Instructor: Instructor:

Dr. Marinella SandrosDr. Marinella Sandros

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NanochemistrNanochemistryy

NAN 601NAN 601

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 The constant, h, is Planck’s constant

◦ has tiny value of: h = 6.6310-34 J·s

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Sunny day (outdoors):◦ 1015 photons per second enter eye (2 mm pupil)

Moonlit night (outdoors):◦ 51010 photons/sec (6 mm pupil)

Moonless night (clear, starry sky)◦ 108 photons/sec (6 mm pupil)

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

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

The quantum wavelength of an object is: = h/p (p is momentum)

◦ called the de Broglie wavelength typical macroscopic objects

◦ masses ~ kg; velocities ~ m/s p 1 kg·m/s◦ 10-34 meters (too small to matter in macro

environment!!) typical “quantum” objects:

◦ 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!

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”

Spring 2008 7

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 8

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

Each atom has a distinct “fingerprint”

Light only comes off at very specific wavelengths◦ or frequencies◦ or energies

Note that hydrogen (bottom), with only one electron and one proton, emits several wavelengths

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Squint and things get fuzzy◦ opposite behavior from particle-based pinhole

camera Eye floaters

◦ look at bright, uniform source through tiniest pinhole you can make—you’ll see slowly moving specks with rings around them—diffraction rings

Shadow between thumb and forefinger◦ appears to connect before actual touch

Streaked street-lights through windshield◦ 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

Lets watch this movie!!!

http://www.youtube.com/watch?v=DfPeprQ7oGc

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

kTE

n

n

lower

upper exp

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 applieswhere is molar absorption (extinction) coefficient (M-1 cm-1); its magnitude reflects probability of absorption and its wavelength dependence corresponds to absorption spectrum

• 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).

clA

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)

So

S1

Fluorescence process: Emission

• The molecule relaxes from the lowest vibrational energy level of the excited state to a vibrationalenergy 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 photonis lower than that of the incidentphotons

So

S1

Stokes shift 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

• For a molecule, the same fluorescence emission wavelength is observed irrespective of the excitation wavelength

So

S1

I. Principles of Fluorescence

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

S0

S1

v=0

v=1

v=2v=3v=4v=5

v’=0v’=1v’=2v’=3v’=4v’=5

Internal conversion vs. fluorescence emission

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

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)

S0

S1T1absorption fluorescence

phosphorescence

Intersystemcrossing

Inte

nsi

ty

Wavelength

Absorbance

DONOR

Absorbance

Fluorescence Fluorescence

ACCEPTOR

Molecule 1 Molecule 2

Fluorescence energy transfer (FRET)In

tensi

ty

Wavelength

Absorbance

DONOR

Absorbance

Fluorescence Fluorescence

ACCEPTOR

Molecule 1 Molecule 2

Non-radiative energy transfer – a quantum mechanical process of resonance between transition dipoles

Effective between 10-100 Å onlyEmission and excitation spectrum must significantly

overlapDonor transfers non-radiatively to the acceptor

Quantum yield of fluorescence, f, is defined as:

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

absorbed photons ofnumber

emitted photons ofnumber f

Quantum yield of fluorescence

Another definition for f is

where kr is the radiative rate constant and k is the sum of the rate constants for all processes that depopulate the S1 state.

The observed fluorescence lifetime, is the average time the molecule spends in the excited state, and it is

k

krf

kf

1

Fluorescence lifetime

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

Inte

nsi

ty

Emission Wavelength (nm)

ExcEmm

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) Which more closely resembles an absorption spectrum an emission or an excitation spectrum?

1) What is the difference between fluorescence and phosphorescence?

2) Define quantum yield?

1) An excitation spectrum is essentially identical to an absorption spectrum.

2) 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 absorbed photons ofnumber

emitted photons ofnumber f