Vibrational spectroscopy. IR absorption spectroscopy Raman spectroscopy UV-Viz absorption Fluorescence spectroscopy Microwave spectroscopy

Transcription

1 Vibational spectoscopy deal with olecules vibations IR absoption spectoscopy Raan spectoscopy UV-Viz absoption Fluoescence spectoscopy Micowave spectoscopy based on optical pinciples and devices (Optical spectoscopy) olecules otations Electoagnetic adiation can deteine a olecule to change his enegy! (otational, vibational, electonic) A lot of enegy levels!!! - otational - vibational - electonic (gound state / excited state)

2 What is spectoscopy? Spectoscopy study the popeties of atte though its inteaction with electoagnetic adiation (diffeent fequency coponents). Latin: specton ghost (o spiit) Gee: σκοπειν (scopie = to see) In spectoscopy, we aen t looing diectly at the olecules (the atte), we study its ghost, obtained fo the inteaction of electoagnetic waves with olecules. Diffeent type of spectoscopy (incident electoagnetic waves with diffeent fequency/wavelength/wavenube/enegy) involve diffeent pictue (diffeent spectu). RMN RES Mico waves Raan IR Visible UV Fluoescence X -Ray Γ - Ray λ[] [c - ] ν[hz] 3x 6 3x 8 3x 3x 3x 4 3x 6 3x 8 3x

3 Fo spectoscopy easueents we can to extact diffeent infoation (enegies of electonic, vibational, otational states; stuctue and syety of olecules; dynaic infoation, etc). Goal: to undestand: - how electoagnetic adiations inteacts with atte and - how we can use the obtained infoation in ode to undestand the saple.

4 Spectoscopy applications Finge pint Functional goups Molecula syety Bond distances Bond angles Electonic stuctue Gas Liquid Solid IR, Raan Micowave IR, Raan MS NMR IR, Raan Micowave e-diffaction IR, Raan Micowave e-diffaction UV-Vis UPS ESR IR, Raan UV-Vis, MS NMR IR, Raan MS NMR IR, Raan MS NMR EXAFS LC-NMR/MS UV-Vis UPS ESR IR, Raan UV-Vis, MS X-Ray diff. IR, Raan MS, NMR Mossbaue IR, Raan MS, NMR Mossbaue X-Ray diff. neuton diff. UV-Vis, UPS, ESR Mossbaue, NQR X-Ray diff. neuton diff. EXAFS: Extended X-Ray Absoption Fine Stuctue, MS: Mass Spectoety, NQR: Nuclea Quadupola Resonance, LC-MNR/MS: Liquid Choatogaph Nuclea Magnetic Resonance Mass Spectoete, UPS: Ultaviolet photoeission spectoscopy

5 Questions: What does light do to saple? How do we poduce a spectu? What does a spectu easue? Inteaction of light with a saple can influence - the saple - the light The basic idea: electoagnetic wave (light) Saple a b Chaacteize light afte saple Chaacteize change in saple (photoacoustic spectoscopy) (bodes on photocheisty) () excitation; () detection

6 In vibational spectoscopy we easue how a saple odifies the incident light, in ode to undestand what light do to the saple! ) Absoption: The saple can absob a pat of incident light A change in the intensity appea: eegent light diffes fo incident light Saple attenuates the incident light (at paticula fequencies). Two type of easueents: absobance A = log(i /I) tansission T = I/I If we easue the absobance of light on entie ange of incident adiation, we will obtained the absoption spectu. A A f ( ) A f ( )` A f ( ) - fequency (Hz, /s) λ - wavelength (n, ) - wavenube (c - ) Micowaves absoption (involve otational tansitions) c c Infaed absoption UV-Vis absoption (involve vibational tansitions) (involve electonical tansitions)

7 ) Eission: Excitation can induces eission of light fo the saple (usually of diffeent fequency fo incident light!). (Eitted in all diections) sae fequency: Rayleigh scatteing diffeent fequency Raan scatteing (vibational tansitions ae involved) Fluoescence (eission fo excited electonic singlet states) Phosphoescence (eission fo excited electonic tiplet states) 3) Optical Rotation: Phase change of light incident on saple (otation of polaization plane) (- no spectoscopy)

8 An electoagnetic wave is coposed fo an electic field (E x ) and a agnetic field (H y ) that ae pependicula each othe, and pependicula to the diection of tavel (Oz). The wave equation fo electoagnetic waves aises fo Maxwell's equations: E x = E sin( t- (/λ) z) H y = H sin(ωt-z) angula fequency (ω = π) [adians/sec] wave vecto ( = π/λ = ω/c) fequency ( = ω/π) [sec -, Hetz] wavelength (n, Ǻ) wavenube (c - ) c c light speed (3 8 /s) E enegy (E = h ) [J], enegy can be expessed as c - using E/hc!

9 Types of olecule otion Motion of whole olecule Tanslational otion: whole olecule changes its location in thee diensional space Rotational otion: whole olecule spins aound an axis in thee diensional space Motion within olecule Vibational otion: otion that changes the shape of the olecule (peiodic otion of atos) - stetching (bonds length defoation) - bending (bonds angle defoation)

10 Molecula vibations A olecula vibation occus when atos in a olecule ae in peiodic otion. The fequency of the peiodic otion is nown as the vibation fequency. A olecula vibation is a peiodic distotion of a olecule fo its equilibiu geoety. The enegy equied fo a olecule to vibate is not continuous (is quantized) and is (geneally) in the infaed egion of the electoagnetic spectu. D-F H-F H-Cl syetical stetching asyetical stetching bending CO N O H O

11 Vibational otion of 3 atos goup: Syetical stetching Asyetical stetching Scissoing Rocing Wagging Twisting In plane vibations - stetching - scissoing - ocing Out of plane vibations - wagging - twisting Molecula vibations can be classified in - stetching - bending - tosion (oe that 3 atos involved)

12

13 Molecula vibations of olecules Isolated olecule total enegy (E), linea oentu (p) and angula oentu (M) ae constants. Z O R CM Fixed O x' z' R α obile y' α d α Y E Ec V const p M R α dr dt α p α const const E c E c - inetic enegy i dr dt V - potential enegy (=?) X OXYZ: fixed efeence fae O x y z : cente of ass efeence fae R CM R

14 Z z' obile In the cente of ass efeence fae (CM), linea oentu (p) and angula oentu (M) ae zeo! O y' p X O R CM Fixed x' R α α d α Y M Ecat conditions: d d - equilibiu position d Only oveent which eet the Ecat conditions ae vibations!

15 The inetic enegy of an isolated olecule in the cente of ass efeence fae (CM): dr dr dt dt d dt Z O' CM z' y' α E c α ato speed (fixed fae) α dr dt tanslational speed α T t T ot otational speed T vib T co elative speed (CM fae) - total inetic enegy O Fixed x' α R α d α Y T t α R - pue tanslational inetic enegy X T ot α (ω α ) α - pue otational inetic enegy T T vib co ω α α (d α α α ) - pue vibational inetic enegy - oto-vibational inetic enegy We alost can sepaate the inetic enegy of the thee type of olecule otion!!!

16 Diatoic olecule vibation The siplest odel to descibe the vibation of a diatoic olecule (two atos lined by a cheical bond) is the classical analog of a sping connecting two bodies. The stength of the bond coesponds to the foce constant of the sping The sping behavio gives us a desciption of how the olecule enegy changes if we distot the bond. When the sping equation (F = -x) is applied to the vibating paticles the fequency of the vibation is elated to the asses of the paticles and to the foce constant. In a siila way, the fequency of the olecule vibation (ν) is elated to the asses of the atos () and to the stength of the cheical bond ().

17 The olecule is consideed isolated, so total enegy (E), linea oentu (p) and angula oentu (M) ae constants. E Ec V(x) const. p R R const R p R p const M E c v v v educe ass x In ode to descibe the olecule vibation we ust define the potential enegy (V) of the olecule. The potential enegy of a haonic oscillato (ideal olecule) is V(x) = / x whee V(x) = potential enegy, = cheical bond (foce constant) x = elongation/copession of the bond fo its equilibiu position At the equilibiu position, the potential enegy is zeo!

18 The vibation otion of a diatoic olecule is odel with a "Siple Haonic Oscillato" (SHO) using Hooe's law as a linea estoing foce. Classically: The Haonic Oscillato Appoxiation Classical desciption d x a dt F x The exact classical solution (depends upon the initial conditions) geneally tae the fo: x(t) Asin(t) Asin( t) The fequency of oscillation is given by: - is the foce constant of the sping in N/ The fequency ν does not depend on the aplitude (A).

19 The vibation of a diatoic olecule (ideal oecule): Siple haonic oscillato the ass is fixed to a wall: The fequency of oscillation is given by: Diatoic olecules thee ae two asses, and. The fequency of vibation is given by: bond foce constant μ educe ass

20 Siple haonic oscillato (SHO) Quantu Mechanical To get the QM solution, we need the potential enegy stoed in the SHO: Potential enegy: Hailtonian: Schödinge equation: V(x) H E c x V p x When we solve the Schödinge equation, we always obtain two things:. a set of wave functions (eigenstates):. a set enegies (eigenvalues): n n,,3... h (n The enegy of a vibating olecule is quantized! E n ) n - quantu nube The vibations enegy levels ae: E v h (v ) o E v hc (v ) v - vibational quantu nube (v =,,, 3,..)

21 Diatoic olecule - one vibation! (stetching) Enegy levels: Wavenube: E v hcν(v c ) E v hν v wavenube fequency educe ass foce constant Wavefunctions Ψ v N x N exp x H x v v 4 h The siple haonic oscillato wave functions (solutions to the one diensional Schödinge equation) ae nown as the "Heite Polynoials". v v! v H v (x) = Heite polynoials H H H x x x x 4x x H3 8x x H v 3 xh v vh v The vibational wave functions of a siple haonic oscillato have altenate paity (even/odd syety/asyety).

22 E v+ - E v = h c ν The distance between two adjacent levels (E v+ - E v ) is h c ν! Fo an ideal olecule, the vibational enegy levels ae equidistant! SHO Wave functions Wave function epesentations fo the fist eight quantu states.

23 Fo the siple haonic oscillato: quantu echanical pedicts the existence of discete, evenly spaced, vibational enegy levels. E v hcν v v,,,3... v - vibational quantu nube Fo the gound state (v = ), E = / h c ν E = / h c E!!! This is called the zeo point enegy. Even in gound state thee is soe ind of vibation!

24 If a oe ealistic potential (V) is used in the Schödinge Equation, the enegy levels get scunched togethe! d dv Using Taylo seies nea equilibiu position: haonic: we conside only te we neglected supeio tes 3, 4, 5,... - în equilibiu position we have a iniu, so - we supposed zeo potential in equilibiu position: x V(x) d V d V() anhaonic: we conside tes 3 and 4 we neglect tes 5,6, ex gx x V(x) Anhaonic oscillato eal olecule! ) ( V... d V d 3! d V d! d dv V V d V d 4! d V d 3! d V d! V

25 Mose potential close to eal olecule potential: V D a e ( e ) V() V(x) d V d x 3 4 gx 3 ex Fo Schödinge equation: 3 d V 3 3! d 4 4 d V 4 4! d Dea ; g Dea e D a e E v = (v+/)h - x e (v+/) h x e h 4D e ν - haonic oscillato fequency x e - anhaonicity constant v - quantu nube D e - dissociation enegy Fo the gound state (v = ): E = / h (- /4 x e ) The distance between two adjacent levels (E v+ - E v ) depend on vibational quantu nube (v): E v+ -E v = h (- x e (v+))

26 The anhaonicity constant is sall: x e ~.5 -. The anhaonicity constant (x e ) and dissociation enegy (D e ) ae lined, they ae specific to olecule! Dissociation enegy = the distance between the iniu of the potential cuve and the continuu! [D e ] = J D x e e D hυ x eh h 4D e 4 [D e ] = c - D x e e D υ x e 4D e 4

27 In haonic appoxiation the nube of vibational levels is infinite! In anhaonic appoxiation the nube of vibational levels is finite! When enegy incease the olecule can dissociate.

28 Vibation of polyatoic olecules. Noal odes Fo a olecule with N atos, each ato has thee otional degees of feedo. Thus, the olecule possesses a total of 3N degees of feedo. Cheical bonds seve to constain the otion of the atos to well defined vibational odes (noal odes). Linea olecules have thee unique tanslations, but only two unique otations. The otation about the bond axis does not count, since it changes neithe positions of the atos, no does it change the angula oentu. Thus, fo the total of 3N degees of feedo, we subtact thee tanslations and two otations, leaving 3N-5 vibational degees of feedo. Non-linea olecules have thee unique tanslations, and thee unique otations. Thus, fo the total of 3N degees of feedo, we subtact thee tanslations and thee otations, leaving 3N-6 vibational degees of feedo. The nube of noal odes is equal to the vibational degee of feedo.

29 Noal odes The vibations of a olecule ae given by its noal odes. A noal ode is a olecula vibation whee soe o all atos vibate togethe with the sae fequency in a defined anne. Noal odes ae basic vibations in tes of which any othe vibation is deived by supeposing suitable odes in the equied popotion. No noal ode is expessible in tes of any othe noal ode. Each one is pue and has no coponent of any othe noal ode (i.e. they ae othogonal to each othe). Linea olecules have 3N - 5 noal odes, whee N is the nube of atos. Non-linea olecules have 3N - 6 noal odes. Non-cicula olecules have N- stetching odes. Linea olecules have N-4 bending odes. Non-linea olecules have N-5 bending odes.

30 The noal odes ae descibed in noal coodinate (Q). catesian coodinate (x i ) cupled oveent equations independent oveent equations pondeat coodinate (q i ) q i i xi Catesian (x i ) efeence fae Noal (Q i ) efeence fae noal coodinate (Q i ): the noal aplitudes depend fo pondeat aplitudes! Α i j A q ij q q q A / ij A ij A ij The aplitude of noal ode ae noal and othogonal to each othe. i A is i A ias i A it A s A as +A a A as + A 3s A 3as = A s A t +A a A t + A 3s A 3t = A t A as +A t A as + A 3t A 3as =

31 Chaacteistics of Noal Modes. Each noal ode acts lie a siple haonic oscillato.. All atos oscillate with sae fequency. A noal ode is a conceted otion of any atos. 3. The cente of ass doesn t ove. 4. All atos pass though thei equilibiu positions at the sae tie. 5. Noal odes ae independent; they don t inteact. Noal odes ae useful in ode to descibe the vibation of polyatoic olecules!

32 All atos oscillate with sae fequency. The cente of ass doesn t ove. All atos pass though thei equilibiu positions at the sae tie.

33 Polyatoic olecules In noal coodinates (Q): h 8 Ec Q V Q E Q Q Schödinge equation can be split in 3N independent diffeential equations. h 8 d dq Q E Total wavefunction: Q,Q,...,Q,... Q Q... Q... Total enegy: Etotal v h An excited vibational state (of a polyatoic olecule) involve oe than one level of enegy (oe than one vibational quantu nube ust be used!). =,,..., 3N-5 =,,..., 3N-6 fo linea olecules; fo nonlinea olecules;

34 Ex: Noal odes of vibation fo CO olecule: - 4 noal odes (3 3-5 = 4), but ae degeneated (bending odes). CO have 3 diffeent vibations (noal odes)! The vibational enegy state of CO olecule can be descibed by thee quantu nubes: (v v v 3 ) v = Syetic stetching quantu nube. v = Bending quantu nube. v 3 = Asyetic stetching quantu nube.

35 (v ) (v 3 ) Syetic stetching ode (v ) - coesponds to a syetic stetching along the intenuclea axis (both oxygen atos oving away fo o towad the cabon ato at the sae tie). Asyetic stetching ode (v 3 ) - coesponds to an asyetic stetching along the intenuclea axis (both oxygen atos oving to the left o ight togethe while the cabon ato oves in the opposite diection between the). Bending ode (v ) - coesponds to a vibational bending otion pependicula to the intenuclea axis. (v ) (v )

36 E() - the vibational gound state of olecule; (is not!) h( E( ) 3 ) Vibational enegy levels in the electonic gound state of CO : E() - the fist excited syetic stetching state; E() - the fist excited asyetic stetching state; E() - the fist excited bending state; E() - two quanta of the excited bending state; and so on. E( v,v,v ) v h v h v3 h 3 3

37 Suay Haonic oscillato Anhaonic oscillato c c E v V(x) D e h (v c c D x = M u ) hυ E v hc (v u =,66-7 g M - ola ass ) u - atoic ass unit (au) E v E v V(x) (v )h (v )hc x D e a 7 D a 4 e e e D e hυ 4D D e xe(v ) xe(v ) gx 3 g D hυ ex e a h e hc h

38 achive.htl

39 Questions:. Fo the following olecules: NH 3, C 6 H 6 (cyclic), C H 8, CH 4, C H (linea). a) find the nube of vibational odes b) find the nube of stetching odes c) find the nube of bending odes. Calculate the vibational fequency of CO given the following data: M C =. u, M O = 6 u, =.86 3 g/s 3. Calculate the vibational enegy in (Joules) of a noal ode in question, in its gound state of v =. 4. Assuing the foce constant to be the sae fo H O and D O. A noal ode fo H O is at 365 c. Do you expect the coesponding D O wave nube to be highe o lowe? Why? 5. The wavenube of the fundaental vibational tansition of 79 B 8 B is 3 c. Calculate the foce constant of the bond (in N/). u =.67-7 g, c = 3 8 /s, h = J s