Transition Dipole Moment and Electron Transfer

[Sina]

Well I am doing a project suffice to say on electron transfer. In protein complexes it has been shown that förster equation gives pretty good results, so I am trying to understand this equation. But there seems to be not much resource on that (I think I will be buying Förster's own book finally...). The thing is there is this emission dipole moment and absorption dipole moment, more commonly seen as transition dipole moments. Can anyone tell me what is this transition dipole moment and how is it different from normal dipole moment (electric ofcourse). Is it the molecules dipole moment when it is excited? Thanks

 

[reilly]

The transition dipole moment, say for i -> f, is the matrix element, <f| P |i>,

where P is the dipole moment operator.
Regards,
Reilly Atkinson

 

[quetzalcoatl9]

you need to review some prerequisite material.

if i were you, i would review Fermi's golden rule, the Franck-Condon principle and then dive into the Marcus theory of non-adiabatic electron transfer.

when you calculate the electron transfer rate you are in essence calculating the golden rule expression where you have replaced the density of states term with (usually) a semi-classical form (in marcus theory is follows from the analytic geometry of a parabolic free energy profile).

 

[Sina]

The thing is my job isn't as hard as calculating the transfer rate. I only need to make comparisons like if the distance is 2 times the initial then transfer rate is 1/2^6 times the initial electron transfer rate, or like if its transition dipole moment changes such then its etr changes such etc...

This is why I need to understand what transition dipole moment is, and I already have a program that will do the calculation for me, I just need to know in which stage of the molecule we call its dipole moment, transition dipole moment (like it could be for example: it is the dipole moment of the molecule in its transition states etc...)

And although I had some introduction to quantum, I really didn't have yet any serious courses on that. I am doing computer, genetics, molecular modelling - there is yet to quantum; maybe in masters degree, but I am into biophysics now and I need some basic information on this topic. That is why I am not going into hard stuff like calculating electron transfer rate from zero. And I didn't understand what you meant by ay for i -> f, is the matrix element, <f| P |i>, what is i and f ? I may be able to derive the rest from that I suppose (I remember this matrix notation from introduction to quantum, I just need to review).

And I need to point out that I am more interested in using the Förster's theory in this project, (which I believe are deried from the theories you counted), I need to simply compare the initial and final distances, the initial and final transition dipole moments, the initial and final overlaps and maybe deltaG's to see the activation energy of electron transfer.

Regards
Sina

 

[Sina]

Okay here is another question, can we say that absopriton dipole moment is the dipole moment of a molecule when it absorbs a photon at its maximum absorbance wavelength?

 

[Arienn]

Hey Sina,
transition dipole moment is a dipole moment the molecule has only when a disturbance is in effect. In interaction with electromagnetic radiation it means only when it is currently absorbing light (i.e. only when you're actually shining on the sample with light). It is not the dipole moment of molecule in the excited state, nor in the ground state. It is a special attribute of the disturbed system (=being hit by photons).
It is calculated as <f|V|i>, f... wavefunction of the final (excited) state of molecule, i... wavefunction of the initial (ground) state of molecule, V... disturbance = transition dipole moment = mu*E (mu ... dipole moment of molecule in ground state, E... electric part of the EM field).
Hope it helps and have fun.

 

[linwenzi]

Okay here is another question, can we say that absopriton dipole moment is the dipole moment of a molecule when it absorbs a photon at its maximum absorbance wavelength?

Please see http://en.wikipedia.org/wiki/Transition_dipole_moment.
There you will find the clear relationship between transition dipole moment and dipole moment.