Electronic Transitions and Absorption in College Transition dipole moments

College 6

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

… Assuming a steady state , 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 Under these conditions the energy density frequency distribution is given by Planck’s radiation law (averaged over polarizations). En dus:

We vinden dus.. Met μ, het overgangsdipoolmoment, een moleculaire eigenschap

Meten van The microscopic quantities are connected to the macroscopic phenomenon of light absorption by a colored sample via Lambert-Beer’s law. If the intensity of the incident light beam is weak and 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:

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 …. This gives Meet K → B12 en μ12 !!!!

… Gewoonlijk wordt gebruikt ipv Met 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 is Thus, 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.

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

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 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

Solvation, Stokes shift The 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: • 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

Electron recombination? 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) 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

Biological electron transfer, Marcus theory (Nobel prize 1992) Born-Oppenheimer benadering: 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)

Biological electron transfer, Marcus theory (Nobel prize 1992)

Biological electron transfer, Marcus theory (Nobel prize 1992) 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 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 Dt=Dl/c 1 mm => 3 x10-12 s = 3 ps

Meten van electron transfer snelheden ES 2 Excited stateaborption ES 1 Stimulated emission Ground state

Ground State Absorption Excited State Absorption Stimulated Emission Difference Absorption Spectrum: A(t)-A(t=0) Meet ultrasnelle verschijnselen via absorptieverschilmetingen tot op een 100 femtoseconde tijdschaal A or DA l

Absorptieverschilmetingenin het bacteriele RC

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 LIGHT Chl dimer + 3 ps - Chl 4 nm Reactie Centrum 1 ps - Ph 200 ms 200 ps - - Q Fe 1 ps =10-12 s

Electronic Transitions and Absorption in College Transition dipole moments