Physical Chemistry (II) CHEM Lecture 25. Lecturer: Hanning Chen, Ph.D. 05/01/2018

Transcription

1 Physicl Chemistry (II) CHEM Lecture 25 Nucler Overhuser Effect nd Electron Prmgnetic Resonnce Lecturer: Hnning Chen, Ph.D. 05/0/208

2 Quiz 24 0 minutes Plese stop writing when the timer stops!

3 Spin Popultion hv X + 2 J hv A + 2 J hv A 2 J hv X 2 J energy digrm of coupled AX system popultion of popultion of the spin popultion difference is the driving force for NMR signls Wht hppens if the spin popultion exchnge cn tke plce? spin exchnge

4 spin exchnge Nucler Overhuser Effect X strong rdition X I A 0 NOE enhncement fctor: η A = I A I A 0 I A 0 J I A enhncement of A due to the sturtion of X J δ δ δ δ A δ δ X A X

5 Spin Sturtion X spin exchnge strong rdition X η A = I A I A 0 I A 0 < 0 I A 0 inter-nucler distnce D AX I A J J δ A δ X δ δ A δ X δ

6 Two-dimensionl NMR A mjor difficulty of trditionl one-dimensionl NMR is its complexity due to too mny spin-spin couplings. δ 2 cn you extrct ny useful informtion? δ free induction decy δ 90 pulse mgnetiztion vector much clerer two-dimensionl picture

7 Correltion Spectroscopy (COSY) 90 pulse the st evolution time 90 pulse 90 pulse the 2nd evolution time wve-mixing time! t t mixing x x!! to llow for spin-spin coupling x t 2 A B coupled "90 pulse": Δt = π 2γ I B I selectively rotte nucleus A M B is long! Z! during the st evolution time: M A,XY = cos 2πv A t ( )! Y + sin( 2πv t)! X A (no spin-spin coupling) fter the second pulse: M A,XY = cos 2πv A t ( )! Z + sin( 2πv t )! X A M A,Z M B,Z spin-spin coupling during the wve-mixing time: M = ( f )cos( 2πv t )! Z M = f cos( 2πv t )! Z A,Z A B,Z A spin exchnge fter the third pulse: M = ( f )cos( 2πv t )! Y M = f cos( 2πv t )! Y A,Y A B,Y A during the 2nd evolution time: M = ( f )cos( 2πv t )cos( 2πv t ) + f cos( 2πv t)cos( 2πv t) AB,Y A A 2 A B

8 Two-dimensionl Fourier Trnsform time-dependent signl: M ( t) = ( f )cos( 2πv t )cos( 2πv t ) + f cos( 2πv t)cos( 2πv t) AB,Y A A 2 A B two peks in 2D spectrum: M ( v,v ) = ( f )[ v,v ]+ f [ v,v ] AB,Y 2 A A A B 2-D Fourier trnsform: F(v,v ) = f (t 2,t )e i2π ( v t +v 2 t ) 2 2 dt dt 2 similrly, the three 90 pulses cn be pplied on nucleus B ( f )[ v,v ]+ f [ v,v ] B B B A The digonl contins the informtion of "non-coupling" nuclei while the off-digonl peks reflect the spin-spin coupling Nucler overhuser effect + Correltion Spectroscopy nucler Overhuser effect spectroscopy (NOESY) ccurtely mesure internucler distnce

9 Electron Prmgnetic Resonnce EPR is less widely used in chemistry due to the bsence of unpired electrons in most orgnic molecules except for rdicl molecules or functionl groups methyl rdicl O 2 oxygen molecule β hv = ΔE p α v = v e Lrmor frequency in condensed phses, g-fctor is very sensitive to n electron's locl chemicl environment g observed g free = the devition of g is subject to the locl current susceptibility e the esiness of generting circulr electric current v = gµ eb e 2π electron mgneton: µ e = J it g fctor: g e = only true for n isolted electron!!! fixed rdio wve frequency vrying mgnetic field g locl = 2πv L µ e B

10 Hyperfine Structure of EPR Spectrum B 0 µ I µ e B locl mgnetic field, B loc = B 0 + B B = m I H (I,m I ) e : hyperfine coupling constnt electron-nucler coupling β gµ e B = ΔE p gµ e (B + 2 ) gµ e (B 2 ) 2π 2π 2π α

11 Hyperfine Coupling with Two Equivlent Spin- Nuclei µ I µ e 4 N B B 0 e B 2 µ I 2 4 N mgneticlly equivlent 4 N nuclei = 2 = µ e µ I coupling: (I =,m I = {,0,+}) (I =,m I = {,0,+}) B = m I B 2 = 2 m I 2 µ e µ I 2 coupling: EPR spectrum: 3 2 2

12 Hyperfine Coupling with Two Inequivlent Spin- Nuclei µ I µ e 4 N B B 0 e B 2 µ I 2 4 N mgneticlly inequivlent 4 N nuclei 2 µ e µ I coupling: (I =,m I = {,0,+}) (I =,m I = {,0,+}) B = m I B 2 = 2 m I 2 µ e µ I 2 coupling: 2 2 EPR spectrum:

13 McConnell Eqution McConnell Eqution: = Qρ e For exmple, =0.375 mt Q = = 2.25 mt If the unpired electron is entirely loclized on single crbon tom benzene nion (C 6 H 6 ) = 2.25 = 2.25 mt the unpired electron is uniformly distributed over the entire romtic ring the density of the unpired electron on crbon tom: ρ C = 6

14 the Origin of the Hyperfine Interction!! locl mgnetic field, B loc = B 0 + m I µ A r µ B Hund's rule!! µ e e e µ I θ E 2!! µi E usully, JNe > 0 µ e e e ( 3cos 2 θ) B B A = µ B 2π 0 r 3 dθ ( 3cos 2 θ) = 0 E2 < E prllel pttern is more energeticlly fvorble (for enhnced stbiliztion) for fst tumbling molecules, no direct contribution electron-nucler coupling cn be medited by other electrons direct mechnism polriztion mechnism

15 Homework 25 Reding ssignment: Chpter 4., 4.2, 4.3, 4.4, 4.5 nd 4.6