4. Molecular spectroscopy

Basel, 2008

4. Molecular spectroscopy

Contents:

1. Introduction

2. Schema of a spectrometer

3. Quantification of molecules mouvements

4. UV-VIS spectroscopy

5. IR spectroscopy

6. MW spectroscopy

7. Magnetic resonance

8. Nullpunct energy

Literature:

• P. Atkins, J. de Paula - Atkins’ Physical Chemistry, 8th Ed., Oxford University Press 2007, chapters13-14.

• P. Atkins, J. de Paula - Physical Chemistry for the Life Sciences, Ed., Oxford University Press 2006, chapter 13.

• C.E. Housercroft, E.W. Constable -Chemistry, Ed. Pearson Education Ltd, 2002, chapters 10-12.

Supplementary material:

• Vibrations of CO2 and H2O (molecules gallery).

• MacSpartan (PC room at groundfloor)

4.1 IntroductionOrigin of spectral lines in molecular spectroscopy: absorption or emission of a photon when the energy of the molecule changes:

- electronic transitions

- rotational states change

- vibrational states change

Absorption spectroscopy: Emission spectroscopy

Ef

Ei

Ei

Ef

ΔE = hν

Emission or absorption spectroscopy:

- give the same information about the energy levels

- practical considerations determine which technique is better to use.

(4.1)

Spectrum

I

λEnergy levels

Spectrum

Particularities:

- lines occur with a variety of intensities

- some lines which are expected to occur, do not appear at all.

Selection rules

4.1.1 Beer-Lamber law

Beer- Lambert law: transmitted intensity varies with the length of the sample, l, and the molar concentration [c], of the absorbing species(Absorption spectroscopy).

I = I010-ε[c]l

ε - molar absorption coefficient (so called extinction coefficient, too)

I0 – incident intensity

I – transmitted intensity

ε - depends on ν of I0, and is greater where the absorption is more intense.

[ε] = dm3 mol-1 cm-1

I0 I

l

sample (4.2)

Beer-Lamber law

Absorbance, A of a sample at a given wavenumber is:

II

A 0log= [ ]lcA ε=

- short for liquids

- very long for gases (multiple passage of the beam between parallel mirrors at each end of the cavity where the sample is introduced)

Transmitance is the ratio between the transmitted light and the incident one:

IIT 0=

Calibration curve(4.3)

(4.4)

(4.5)

l :

4.1.2 LinewidthsSpectral lines: individual transitions between two energy levels.

Spectral bands: simultaneous transitions between very close energy levels,thus the summ of many spectral lines.

Lifetime broadening: finite lifetime of the states involved in the transition are inducing abroadening of the spectral lines:

τδ h

=E

pscm/

3.5~1

τνδ

−

=

νδδ ~hcE =

Ef

δEi

Example: the width of a transition from astate with a lifetime of 5.0 ps is 1.1 cm-1.

Why lifetimes?- collisional deactivation(intermolecules or with the walls)

- spontaneous emission

Uncertainty principle(Heisenberg)

(4.6)(4.8)

(4.7)

Absorption coefficient of a transition

Maximum value of the molar absorption coefficient, εmax represents a measure of the intensity of a transition.

Absorption bands

Integrated absorption coefficient: area under the plot of the molar absorption coefficient against of the incident radiation.

ν~

Integrated absorption coeficient, A : summ of the absorption coeficients over the entire spectral band.

( ) ννε ~~ dband∫=A

A is proportional to the heights of the lines if they have similar widths

(4.9)

4.1.3 Electromagnetic energy domain

Frequency: ν

Wavelength: λ = c/ν

Energy: ΔE = h ν

4.2 Schema of a spectrometer

Sourse Mono-chromator

Sample

cDetector

d

λ

I0 I

I

λOy axis

Ox axis

Spectrometer: an instrument that detects the characteristics of light which is emmited, absorbed or scattered by atoms or molecules

Absorption spectrometer

Absorption Spectrometer

Source:

- Far IR (35 cm-1 <<200 cm-1): mercury arc inside a quartz envelope

- Vis: tungsten iodine lamp (white light)

- Near UV: deuterium lamp

- MW: klistron

ν~

Detectors:

- photodiode (photoelectric effect) (Uv-VIS)

- CCD camera (charged couple device) - 2D array of photodiodes

- photovoltaic device of Hg-Cd-Te (IR)

- Detector sensitive to the phase (EPR)

UV-Vis

If the source is emmiting only one frequency, the monocromator in not needed, for example in the case of a klistron. Monocromator can be replaced by an interferometer, if necessary.

4.2.1 Aims of spectroscopy

1. Qualitative analysis of a new substance/mixture (to identify the molecular species present)

2. Quantitative determination of a known substance (Beer-Lamber law)

3. Structural characterisation of a substance (from the energy levelsand various transitions > establish the physical and chemical properties of the substance).

Molecular spectroscopy

λν

hν

ν~

Types of spectroscopy

Domain Spectroscopy

10-8m bis 10-10m X-ray Electron spectroscopy

10-6m bis 10-8m UV-VIS Electron spectroscopy

10-4m bis 10-6m IR Vibration spectroscopy

10-2m bis 10-4m MW Rotation spectroscopy

10-2m bis 1m Magnetic resonance - EPR

>1m Radio ν Magnetic resonance - NMR

λ

4.2.2 Physical background for transitions

X-ray Electron spectroscopy Internal electrons are excited, and after the rearrangement of the electronic configuration, photons are emitted.

UV-VIS Electron spectroscopy Electrons of valence are excited (possible ionization), and atoms will emit photons with the difference in energy between the two states where the transition took place.

IR Vibration spectroscopy Oscillations of atoms in a molecule modify its energy levels between which transitions occur > vibration modes

MW Rotation spectroscopy Molecules as rigid rotors have a rotation movement associated with various rotational energy levels, between which transitions occur (for gas phase molecules).

MW EPR The spins of unpaired electrons of a paramagnetic substance placed in a magnetic field change their orientation when they are irradiated with microwave energy equal to the difference between two energy levels of the system.

Radio ν NMR The spins of the nuclei placed in a magnetic field change their orientation when they are irradiated with a energy which corresponds to the difference between two energy levels.

4.3 Quantification of the mouvement

E =h2

8mL2 n2

ΔE =3h 2

8mL2

ν =3h

8mL2

λ =8mL2c

3h

˜ ν = 1λ

=3h

8mL2c

(4.10)

3.5.5.- a particle in a box, formula 3.32, and (K3-12 – Huber course)

Energy levels structure: m - particle mass (electron, atom, molecule)

n - principal quantum number = 1,2,...

h – Planck constant

L – dimension of the „box“ where de Broglie wave of the particle is confined.

Example For: n =1 > n =2

(4.11)

(4.12)

(4.13)

Mouvement > spectroscopy

Electronic Groundstate

Vibration

Rotation

ν~Mouvement Domain λ [m] [cm-1] Observations

Electron excitation

UV-VIS 4.5.10-8 224600 mel = 0.001/1800 kg /NA; L (molecule) = 200 pm

Vibration IR 4.5.10-6 2218 Red. Weight: 0.01Kg/NA;L(10%bondlenght)=15pm

Rotation MW 0.008 1.25 MW=0.1Kg/NA; L(molecule)= 200pm

Translation continuum 2.1015 5x10-18 MW=0.1Kg/NA; L(box lenght)=0.1m

Using 4.12 and 4.13 for specific values of particle mass and box lenght:

Rotation energy levels

Vibration energy levels

Electronic groundstate energy

Schema is not at scale concerning various energy levels for different types of movement.

To calculate the energies for these experimental values !!!

4.3.1 Selection rules

τμ dfi ΨΨ∫μ - dipol moment operator

Ψi/f – wavefunctions

For a transition involving the absorption of a photon (IR, optical etc.) there must be a change in dipole moment on going from the ground (i) to the excited state (f):

Transition probability:

(4.14)

Allowed transition:

Forbidden transition:

0≠ΨΨ∫ τμ dfi

0=ΨΨ∫ τμ dfi

(4.15)

(4.16)

The integral is nonzero only if the integrand is unchanged by any operation of symmetry of the molecule.

Selection rules

Laporte selection rules (for UV-Vis spectra):

For centrosymmetric species (free ions and octahedral complexes):

u → g and g → u transitions are allowed

g → g and u → u transitions are forbidden

The integral is non-zero only when the overall product ψ1µψ2 has g symmetry.Conditions:

- µ transforms like the functions x, y and z, (u symmetry for a centrosymmetric species).

- Ψ1 and ψ2 differ or not in symmetry, and can be: centrosymmetric (g) or anticentrosymmetric (u).

4.4 UV-Vis spectroscopyGround state of the molecule: a given configuration of nuclei of the atoms forming the molecular structure.

Excitated state of the molecule: an electon has migrated in an other molecule region > rearrangement of the nuclei configuration by vibration.

hν

Vibrational structure of an electronic transition

Electronic transitions

- in solutions > broad bands- in gas phase > resolved vibrational structure.

Vibrational structure of an electronic transition:

A

λ/nm

Absorption spectra of chlorophylls a and b, the main pigments in the visible region of the electromangnetic spectrum.

Absorption spectrum of I2 molecule in gas phase.

4.4.1 Franck-Condon principle

Franck-Condon principle explains the vibrational structure of anelectronic band by considering that the electronic transition takes place faster than the change of the nuclear configuration in the excited stateof the molecule.

Predict the most likely vibrational state (in the excited electronic state).

All other vibrational states in the excited state of the molecule are less probable(less intense):

Absorption band

4.4.2 Electronic transitions

Chromophore: molecular groups with characteristic optical absorptions > Presence of a chromophore induces the color of many substances.

Electronic transitions:

• n-to-π* transitions – transition form a non-bonding orbital to an antibonding π* orbital (energy = 4eV > λ = 290nm)

• π-to-π* transition – electron from a π orbital moves to a π* orbital (energy = 7eV > λ = 180nm for unconjugate double bonds, and higher λ for conjugate double bonds )

• d-d transitions in metal complexes where d orbitals of the metal ar involved.

•CT transitions – transfer of an electron from ligend to the metal d orbitals or inverse (LMCT or MLCT)

Examples of chromophores

n to π* transition for carbonyl groups (excitation of a nonbonding O lone-pair electron to an antibonding CO π* orbital).

π to π* transition for carbon-carbon double bond (excitation of an electron from a π orbital to an antibonding π* orbital).

4.4.3 Transition intensity: experimental

• CT bands are often very strong: ε ~ 1000 - 50000 L mol-1 cm-1

• d-d transitions are intermediate in intensity:

» centrosymmetric molecules: ε ~ 20 - 100 L mol-1 cm-1

» non-centrosymmetric molecules: ε ~ 250 L mol-1 cm-1

• n-to-π* transitions are usually weak, for example in carbonyls they are symmetry forbidden.

Selection rules:

•ΔS = 0

•the intensity of a transition depends on the symmetry of the states involved (Laporte selection rules).

Transition intensity- example

Explanation:

Complexes undergo vibrational motion that can distort the complex so as to remove its center of symmetry.

Coupling between these vibration modes and the electronic transition leads to the transitions being weakly allowed (essentially we excite the complex to a final state that is both electronically excited and vibrationally excited in such as way that the vibration removes the center of symmetry).

This interaction is called vibronic coupling that leads to the rather broad nature of most d-d transitions.

d-d transitions in octahedral complexes are formally forbidden as they are g→ g.

But, d-d transitions in octahedral complexes appear, even if they are weak.

Transition intensity- examplesTransition ε Complexes, CX

Spin forbiddenLaporte forbidden

10-3 – 1 CX, as [Mn(OH2)6]2+

Spin allowedLaporte forbidden

1-1010-100100-1000

Cx, as [Ni(OH2)6]2+square planar Cx, as [PdCl4]2-6-coordinate Cx of low symm.

Spin allowedLaporte allowed

102-103

102-104

103-106

MLCT bands in Cx with unsaturare ligands

non-centrosymm. CX with P atoms

CT in organic compounds

4.4.4 Radiative and non-radiative decay

Excitation energy of a molecule is degraded by:

- termal motion of the surrounding

- radiative decay (electronic transition to a lower-energy orbital and emission of a photon)

-Dissociation (fragmentation of the molecule)

Radiative decay:

1. Fluorescence: spontaneously emmited radiation which ceases very soon after the exciting radiation is extinguish

2. Phosphorescence: spontaneously emmited radiation which may persist long periodes after the exciting radiation is extinguish(energy storage in a reservoir from which is slowly released).

Fluorescence radiation

CLSM micrograph of convolaria

Fluorescence microscopy

The excited molecule:

- is subject to collisions with the surrounding molecules and gives up energy by decreasing the vibrational levels (vibrational relaxation).

- the rest of energy is released by emission of a photon > fluorescence occur at a lower frequency that of the incident radiation!

Fluorescence correlation spectroscopy