Notes 7
Spectroscopy
Spectroscopy involves wavelength and frequency
Certain frequencies correspond to certain types of molecular excitation
Figure
Experimental Particulars: ...................... Emission vs Absorption
1) Sources:
Microwaves:
Far IR
Visible
UV
Far UV
X-ray
Gamma
2) Dispersing Elements a) Prism
b) Diffraction Grating
c) Fourier Transform
3) Detectors:
1) PMT
2) CCD
3) Crystal Diode
Signal Modulated to help in detection
Einstein said three ways for transitions to occur between states!
Stimulated Absorption “B”
Stimulated Emission “B”
Spontaneous Emission “A”
LASER - light amplification by stimulated emission of radiation
Electric dipole moment operator
=er
permanent vs transition dipole moments
A transition from one state to another occurs when the radiation field connects the two
states.
Spectroscopic Relations Table 10.3
As seen before the rates of stimulated and spontaneous emission are related by
A=8
Spectra are seen as transition bands in a plot of intensity vs wavelength
Why aren’t they just stick spectra. Why are they bands with a finite width?
The band has a width due to:
A. Doppler Broadening
B. Lifetime Broadening
.................1) collisional lifetime
................2) natural lifetime
Natural linewidths increase with the magnitude of the Spontaneous Emission
Coefficient
What is A?
Experiments measure Intensity changes
Absorption
Beer-Lambert Law
T=
A = log10(I/Io)
A= cl
c=
l=
In base e: .....................................
 =  ln10 .................................Naperian molar absorptivity
Max value max gives indication of intensity of transition. Also talk about integrated
absorption coefficient:
The wavelength at which two or more components have the same extinction coefficient is
called the isobestic wavelength.
The absorbance is additive. It can be generalized to any number of components.
The occurrence of two or more isobestics in the spectra of a series of solution of the same
total concentration demonstrates the presence of two and only two components absorbing
in that region.
Absorption Spectra of Building Blocks (Proteins and Nucleic Acids)
Most proteins and all nucleic acids are colorless in the visible region of the spectrum, but
thay absorb in the near-UV region.
See Fig
weaker transition at 280 is a ______________________---
stronger transition at 200 nm is ____________________________________
Proteins are natural poly amino acids
Nucleic acids are poly nucleotides
To understand the UV absorption of proteins and/or nucleic acids, one needs to examine
the various contributions to the spectra - Important Factors
a.
b.
c.
d.
Amino Acid Specta Fig
Polypeptide Spectra
Contribution to absorption spectra from the amide linkages can be seen
Fig (side chains are important)
Secondary Stucture
Describes which residues are in helices or other ordered conformations. The
conformation of a protein is sensitively detected by UV spectroscopy.
pH effects: raising the pH induces helix formation due to a reduction of the net positive
charge.on the lysine side chains Fig
Raising the temp converts the polypeptide to the B sheet structure.
Denaturation destroys much of the secondary structure so that
_______________________
___________ occur.
Nature of the Spectroscopic Changes
Changes in the environment of amino acid changes the secondary structure and changes
the spectroscopy.
Electrical in origin. Ground and excited electronic states are sensitive to:
a.
b.
c.
d.
Nucleic acids
Aromatic bases attached to the ribose OR deoxyribose-phosphates all have absorption
near ______________________.
The free base, the nucleoside (the base attachéd to the sugar), the nucleotide (the base
attached to the sugar-phosphate, and denatured poly nucleotide, all have similar
absorption spectra in this region.
Example:
In general polynucleotides and nucleic acids absorb less per nucleotide than their
constituent nucleotides. Native double stranded DNA absorbs less per nucleotide than
denatured DNA stands.
Decreased absorptivity is called _________________ or
__________________________
Increased absorptivity is called _____________________ or
_________________________
The hypochromicity of the polynucleotides or relative to the nucleotides results primarily
from
Fluorescence
Many biological substances emit characteristic fluorescence. Chlorophyll - red
fluorescence, etc.
Other examples:
Fluorescence labels
Bioluminescence
Theory of fluorescence
Frank-Condon principle - the transition is vertical: Nuclei do not change position.
Internal conversion
Solvent Effects
Excited State Properties
Decay of the electronic excited state is usually 1st order.
Thus there is a decay constant, a fluorescence decay time or lifetime given by:
Can be other radiative processes that lead to deactivation from the excited state
The quantum yield - the fraction of the absorbed photons that lead to fluorescence; it is
the number of photons fluoresced divided by the number of photons absorbed.
Relationship between the quantum yield and the fluorescence lifetime.
Fluorescence almost always occurs from the lowest excited state of the molecule.
Quenching
Collision processes with specific quenching molecules leads to a change in the lifetime
Stern-Volmer Relation
Concentration quenching can be quite dramatic.
Excitation Transfer
FRET
Molecular Rulers
Polarization of Fluorescence
Phosphorescence
Single Molecule Fluorescence
Optical Rotary Dispersion and Circular Dichroism
Polarized Light
unpolarized light
plane polarized light
circularly polarized light
elliptically polarized light
Birefringence
Linear birefringence - difference in refractive index for light polarized in planes
perpendicular to each other
Circular birefringence - the difference in refractive index for right circularly polarized
light and left circularly polarized light.
Optical Rotation and Circular Dichroism
Optical rotation by chiral samples results from and is a measure of their circular
birefringence. Comes from the usual experimental measurement
Note that phi is given per cm of pathlength in the sample. The actual rotation increases
linearly with the pathlength through the sample.
The rotation is measured.
Circular Dichroism results from a differential absorption of left an right circularly
polarized light by a sample that exhibits molecular asymmetry.
The passage of plane polarized light through a circularly polarized dichroic sample
produces not only a phase shift due to the circular birefringence but also a differential
decrease of the amplitudes of the right and left circularly polarized components. The
emerging beam is found to be elliptically polarized with ellipticity defined as
See Fig and
table
Nucleic Acids and proteins and optical activity
Circular dichroism of the synthetic polynucleotide poly (dG-dC) poly (dG-dC) Fig
Vibrational Spectra
Infrared Absorption
Ideal Model is ___________ ______________________. The vibrational frequency is
equal to:
Non-ideal part occurs at high quantum numbers.
It can be modeled by the Morse potential.
The selection rule is based on a difference in dipole as a result of vibration.
Resulting selection rules are:
Pure Rotational Motion
All J are forbidden unless there is a permanent dipole moment
Rotational Transisitons - photons in wavelength region
h = E = Epnoton =
In rotation, at high quantum numbers, one can also deviate from the ideal case due to
centrifugal force. This will effectively cause changes in the "Rigid" bond length at higher
rotational energy.
Vibration-Rotation
Usually express the energy in cm-1: (wavenumbers) or 1/wavelength in cm =
Need EvJ
Ev,J =
OR
EvJ/h = e(v + ½) + Be J(J+1) - D J2(J+1)2 .............................. A1
Be = rotational constant =
D = centrifugal distortion constant (corrects for ..............................................................) =
So far we have made a correction for non-ideality in the Rotor (Rotation) but vibrational
energy is still based on the Harmonic Oscillator
One correction is to use the Morse Function for the Vibrational Kinetic Energy
V(r) - V(re) = De [1 - exp(-a(r-re)]2
De = Dissociation Energy - energy required to dissociate the molecule from the state of
minimum
potential B
Figure
Corrections for the anharmonicity and for interaction between vibration and rotation give:
EvJ =
All three of the correction terms cause the energy levels to be lower for large values of
the quantum #. At low values the terms in e, , and D may be neglected!
NOW READY FOR SPECTRA
Pure Rotational Spectrum
E rot (in cm-1) =
see fig
How is this related to the bond length? How can we get the bond length from this
information?
Vibration Rotation Spectrum
Vibrational Transitions - Infrared Region
For Diatomics
Selection Rules
x = r-re and (x) is operator for molecular transition dipole moment. Using the Harmonic
Oscillator Wavefunctions find that the selection rules are:
v = 0, +/- 1 .... and .... J not = 0
v = 0 (pure rotation)
v = +/- 1 (vibration - rotation)
Allowed transitions between ground vibrational state (v=0) and 1st excited vibrational
state.
Figure
Set of spectral lines result - BAND
Spectral lines for which J in upper state is larger are called R branch of the band
E is Higher energy, higher frequency
Spectral lines for which J in upper state is smaller are
If lines occurred for values of J in both states the same this would be called the Q-branch
NOT OBSERVED FOR DIATOMICS - Forbidden by Selection Rules
However, may be observable for polyatomics.
Thus spectrum looks like:
Figure
Spectral peaks corresponding to v = +/-1 are called fundamentals.
Vibrational selection rules are less well obeyed than rotational selection rules and often
one can observe in a spectrum the transitions corresponding to
v = +/- 2 ...... first overtone
v =  3 ..... second overtone
And in polyatomics where several vibrational modes exist can get combination bands.
If we neglect the anhamonicity, the centrifugal distortion, and the coupling
then the wavelength of a line of the Branches is:
Light Scattering - Elastic and Inelastic light scattering
Rayleigh Scattering and Raman Scattering
Rayleigh Scattering
Raman Scattering
Stokes
Anti-Stokes
Resonance Raman
NMR (Nuclear Magnetic Resonance Spectroscopy)
NMR monitors changes in the nuclear spin state.
Nuclei have intrinsic spins like electrons do. Nuclei can have integral or half integral
spin states. (O, ½, 1 ….) others. Nuclei with spin ½ include H-1, C-13, N-15, and P-31.
In the absence of an externally applied magnetic field, different nuclear spin states are
degenerate, but in the presence of an externally applied magnetic field, the spin states hav
different energy.
The spin quantum numbers are related to the magnetic moment along the z-axis by
The energy of a spin state in a magnetic field is:
Bo is the strength of the magnetic field in Tesla directed along the z-axis.
The energy difference between these two states is
The energy difference is related to a frequency for the transition (spectroscopy), called
the ______________________ frequency.
For a proton in a field of Bo of 11.7T, the frequency is 500MHz. This frequency
corresponds to radiowaves in the electromagnetic spectrum.
NOTE: These are very-low energy transitions, compared with electronic or vibrational
transitions. For a large number of nuclear spins, the lower and upper spin state will be
nearly equally populated, since the energy splitting is much smaller than the thermal
energy (kT) at room temp. Since the intensity of the absorption is related to the
difference in the population of the two states, NMR is much less sensitive than IR or UVVis Absorption Spectroscopy.
The energy splitting can be increase by increasing the magnetic field strength. Magnets
as lar as 18.1 T are in us. Here the Larmor frequency for a proton is 800 MHz) So the
vernacular is that an instrument with an 18.1 T magnet is called an 800MHz NMR.
Spectrum results as a result of the nuclei absorbing energy when the radiation matches
the Larmor frequency.
Classical picture of NMR - Vector Model
free induction decay is the return of the system to equilibrium in which a large number of
spins behave in a coherent fashion. Wavefunctions, like waves, have a phase associated
with them, and the wavefunctions may add together if their phases are aligned correctly.
Interactions in NMR
1. Chemical Shifts - the magnetic field experienced by a nucleus is slightly different from
that of the applied external field and depends on the local environment. The energy level
separation between the two spin states is thus slightly changed from that causes by the
applied field.
As a result of this, different protons will have different resonant frequencies.
The frequency of an NMR peak is usually expressed with respect to a reference
frequency, using protons that resonate at a high frequency extreme of the spectrum.
The resonance position is expressed in terms of a frequency difference between the
reference peak and the observed peak so that it is independent of the magnitude of the
applied field. This measure of resonance frequency is called the Chemical Shift. It is:
Local magnetic fields that give rise to chemical shift are caused by the electrons in the
molecule.
Electron currents depend on the orbital configuration of the molecule.
See figure
2. Spin-Spin Coupling. Scalar Coupling, or J-Coupling:
The interaction of nuclei through electrons in connecting bonds depends on whether the
spin state is aligned or against the magnetic field. The spin state of one nucleus affectss
the spin energies of the neighboring nuclei (Spin coupling or J-coupling). The two
possible orientations of a spin = ½ nucleus in a magnetic field can split the energy levels
of neighboring nuclei. Thus the absorption line of a set of equivalent nuclei is split into a
multiplet. The frequency of separation between the lines of the multiplet is the spin-spin
splitting, J in Hertz, if the spin-spin splitting is less than one-tenth the frequency differenc
due to the chemical shifts, simple first-order theory, the effects of the chemical shifts and
the spin-spin splittings are additive. If the splitting between protons is comparable or
larger than the difference in chemical shifts, then the spectrum depends on the ratio of J
to the frequency difference.
See fig
The spin-spin splitting in Hertz (ulike the chemical shift) is independent of the applied
magnetic field. The values of J for protons range from 0 to about 20 Hz. Proton NMR
measured in a hydrocarbon or carbohydrate are not affected by the carbon or oxygen
nuclei as they have no magnetic moment except a very small amont of C-13 or O-17.
See Figures
3. Relaxation Mechanisms
Once the energy is absorbed to change the nuclear spin state, a return of the spin
population follows first-order kinetics: its relaxation time is calls the:
Spin Lattice Relaxation Time, T1
Measurement of the relation rates for nuclear spin probes the local environment and
dynamics of a molecule. Relaxation measurements can be used to determine whether a
biological macromolecule moves together rigidly or fluidly in a solution.
Another characteristic relaxation time tha is measurable in NMR is the spin-spin
relaxation time, T2, which characterizes the interactions between spins on equivalent
nuclei, it does not involve change of energy with the environment (the lattice). It can be
measured from the width of the NMR peak.
Nuclear Overhauser Effect (NOE) can be sued to determine which nuclei are near each
other. Intense radiation corresponding to the transition frequency of one type of proton
is applied to the sample. The NMR peak is saturated changing the spin population of
those protons so there are an equal number of nuclei in the upper and lower energy levels.
These nuclei interact with neighboring nuclei and change the spin population of the
neighboring nuclei from their equilibrium distribution. The intensity of the NMR peak of
each nearby nucleus will change
Since the interaction between magnetic nuclei depends on 1/r to the 6th power, the
Overhauser effect is appreciable only for very close neighbors (usually closer than 5
angstroms away).
Multidimensional NMR
COSY - correlated spectroscopy - two short pulses separated by a delay period T1. After
the second pulse the free-induction decay is detected during the period T2
Figure
NOESY - monitor through space NOE interactions between protons that are less than 5-6
angstroms apart. This is a powerful means of gaining structural information by solution
NMR
Fig
EPR Electron paramagnetic Resonance
MRI
Molecules have a range of conformations produced by vibrations of all the bonds and the
torsional rotations around the single bonds as discussed previously
Binding of small molecules to many sites on a macromolecule and the disruption of
hydrogen bonding which leads to helix-coil transitions of polynucleotides and
polypeptides.
Binding of Small Molecules by a Polymer
Langmuir Adsorption Isotherm
Statistical Thermodynamics
Derivation of the Boltzmann Distribution for Individual Particles
Use of the Boltzmann Distribution for Statistical Thermodynamics
BUT WITH RESPECT TO SPECTROSCOPY, THE BOLTZMANN DISTRIBUTION
TELLS US THE RELATIVE POPULATION OF THE STATES INVOLVED IN THE
SPECTRAL TRANSITION. And since the intensity is related to the population of the
initial state, then the Boltzmann Distribution is related to the intensity of a peak in a
spectrum.
Consider a system of N molecules
Total Energy of the system is E
We say that the energy is distributed over the molecules.
Collisions take place - there is a ceaseless redistrubution of energy - not oly between the
molecules, but also among their different modes of motion.
If several energy states:
translational, rotational, vibrational, electronic
then the closest we can come to describing the DISTRIBUTION OF ENERGY is to
STATE THE POPULATION IF EVERY ENERGY STATE or LEVEL
From Quantum Mechanics we know that the energy of a molecule is not a continuous
function.
Remember that the energy of vibration is restricted.
For our DISTRIBUTION we make the following definitions and assumptions:
1) on average there are ni molecules in a state of energy i or energy level i.
2) Population - average # may be relatively constant in a level even though collisions
occur.
3) Principle of equal a priori probabilities:
“All Possibilities for the distribution of Energy are equally probable ie vibrational states, rotational states, electronic states
4) Ergodic Hypothesis (Why are we interested in the distribution - defines equilibrium
situation)
“ The long time average of a Mechanical variable, M, of interest is equal to the ensemble
average of M in the limit that N infinity, provided that the ensemble replicates the
thermodynamic state.
So we need a statistical treatment of an assembly of molecules to find there average
arrangement, and that will represent the equilibrium thermodynamic state.
Statistics shows that although there are many possible arrangements of the energy quanta
within the molecules of the assembly, that only one configuration has an extremely high
probability. That is the arrangement of the energy into the molecules defined by one
configuration is many - many times more likely to happen than any other configuration.
This particular configuration is defined by the Boltzmann Distribution:
One form of the Boltzmann distribution is:
The probability that a molecule is in the ith energy state (pi) is given by:
pi = expi) / j exp(-j)) ............................... where = 1/kT
and ni (the number of molecules in the ith level is given by: N pi ...... (where N is the total
# of molecules)




j exp(-j) is often denoted by Q and is called the partition function
Also note that the relative probability that a molecule is in the ith level relative to the jth
level is given by:
ni /nj = exp (-i - j))