-
IPC Friedrich-Schiller-Universität Jena 1
Hamiltonian for a polyatomic molecule treated as Coulomb system with N nuclei
(coordinates {R}) and n electrons (coordinates {ri}) :
In atomic units i.e. ~ = qe = me = 1
Kinetic energy operator for nuclei
Kinetic energy operator for electrons
Nuclei-electron interaction operator
Electron-electron interaction operator
Nuclei-nuclei interaction operator
Molecular many electron systems: electronic & nuclear movement
-
IPC Friedrich-Schiller-Universität Jena 2
(3N + 3n)-dimensional problem:
Born-Oppenheimer Approximation: separate treatment of electronic and nuclear
motion allows the total wavefunction of a molecule to be broken into its electronic
and nuclear components:
Decomposition of Hamiltonian:
= adiabatic potential energy surfaces
Schrödinger equation for complete problem:
Molecular many electron systems: electronic & nuclear movement
Does not depend on {ri} =
constant for given nuclear
geometry
-
IPC Friedrich-Schiller-Universität Jena 3
Multiplikation with and integration over electron coordinates
Schrödinger equation for nuclear motion:
C describe coupling between nuclear and electron motion thus the resulting
coupling of electronic states (non-adiabatic coupling)
Molecular many electron systems: electronic & nuclear movement
-
IPC Friedrich-Schiller-Universität Jena 4
Born-Oppenheimer approximation neglects coupling between nuclear and electron
motion
C = 0
Electrons adjust immediately or adiabatic to any nuclear motion:
displays the potential for nuclear motion
Within the Born-Oppenheimer approximation the nuclear dynamic is treated
in a way that the nuclear motion is described on adiabatic potential energy
surfaces
Molecular many electron systems: electronic & nuclear movement
-
IPC Friedrich-Schiller-Universität Jena 5
Molecular many electron systems: electronic & nuclear movement
-
IPC Friedrich-Schiller-Universität Jena 6
Description of quantized molecular electronic energy states by many-electron
wavefunctions:
Approximation of many electron wavefunctions as Slater determinant
(antisymmetrized product) of one electron wavefunctions called molecular orbitals
(MOs):
Electronic states can be approximated by a single electronic configuration which is
commonly displayed by a MO diagram
MO
UV-Vis-Absorption
-
IPC Friedrich-Schiller-Universität Jena 7
In a MO diagram (representing a single electronic configuration) the highest occupied
MO is called HOMO and the lowest unoccupied MO is called LUMO
MOs are represented as linear combination of atomic orbitals (AOs)
Bonding MOs result when AOs enhance each other in the nuclei region
Antibonding MOs are formed when AOs cancel each other in the nuclei region
Classification of MOs:
s-orbitals: bonding orbitals which are symmetric with respect to rotation around
the molecular axis
s*-orbitals: antibonding orbitals with nodal plane within molecular axis
p-orbital: results from overlap of two lobes of one AO with the two lobes of
another AO
Nonbonding MOs contain lone pairs of electrons which do not participate in bonding
atoms together since they are unshared
UV-Vis-Absorption
-
IPC Friedrich-Schiller-Universität Jena 8
Molecular electronic transitions
UV-Vis-Absorption
Molecular electronic transitions take place when valence electrons in a molecule
are excited from one energy level to a higher energy level.
Electrons residing in the HOMO of a sigma bond can get excited to the LUMO of
that bond. This process is written down as a σ → σ* transition.
Likewise promotion of an electron from a π-bonding orbital to an antibonding π
orbital* is denoted as a π → π* transition.
Auxochromes with free electron pairs denoted as n have their own transitions, as
do aromatic pi bond transitions.
The following molecular electronic transitions exist:
σ → σ* π → π* n → σ* n → π* aromatic π → aromatic π*
p,p* np* ns*
(C=C, C=O) (C=O, C=N, C=S) (–Hal, -S-, -Se- etc.)
-
IPC Friedrich-Schiller-Universität Jena 9
Molecular orbital or electronic configuration (z.B. Formaldehyd)
Energetic order of transitions:
p* ← n < p* ← p < s* ← n < p* ← s < s* ← s
UV-Vis-Absorption
-
IPC Friedrich-Schiller-Universität Jena 10
spin multiplicity
• Total spin quantum number S = ∑ si
with si = +½ or - ½
• Multiplicity M = 2S + 1
• M = 1: Singulet
• M = 2: Dublet
• M = 3: Triplet
HOMO
LUMO
UV-Vis-Absorption
-
IPC Friedrich-Schiller-Universität Jena 11
Molecular
orbital
Electronic
configuration
Electronic
states
UV/Vis-absorption spectrum
UV-Vis-Absorption
-
IPC Friedrich-Schiller-Universität Jena 12
J = 0
J = 1
J = 2
J = 3
J = 4
Ro
tatio
na
l le
ve
ls
v = 0
v = 1
v = 0
v = 1
v = 3
v = 4
Vib
ratio
na
l le
ve
ls
Excitation [
10
-15 s
]
Internal conversion
[10-14 s]
Fluorescence
[10-9 s]
Intersystem crossing
Phosphorescence
[10-3 s]
S0
S1
S2
S3
S4
T1
Tn
IR- & NIR-
spectroscopy
UV-VIS-spectroscopy Microwave-
spectroscopy
Molecular many electron systems: electronic & nuclear movement
Jablonski-Scheme
-
IPC Friedrich-Schiller-Universität Jena 13
Principle to interpret electronic absorption spectra based on the probability distrubtion
||2 of the vibrational levels within the electronic states.
The basis of this principle is that
electronic transitions happen on a
timescale (~10-16s) that is
significantly smaller than the
vibrational period (~10-13s) of a
given molecule and therefore the
distance at which they happen can
be assumed to be fixed during the
transition.
Franck-Condon principle
UV-Vis-Absorption
-
IPC Friedrich-Schiller-Universität Jena 14
Transition dipole moment for a transition between the states |i and |f:
For excitation follows:
Electronic transition dipole moment is developed in a rapidly converging Taylor
expansion about nuclear displacements from the equilibrium position
Condon approximation neglects higher order terms i.e. electronic transition dipole
moment is assumed to be constant i.e. nuclear coordinates correspond to
equilibrium geometry
Condon approximation:
Transition dipole moment:
B.O.-approximation
Franck-Condon principle
UV-Vis-Absorption
-
IPC Friedrich-Schiller-Universität Jena 15
= degree of redistribution of electron density during transition
= degree of similarity of nuclear configuration between vibrational
wavefunctions of initial and final states.
Intensity of a vibronic transition is direct proportional to the square modulus of the
overlap integral between vibrational wavefunctions of the two electronic states =
Franck-Condon-Factor:
Franck-Condon principle
UV-Vis-Absorption
-
IPC Friedrich-Schiller-Universität Jena 16
|i
|f |i
|f
Franck-Condon principle
UV-Vis-Absorption
-
IPC Friedrich-Schiller-Universität Jena 17
Transition metal complexes
A biologically very important group of metal complex bonds are the porphyrin
pigments such as:
Hemoglobin (pigment of the blood, central ion Fe2+)
Cytochromes of respiratory chain
Chlorophyll (green molecules in leaves, central atom Mg)
UV-Vis-Absorption
In these molecules the octahedron
structure with a central atom is
incorporated into particular proteins
The four ligand positions of the base of
the pyramid are occupied by the lone
electron pairs of nitrogen atoms of the
plane porphyrin ring system
The two corners of the pyramid are
occupied by specific amino acids
(histidine) and/or by an oxygen molecule
(hemoglobin)
Heme-group
-
IPC Friedrich-Schiller-Universität Jena 18
Cytochrome c:
Pyramid corners of heme unit are occupied by N-atom of a histidine residue and
S-atom of a mezhionine residue
Redox change of cytochromes predominatly occurs at the central iron atom
[(Fe2+) ↔ (Fe3+)]
-Peaks
= sensitive for redox change
(analysis of mitochondria)
Transition metal complexes
UV-Vis-Absorption
-
IPC Friedrich-Schiller-Universität Jena 19
Transition metal complexes
Hemoglobin (iron is always found as Fe2+)
Arterial oxygen-loaded blood = light red
Blood in veines free of oxygen = deep red
Desoxy Hemoglobin
(Fe2+ / 92 pm / high spin)
End-on coordination of O2 (Fe2+ / 75 pm / low spin)
0,4 A °
B
UV-Vis-Absorption
-
IPC Friedrich-Schiller-Universität Jena 20
Fundamental terms:
Polarimetry, optical rotation, circular birefringence:
turning of the plane of linearly polarized light
Optically active molecules exhibit different refractive indices for right nR and
left nL polarized light nR ≠ nL
Optical rotatory dispersion (ORD):
Wavelength dependency of rotation
Allows determination of absolute configuration of chiral molecules
Circular dichroism:
linearly polarized light is transformed into elliptically polarized light upon traveling
through matter
Different absorption coefficients for left and right circular polarized light
(eR ≠ eL ).
Polarimetry & Optical rotatory dispersion & Circular dichroism
UV-Vis-Absorption
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IPC Friedrich-Schiller-Universität Jena 21
Polarimetry
What happens if light interacts with chiral molecules?
Enantiomeric molecules interact differently with circular polarized light.
Polarizability depends on direction of rotation of incoming circular polarized light
Optically active substances exhibit different refractive indices for right nR and
left nL polarized light nR ≠ nL
UV-Vis-Absorption
Polarimetry & Optical rotatory dispersion & Circular dichroism
-
IPC Friedrich-Schiller-Universität Jena 22
Polarimetry:
Incoming linear polarized light beam experiences different refractive indices for its
left and right circular components.
Phasing of left and right rotating component of exiting light beam is shifted while
the absolute E-field vectors do not change
Vector addition leads to linear polarized light with rotated polarization plane
UV-Vis-Absorption
Polarimetry & Optical rotatory dispersion & Circular dichroism
-
IPC Friedrich-Schiller-Universität Jena 23
Polarimetry:
For follows:
Na-D line l = 589 nm
2-Butanol = 11.2° (Messwert)
T = 20°C
l = 1dm
Difference is rather small!
Due to the different refractive indices a phase difference d = jL –jR builds up in the active medium which is proportional to the path
length l.
When exiting the medium linear polarized light where the oscillation
plane is rotated by d/2 arises
It follows:
l
UV-Vis-Absorption
Polarimetry & Optical rotatory dispersion & Circular dichroism
-
IPC Friedrich-Schiller-Universität Jena 24
Optical rotatory dispersion(ORD)
ORD measures molar rotation [F] as function of the wavelength!
If the substance to be investigated has no
electronic absorption within the
investigated spectral region the following
ORD spectra are obtained
Reason:
refractive indices for left and right
polarized light change differently with
wavelength (rotatory dispersion is
proportional to refractive index
difference).
ORD-spectra of 17ß- and 17-
hydroxy-5-androstan
UV-Vis-Absorption
Polarimetry & Optical rotatory dispersion & Circular dichroism
-
IPC Friedrich-Schiller-Universität Jena 25
Optical rotatory dispersion(ORD)
Refractive indices for left and right polarized light exhibit anomalous dispersion in
the range of an absorption band
Cotton effect
Positiv negativ Cotton effect
UV-Vis-Absorption
Polarimetry & Optical rotatory dispersion & Circular dichroism
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IPC Friedrich-Schiller-Universität Jena 26
Circular Dichroism (CD)
Enantiomeric molecules exhibit besides different refractive indices for left and right
circular polarized light also different absorption coefficients:
It follows:
For pure ORD bands left and right circular polarized components of linear polarized
light experience only different retardation when passing through the sample while for a
CD band also one component gets more absorbed than the other
Exiting light is elliptically polarized.
Circular Dichroism
UV-Vis-Absorption
Polarimetry & Optical rotatory dispersion & Circular dichroism
-
IPC Friedrich-Schiller-Universität Jena 27
Circular Dichroism (CD)
[10-1 × deg × cm2 × g-1]
[10 × deg × cm2 × mol-1]
The ratio between short and the long elliptical axis is defined as tangent of an
angle , the so called ellipticity (tan = b/a):
a = ER + EL
b = ER - EL
The specific ellipticity is defined as:
where 0bs is the experimentally determined
ellipticity.
The molar ellipticity is defined as:
UV-Vis-Absorption
Polarimetry & Optical rotatory dispersion & Circular dichroism
-
IPC Friedrich-Schiller-Universität Jena 28
Circular Dichroismus (CD) Simple model:
For an electronic transition to be CD active the following must be true:
µe is the electronic transition dipole moment (corresponds to a linear displacement
of electrons upon transition into an excited state)
µm is the magnetic transition moment (corresponds a radial displacement of
electrons upon excited state transition)
Scalar product is characterized by a helical electron displacement.
Depending on the chirality of the helix preferably more right or left circular
polarized light will be absorbed, respectively.
Electronic transition Magnetic transition Optical activity
UV-Vis-Absorption
Polarimetry & Optical rotatory dispersion & Circular dichroism
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IPC Friedrich-Schiller-Universität Jena 29
Circular Dichroism (CD)
Application field:
b-sheet
random coil
-helix
UV-Vis-Absorption
Polarimetry & Optical rotatory dispersion & Circular dichroism
-
IPC Friedrich-Schiller-Universität Jena 30
Circular Dichroism (CD)
Application field:
Typical reference CD spectra:
Poly-L-Lysine in different conformations:
-Helix, b-sheet and random coil.
Temperature
dependent CD
spectra of insuline:
For increasing
temperature the
molecule changes
form -helix into the
denaturated random
coil form with ß-sheet
contributions.
UV-Vis-Absorption
Polarimetry & Optical rotatory dispersion & Circular dichroism
-
IPC Friedrich-Schiller-Universität Jena 31
Vibrational microspectroscopy
Polyatomic molecules – Normal modes
Number of vibrational degrees of freedom:
For a non-linear molecule consisting of N atoms
there are 3N – 6 vibrational degrees of freedom =
Normal modes.
Normal modes can be excited independently (they
are decoupled).
Every normal mode q is a harmonic oscillator
independent of the rest of the molecule:
q = effective mass of the vibration = measure of the mass,
which is moved during the vibration. amplitude, x
Possib
le e
nerg
y levels
, E
qv Potential energy
V
0
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IPC Friedrich-Schiller-Universität Jena 32
Vibrational microspectroscopy
Polyatomic molecules – Normal modes
Example Water: 3 normal modes
d (1595 cm-1) as (3756 cm-1) s (3652 cm
-1)
Adenine
ar ring breathing
Thymine
(C=O) ar
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IPC Friedrich-Schiller-Universität Jena 33
Vibrational microspectroscopy
Polyatomic molecules – band assignment
-
IPC Friedrich-Schiller-Universität Jena 34
Raman vs. IR and NIR Absorption spectroscopy
v = 1
v = 0
a(R-R eq )
IR
V
v = 1
v = 0
a(R-R eq )
V
NIR
IR Absorption NIR Absorption
v = 1
v = 0
a(R-R eq )
V
Raman-Signal
(Stokes)
Raman scattering
Vibrational microspectroscopy
-
IPC Friedrich-Schiller-Universität Jena 35
Raman microspectroscopy
Vibrational microspectroscopy
Classical description
Incident electromagnetic field: (1)
Induced dipole moment: (2)
(1) in (2): (3)
Oscillating molecule: (4)
Expansion of around q = 0:
(5)
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IPC Friedrich-Schiller-Universität Jena 36
(5) in (3): (6)
Anti-Stokes-Raman-Streeung
Rayleigh-Streuung Stokes-Raman-Streuung
Vibrational microspectroscopy
Raman microspectroscopy
Classical description
Trigonometric transformation:
(7)
-
IPC Friedrich-Schiller-Universität Jena 38
Vibrational microspectroscopy
Raman microspectroscopy – quantum mechanical description
v = 0
v = 1
laser – vib laser + vib
virtual states
v = 0
v = 1
v = 2
v = 3
vibrational
states
Rayleigh scattering
Stokes-Raman
scattering
Anti-Stokes-Raman scattering
-
IPC Friedrich-Schiller-Universität Jena 40
Vibrational microspectroscopy
Raman microspectroscopy
3500 3000 2500 2000 1500 1000 5000
5000
10000
15000
20000
25000
30000
wavenumber / cm-1
Ra
ma
n in
ten
sity / a
rb. u
.
(C=C)
(=C-H)
s(CH2)
s(CH3)
as(CH2)
s(CH)
as(CH)
as(CH3)
d(CH3/CH2)
Pyridin – ring breathing
N
N
C H 3
H
H
H H
H
H
H
H H
H
H
Pyrrolidin – ring breathing
Raman spectrum of nicotine
-
Vibrational microspectroscopy
Raman microspectroscopy
Raman spectra of cells
3000 2500 2000 1500 1000
(C
-H)
(C
-C)
(C
-O)
(C
H2)
(P
O2
- )sym
d(C
H2,C
H3)
d(C
H2,C
H3)
d(C
H2,C
H3)
s(O
-H)
(C
=O
)
d(O
-H)
water
protein
lipide
polysaccharide
Ra
ma
n In
ten
sity
Wavenumber / cm-1
dna
T A
, G
A. C
, U
C, U
A, G
A, G
T
Phe, T
rp
am
ide III
Tyr,
Trp
, H
is
Trp
, am
ide II
Trpam
ide I
(C
-C) s
cele
tal
(C
-C) s
cele
tal
(C
=C
) cis
d(=
CH
) in p
lane
(C
H2)
(C
-H)
(C
-H)
(C
-H)
endoplasmic
reticulum
nucleus
ribosome
mitochondria
DNA/RNA
polysaccharides
lipids
proteins
water
-
Vibrational microspectroscopy
Raman microspectroscopy
Raman spectra of cells
endoplasmic
reticulum
nucleus
ribosome
mitochondria
DNA/RNA
polysaccharides
lipids
proteins
water
3000 2500 2000 1500 1000 500
Experimentell bacterial spectrum
Simulated bacterial spectrum
Linearcombination of the main components
Ra
ma
n In
ten
sity
Wavenumber / cm-1
* *
Quartz *
-
Raman microscopy
Vibrational microspectroscopy
Raman microspectroscopy
CCD spectrometer
laser
microscope
L
BS1
BS2
M
MO
S
N IF
C
W
High specificity
High spatial resolution ( < 1 µm)
Minimal sample preparation
All solvents can be applied
(inclusive water)
-
44
Vibrational microspectroscopy
Requirement of statistical models
Biological samples
Biopolymers (proteins, DNA, …)
Similar vibrations
Similar spectra
Classification model
Calculating a marker for groups
0
Classification models:
Artificial neural networks
Linear discriminant analysis
Support vector machines
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IPC Friedrich-Schiller-Universität Jena 45
Vibrational microspectroscopy
788
DNA
1005
phe
1575
G, A
1800 1600 1400 1200 1000 800 600
Ra
ma
n-I
nte
nsity
Wavenumber / cm-1
Breast cancer cell lines (MCF-7, MCF-10A) as model system
finger print region with chemical
information
Univariate analysis show the chemical
information
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IPC Friedrich-Schiller-Universität Jena 46
Vibrational microspectroscopy
Multivariate Analysis Strategy for Cancer Diagnosis
In order to compare two eukaryotic cells it is necessary to focus on one compartment.
The nucleus was chosen because major differences arise while tumorgenesis.
All spectra which exhibit a higher DNA/RNA content were
used to build a classification model for MCF-7/-10A.
The decision malignant cell (MCF-7) / benign cell (MCF-
10A) was possible with a accuracy of 99,11%.
-
Raman microscopy
Raman spectroscopy of a colon tissue section. A, representative Raman spectra of connective tissue (1),
muscle layer (2) and epithelial tissue (3). B, 79 x 79 Raman map with a step size of 2,5 µm. The colors of
the Raman represent cluster memberships. C, the arrow in the photograph shows the position of a
ganglion. E, enlarged ganglion from C.
47
Vibrational microspectroscopy
Biomedical diagnostics
-
Special properties of Raman spectroscopy:
Stokes ( = 0 – R) Raman scattering intensity:
Increase of the
laser intensity
or by
SERS
Use of higher
excitation frequency
(shorter wavelengths)
Excitation of the electronic
resonance
Resonance Raman scattering
48
Vibrational microspectroscopy
-
IPC Friedrich-Schiller-Universität Jena 49
inte
nsity
400 450 500 550 600 650 700 750
wavelength / nm
Fluorescence Raman
Resonance
Raman
Resonance Raman spectroscopy
Vibrational microspectroscopy
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IPC Friedrich-Schiller-Universität Jena 52
Advantages of resonance Raman spectroscopy
Resonance enhancement of the scattering intensities by a factor 106 – 108
Improved S/N ratio
Allows detection of low concentrated substances in solution
Resonance-Raman spectra are dominated by modes characteristic for the
geometrical changes of the molecules during the electronic transition
Selective excitation (e.g. of chromophores pivotal for the biological activity of the
molecule) possible due to variation of the excitation wavelength
simplified spectrum, since less vibrations contribute to the spectrum; only
Franck-Condon active modes are enhanced
Vibrational microspectroscopy
Resonance Raman spectroscopy
-
IPC Friedrich-Schiller-Universität Jena 53
Excitation of different chromophors within a molecule
Guanosin-5‘-Mono-Phosphat
Vibrational microspectroscopy
Resonance Raman spectroscopy
-
IPC Friedrich-Schiller-Universität Jena 54
Vibrational microspectroscopy
Resonance Raman spectroscopy
3000 2500 2000 1500 1000
wavenumber / cm-1
AG
-Vort
rag
NIR
-bandassig
nm
ent
grating: 300 l/mm
Hole: 1000 m
central spectral
position: 2000 cm-1
wavebumbercorrection:
+ 2cm-1
IR spectrum
Raman spectrum (532 nm)
UV resonance Raman spectrum (244 nm)
phospho
die
ste
r
(C
C/C
N)
d(C
H)
Am
id II
Am
id I
satu
rate
d e
ste
rscarbohydrates
proteins
lipids
Tyr
A +
G +
Tyr
T +
AA
+ G
G +
AC
G +
AT
yr+
Trp
T
S. pseudovenezuela DSM 40212
(C
H)
G+A
Am
id III
DNA – components
&
Proteins
Contribution from
whole cell
5 µm
10
20
30
40
50
20 30 40 50 60 70
bulk
single cell
Applied vibrational spectroscopic methods Retrieved information
-
IPC Friedrich-Schiller-Universität Jena 55
SERS = Surface Enhanced Raman Scattering
Vibrational microspectroscopy
Stokes ( = 0 – R) Raman scattering intensity:
Increase of the
laser intensity
or by
SERS
Use of higher
excitation frequency
(shorter wavelengths)
Excitation of the electronic
resonance
Resonance Raman scattering
-
IPC Friedrich-Schiller-Universität Jena 57
Electromagnetic enhancement
Localized surface plasmon resonance (LSPR)
Plasmons can be described in the classical picture as an oscillation of free electron
density against the fixed positive ions in a metal. Surface plasmons are surface
electromagnetic waves (evanescent wave) that propagate in a direction parallel to
the metal/dielectric (or metal/vacuum) interface.
+
-
+
-
Electric field
Electron cloud
Gold sphere
Vibrational microspectroscopy
SERS = Surface Enhanced Raman Scattering
-
IPC Friedrich-Schiller-Universität Jena 58
ELM
EDIP
ESC
R
Molecule = Etot
mit Etot = E0 + ELM
Observator
EDIP
EO
Raman intensity IR
IR ER2
ER = EDIP + ESC
Vibrational microspectroscopy
SERS = Surface Enhanced Raman Scattering
Electromagnetic enhancement
Localized surface plasmon resonance (LSPR)
-
IPC Friedrich-Schiller-Universität Jena 60
SERS increases detection limit!
Vibrational microspectroscopy
SERS = Surface Enhanced Raman Scattering
-
IPC Friedrich-Schiller-Universität Jena 62
L
L - S = R
R
Excitation of coherent molecular vibrations
within common focus of two laser beam whose
difference frequency L - S matches a
molecular vibration.
Non-linear Raman microspectroscopy
Coherent Raman spectroscopy
Fundamental concepts of coherent anti-Stokes Raman scattering (CARS)
-
IPC Friedrich-Schiller-Universität Jena 68
Coherent molecular
vibrations excited by
the two laser fields L
and S modulate a
third laser field (L)
and thus generate a
coherent light beam at
anti-Stokes frequency
aS = 2L - S
Non-linear Raman microspectroscopy
Fundamental concepts of coherent anti-Stokes Raman scattering (CARS)
-
IPC Friedrich-Schiller-Universität Jena 72 Stokes pulse
Pump pulse 1
Pump pulse 2
CARS-Signal
Energy conservation
Momentum
conservation
Non-linear Raman microspectroscopy
Fundamental concepts of coherent anti-Stokes
Raman scattering (CARS)
-
IPC Friedrich-Schiller-Universität Jena 73
CARS intensity
starting point for derivation of CARS intensity is non-linear wave equation for anti-
Stokes amplitude EaS
for k = 0 CARS intensity increase for L2
for k 0 build up of CARS signal over limited coherence
length lPh p/k; thereafter spatial-time-periodic intensity
modulation due constructive and destructive interference.
CARS signal oscillates as function of L with periodicity
laS/2n
Non-linear Raman microspectroscopy
Fundamental concepts of coherent anti-Stokes Raman scattering (CARS)
L
IaS
lPh
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IPC Friedrich-Schiller-Universität Jena 77
CARS line profiles
Besides resonant susceptibility due
to molecular vibrations also a non-
resonant contribution NR due to
electronic structure of medium must
be considered. NR is a real value
and does not show a strong
frequency dependency i.e. can be
considered as constant in vicinity of
vibrational ferquency.
resonant
susceptibility
Non-resonant
susceptibility
Non-linear Raman microspectroscopy
Fundamental concepts of coherent anti-Stokes Raman scattering (CARS)
-
IPC Friedrich-Schiller-Universität Jena 79
Collinear CARS microscopy:
Phase-matching for strong focusing with microscopy objective
Phase-matching uncritical because:
For every wave vector component of
pump beam the corresponding
component of Stokes beam needed
to fulfill phase-matching can be found
in focus.
CARS signal is only generated for
short interaction length. Focusing with
objective goes below coherence
length. Interaction length is too short
in order for a large phase mismatch
to occur.
Wavevector mismatch in water for collinear CARS geometry
as a function of NA. Solid line: pump wavelength: 600 nm,
Raman shift: 4167 cm-1; dashed line: pump wavelength:
500 nm, Raman-Shift: 7500 cm-1; L is defined as FWHM of
the focal excitation intensity along optical axis
CARS microscopy
Non-linear Raman microspectroscopy
-
IPC Friedrich-Schiller-Universität Jena 80
Collinear CARS microscopy:
Beam geometries in CARS microscopy
F-CARS
E-CARS
p
S aS
aS F-CARS = Forward CARS
E-CARS = Epi CARS
E-CARS signal for scattering
objects smaller than half anti-
Stokes wavelength
Magnitude of phase mismatch
acts as filter for scattering
objects of certain size.
Non-linear Raman microspectroscopy
CARS microscopy
-
IPC Friedrich-Schiller-Universität Jena 81
CARS signal dependence on the size of
a sphere placed in vacuum at the origin
of tightly focused excitation beams for
different experimental geometries.
F-CARS signal increases quadratically with D
until it reaches a constant value where the
diameter of the sphere exceeds the longitudinal
dimension of the focal volume.
E-CARS signal has the same amplitude as F-
CARS signal for sphere diameters smaller than
the pump wavelength and reaches a maximum
for~ 0.3lp. E-CARS amplitude decreases quickly
for increasing sphere diameters and oscillates as
function of D with periodicity laS/2n as a result of
interference effects due to a large phase
mismatch . For large D (= bulk) no E-CARS
signal can be observed anymore.
Collinear CARS microscopy:
Beam geometries in CARS microscopy
Non-linear Raman microspectroscopy
CARS microscopy
-
IPC Friedrich-Schiller-Universität Jena 82
Collinear CARS microscopy:
CARS microscopy is not background free
Contrast reduction due to:
Non-resonant background signals.
Water as solvent leads due to ist broad
Raman bands strong resonant
background signals
CARS field of object in F-CARS geometry is superimposed on much stronger CARS signal of medium
(due to larger interaction length).
Low contrast of CARS image of object
E-CARS detection allows imaging with much better contrast because E-CARS signal of medium
disappears due to destructive interference. However, this is not true for E-CARS signal of object if its size
is comparable to anti-Stokes wavelength where only the object leads to image contrast.
Non-linear Raman microspectroscopy
CARS microscopy
-
IPC Friedrich-Schiller-Universität Jena 83
Comparison of contrast in F-CARS
and E-CARS images of unstained
live epithelial cells taken with 5 ps
pulse trains at a repetition rate of
400 kHz. (a) F-CARS image
recorded with parallel-polarized
pump and Stokes beams with
average powers of 0.4mW and
0.2mW, respectively, at a Raman
shift of 1579 cm−1 (protein vibration).
(b) E-CARS image recorded with
average pump and Stokes powers
of 2.0mW and 1.0mW, respectively,
at a Raman shift of 1570 cm−1.(DNA
vibration).
Larger water background Background supression! Small
features (~ 100 nm) become visible.
Non-linear Raman microspectroscopy
CARS microscopy
Collinear CARS microscopy:
CARS microscopy is not background free
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Raman images 1659cm-1; 32 x 32 data points; Measuring time 9 h
Bright field
CARS image
CARS images at 1660cm-1; 512 x 512 data points; Measuring time 5.4s,
A comparative study on colon tissue by means of CARS and Raman imaging
Non-linear Raman microspectroscopy
CARS microscopy
-
IPC Friedrich-Schiller-Universität Jena 90
Multimodal Optical Imaging
Future trends in non-linear microscopy
-
IPC Friedrich-Schiller-Universität Jena 91
Multimodal image:
Composite of
CARS, SHG and TPEF
Cerebellum of a domestic pig:
Multimodal image retrieves simlar information as
H&E
In-vivo detection of tumor
H&E CARS CH SHG (collagen)
Purkinje cells
White matter
arachnoidea
Granule layer
TPEF
Grey matter
Multimodal Optical Imaging
Future trends in non-linear microscopy
-
IPC Friedrich-Schiller-Universität Jena 92
Multimodal Optical Imaging
Brain metastasis of lung carcinoma:
Detection of tumor by CARS
Detection of tumor boundary by spectral profile
Subcellular details (cell cores)
Multimodal information of the tissue morphochemistry
H&E
Future trends in non-linear microscopy
-
IPC Friedrich-Schiller-Universität Jena 95
Multimodal Optical Imaging
Multi-modal imaging
Various methods are necessary in order to achieve molecular contrast
as well as multivariate information (absorption, fluorescence based
methods, SHG, THG, Raman and FTIR, CARS, etc.)
Implementation of in-vivo multimodal imaging for clinical detection and
ultimately to the diagnosis of disease
Multi-modal imaging
Future trends in non-linear microscopy