = 3/2

l s

√15/2ħ jz = -3/2ħ j

√15/2ħ

jz = -3/2ħ j

S-O coupling

lz = +1 and sz = +1/2

lz = +1 and sz = -1/2

lz = 0 and sz = +1/2

lz = 0 and sz = -1/2

lz = -1 and sz = +1/2

lz = -1 and sz = -1/2

Hydrogen atom fine spectrum

From Banwell, page No. 138

Compound doublet

From Banwell, page No.138

Lithium atom fine spectrum From Banwell, page No. 141

Helium atom fine spectrum From Banwell, page No. 147, Fig. 5.11

Compound Triplet

From Banwell, page No. 148, Fig. 5.12

Validation/Application of Atomic Spectroscopy: 1. Zeeman Splitting

m = -e/2m J joules/tesla

m = -eg/2m J joules/tesla

m = -eg/2m J(J+1) ħ J/T

For a point charge of mass m, the magnetic dipole vector is given by,

But electron is not a point charge, so need to include a numerical factor, g, called Landé factor

Substituting value of J;

g = 3/2 + S (S+1) – L(L+1)

2J(J+1) g lies in between 0 and 2

Now, assume that the external magnetic filed is in the z direction, then J assigns the Jz values.

mz = -egh/4pm Jz J/T

Extent of splitting: DE = mz . Bz joules = -egh/4pm Jz Bz joules

DE a Jz . Bz

Jz= ± J, ± (J-1), ± (J-2)……0, for integer values of J OR ± J, ± (jJ1), ± (J-2)……..1/2, for half-integer values of J

-eh/4pm = Bohr Magneton

Example 1 Singlet term transitions

1S0

1P1

MJ or Jz +1 0 -1

wo

w

wo

I I

w

DE is same and depend on Bz

For singlet term transitions, S = 0 and L = J. So g = 1 So splitting is simple and is called “Normal Zeeman effect”

DE = eh/4pm Bz; Jz = 1, g =1

DE = -eh/4pm Bz; Jz = -1, g =1

Bz

MJ or Jz +1

-1

0

DS = 0 DL = ±1 DJ = 0, ± 1 DMJ = 0, ± 1

Example 2 Sodium doublet under magnetic field

Transitions between n=3, l=1 to n=3, l= 0

2S1/2

2P3/2

I

2P1/2

w

I

w Positions of spectra lines in

the absence of applied field

Doublet 10 lines

DS = 0 DL = ±1 DJ = 0, ± 1 DMJ = 0, ± 1

3s1

3p1

MJ or Jz

-1/2

+1/2

+1/2

-1/2

-1/2 +1/2

-3/2

+3/2

Bz Spin orbit coupling

I

w

Coarse spectrum

Fine spectrum Hyperfine

spectrum

DE will be in the ratio 3:1:2 for 2S1/2 : 2P1/2 : 2P3/2 states, since g = 2, 2/3 and 4/3 respectively. Complicated spectrum: “Anomalous Zeeman effect”

Validation/Application of Atomic Spectroscopy: 2. Photoelectron Spectroscopy (PES)

hn = Binding energy + Kinetic Energy

Binding energy = hn - Kinetic Energy

For n = 1, 2, 3, 4, 5, …….etc.

X-ray notations K, L, M, N, O…… etc.

Binding Energy

Kinetic Energy

hn

Principle of PES

K

L

M N

If source is UV, Ultra-violet Photoelectron Spectroscopy (UPES)

If source X-ray, X-ray Photoelectron Spectroscopy (XPES)

PES Example 1: Ar ion

1S22S22P5 1S22S22P63S1

Interpretation of spectrum

Electron from 2P terms show higher B.E.

Ratio of peak area between3s to 3p state is 1:3

Ratio of peak between 2P3/2 and 2P1/2 is 2:1

From Banwell, page No. 155

Summary: Atomic Spcetrosocpy

Electromagnetic radiation – Sources- Wien’s Law ( l = 0.0029/T meters)

HΨ = EΨ; Time independent one dimensional Schrödinger equation HΨ = EΨ; solving for E

E = -RH/n2 Joules (RH = Rydberg constant = 2.18 x 10-18 Joules)

E = -Z2RH/n2 Joules; for any one electron system (H-like system He1+, Li2+ etc.).

DE = RH/h [1/nf2 – 1/ni

2]; for emission spectroscopy

DE = RH/h [1/ni2 – 1/nf

2]; for absorption spectroscopy\

For any one electron system , there will a Z2 term in the numerator

Validation of E Ionization energy Atomic spectroscopy

UV

Visible

NIR

IR

Pfund series : E(n) to E(n=5)

Humphrey series: : E(n) to E(n=6)

And so on…..

HΨ = EΨ; solving for Ψ n, l and m quantum numbers 1s = Ψ100, 2pz = Ψ211 etc… Spin-orbit coupling

Orbital angular momentum, l

Spin angular momentum, s

l (L) = orbital angular momentum quantum number l (L) = Total orbital angular momentum (vector), lz = Projection of l on z-axis (ml) lz = ± l, ± (l -1), ± (l -2)……..0. s (S) = Spin angular momentum quantum number s (S) = Total spin angular momentum (vector) sz (Sz) = Projection of S on z-axis (ml) sz (Sz) = ± s, ± (s-1), ± (s-2)……..0., for integer values of S OR ± s, ± (s-1), ± (s-2)……..1/2, for half-integer values of S j (J) = Total angular momentum quantum number j (J) = Total angular momentum (vector) jz (Jz) = Projection of J on z-axis (ml) jz (Jz) = ± j, ± (j-1), ± (j-2)……0, for integer values of J OR ± j, ± (j-1), ± (j-2)……..1/2, for half-integer values of J

Many electron system L-S coupling (Russell Saunder’s coupling) Z >30, jj coupling

Term symbol (Russell Saunder’s coupling)

2S+1LJ

lower J value, for less than half filled orbitals higher J value, for more than half filled orbitals

Non-equivalent : Examples done in class Sodium, Fluorine, 2s1, 2p1 and 2p1, 3p1

Equivalent electrons: Examples done in class Carbon

3P0

3P1

1D2

1S0

3P2

p2 state (carbon) 15 microstates

http://isites.harvard.edu/fs/docs/icb.topic979814.files/Lecture%2017.pdf

Application/validation of atomic spectroscopy Zeeman effect Photoelectrons pectrosocpy (PES)

Molecular Spectroscopy

Molecular energy levels

Molecular Orbital Theory

Homonuclear diatomic molecules originating from s orbitals

Homonuclear diatomic molecules originating from s and p orbitals

Heteronuclear diatomic molecules

Molecular Term symbols

Selection rules

Hydrogen molecule spectrum

Vibrational coarse structure:

Born-Oppenheimer approximation

Franck-Condon Principle

Dissociation

Rotational fine structure

Predissociation

Fluorescence and Phosphorescence

Spectrophotometer

Beer-Lambert law.

Molecular energy level


Homonuclear diatomic molecules originating from s orbitals

+

In MO theory, the valence electrons are delocalized over the entire molecule, not

confined to individual atom or bonds

MO (Ψ) arise by the interaction of atomic orbitals (Ψ). The atomic orbitals can interact

constructively or destructively to form bonding MO and antibonding MO, respectively.

1s orbital, constructive interference

1sa 1sb

View along the inter-nuclear axis

σ1sg

σ: Cylindrically symmetrical along the bond axis

Bonding molecular orbital

σ

Ψ2 = (Ψ1sa + Ψ1sb)2 = Ψ21sa + Ψ21sb + 2 Ψ1saΨ1sb

Constructive interference term

-

1sa 1sb

View along the inter-nuclear axis

σ*1su

σ: Cylindrically symmetrical along the bond axis

Antibonding molecular orbital

1s orbital, destructive interference

σ

Ψ2 = (Ψ1sa - Ψ1sb)2 = Ψ21sa + Ψ21sb - 2 Ψ1saΨ1sb

Destructive interference term

Arranging the M.O. (Ψ ) in energy diagram

1sa 1sb

σ1sg

(Bonding molecular orbital)

σ*1su

(Antibonding molecular orbital)

Bonding MO: High electron density accumulates between the two nuclei

More stable than individual atoms

Antibonding MO: Less electron density accumulates between the two nuclei

Creates an effect exactly opposite to a bonding –Antibonding, NOT non-bonding

Less stable than individual atoms

1s 1s

σ1sg

σ*1su

Example 1: MO diagram of Hydrogen molecule

Atomic configuration: 1s1

Bond order: ½ (# of bonding MO electrons - # antibonding MO electrons)

For H2 = ½ (2-0) = 1; single bond, diamagnetic

Molecular configuration: (σ1sg)2

Energy

Example 1: MO diagram of He molecule

Atomic configuration: 1s2

Bond order: ½ (# of bonding MO electrons - # antibonding MO electrons)

For He2 = ½ (2-2) = 0; No bond.

Molecular configuration: (σ1sg)2(σ*1su)2

1s 1s

σ1sg

σ*1su

Does He molecule exist????

He-He Not a bond that is seen that often

Weakest chemical bond known

DEd = 0.01 kJ/mol for He2

DEd = 432 kJ/mol for H2

Energy

Example 1: MO diagram of Li2 molecule Atomic configuration: 1s22S1

Bond order: ½ (# of bonding MO electron - # antibonding MO electrons)

For Li2 = ½ (4-2) = 1; single bond, diamagnetic

1s 1s

σ1sg

σ*1su

2s 2s

σ2sg

σ*2su

Molecular configuration: (σ1sg)2(σ1s*u)2 (σ2sg)

2

Energy

DEd = 105 kJ/mol for Li2

Example 1: MO diagram of Be2 molecule

Atomic configuration: 1s22s2

Bond order= ½ (4-4) = 0; No bond

1s 1s

σ1sg

σ*1su

2s 2s

σ2sg

σ*2su

Molecular configuration: (σ1sg)

2(σ*1su)2 (σ2sg)2(σ*2su)2

Energy

DEd = 9 kJ/mol for Be2

Molecular Term Symbol

Comparison of notations

From Banwell, page No.183

Molecular Term Symbol

Where, S is the total spin quantum number Λ is the projection of the orbital angular momentum along the internuclear axis Ω is the projection of the total angular momentum along the internuclear axis u/g is the parity +/− is the reflection symmetry along an arbitrary plane containing the internuclear axis

= I l1 + l2I and Il1 – l2I S = I s1 + s2I and Is1 – s2I Ω= Il1+ S1I and Il1- S1I

Only the projection (orbital, spin and total angular momentum) on z-axis is considered in molecular term symbol assignment

Molecular energy level


Homonuclear diatomic molecules originating from p orbitals

g, Gerade parity

u, ungerade parity

The probability density function can be calculated as did in the s orbital case

pz orbital

The internuclear axis (bond axis) is taken as the z-axis

px orbital (or py)

u, Ungerade parity

g, Gerade parity

Antibonding

Bonding

Orbital parity – gerade (g) and ungerade (u)

Symmetry of orbitals and molecules is of great importance, and we should be able to determine whether orbitals are gerade (g) or ungerade (u) (from German for even or odd).

a a a

b b b

center of

inversion

a = b

not a

center of

inversion

a ≠ b

Parity (g or u) of atomic orbitals:

s-orbital

gerade (g) p-orbital

ungerade (u)

d-orbital

gerade (g)

Parity (g or u) of molecular orbitals:

σ*(1s)u

σ(1s)g

The test for whether an MO is g or u is to find the possible center of inversion

of the MO. If two lines drawn out at 180o to each other from the center, and of

equal distances, strike identical points (a and b), then the orbital is g.

center of

inversion

a = b

a

b

a

b

not a center

of inversion

a ≠ b (sign of wave-

function is

opposite) u

g g

u

Parity (g or u) of molecular orbitals:

π*(2p)g

π(2p)u

The test for whether an MO is g or u is to find the possible center of inversion

of the MO. If two lines drawn out at 180o to each other from the center, and of

equal distances, strike identical points (a and b), then the orbital is g.

center of

Inversion

a = b

not a center of

inversion

a ≠ b

a

b

a

b

Bonding p orbital

antibonding p orbital

g

u

Test 1

σ*pu

π*pg

σ*su

πpu

σsg

σ(1s)

+/- reflection plane symmetery element

“+” “+”

“u”

“g” “g”

“u”

Do a reflection operation in a plane containing the bond axis

p2py M.O p2px M.O

+/- reflection plane assignment

“-” “+”

“u”

“g”

“u”

Do a reflection operation in a plane containing the bond axis

Selection rules

DS = 0 D = 0, ±1 (because DJ = 0, ±1 DΩ = 0, ± 1 S+ ↔ S+ , S-↔ S-

g ↔ u, change of parity during transition is required. So ‘u’ to ‘u’ and ‘g’ to ‘g’ are not allowed.

All selection rules (electronic, vibration and rotational) are based on conservation of angular momentum.

Selection rules are quantum mechanically based on transition moment integral, P = < Ψ*m Ψ>

u x u = g g x u = u x g = u g x g = g

Dipole moment operator, m = mx . my . mz ; = u . u. u = u parity

Molecular Term Symbol Examples

H2 : (σ1sg)2 = 1S+

g

H-2 : (σ1sg)

2 (σ*1su)1 = 2S+u

He2 : (σ1sg)2 (σ*1su)2 = 1S+

g

B2 : (σ1sg)2 (σ*1su)2 (σ2sg)

2 (σ*2su)2 (p2pxu)1 (p2pyu) 1 = 1Dg, 3S-

g and 1S+

u

O2 molecule, bond order = 2

O O2 O

BO = (6-2)/2 = 2

(disregardiing overlap of 2s orbitals)

The ability to predict the number of unpaired electrons in molecules is where MO excels, and Lewis-approach fails.

molecules with unpaired electrons are paramagnetic

Singlet oxygen (1O2)

O O2 O

BO = (6-2)/2 = 2

Singlet Oxygen is an excited state of the ground state triplet 3O2

molecule. It is much more reactive, and will readily attack organic molecules.

The O2 molecule in its excited singlet state which is 25 kcal/mol in energy above the ground triplet state. Irradiation with IR light causes excitation to the singlet state, which can persist for hours because the spin-selection rule inhibits transitions that involve a change of spin state.

Born-Oppenheimer Approximation

ΨTot = ψNuc . ψele

ΨNuc. = Ψvib . Ψrot . Ψtans

ΨNuc. = Ψvib . Ψrot

Since Ψtrans , is negligible

So

Ψtot = Ψvib . Ψrot . Ψele

Mass (nuc) >> mass (ele) V(nuc) << V(ele)

(a) For electron, nucleus is stationary and fixed (b) For nucleus, electron is delocalized

Etotal = Eelectronic + Evibration + Erotation in Joules

εtotal = εelectronic + εvibration + εrotational in cm-1

ΔEtotal = ΔEelectronic + ΔEvibration + ΔErotation

Etotal = Eelectronic + Evibration εtotal = εelectronic + εvibration in cm-1

Vibrational Coarse structure

No restriction in vibronic transition.

Progressions

From McQuarrie and Simon, Fig. 13.8

Absorption spectrum of I2 (g) in the visible region

This spectrum is a n’ progression

From McQuarrie and Simon, Fig. 13.9

The Franck–Condon principle is a rule in spectroscopy and quantum chemistry that explains the intensity of vibronic transitions.

Classical form: Franck-Condon principle states that an electronic transition takes place so rapidly that a vibrating molecule does not change its internuclear distance appreciably during the transition. So the electronic transition occurs vertically in P. E. diagram.

The Franck–Condon principle

Classical form: Vertical transitions



Quantum mechanical form:

The intensity of a vibronic transition is proportional to the square of the

overlap Integral between the two vibrational states wave functions (ψ2) that are

involved in the transition.

ψ=ψe ψN

ψf = ψe,f ψN,f

ψi = ψe,i ψN,i

µ = µe +µN

As ψe,f and ψe,i are orthogonal to each

other so <ψe,f | ψe,i> = 0

Franck Condon factor

Transition moment integral (selection rules)

Quantum mechanical form

<µ> = <ψf |µ|ψi>

= <ψe,f ψN,f |µe+µN| ψe,i ψN,i>

= <ψe,f ψN,f |µe| ψe,i ψN,i>

+ <ψe,f ψN,f |µN| ψe,i ψN,i>

= <ψN,f | ψN,i> <ψe,f |µe| ψe,i>

+<ψe,f | ψe,i> <ψN,f |µN| ψN,i>

= <ψN,f | ψN,i> <ψe,f |µe| ψe,i> + 0


Transition moment integral <µ> = <ψf |µ|ψi>






= <ψN,f | ψN,i> <ψe,f |µe| ψe,i> + 0


<µ> = <ψf |µ|ψi>






= <ψN,f | ψN,i> <ψe,f |µe| ψe,i> + 0


<µ> = <ψf |µ|ψi>






= <ψN,f | ψN,i> <ψe,f |µe| ψe,i> + 0


<µ> = <ψf |µ|ψi>






= <ψN,f | ψN,i> <ψe,f |µe| ψe,i> + 0


Quantum mechanical form (in integral terms)

P = ʃ ψN,f . ψN,i dζ ʃ ψe,f µ ψe,i dζ

Franck Condon factor

Transition moment integral (selection rules)

P = ʃ ψ vib,f ψ vib,i dζ ʃ ψe,f µ ψe,i dζ

So the final form is

ΨN = Ψvib . Ψrot . Ψtans

ΨN = Ψvib . Ψrot

ΨN = Ψvib



Quantum mechanical form:

The intensity of a vibronic transition is proportional to the square of the

overlap Integral between the two vibrational states wave functions (ψ2) that are

involved in the transition.

QM form: Max. overlap between ψ2

Case 1: When Re’ = Re”

The Franck–Condon principle Different possibilities

Re = Equilibrium internuclear distance

(0,0) most intense transition

When Re’ = Re”

The Franck–Condon principle Different possibilities




Intensity profile

(0,0) NOT most intense transition (2,0) most intense transition

Actual intensity profile

Molecule spent most of the time at the edges as vibration energy level increases

Case 2: When Re’ > Re”

N2 molecule: Re” = 1.098 Å. Re’ = 1.22Å & 1.2126 for 1Pg and 3Pg



(0,0) NOT most intense transition

Case 2: When Re’ >> Re”

Intensity profile

I2 molecule: Re” = 2.667 Å. Re’ = 3.025 Å



(0,0) NOT most intense transition (2,0) is the most intense

Case 2: When Re’ < Re”

Intensity profile

Transitions b/n two excited states: Antibonding to bonding or non-bonding

Rotational Fine structure of Electronic-Vibration Transition

Etotal = Eelectronic + Evibration + Erotation in Joules

εtotal = εelectronic + εvibration + εrotational in cm-1

ΔEtotal = ΔEelectronic + ΔEvibration + ΔErotation

εtotal = εelectronic + εvibration + BJ (J+1) ; (J = 0,1, 2, 3 …) B = h/8p2Ic

Dεtotal = D (εelectronic + εvibration) + D {BJ (J+1)} in cm-1

Rotational Selection rule

DJ = 0, ±1; J is the rotational energy level

DJ = ±1; for 1S ↔ 1S transitions DJ = 0, ±1; for 1S ↔ 1D or 1P ↔ 1D transitions

Based on conservation of angular momentum

DJ = +1; R branch DJ = 0; Q branch DJ = -1; P branch

Rotational Fine structure of Electronic-Vibration Transition

Dεtotal = D (εelectronic + εvibration) + D {BJ (J+1)} in cm-1

Dεrotational = B ̍ J ̍(J ̍+1) – B ̎ J ̎(J ̎+1) ----- (1)

Where B’’, B ̍ are Rotational constants in electron ground state and excited state respectively

DJ= +1 J ̍ = J ̎ +1 ------- (2)

DEr = B ̍ (J ̎ +1)(J ̎ +2) – B ̎ J ̎ (J ̎ +1)

Substitute eq 2 in 1

= (J ̎ +1){ B ̍ (J ̎ +2) - B ̎ J ̎ } = (J ̎ +1){ B ̍ J ̎ + 2B ̍ - B ̎ J ̎}

= (J ̎ +1){ B ̍ J ̎ - B ̎ J ̎ + B ̍ + B ̎ + B ̍ - B ̎ } (add and subtracting B ̎)

= (J ̎ +1){ (B ̍- B ̎ )J ̎ + B ̍ - B ̎ + B ̍ + B }

DEr = (B ̍+ B ̎ ) (J ̎ +1) + (B ̍- B ̎ ) (J ̎ +1) 2 -------- (3)


Total energy DET = (DEe + DEv ) + (B ̍+ B ̎ ) (J ̎ +1) + (B ̍- B ̎ ) (J ̎ +1) 2

R- branch

R- branch

DJ= -1 J ̎ = J ̍+1 ------- (4)

DEr = B ̍ J ̍ (J ̍+1) – B ̎ (J ̍+1)(J ̍ + 2)


= (J ̍ +1){ B ̍ J ̍ – B ̎ (J ̍ + 2) } = (J ̍ +1){ B ̍ J ̍ – B ̎ J ̍ – 2B ̎ ̍}

= (J ̍ +1){ B ̍ J ̍ – B ̎ J –̍ B ̎ + B ̍ – B ̍ – B ̎ } (add and subtracting B ̍)

= (J ̍ +1){ (B ̍- B ̎ )J ̍ +( B ̍ - B ̎ )- (B ̍ + B ̎ ) }

DEr = (B ̍- B ̎ ) (J ̍ +1)2 - (B ̍+ B ̎ ) (J ̍+1) -------- (5)


Total energy DET = (DEe + DEv ) - (B ̍+ B ̎ ) (J ̍+1) + (B ̍- B ̎ ) (J ̍ +1)2

P- branch

P- branch

DJ= 0 J ̎ = J ̍ ------- (6)

DEr = B ̍ J ̍ (J ̍+1) – B ̎ J ̍ (J ̍+1)


= J ̍ (J ̍ +1)( B ̍ - B ̎ ) = (B ̍ - B ̎ ) (J ̍ 2+J ̍ )

DEr = (B ̍ - B ̎ ) J ̍ 2 + (B ̍ - B ̎ ) J ̍ ------- (7)


Total energy DET = (DEe + DEv )+ (B ̍ - B ̎ ) J ̍ + (B ̍ - B ̎ ) J ̍ 2

Q- branch

Q- branch

Total energy DET = (DEe + DEv ) + (B ̍+ B ̎ ) (J ̎ +1) + (B ̍- B ̎ ) (J ̎ +1) 2 R- branch

B’ < B”

Total energy DET = (DEe + DEv ) - (B ̍+ B ̎ ) (J ̍+1) + (B ̍- B ̎ ) (J ̍ +1)2 P- branch

Total energy DET = (DEe + DEv )+ (B ̍ - B ̎ ) J ̍ + (B ̍ - B ̎ ) J ̍ 2 Q- branch

Overall

Band head

Few example

Dissociation and Pre-dissociation

Molecular abs.

Atomic abs.

Dissociation and Pre-dissociation

Pre-dissociation

Molecule spent most of the time at the edges as vibration energy level increases

Tells the fate of an excited electron…

Jablonski Diagram

S0

v0

vn

vn

v0

vn

v0

vn

v0

v0

S1

S2

Sn

T1

Electronic ground state

Abso

rpti

on

(10

-15 s

)

VC (10-12 s)

ISC (10-12 s)

Fluorescence (10-9 s)

Phosphorescence (10-6 s)

Ener

gy

IC (10-12 s)

Implication of excited state dynamics

1. Photosynthesis

2. Solar energy research

L branch polar glutamate side chain

M branch nonpolar valine side chain

Unidirectional charge separation in Reaction Centre

Electron transfer processes occurs in ns/ps

Spectrophotometers

Absorption spectrophotometer

Diode array spectrophotometer

Monochromator: Grating, prism

Detector: Photographic plate, Photodiode, Photomultiplier tube

(~350 to 800 nm)

(~ 190-350 nm)

Atomic Absorption Spectrophotometer (AAS)

ICP-AES, ICP-OES, ICP-MS

According to the Beer-Lambert law

−𝑑𝐼

𝐼∝ 𝐶 𝑙

−𝑑𝐼

𝐼= 𝑎𝐶 𝑙

− 𝑑𝐼

𝐼= 𝑎𝐶 𝑑𝑙

𝐿

0

𝐼

𝐼𝑜

− ln𝐼

𝐼𝑜

= 𝑎𝐶 𝐿

− log𝐼

𝐼𝑜

= a C L/2.303

−𝑙𝑜𝑔𝐼

𝐼𝑜

= ∈ 𝐶 𝐿

log T = − ∈ 𝐶 𝐿

Where T is known as Transmittance now, Absorbance (A) A = - log T = - (- ∈ 𝐶 𝐿) A = ∈ 𝐶 𝐿

0 L

Io I

Io = Intensity of incident light I = intensity of transmitted light

‘∈’ is called the molar absorptivity or molar extinction coefficient. This is a Parameter defining how strongly a substance absorbs light at a given wavelength per molar concentration

Education

Atomic and molecular spectroscopy chm323