Instructor: Dr. Marinella Sandros

Nanochemistry NAN 601 • Instructor: • Dr. MarinellaSandros Lecture 7: Quantum Chemistry_Fluorescence

Let’s start with photon energy • 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10-34 J·s

How come I’ve never seen a photon? • Sunny day (outdoors): • 1015 photons per second enter eye (2 mm pupil) • Moonlit night (outdoors): • 51010 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

Waves http://www.ars-chemia.net/Classes/101/PPT/08_Quantum_Chemistry.pdf

Quantum Wavelength • 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!

Quantum Mechanics View • 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”

Quantum problems….. • 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

Problems, cont. • 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

Diffraction in Our Everyday World • 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

The Double Slit Experiment wave? particle?

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

Dr. Quantum • Lets watch this movie!!! http://www.youtube.com/watch?v=DfPeprQ7oGc

Bohr and the Atom http://www.ars-chemia.net/Classes/101/PPT/08_Quantum_Chemistry.pdf

Bohr and the Emission Spectrum http://www.ars-chemia.net/Classes/101/PPT/08_Quantum_Chemistry.pdf

Explaining Emission Spectrum http://www.ars-chemia.net/Classes/101/PPT/08_Quantum_Chemistry.pdf

I. Principles of Fluorescence Luminescence • Emission of photons from electronically excited states • Two types of luminescence: Relaxation from singlet excited state Relaxation from triplet excited state

I. Principles of Fluorescence 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

I. Principles of Fluorescence 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

I. Principles of Fluorescence Energy level diagram (Jablonski diagram)

I. Principles of Fluorescence 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*10-23 JK-1 (Boltzmann’s constant) DE = 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 e 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 highervibrational 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).

I. Principles of Fluorescence 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 So

S1 So I. Principles of Fluorescence 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

I. Principles of Fluorescence 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

S1 So I. Principles of Fluorescence 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

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 S1 v’=1 v’=0 v=5 v=4 v=3 v=2 v=1 S0 v=0

I. Principles of Fluorescence 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) Intersystem crossing S1 T1 absorption fluorescence phosphorescence S0

I. Principles of fluorescence

Fluorescence energy transfer (FRET) Molecule 1 Molecule 1 Molecule 2 Molecule 2 Fluorescence Fluorescence Fluorescence Fluorescence ACCEPTOR ACCEPTOR DONOR DONOR Intensity Intensity Absorbance Absorbance Absorbance Absorbance Wavelength 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 • Quantum yield of fluorescence, Ff, 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

II. Quantum yield and life time Fluorescence lifetime • Another definition for Ff is where kr is the radiative rate constant and Sk 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

Exc Emm Intensity Emission Wavelength (nm) 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

Quantum Yield and Lifetime Effect on fluorescence emission • Suppose an excited molecule emits fluorescence in relaxing back to the ground state • If the excited state lifetime, t is long, then emission will be monochromatic (single line) • If the excited state lifetime, t is short, then emission will have a wider range of frequencies (multiple lines)

Quiz 5 • Which more closely resembles an absorption spectrum an emission or an excitation spectrum? • What is the difference between fluorescence and phosphorescence? • Define quantum yield?

Quiz 5-Answers • 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 • Quantum yield is

Instructor: Dr. Marinella Sandros