 Instructor:  Dr. Marinella Sandros 1 Nanochemistry NAN 601 Lecture 7: Quantum Chemistry_Fluorescence

2  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 = 6.63  J·s

3  Sunny day (outdoors): ◦ photons per second enter eye (2 mm pupil)  Moonlit night (outdoors): ◦ 5  photons/sec (6 mm pupil)  Moonless night (clear, starry sky) ◦ 10 8 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

5  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 ◦  meters (too small to matter in macro environment!!)  typical “quantum” objects: ◦ electron ( kg) at thermal velocity (10 5 m/s)   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  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  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

9  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

10 particle? wave?

11  The pattern on the screen is an interference pattern characteristic of waves  So light is a wave, not particulate

 Lets watch this movie!!! oGc

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 k=1.38* 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 where  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 S 1 or S 2 The absorption process takes place on a time scale ( 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 S 1 potential energy curve → electron is promoted to higher vibrational level in S 1 state than the vibrational level it was in at the ground state Vibrational deactivation takes place through intermolecular collisions at a time scale of s (faster than that of fluorescence process) SoSo S1

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 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 S 1 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 S0S0 S1S1 v=0 v=1 v=2 v=3 v=4 v=5 v’=0 v’=1 v’=2 v’=3 v’=4 v’=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 S n-1 and low vibrational energy levels of S n  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 s (faster than that of fluorescence process)  The energy gap between S 1 and S 0 is significantly larger than that between other adjacent states → S 1 lifetime is longer → radiative emission can compete effectively with non-radiative emission

Mirror-image rule typically applies when only S 0 → S 1 excitation takes place Deviations from the mirror-image rule are observed when S 0 → S 2 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  T 1 → S 0 transition is also forbidden → T 1 lifetime significantly larger than S 1 lifetime ( s) S0S0 S1S1 T1T1 absorption fluorescence phosphorescence Intersystem crossing

Intensity Wavelength Absorbance DONOR Absorbance Fluorescence ACCEPTOR Molecule 1Molecule 2 Fluorescence energy transfer (FRET) Intensity Wavelength Absorbance DONOR Absorbance Fluorescence ACCEPTOR Molecule 1Molecule 2 Non-radiative energy transfer – a quantum mechanical process of resonance between transition dipoles Effective between Å only Emission and excitation spectrum must significantly overlap Donor 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 Quantum yield of fluorescence

 Another definition for  f is where k r is the radiative rate constant and  k is the sum of the rate constants for all processes that depopulate the S 1 state.  The observed fluorescence lifetime, is the average time the molecule spends in the excited state, and it is 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 Intensity Emission Wavelength (nm) Exc Emm

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