Molecular spectroscopy II: Electronic transitions. Characteristic frequencies and wavelengths. Hierarchy of energy levels. E el >> E rot >> E vib

Transcription

1 Molecular spectroscopy II: Electronc transtons Characterstc requences and wavelengths Herarchy o energy levels E el >> E rot >> E vb Electronc transtons Vbratonal transtons Rotatonal transtons Energy Energy Energy derent electronc states derent vbratonal states derent rotaton states E el E rot E vb Internuclear dstance Internuclear dstance Internuclear dstance = nm UV vsble regon = m nrared regon = 1 mm 10 cm mcrowave regon

2 The nucle ater an electronc transton are subected to derent orces and the molecule may respond by startng to vbrate. The resultng vbratonal structure o electronc transtons can be resolved or gaseous samples, but n a lqud or sold the lnes usually merge together and result n a broad, almost eatureless band. Supermposed on the vbratonal transtons that accompany the electronc transton o a molecule n the gas phase s an addtonal branch structure that arses rom rotatonal transtons. Ultravolet spectrum o gaseous SO 2 The absorpton spectrum o chlorophyll n the vsble regon. Vbratonal structure n electronc spectra o molecules: Franck Condon prncple Franck Condon prncple: Because the nucle are so much more massve than the electrons, an electronc transton takes place very much aster than the nucle can respond. vertcal transton: Nuclear coordnates do not change! Note that the upper curve s usually dsplaced to greater equlbrum bond lengths because electroncally excted states usually have more antbondng character than electronc ground states. Accordng to the Franck Condon prncple, the most ntense vbronc transton s rom the ground vbratonal state to the vbratonal state lyng vertcally above t. Transtons to other vbratonal levels also occur, but wth lower ntensty. As a result o the transton, electron densty s rapdly bult up n new regons o the molecule and removed rom others. The ntally statonary nucle suddenly experence a new orce eld, to whch they respond by begnnng to vbrate F = grad (V)

3 Franck Condon actors A typcal absorpton spectrum o a molecule R e What determnes ntenstes o derent spectral transtons? Several nearby states have an apprecable probablty o the nucle beng at the ntal separaton R e. Thereore, transtons occur to all the vbratonal states n ths regon, but most ntensely to the state wth a vbratonal waveuncton that peaks most strongly near R e. e rk e k e Franck Condon actors Dpole moment operator s a sum over all nucle at R and electrons at r k n the molecules S,, ) ( Z R * d e rk e Z R k ( r, R) ( r) ( R) d rk d d e Z R d d k e k rk d Born Oppenhemer approxmaton: d total wave uncton S(, ), = Transton dpole moment arsng rom the redstrbuton o electrons electron part vbratonal part Electronc states are orthogonal = Overlap ntegral between the vbratonal state n the ntal electronc state and the vbratonal state n the nal electronc state The ntensty o the transton s proportonal to the square modulus, μ 2,

4 Example: Calculatng a Franck Condon actor Consder the transton rom one electronc state to another, ther bond lengths beng R e and R e and ther orce constants equal. Calculate the Franck Condon actor or the 0 0 transton and show that the transton s most ntense when the bond lengths are equal. Soluton: we need to calculate S(0,0), the overlap ntegral o the two ground state vbratonal waveunctons, and then take ts square. Use the waveunctons or a harmonc oscllator: 1/2 Orgn o colours: Chromophore A chromophore s the part o a molecule responsble or ts color. (χρῶμα means colour, φέρω means to carry ) The color arses when a molecule absorbs certan wavelengths o vsble lght and transmts or relects others. The chromophore s a regon n the molecule where the energy derence between two derent molecular orbtals alls wthn the range o the vsble spectrum. Vsble lght that hts the chromophore can thus be absorbed by exctng an electron rom ts ground state nto an excted state. One o the most mportant chromophores are conugated p bond systems. Example: carotene

5 The chlorophyll Chlorophyll (also chlorophyl) s a green pgment plants. Its name s derved rom the Greek words χλωρος, chloros ("green") and φύλλον, phyllon ("lea"). Chlorophyll allows plants to absorb energy rom lght. Chlorophyll absorbs lght most strongly n the blue and red regons o spectrum. However, t s a poor absorber o green and near green portons o the spectrum, hence ts green color. Structure o chlorophyll c1 Conugated p bond systems: * transton A C=C double bond n a molecule acts as a chromophore. One o ts mportant transtons s the * transton, n whch an electron s promoted rom a orbtal to the correspondng antbondng orbtal. LUMO= 2* In Ethene, the energy needed to excte electroncally the molecule, rom the ground state 1 2 to the rst excted state *1 s provded by 7 ev: Ethene absorbs the UV lght (=170 nm). HOMO= 1 When the conugaton pathway n the molecule s extended, the HOMO LUMO separaton energy, E L H decreases. I E L H s on the order o the energy o vsble lght E=h, then the molecules, such as the long carotenod molecules, absorb vsble lght at a certan requency (n the green). The photons wth another energy,.e. the radatons wth other requences, are relected towards our eyes and that gves the orange color o carrots that contans a lot o carotenes. carotene

6 The ates o electroncally excted states Beore Molecule n excted state Ater A radatve decay process s a process n whch a molecule dscards ts exctaton energy as a photon. Ater Molecule n ground state Beore Molecule n excted state Ater Ater Molecule n ground state A nonradatve decay, s a process n whch the excess energy s transerred nto the vbraton, rotaton, and translaton o the surroundng molecules due to collsons Radatve decay: Fluorescence and phosphorescence In luorescence, spontaneous emsson o radaton occurs wthn a ew nanoseconds ater the exctng radaton s extngushed. In phosphorescence, the spontaneous emsson may persst or long perods (even hours, but characterstcally seconds or ractons o seconds). The derence suggests that phosphorescence nvolves the storage o energy n a reservor rom whch t slowly leaks. Fluorescence The sequence o steps leadng to luorescence. Ater the ntal absorpton, the upper vbratonal states undergo radatonless decay by gvng up energy to the surroundngs. A radatve transton then occurs rom the vbratonal ground state o the upper electronc state.

7 Energy Energy Internuclear dstance Internuclear dstance An absorpton spectrum shows a vbratonal structure characterstc o the upper state. A luorescence spectrum shows a structure characterstc o the lower state; t s also dsplaced to lower requences Phosphorescence The sequence o events leadng to phosphorescence or a molecule wth a snglet ground state. The rst steps are the same as n luorescence, but the presence o a trplet excted state plays a decsve role. Due to the spn orbt couplng the molecule may undergo ntersystem crossng, a transton between states o derent multplcty, and become a trplet state. Ths happens at the pont where the snglet and trplet excted states have the same energy. We can expect ntersystem crossng to be mportant when a molecule contans a moderately heavy atom (such as S, sulur), because then the spn orbt couplng s large. When an excted molecule crosses nto a trplet state, t s now steppng down the trplet s vbratonal ladder. Reachng the lowest vbratonal state, the molecule cannot radate ts energy because return to the ground electronc state s spn orbdden. The radatve transton, however, s not totally orbdden because the spn orbt couplng that was responsble or the ntersystem crossng also breaks the selecton rule. The molecules are thereore able to emt weakly, and the emsson may contnue long ater the orgnal excted state was ormed.

8 Curosty: The term "phosphorescence", meanng glow o phosphorus (P) ater llumnaton, orgnally derves rom ths property o phosphorus, although ths word has snce been used or a derent physcal process that produces a glow. The glow o phosphorus tsel orgnates rom oxdaton o the whte (but not red) phosphorus a process now termed chemlumnescence. Dssocaton A dssocaton s characterzed by an absorpton spectrum composed o two parts: a vbratonal progresson a contuum absorpton When absorpton occurs to unbound states o the upper electronc state, the molecule dssocates and the absorpton s a contnuum. Below the dssocaton lmt the electronc spectrum shows a normal vbratonal structure.