College 6. Transition dipole moments & absorption.

College 6

Transition dipole moments & absorption

When a beam of light impinges on a sample of (bio)molecules, part of the light may be absorbed, the precise amount depending on the wavelength. For instance, chlorophyll, the pigment of plants displays two major transitions around 670 nm (red) and 430 nm (blue). In addition several weaker transitions are visible.

fEEdtdN ififi2222

cos

For a single molecule:

The quantity that determines the probability of a transition to take place is the transition dipole moment: if

ifE

Where is a lineshape function f

Absorption

Electronic transitions

The electronic transitions are associated to transition dipole moments with different strengths and orientations. The longest-wavelength transition is invariably polarized along the y-axis of the molecule and is therefore known as the Qy transition. This means that the absorption will be strongest if the electric field vector of linearly polarized light is parallel to the y molecular axis of the pigment. The exciting light couples to the π-electrons of the molecule and transiently arranges them somewhat during the transition. The Qy transition causes a shift in electron density that is directed along the y molecular axis of the molecule

Electronic density changes associated with Qx and Qy transitions in bacteriochlorophyll a. Note that the signs are chosen arbitrarily, the charge density changes oscillate with the incident light field.

Einstein coefficients

2212211121 NAWNBWNB

dt

dN

W(ω) = ‘light’ =energy density of radiation in range ω +dω

…

Assuming a steady state , 01 dt

dN

212112

21

BNNB

AW

If we now take the situation that there is no external radiation field and that the system is in thermal equilibrium at a temperature T, then the ratio follows from the Boltzmann distribution between states of different energies

kTeN

N 2

1

Under these conditions the energy density frequency distribution is given by Planck’s radiation law (averaged over polarizations).

1

132

3

kTecW

32

3

21

21

2112

cB

A

BB

En dus:

We vinden dus..

32

3

21

21

2112

cB

A

BB

2

120

3

3

21 3

c

A

Met μ, het overgangsdipoolmoment, een moleculaire eigenschap

20

2

2112 3 B

Meten van 21211221 ,,, ABB

The microscopic quantities are connected to the macroscopic phenomenon of light absorption by a colored sample via Lambert-Beer’s law.

2211121 NANWB

dt

dN 21 NN

If the intensity of the incident light beam is weak and

dFV

adzWBNadzd

t

W121

It then follows from energy conservation that the rate of decrease of the beam energy must be equal to the rate at which the energy is removed from the light beam by absorption:

….

This gives V

WBFNt

W 121

we rewrite this in terms of the change in intensity I in Wm-2 of the light beam upon passage through the sample slice. Inspection of Fig.6.4 shows that the difference between the amount of energy entering and leaving the sample slice per unit of time precisely equals the rate of decrease of the beam energy. Thus we obtain Moreover, , with c the speed of light and n the index of refraction of the medium

zItW cnIW

I

Vnc

FNB

z

I 112

KzeIzI 0 Vcn

FBNK

121

Meet K → B12 en μ12 !!!!

…

Gewoonlijk wordt gebruikt ipv ODIlI 100 KzeIzI 0

Met lCOD

Here ε is the molar extinction coefficient (usually expressed in dm3mol-1cm-1), l the pathlength (usually in cm) and C the concentration of the sample (usually expressed in moldm-3).

For example, in a leaf chlorophyll a, at 680 nm, extinction coefficient is 105 dm3mol-1cm-1. The chl concentration is about 10-3 mol dm-3 and the pathlength is about 0.02 cm. Thus, the OD of a single leaf at 680nm isThus, the reduction in intensity of 680 nm light upon passage through a leaf is about a factor of 100. As a consequence no red light is detected below the outer array of leaves of a tree.

21021010 235 OD

d

band 612

12 1001.1

Light, Spectrum and Absorption

i

f

I0()

I)

lCOD

IIOD

0log

l

C =concentration

Beer-Lambert’s law:

I0()

Franck Condon principle

Fig 6.6 In the quantum mechanical version of the Franck-Condon principle, the molecule undergoes a transition to the upper vibrational state that most closely resemble the vibrational wavefunction of the lower electronic state. The two wavefunctions shown here have the greates overlap integral of all the vibrational states of the upper electronic electronic state and hence are most similar

Because the nuclei are so much more massive than the electrons, an electronic transition takes place very much faster than the nuclei can respond.

Jablonski diagram

Fig 6.7 Potential energy diagrams and spectra for absorption and fluorescence electronic transitions in organic molecules. (a) The initial state for absorption is usually the ground vibrational state of the ground electronic state, while the final state is usually an excited vibrational state of the excited electronic state. (b) The initial state for fluorescence is the ground vibrational state of the first excited state, while the final state is an excited vibrational state of the ground electronic state. (c) Absorption and emission spectra that result from the transitions shown in (a) and (b).

The Fates of the Electronic Excited States

Radiationless decay and fluorescence

10-12 s

10-9 s

Fig 6.23 Left: The sequence of steps leading to fluorescence. After the initial absorption, the upper vibrational states undergo radiationless decay by giving up energy to the surroundings. A radiative transition then occurs from the vibrational ground state of the upper electronic state. Right: Absorption spectrum (a) shows a vibrational structure characteristic of the upper state. A fluorescence spectrum (b) shows a structure characteristic of the lower state; it is also displaced to lower frequencies (but the 0-0 transitions coincide) and resembles a mirror image of the absorption

Stokes’shift:Solvent Relaxation

Solvation, Stokes shiftThe 0-0 absorption and fluorescence peaks are not always exactly coincident because the solvent may interact differently with the molecule in the ground and excited states (for instance the H-bonding pattern may be different). Because the solvent molecules do not have the time to rearrange during the transition, the absorption occurs in an environment characteristic of the solvated ground state; however, the fluorescence occurs from in an environment characteristic of the solvated excited state

All decay processes:

Jablonski Diagram

Internal conversion: 10-12 sec

Fluorescence: 10-8 sec

Intersystem Crossing: 10-8 sec

S0

S1

S3

S2 21

21

AkkA

F iscic

Quenching process

Qiscic kAkkA

F 21

21

•Radiative decay (fluorescence)•Intersystem crossing(triplet formation)•Internal conversion(heat)•Quenching process(electron transfer, …)

Electron transfer

The chemical properties of an excited pigment molecule may be very different from those of the same molecule in the ground or lowest energy state. In particular the oxidation-reduction potential for electrons either being added to the molecule or given up by it is very different in the excited state compared with the ground state

1

When light raises a molecule to an excited electronic state, themolecule becomes a stronger reductant

LIGHT

Incr

easi

ng

En

erg

y

A* BA B

HOMO

LUMO

LUMO

HOMO

electrons

Electron recombination?

1

The electron carriers in the bacterial reaction center are arranged around an axis of approximate rotational symmetry

Axis of approximate rotational symmetry

BChl dimer

BPh

Q

Fe

BChlBChl

BPh

Q

BChl = bacteriochlorophyll

BPh = bacteriopheophytin(BChl with 2 H in place of Mg)

Q = ubiquinone

Two of the four BChlsform a dimer (P870) that acts as the initial electron donor

The oxidized primary electron donor is positioned next to the reduced acceptor. Most likely outcome according to the laws of thermodynamics is for the electron to simply transfer back to the donor = recombination, energy lost.

To avoid this: a series of ultrafast secondary electron transfer reactions to separate the oxidized and reduced species in space. The result is that the positive and negative charges become separated from each other, and the probability of recombination is greatly reduced.

Biological electron transfer, Marcus theory (Nobel prize 1992)

redoxoxred ADAD

fifiet EEVk 22

Nuclear Dynamics and Electron Transfer

DA

D+A-

Nuclear Configuration

FCVW RP

22

Rate of electron Transfer:

RDA RD+

A-

R#

V is the electronic coupling between the two states and has units of energy, usually given in wave numbers (cm-1). The delta function ensures conservation of energy



DA

D+A-


FCVW RP

22


RDA RD+

A-

R#

Born-Oppenheimer benadering:

fifii

iet EEVPk 2

FCVk elet22

V is the square of the electronic coupling matrix element between the electronic states of the reactant and those of the product, and FC is the Franck-Condon factor (implicitly including the summation over all states)


Correspondence between the electronic energy levels (shown on the left) and the nuclear energy levels (shown on the right).

(a) At the nuclear configuration q0R the

electron to be transferred in DA is in an occupied electronic energy level (denoted by the blue circle) and the lowest unoccupied of D+A- (denoted by an unfilled circle) is too high in energy to be a good electron acceptor. (b) As the nuclei rearrange to a configuration represented by q*, DA and D+A- become degenerate and electron transfer occurs by electron tunneling through a barrier of height V and width r, the edge-to-edge distance between D and A. (c) The system relaxes to the equilibrium position of D+A- denoted by q0

P in which the lowest unoccupied electronic level of DA is higher in energy than the highest occupied electronic level of D+A-

Rq0



DA

D+A-


FCVW RP

22


RDA RD+

A-

R#

FCVk elet22

The electronic coupling matrix element experimentally depends primarily on the distance and orientation of the reacting species. A variety of evidence indicates that this parameter depends exponentially on the distance between the reacting groups

)exp(20,

2 dVV elel

A consensus seems to have been reached that a value of 1.4Å-1 is reasonable for protein-mediated electron transfer processes

Femtoseconde pump-probe

t=l/c

1 mm => 3 x10-12

s

= 3 ps

Stimulated emission

Excited stateaborption

Ground state

ES 1

ES 2

Meten van electron transfer snelheden

Ground State Absorption

Excited State Absorption

Difference Absorption Spectrum: A(t)-A(t=0)

AorA

Stimulated Emission

Meet ultrasnelle verschijnselen via absorptieverschilmetingen tot op een 100 femtoseconde tijdschaal

Absorptieverschilmetingenin het bacteriele RC

Chl dimer

Ph

Q

Fe

Chl

3 ps

1 ps

200 ps

LIGHT

When the complex is excited with light, an electron moves from the Chl dimer to a Pheophytin (looks like Chlorophyll) and then to a quinone

1 ps =10-12 s

Reactie Centrum

200 s

+-

-

--

4 nm

College 6. Transition dipole moments & absorption.

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Transcript of College 6. Transition dipole moments & absorption.