Photochemistry Lecture 2 Fates of excited states of polyatomic molecules

Polyatomic molecule electronic states  Use of group theory to define irreducible representations for MOs  e.g., benzene

Benzene electronic excited states  Ground state ….(1a 2u ) 2 (1e 1g ) 41 A 1g  First excited configuration …..….(1a 2u ) 2 (1e 1g ) 3 (1e 2u ) 1  Use direct product tables to generate the term symbols  e 1g x e 2u = B 1u + B 2u + E 1u  Resultant spin 1 or 0 (triplet/singlet)  Lowest excited state is 3 B 1u  Lowest singlet excited state 1 B 2u

Selection rules for allowed electronic transitions  () x ()  (T x ) and/or (T y ) and/or (T z )  For benzene (D 6h ) (T x ),(T y ) E 1u, (T z )  A 2u  Transition to lowest excited state formally forbidden because A 1g x B 2u = B 2u

Chromophores  Larger molecules may have very few symmetry elements  Excitation can often be traced to electrons belonging to a small group of atoms known as a chromophore  Typically label excitation as e.g., *  n (e.g., carbonyl group) *   (e.g., alkene or carbonyl) *  n indicates a non-bonding electron usually localised (e.g, lone pair on oxygen for carbonyl)

Chromophores (cont)  Likewise, excited states may be labelled e.g., 1 (*,) or 3 (*,n) indicating which electrons are unpaired.  *   transitions may lie deep into the ultraviolet (7 eV or = 180 nm) for unconjugated double bonds, but shift towards visible as conjugation increases (cf particle in 1D box)  *  n transitions in carbonyl group also in UV at around 290 nm (4 eV)

Photochemical mechanism of vision: *   of 11-cis retinal Isomerization in 200 fs

* n transition is forbidden to first-order approximation on grounds of symmetry (p x  p y on oxygen – transition moments zero)

Simplified nomenclature for polyatomic molecules  S 0 ground state  S 1 lowest excited singlet state (S=0)  T 1 lowest triplet state (S=1) S0S0 S1S1 S2S2 T1T1 T2T2

Vibrational modes of polyatomic molecules  3N-6 degrees of vibrational freedom (or 3N-5 for a linear molecule)  Normal modes from group theory analysis e.g., for ammonia -

Vibronically allowed transitions  In benzene, transition to lowest excited state 1 B 2u formally forbidden because it has A 1g x B 2u = B 2u whereas (T x ),(T y ) E 1u, (T z )  A 2u However, if an E 2g vibration is simultaneously excited then overall symmetry of excited state is B 2u x E 2g = E 1u Hence excitation is weakly allowed, provided there is simultaneous excitation of vibration of appropriate symmetry mode. (distortion of symmetry causes mixing of excited electronic states)

Potential energy surface  Potential energy of molecule varies as a function of 3N-6 co- ordinates for polyatomic. PE surface, not just simple curve.  Can represent a “cut” through this multi- dimensional surface by freezing all co-ordinates except one of interest e.g., for umbrella bending mode of ammonia PE surface for triatomic – bending angle fixed (linear)

Franck Condon principle as applied to polyatomic molecules  For those vibrational modes that are allowed by symmetry, whether a long or short progression is observed is determined by Franck Condon principle  Need to consider whether there is a large change in geometry on excitation along the direction of the normal co-ordinate for the mode in question  e.g., for NH 3 molecule becomes more planar in excited states, hence a long progression in the umbrella bending mode is excited. For benzene the ring bond length increases, hence ring breathing mode is excited.

Ring breathing mode vibrational progression of Benzene

Vibrational states of polyatomic molecules  3N-6 Normal modes of e.g., H 2 O  Represent number of quanta in each mode as (v 1, v 2….. )  v 1 quanta in mode 1 etc.  (0,0,0..) is the ground vibrational state.  Energy, E is  the sum of vibrational energies in each mode (harmonic approx).  E= (v 1 + ½) h 1 + (v 2 +½)h 2 + ….

Density of vibrational states for hexafluorides  Density of vibrational states defined as number of vibrational states per wavenumber  Estimate from number of ways of distributing j quanta in s equivalent oscillators

Jablonski diagram Vibrational levels at high energy are pseudo- continuous Levels of S 1 are degenerate with pseudo-continuum of high vibrational levels of S 0 and T 1

Fates of excited states III: Polyatomic molecules

Vibrational relaxation in solution  Molecules excited to excited vibrational levels of S 1 undergo rapid degradation to lowest vibrational level of S 1.  Energy is transferred to the solvent molecules (translation primarily) by collision i.e., V-T  Subsequent processes begin from this lowest level and are thus independent of the vibrational level that is originally excited.

Absorption spectrum determined by (a) vibronic selection rules and (b) Franck-Condon overlap Emission (fluorescence) or other processes follow relaxation to lowest vibrational level of S 1 Energy transfer etc

Intramolecular energy transfer  Collision free radiationless process; molecule evolves into different electronic state without loss or gain of energy  Excess electronic energy transferred to vibrations, followed by fast relaxation.  Represented by horizontal line on Jablonski Diagram

Different intramolecular processes  Internal Conversion (IC) No change of spin state e.g., S 0  S 1  Intersystem Crossing (ISC) Change of spin state e.g., T 1 S 0 or S 1 T 1  Intramolecular Vibrational Redistribution (IVR) No change of electronic state but change of vibrational state (more important in gas phase) S 1 (v 1,v 2,v 3 ….)  S 1 (v 1 ’,v 2 ’,v 3 ’)