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Chemistry 2 Lecture 10 Vibronic Spectroscopy

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Learning outcomes from lecture 9 Excitations in the visible and ultraviolet correspond to excitations of electrons between orbitals. There are an infinite number of different electronic states of atoms and molecules. Assumed knowledge Be able to qualitatively explain the origin of the Stokes and anti- Stokes line in the Raman experiment Be able to predict the Raman activity of normal modes by working out whether the polarizability changes along the vibration Be able to use the rule of mutual exclusion to identify molecules with a centre of inversion (centre of symmetry)

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Which electronic transitions are allowed? The allowed transitions are associated with electronic vibration giving rise to an oscillating dipole

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E lectronic spectroscopy of diatomics For the same reason that we started our examination of IR spectroscopy with diatomic molecules (for simplicity), so too will we start electronic spectroscopy with diatomics. Some revision: –there are an infinite number of different electronic states of atoms and molecules –changing the electron distribution will change the forces on the atoms, and therefore change the potential energy, including k, e, e x e, D e, D 0, etc

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Depicting other electronic states Ground Electronic State Excited Electronic States 1. Unbound 2. Bound There is an infinite number of excited states, so we only draw the ones relevant to the problem at hand. Notice the different shape potential energy curves including different bond lengths…

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Ladders upon ladders… Each electronic state has its own set of vibrational states. Note that each electronic state has its own set of vibrational parameters, including: - bond length, r e - dissociation energy, D e - vibrational frequency, w e re’re’re”re” De”De” De’De’ e”e” e’e’ Notice: single prime ( ’) = upper state double prime (”) = lower state

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The Born-Oppenheimer Approximation The total wavefunction for a molecule is a function of both nuclear and electronic coordinates: (r 1 …r n, R 1 …R n ) where the electron coordinates are denoted, r i, and the nuclear coordinates, R i. The Born-Oppenheimer approximation uses the fact the nuclei, being much heavier than the electrons, move ~1000x more slowly than the electrons. This suggests that we can separate the wavefunction into two components: (r 1 …r n, R 1 …R n ) = elec (r 1 …r n ; R i ) x vib (R 1 …R n ) Electronic wavefunction at × each geometry Total wavefunction = Nuclear wavefunction

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The Born-Oppenheimer Approximation (r 1 …r n, R 1 …R n ) = elec r 1 …r n ; R i ) x vib R 1 …R n ) The B-O Approximation allows us to think about (and calculate) the motion of the electrons and nuclei separately. The total wavefunction is constructed by holding the nuclei at a fixed distance, then calculating the electronic wavefunction at that distance. Then we choose a new distance, recalculate the electronic part, and so on, until the whole potential energy surface is calculated. While the B-O approximation does break down, particularly for some excited electronic states, the implications for the way that we interpret electronic spectroscopy are enormous! Electronic wavefunction at × each geometry Total wavefunction =Nuclear wavefunction

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Spectroscopic implications of the B-O approx. 1. The total energy of the molecule is the sum of electronic and vibrational energies: E tot = E elec + E vib E elec E tot E vib

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Spectroscopic implications of the B-O approx. In the IR spectroscopy lectures we introduced the concept of a transition dipole moment: |1 |2 upper state wavefunction lower state wavefunction transition dipole moment dipole moment operator integrate over all coords. using the B-O approximation: 2. The transition moment is a smooth function of the nuclear coordinates.

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Spectroscopic implications of the B-O approx. |1 |2 2. The transition moment is a smooth function of the nuclear coordinates. If it is constant then we may take it outside the integral and we are left with a vibrational overlap integral. This is known as the Franck-Condon approximation. 3. The transition moment is derived only from the electronic term. A consequence of this is that the vibrational quantum numbers, v, do not constrain the transition (no v selection rule).

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Electronic Absorption There are no vibrational selection rules, so any v is possible. But, there is a distinct favouritism for certain v. Why is this?

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Franck-Condon Principle (classical idea) Classical interpretation: “Most probable bond length for a molecule in the ground electronic state is at the equilibrium bond length, r e.”

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Franck-Condon Principle (classical idea) The Franck-Condon Principle states that as electrons move very much faster than nuclei, the nuclei as effectively stationary during an electronic transition. In the ground state, the molecule is most likely in v=0.

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Franck-Condon Principle (classical idea) The Franck-Condon Principle states that as electrons move very much faster than nuclei, the nuclei as effectively stationary during an electronic transition. The electron excitation is effectively instantaneous; the nuclei do not have a chance to move. The transition is represented by a VERTICAL ARROW on the diagram (R does not change).

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Franck-Condon Principle (classical idea) The Franck-Condon Principle states that as electrons move very much faster than nuclei, the nuclei as effectively stationary during an electronic transition. The most likely place to find an oscillating object is at its turning point (where it slows down and reverses). So the most likely transition is to a turning point on the excited state.

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Quantum (mathematical) description of FC principle approximately constant with geometry Franck-Condon (FC) factor μ 21 = constant × FC factor FC factors are not as restrictive as IR selection rules ( v=1). As a result there are many more vibrational transitions in electronic spectroscopy. FC factors, however, do determine the intensity.

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Franck-Condon Principle (quantum idea) In the ground state, what is the most likely position to find the nuclei? Max. probability at R e

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Franck-Condon Factors If electronic excitation is much faster than nuclei move, then wavefunction cannot change. The most likely transition is the one that has most overlap with the excited state wavefunction. v’ = 0 1 2 v” = 0

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Look at this more closely… Excellent overlap everywhere Negative overlap to left, postive overlap to right overall zero overlap Negative overlap in middle Positive overlap at edges overall very small overlap

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Franck-Condon Factors

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v=10 Note: analogy with classical picture of FC principle! v. poor v=0 overlap

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Electronic Absorption There are no vibrational selection rules, so any v is possible. μ 21 = constant × FC factor Relative vibrational intensities come from the FC factor

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Absorption spectrum of binaphthyl Example of real spectra showing FC profile

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Absorption spectrum of CFCl

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If the excited state is dissociative, e.g. a * state, then there are no vibrational states and the absorption spectrum is broad and diffuse. Unbound states (1)

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Even if the excited state is bound, it is possible to access a range of vibrations, right into the dissociative continuum. Then the spectrum is structured for low energy and diffuse at higher energy. Unbound states (2)

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Some real examples… A purely dissociative state leads to a diffuse spectrum. HI

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The dissociation limit observed in the spectrum! I2I2 Some real examples…

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Analyzing the spectrum… All transitions are (in principle) possible. There is no v selection rule Vibrational structure

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cm -1 18327.8 18405.4 18480.9 18555.6 18626.8 18706.3 18780.0 18846.6 18911.5 18973.9 19037.5 v’ 25 26 27 28 29 30 31 32 33 34 35 v” 0 0 0 0 0 0 0 0 0 0 0 How would you solve this? (you have too much data!) 1. Take various combinations of v’ and solve for e and e x e simultaneously. Average the answers. 2. Fit the equation to your data (using XL or some other program). Analysing the spectrum…

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cm -1 18327.8 18405.4 18480.9 18555.6 18626.8 18706.3 18780.0 18846.6 18911.5 18973.9 19037.5 v’ 25 26 27 28 29 30 31 32 33 34 35 v” 0 0 0 0 0 0 0 0 0 0 0 E elec = 15,667 cm -1 e = 129.30 cm -1 e x e = 0.976 cm -1 Dissociation energy = 19950 cm -1 Analyzing the spectrum…

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Learning outcomes Be able to draw the potential energy curves for excited electronic states in diatomics that are bound and unbound Be able to explain the vibrational fine structure on the bands in electronic spectroscopy for bound excited states in terms of the classical Franck-Condon model Be able to explain the appearance of the band in electronic spectroscopy for unbound excited states The take home message from this lecture is to understand the (classical) Franck-Condon Principle

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Next lecture The vibrational spectroscopy of polyatomic molecules. Week 12 homework Vibrational spectroscopy worksheet in tutorials Practice problems at the end of lecture notes Play with the “IR Tutor” in the 3 rd floor computer lab and with the online simulations: http://assign3.chem.usyd.edu.au/spectroscopy/index.php

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Practice Questions 1.Which of the following molecular parameters are likely to change when a molecule is electronically excited? (a) ω e (b) ω e x e (c) μ (d) D e (e) k 2. Consider the four sketches below, each depicting an electronic transition in a diatomic molecule. Note that more than one answer may be possible (a)Which depicts a transition to a dissociative state? (b)Which depicts a transition in a molecule that has a larger bond length in the excited state? (c)Which would show the largest intensity in the 0-0 transition? (d)Which represents molecules that can dissociate after electronic excitation? (e)Which represents the states of a molecule for which the v”=0 → v’=3 transition is strongest?

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