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QuantumChemistryandSpectroscopy
Text book Engel: Quantum Chemistry and Spectroscopy (3 ed., QCS) or
Engel and Reid: Physical Chemistry (3 ed.)
Chapter7.Molecularspectroscopy(Engel:QCSchapter
14)
Now we have rather good understanding of electronic structure of
simple molecules. Now we can start thinking how the molecular
spectra will look. Of course every molecule is different and a
general discussion is impossible but we can learn a lot form few
simple examples. Let us start from O2 molecule. We know it’s
ground state. The highest state is the p* and it is degenerated
s*
---
p* -↑p
s
thus the ground state is triplet. What kind
of molecular excitations the O2 will have.
-↑-
-↑↓- -↑↓- ↑↓-
The first excitation is a singlet state with
same orbital as in the ground state. The
ground state is marked with
3S g
and the
excited state as 1Dg . Then in the next excitation the electron is
p* -↑p
s
-↓-
-↑↓- -↑↓- ↑↓-
still in a singlet state but on different
atom orbital. This is marked as
1S +
g
(Warning
the assignment of the states can be
Incorrect, I was confused when reading Engel but the labels are
correct). The next excitation comes from an electron exited to
p* -↑↓p
---
-↑↓- -↑↓-
s* state. Using Hund’s rule the total spin is
1 and the state is triplet. It is marked with
s
3S + .
u
- ↑↓-
This state is very close to O2
dissociation limit. Now it is important that there are several
s*
-↑-
p* -↑--
molecular excited states. This is very
---
p
-↑↓- -↑↓-
s
- ↑↓-
general feature. Also these states can have
different spin states. Next the selections
rules are rather complex. First the spin
cannot change, DS=0, the angular momentum L can change 0,±1. For
homoatomic dimers u ↔ u, g ↔ g transition are forbidden, the u ↔
g transition is allowed. Also
the S- ↔ S+ transition is
forbidden. (The S- ↔ S- and S+ ↔
react with O2
O2 + hv → 2O∙
S+ transition are allowed). At
the end the O2 cannot be exited
to any of the bound states. The
fist allowed transition is to
the 3S-u state. The needed energy
is corresponds to radiation of
wavelength around 175 – 200 nm.
This is a strong UV region. Is
the transition to the lower
states would be allowed O2 would
adsorb at the visible light
region and the atmosphere would
not be transparent. The O2
cannot dissociate at lower part
of the atmosphere but at
stratosphere there is much more
strong UV-radiation. The
dissociated oxygen atoms will
molecules to produce ozone, O3.
O∙ + O2 + M → O3 + M
This is the most important ozone production reaction in the
atmosphere.
In the energy diagrams the small side marks denote the
vibrational levels.
Vibrational fine structure in electron spectra
The vibration lines can be seen well in the electron spectra. As
in the roto-vibrational spectra different quantum states cannot
be separated. The transition dipole is now rather complex. We
need to deal at the same time the atomic and electronic wave
functions.
Y = fvib, ground ( R1 ,..RM )jel , ground ( r1..rN )
This is technically rather complex object and now we need to
compute the transition dipole. Note that the electrons are
excited so the dipole operator affect (mostly) to the electronic
wave functions. From the atomic wave functions the overlap
integral is relevant. We can assume that the atomic wave
functions are close to harmonic oscillator wave functions.
òf
vib , ground
( R )fvib ,excited ( R ) dR × ò jel , ground ( r1..rN ) mˆjel ,excited ( r1..rN ) d 3r1..d 3rN
Note that the selection rule from harmonic oscillator (Dn=±1) is
not valid. I do not have a good explanation, but the electrons
couple stronger to the electric field.
There is also another phenomena which is due to the mass
difference between electrons and atoms. The electron transitions
are so quick that the atoms do
not have time to move. This
Franck-Condon principle is
general. It is easy to utilize in
the potential energy diagrams.
When the minima of the potential
energy curves are not at the same
position, the excitation line
goes straight up and the most
likely energy excitation is not
from vibrational ground state to
ground state. The overlap
integral can be used to estimate
the intensity of the transition
òf
vib , ground
( R)fvib , excited ( R) dR
2
Note: in the case of O2 the minima
were almost at the same position
so then the 0 -> 0 transition is
the most likely. The side spectra
is very useful. From it the
molecular vibration connected to the electronic excitation can
be determinate. (In many atom molecule it is not easy to know
which vibration is really measured.)
Fluorescence spectra
The Franck-Condon principle is useful in fluorescence spectra.
There we are looking both the molecules adsorption and emission
spectra, usually at visible or UV-light range. Both the
adsorption and emission spectra have several almost equally
spaced peaks. The spectra are almost mirror images of each other
and emission spectra is higher in energy. The spectra is easy to
understand with the energy level diagrams. In the example below
the potentials are slightly off-set so the 0 -> 4 peak is more
probable. Once the system is at the excited state, S 1, the
vibrational states will release energy at IR region. The
relaxation to vibrational ground state is rather fast. After the
molecule is at state S1 vibrational ground state it can relax
back to S0 state. This relaxation can end to different
vibrational states.
Time scales of the different processes. Note that the
fluorescence process have to be much slower than the vibrational
processes.
From:
http://micro.magnet.fsu.edu/primer/techniques/fluoresce
nce/fluorescenceintro.html
The fluorescence spectroscopy is very useful in biology and it
has several every day applications. One of the most common are
the fluorescent lights. Inside of these lamps are mercury vapor
that emits mild UV light. The fluorescent material on the lamps
surface will turn the UV lights to white light. These lamps are
more energy efficient than normal light bulbs. Also the color of
the light can be tuned with different fluorescent materials.
Some of the least pleasant light comes from tubes containing the older, halophosphate-type phosphors
(chemical formula Ca5(PO4)3(F, Cl):Sb3+, Mn2+).
From: https://en.wikipedia.org/wiki/Fluorescent_lamp
Chromophores
All chemical molecules adsorb at some wave length, mostly at UV.
But we are interested of chemical groups that adsorbs are (near)
visible range. These are usually called chromophores. As an
example we can look C=O group in formaldehyde H2CO. The carbon is
sp2 hybridized, two of the hybrid orbital form the C-H s-bonds
and one will participate to the C=O bond. The sp2 orbital and
O:2pz orbital will form a s-bond. The px orbitals from the C and
O will form a p-bond and the electron pair on the O:py orbital
does not interact much with the carbon, it is marked with n O.
(The O:2s orbital does not interact much with the C.)
(2sO)2(sCH1)2(sCH2)2(sCO)2(pCO)2(nO)2(pCO*)0
Now we have the electronic structure of C=O group.
The transition rules are again rather complex but the lowest
transition is n → p* the next one is p → p*, and the highest one
is s → s* . There is also the triplet states.
The description is mostly valid to any C=O group. Below is a
table of few common chromophores. As one can see most of them
are on the UV range. Well we know that, most of organic
compounds are transparent. And UV radiation, especially strong
UV, will broke most molecules. (Visible light 400 -700 nm.) The
table contain the lowest excitation and there are other
transitions higher in energy.
The chromophores below are simple but nature is full of more
complex chromophores. One very interesting class is conjugated pbond systems, like beta-carotene and 11-cis-retinal. The 11-cisretinal is the prime molecule responsible in vision. In retinal
it is important that is changes its shape in the excitation. The
long p-bonded systems have adsorption at longer wave lengths.
This can be understood using the Huckel model. We can solve the
Huckel matric for longer p-bonded chain and we will see that the
NxN matrix
−
ℎ
0
0
0
0
ℎ
−
ℎ
0
0
0
0
ℎ
−
ℎ
0
0
0
0
ℎ
−
ℎ
0
…
…
..
..
…
..
0
0
0
0
ℎ
−
=0
Will have solution of En= H11 + 2h cos(np/(N+1)). When N is large
we will have several states in the range of H11 ± 2h. Half of
them are occupied and for even N the HOMO-LUMO gap is 2h
[cos(Np/(2(N+1))- cos((N+2)p/(2(N+1))] ≈ 4h/(N+1) so the gap
shrinks when the N increases
retinal
From: https://en.wikipedia.org/wiki/Chromophore
Carotene
Last also the metal complexes are often colorful and basis of
many pigments. Blood’s red color comes from the iron porphyrin.
Many of these pigments are toxic due to the metal.
·
·
·
·
·
·
·
·
·
·
Cadmium pigments: cadmium yellow, cadmium red, cadmium green, cadmium orange,
cadmium sulfoselenide
Chromium pigments: chrome yellow and chrome green
Cobalt pigments: cobalt violet, cobalt blue, cerulean blue, aureolin (cobalt yellow)
Copper pigments: Azurite, Han purple, Han blue, Egyptian blue, Malachite, Paris green,
Phthalocyanine Blue BN, Phthalocyanine Green G, verdigris, viridian
Iron oxide pigments: sanguine, caput mortuum, oxide red, red ochre, Venetian red, Prussian
blue
Lead pigments: lead white, cremnitz white, Naples yellow, red lead, lead-tin-yellow
Manganese pigments: manganese violet
Mercury pigments: vermilion
Titanium pigments: titanium yellow, titanium beige, titanium white, titanium black
Zinc pigments: zinc white, zinc ferrite
Phthalo blue (from: https://en.wikipedia.org/wiki/Pigment)
Problem: what might be the transition in metals that give them
color.
Phosphorence spectra
If the ground state is a singlet state the excited state is also
a singlet but the (with heavier elements) there can be
transition from the excited singlet
state to triplet state. Only small
fraction of the molecules will make
the singlet -> triplet transition but
then the triplet state is very
stable. The transition T1 state to the
ground state can take minutes. The
phosphorence phenomena is used
commonly to illuminate the clock
hands even when they are not
illuminated.
Applications of fluorescence
Fluorescence has become a very useful tool for biological
samples. In those (different) fluorescensing molecules are
attached to the samples and they can be imagined with very high
accuracy (Nobel Prize 2014). It is important that the
fluorophores can be attach to different parts of the samples,
like the nucleus of the cell, or cancer cells, etc..
From: https://en.wikipedia.org/wiki/Fluorescence_microscope