Transcript Lecture 7_Quantum Chemistry

Nanochemistry
NAN 601
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Instructor:
 Dr.
Marinella Sandros
Lecture 7: Quantum Chemistry_Fluorescence
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Light is quantized into packets called photons
Photons have associated:
◦
◦
◦
◦
frequency,  (nu)
wavelength,  ( = c)
speed, c (always)
energy: E = h
 higher frequency photons  higher energy  more
damaging
◦ momentum: p = h/c
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The constant, h, is Planck’s constant
◦ has tiny value of: h = 6.6310-34 J·s
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Sunny day (outdoors):
◦ 1015 photons per second enter eye (2 mm pupil)
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Moonlit night (outdoors):
◦ 51010 photons/sec (6 mm pupil)
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Moonless night (clear, starry sky)
◦ 108 photons/sec (6 mm pupil)
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Light from dimmest naked eye star (mag
6.5):
◦ 1000 photons/sec entering eye
◦ integration time of eye is about 1/8 sec  100
photon threshold signal level
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http://www.ars-chemia.net/Classes/101/PPT/08_Quantum_Chemistry.pdf
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Every particle or system of particles can be defined
in quantum mechanical terms
◦ and therefore have wave-like properties
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The quantum wavelength of an object is:
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typical macroscopic objects
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typical “quantum” objects:
 = h/p
(p is momentum)
◦ called the de Broglie wavelength
◦ masses ~ kg; velocities ~ m/s  p  1 kg·m/s
◦   10-34 meters (too small to matter in macro
environment!!)
◦ electron (10-30 kg) at thermal velocity (105 m/s)    10-8
m
◦ so  is 100 times larger than an atom: very relevant to an
electron!
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All matter (particles) has wave-like
properties
◦ so-called particle-wave duality
Particle-waves are described in a
probabilistic manner
◦ electron doesn’t whiz around the nucleus,
it has a probability distribution describing
where it might be found
◦ allows for seemingly impossible “quantum
tunneling”
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Why was red light incapable of knocking electrons out of
certain materials, no matter how bright
◦ yet blue light could readily do so even at modest intensities
◦ called the photoelectric effect
◦ Einstein explained in terms of photons, and won Nobel Prize
Spring 2008
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What caused spectra of atoms
to contain discrete “lines”
◦ it was apparent that only a small
set of optical frequencies
(wavelengths) could be emitted
or absorbed by atoms
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Each atom has a distinct
“fingerprint”
Light only comes off at very
specific wavelengths
◦ or frequencies
◦ or energies
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Note that hydrogen (bottom),
with only one electron and one
proton, emits several
wavelengths
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Squint and things get fuzzy
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Eye floaters
◦ opposite behavior from particle-based pinhole
camera
◦ look at bright, uniform source through tiniest
pinhole you can make—you’ll see slowly moving
specks with rings around them—diffraction
rings
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Shadow between thumb and forefinger
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Streaked street-lights through windshield
◦ appears to connect before actual touch
◦ point toward center of wiper arc: diffraction
grating formed by micro-grooves in windshield
from wipers
◦ same as color/streaks off CD
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particle?
wave?
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The pattern on the screen is an interference
pattern characteristic of waves
So light is a wave, not particulate
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Lets watch this movie!!!
http://www.youtube.com/watch?v=DfPeprQ7
oGc
http://www.ars-chemia.net/Classes/101/PPT/08_Quantum_Chemistry.pdf
http://www.ars-chemia.net/Classes/101/PPT/08_Quantum_Chemistry.pdf
http://www.ars-chemia.net/Classes/101/PPT/08_Quantum_Chemistry.pdf
http://www.ars-chemia.net/Classes/101/PPT/08_Quantum_Chemistry.pdf
Luminescence
• Emission of photons from electronically excited states
• Two types of luminescence:
Relaxation from singlet excited state
Relaxation from triplet excited state
Singlet and triplet states
• Ground state – two electrons per orbital; electrons
have opposite spin and are paired
• Singlet excited state
Electron in higher energy orbital has the opposite
spin orientation relative to electron in the lower
orbital
• Triplet excited state
The excited valence electron may spontaneously
reverse its spin (spin flip). This process is called
intersystem crossing. Electrons in both orbitals
now have same spin orientation
Types of emission
• Fluorescence – return from excited singlet state to
ground state; does not require change in spin
orientation (more common of relaxation)
• Phosphoresence – return from a triplet excited state
to a ground state; electron requires change in spin
orientation
• Emissive rates of fluorescence are several orders of
magnitude faster than that of phosphorescence
Energy level diagram (Jablonski diagram)
Fluorescence process: Population of energy
levels
• At room temperature (300 K), and for typical
electronic and vibration energy levels, can
calculate the ratio of molecules in upper and
lower states
nupper
nlower

 exp  E

kT
k=1.38*10-23 JK-1 (Boltzmann’s constant)
E = separation in energy level
Fluorescence process: Excitation
• At room temperature, everything starts out at
the lowest vibrational energy level of the ground state
• Suppose a molecule is illuminated with light at a
resonance frequency
• Light is absorbed; for dilute sample, Beer-Lambert
law applies
A  cl
where e is molar absorption (extinction) coefficient
(M-1 cm-1); its magnitude reflects probability of absorption and
its wavelength dependence corresponds to absorption spectrum
e
• Excitation - following light absorption, a chromophore is excited
to some higher vibrational energy level of S1 or S2
• The absorption process takes place on a time scale (10-15 s) much
faster than that of molecular vibration → “vertical” transition
(Franck-Condon principle).
Fluorescence process: Non-radiative
relaxation
• In the excited state, the electron is
promoted to an anti-bonding orbital→
atoms in the bond are less tightly held
→ shift to the right for S1 potential
energy curve →electron is promoted to
higher vibrational level in S1 state than
the vibrational level it was in at the
ground state
• Vibrational deactivation takes place
through intermolecular collisions at a
time scale of
10-12 s (faster than that of
fluorescence process)
S1
S
o
Fluorescence process: Emission
• The molecule relaxes from the
lowest vibrational energy level
of the excited state to a vibrational
energy level of the ground state
(10-9 s)
• Relaxation to ground state occurs
faster than time scale of molecular
vibration → “vertical” transition
• The energy of the emitted photon
is lower than that of the incident
photons
S1
So
Stokes shift
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The fluorescence light is red-shifted (longer
wavelength than the excitation light) relative to the
absorbed light ("Stokes shift”).
Internal conversion (transition occurring between
states of the same multiplicity) can affect Stokes
shift
Solvent effects and excited state reactions can also
affect the magnitude of the Stoke’s shift
Invariance of emission wavelength with
excitation wavelength
• Emission wavelength only
depends on relaxation back
to lowest vibrational level of S1
S1
• For a molecule, the same
fluorescence emission wavelength
is observed irrespective of the
excitation wavelength
So
I. Principles of Fluorescence
v’=5
v’=4
Mirror image rule
• Vibrational levels in the excited states
and ground states are similar
• An absorption spectrum reflects the
vibrational levels of the electronically
excited state
• An emission spectrum reflects the
vibrational levels of the electronic
ground state
• Fluorescence emission spectrum is
mirror image of absorption spectrum
v’=3
v’=2
v’=1
v’=0
S1
v=5
v=4
v=3
v=2
v=1
v=0
S0
Internal conversion vs. fluorescence emission
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As electronic energy increases, the energy
levels grow more closely spaced
It is more likely that there will be overlap
between the high vibrational energy levels of
Sn-1 and low vibrational energy levels of Sn
This overlap makes transition between states
highly probable
Internal conversion is a transition occurring
between states of the same multiplicity and it
takes place at a time scale of 10-12 s (faster
than that of fluorescence process)
The energy gap between S1 and S0 is
significantly larger than that between other
adjacent states → S1 lifetime is longer →
radiative emission can compete effectively
with non-radiative emission
Mirror-image rule
typically applies when
only S0 → S1 excitation
takes place
Deviations from the
mirror-image rule are
observed when S0 →
S2 or transitions to even
higher excited states
also take place
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Intersystem crossing refers to non-radiative transition between states of
different multiplicity
It occurs via inversion of the spin of the excited electron resulting in two
unpaired electrons with the same spin orientation, resulting in a state
with Spin=1 and multiplicity of 3 (triplet state)
Transitions between states of different multiplicity are formally
forbidden
Spin-orbit and vibronic coupling mechanisms decrease the “pure”
character of the initial and final states, making intersystem crossing
probable
T1 → S0 transition is also forbidden → T1 lifetime significantly larger than
S1 lifetime (10-3-102 s)
Intersystem
crossing
S1
absorption
T1
fluorescence
phosphorescence
S
Fluorescence energy transfer (FRET)
Molecule 1
Molecule 2
Fluorescence
Fluorescence
ACCEPTOR
DONOR
Absorbance
Absorbance
Wavelength
Non-radiative energy transfer – a quantum mechanical process
of resonance between transition dipoles
Effective between 10-100 Å only
Emission and excitation spectrum must significantly overlap
Donor transfers non-radiatively to the acceptor
Quantum yield of fluorescence
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Quantum yield of fluorescence, Ff, is defined as:
number of photons emitted
Ff 
number of photons absorbed
In practice, is measured by comparative measurements with
reference compound for which has been determined with high
degree of accuracy.
Ideally, reference compound should have
◦ the same absorbance as the compound of interest at given
excitation wavelength
◦ similar excitation-emission characteristics to compound of interest
(otherwise, instrument wavelength response should be taken into
account)
◦ Same solvent, because intensity of emitted light is dependent on
refractive index (otherwise, apply correction
◦ Yields similar fluorescence intensity to ensure measurements are
taken within the range of linear instrument response
Fluorescence lifetime
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Another definition for Ff is
Ff 
kr
k
where kr is the radiative rate constant and Sk is the sum of
the rate constants for all processes that depopulate the S1
state.
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The observed fluorescence lifetime, is the average time the
molecule spends in the excited state, and it is
1
f 
k
Fluorescence emission distribution
•For a given excitation wavelength,
the emission transition is
distributed among different
vibrational energy levels
•For a single excitation wavelength,
can measure a fluorescence
emission spectrum
Intensity
Exc
Emm
Emission Wavelength (nm)
Effect on fluorescence emission
• Suppose an excited molecule emits fluorescence
in relaxing back to the ground state
• If the excited state lifetime,  is long, then
emission will be monochromatic (single line)
• If the excited state lifetime,  is short, then
emission will have a wider range of frequencies
(multiple lines)
1)
1)
2)
Which more closely resembles an absorption
spectrum an emission or an excitation
spectrum?
What is the difference between fluorescence
and phosphorescence?
Define quantum yield?
1)
2)
An excitation spectrum is essentially
identical to an absorption spectrum.
Fluorescence – return from excited singlet state
to ground state; does not require change in spin
orientation (more common of relaxation)
Phosphoresence – return from a triplet excited
state to a ground state; electron requires change
in spin orientation
3)
Quantum yield is
number of photons emitted
Ff 
number of photons absorbed