I 2 Vapor Absorption Experiment and Determination of Bond Dissociation Energy.

Transcription

1 I 2 Vapor Absorption Experiment and Determination of Bond Dissociation Energy. What determines the UV-Vis (i.e., electronic transitions) band appearance? Usually described by HOMO LUMO electron jump LUMO has one more node than the HOMO causes geometry changes: bonds get longer on average (although some may get shorter)

2 The Franck Principle, Condon approximation, and Franck-Condon Factors. Excitation of a diatomic molecule to its lowest excited electronic state, most often is well described by removing an electron from the highest occupied MO (HOMO) and placing it in the lowest unoccupied MO (LUMO). Usually the LUMO has one more node than the HOMO, typically causing more bonds to be more antibonding relative to the HOMO. In any case, the bond orders are instantly changed (a so called vertical transition ), while the nuclei hardly move during the excitation process ( Franck Principle ). Initially following the electronic excitation, the nuclei are in a non-stationary vibrational quantum state that may be described as a superposition of the excited state vibrational eigenstates. Also in 1926, Edward Condon worked out the quantum mechanics that gave the relative intensities of the vibronic transitions which contained the approximation that the electronic transition dipole moment is essentially independent of the vibrational levels involved (the Condon approximation), which leads to the relative absorbance of an vibronic transitions to be given by the square of the overlap integral of the final state vibrational wave function with the initial ground state vibrational wave function, now known as the Franck-Condon factor. Handout #2 indicates how the Franck-Condon factors, and thus the appearance of the spectrum will vary as a function of the bond length change upon excitation and the excited vibrational state for a single vibrational mode. This is depicted in terms of λ. Here, λ is not wavelength, but a dimensionless measure of the stored harmonic spring potential energy in units of the harmonic energy level spacing, i.e., ½ k r 2 /hν, where r = the change in bond length upon the vertical excitation. For I 2, λ is quite large, ~3. In other words, the vertical vibronic transition from the ground state will reach v = ~3 vibrational quantum number of the excited state.

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4 PURE ANTIBONDING LUMO Mostly ANTIBONDING HOMO Mostly BONDING PURE BONDING

5 Chlorophyll

6 Absorbance (1 cm path) I 2 Vapor Absorption nm nm nm 7 nm 5 nm "wavenumbers" cm

7 PURE ANTIBONDING I 2 LUMO HOMO PURE BONDING shop/molecular_orbital_theory.htm VERY LARGE BOND LENGTH INCREASE!

8 Relative intensities are given by Franck-Condon Factors: the square of the overlap integral of the initial vibrational wavefunction and the final vibrational wavefunctions. For the simple model of same harmonic oscillator potential energy in both states: Franck - Condon Factor from v" = to v' This happens to be the same as the Poisson Distribution (coincidental) = v' λ e λ v'! λ is the increase in vibrational potential energy caused by the vertical transition divided by hν vib (the vibrational energy level spacing.) i.e., λ=[1/2 k( x e ) 2 /hν vib ]

9 v" = = v' to v' λ e λ v'!

10 Cartoon NO bond length change λ=2 bond length change

11 small overlap because negative part cancels positive part LARGEST overlap because large positive overlap and small negative part. small overlap because excited state potential energy is centered at a longer equilibrium bond length

12 But, real molecules NOT HARMONIC. Bonds get weak when stretched Energy levels get closer together with increasing energy. Why?

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14 assumingν Hot Bands ratio of populations of ground vibrational levels = 27 cm recall that for harmonic oscillator : P P 1 P P 2 -( E1 E -( E2 E 2 vib ) ) -( E1 E -( E2 E ) ) hν vib 2hν 2hν e e 27 cm 27 cm 2 27 cm 27 cm 27 cm 51cm 2 27 cm 27 cm at 298 K, E (v - = v = =.18 = =.18 which is close to true for I / 2 At T = 75 K, (liquid nitrogen temperture), = 52 cm P1 P P P hν vib e e 2 )hν vib =.135 Hot bands are neglegible at liquid nitrogen temperature for I : =

15 HOT HOT 2 v 1 v v Only these seen at LOW T Abs v'=25 v"= v'=2 v"= v'=25 v"=1 v' 15 v"= v'=2 v"=1 v' 2 v"= nm