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Chp 10 Notes 1
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 10.10
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 ot examin the
various contributions to the spectra - Important Factors
a.
b.
c.
d.
Amino Acid Specta Fig 10.2 and 10.3
Polypeptide Spectra
Contribution to absorption spectra from the amide linkages can be seen
Fig 10.14 (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 10.4
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 form
Interactions between adjacent bases in their stacked arrangement in the helical polymer.
The origin of the hypochromism is electromagnetic in origin
Chapter 10 Notes 2
Chromophoric Proteins
Many proteins include groups other than amino acids
These are chromophoric groups or ___________________. Examples of chromophoric groups
include:
a. glycoproteins (sugars)
b. hemeproteins (iron porphyrins)
c. flavoproteins (flavin)
d. rhodopsin
b,c,d contribute to absorption spectrum in the visible or near-UV regions.
Fig 10.15
Conjugated double bonds of the aldehyde in in the retinal can be treated as a mobile particle in a
box with the pi electrons moving in the box. This long wavelength absorption then is a pi to pi*
transition.
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 10.23 and table 10.6
Nucleic Acids and proteins and optical activity
Circular dichroism of the synthetic polynucleotide poly (dG-dC) poly (dG-dC) Fig 10.25
Vibrational Spectra
Infrared Absorption
Ideal Model is ___________ ______________________. The vibrational frequency is equal
to:
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 =
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 nergy 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 UV-Vis 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 poeition is expressed in terms of a frequency difference between the reference
peak an dthe 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 10.31
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 firstorder 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 10.34.
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 10.33 and 10.34
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 10.36
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 10.39
EPR Electron paramagnetic Resonance
MRI
Chapter 11
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))