I2 Vapor Absorption Experiment and Determinationof 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)

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, λis 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∆r2/hν , where ∆r = the change in bond length upon the “vertical excitation”. For I2, λ is quite large, ~30. In other words, the vertical vibronic transition from the ground state will reach v’= ~30 vibrational quantum number of the excited state.

HOMO

LUMO

PURE ANTIBONDING

PURE BONDING

Mostly BONDING

Mostly ANTIBONDING

Chlorophyll

14000 16000 18000 200000.05

0.10

0.15

0.20

0.25

0.30Ab

sorb

ance

(10

cm p

ath)

"wavenumbers" cm-1

I2 Vapor Absorption

700 nm 500 nm588.24 nm 555.55 nm 526.32 nm

http://www.mpcfaculty.net/mark_bishop/molecular_orbital_theory.htm

I2HOMO

LUMO

PURE ANTIBONDING

PURE BONDING

VERY LARGE BOND LENGTH INCREASE!

λλ e!'v

v' to0 v"fromFactor Condon -Franck'v

==

Relative intensities are given by Franck-Condon Factors:the square of the overlap integral of the initial vibrationalwavefunction and the final vibrational wavefunctions.

For the simple model of same harmonic oscillator potentialenergy in both states:

λ is the increase in vibrational potential energy causedby the vertical transition divided by hνvib (the vibrationalenergy level spacing.) i.e., λ=[1/2 k(∆xe)2/hνvib]

This happens to be the same as the Poisson Distribution (coincidental)

λλ e!'v

v' to0v"'v

=

=

Cartoon

NO bond lengthchange

λ=2 bond lengthchange

small overlap because negative partcancels positive part

small overlap because excited statepotential energy is centered at alonger equilibrium bond length

LARGEST overlap because large positive overlap and small negative part.

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

“Hot Bands”

135.00.368

0.368

)h-v(E :oscillator harmonicfor that recall Ifor true toclose is which K, 298at cm 207 kT assuming

levels al vibrationground of spopulation of ratio

22cm 207cm 20722)(-

0

2

1cm 207cm 207)(-

0

1

v

21-

1-

1-02

1-

1-01

21

===≈==

==≈==

==≈

−×−−−

−−−−

eeeePP

eeeePP

kTh

kTEE

kTh

kTEE

vib

vib

vib

/

ν

ν

νν

2

22cm 207cm 20722)(-

0

2

4cm 51cm 207)(-

0

1

-1

Ifor emperaturenitrogen t liquidat neglegible are bandsHot

00034.00.018

018.0

:cm 52 kT ,emperture)nitrogen t (liquid K, 75TAt

1-

1-02

1-

1-01

===≈==

==≈==

==

−×−−−

−−−−

eeeePP

eeeePP

kTh

kTEE

kTh

kTEE vib

ν

ν

588 584 580 576 572 568 564 560 556 552 548 544 5400.05

0.10

0.15

0.20

0.25

0.30

v'=20 v"=1

v'=25 v"=1

v'=25 v"=0

v' 20 v"=2

v' 15 v"=0

Abs

nm

v'=20 v"=0

2”v’ 1”v’ 0”v’ Only these seen at LOW THOT HOT