NMR Spectroscopy In Structural Analysis

Transcription

1 NR Spctroscop In Structural Analsis rciss wrkcollg arlos Schurink Hans Wink Rainr Wchslbrgr NR Spctroscop Rsarch Group

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3 Nots. Erciss labld with a B ar supplmntar. Som ar a bit mor difficult, othrs ar just additional rciss. Good practic matrial for th am! Answrs to qustions ar includd at th nd of this book. Answr th qustion ourslf, bfor turning to th answrs! Ask! h assistants ar thr to hlp ou. Chaptr. Introduction B. NR dals with nuclar magntism, arising from th magntic momnt of th nuclus of som tps of atoms. h vrda form of (macroscopic) magntism as manifstd b prmannt magnts and magntiabl matrials, has a diffrnt sourc. Find out which. Chaptr 2. Basic NR hor 2. a) Draw th nrg diagrams and indicat th α and β spin stats for th following nucli: 3 H γ 3 H = ( s) (I = /2) 3 Cd γ 3 Cd = ( s) (I = /2) b) At what frqunc do ths nuclar spins rsonat givn a.5 sla () magntic fild? c) What ar th corrsponding angular frquncis ( hoksnlhid ) of th prcssion motion? 3. A proton at.7 rsonats at 500 H. o what valu must th magntic fild b raisd in ordr to obtain rsonanc at 600 H? 4. Prov that th nrg of a randoml orintd magntic momnt in th static B 0 fild is onl dpndnt on th -componnt of th magntic momnt (s radr q. 2.6 and 2.7). 5. Considr th compound chloroform (CHCl 3 ) whr all carbon-atoms ar of th 3 C- isotop. h diffrnc in th Larmor frqunc of th 3 C spin and H spin is 675 H. What is fild strngth of th B 0 fild? What is th proton Larmor frqunc? Us abl on radr p h quation of motion (radr q. 2. on p. 0) is crucial to dscrib NR phnomna. Driv radr q. 2.2 from q. 2. and vrif that q. 2.3 is a corrct solution (p. 0/). 3

4 B7. h arth magntic fild has a strngth of roughl 45 μ. a) What is th proton rsonanc frqunc in th arth magntic fild? b) What is th wavlngth of th lctromagntic radiation that can b absorbd at this fild? Chaptr 3. An nsmbl of Nuclar Spins 8. a) Considr an nsmbl of H nuclar spins. What is th ratio of th populations of th uppr and lowr stats at 25 C and a magntic fild of 2.35? b) What is th population diffrnc btwn th two spin stats pr 0 6 spins? c) What is th population diffrnc for 3 C, undr th sam conditions, pr 0 6 spins? 9. A sampl of chloroform is placd in a NR spctromtr with a fild strngth corrsponding to a proton rsonanc frqunc of 500 H. a) Sktch th nt-magntiation vctor of th proton spins in th laborator fram undr quilibrium conditions. W want to giv a 90 -puls to crat transvrs magntiation. b) What should b th frqunc of th B -puls? c) Assum that strngth of th B -fild is 0.60 m. What should b th duration (t p ) of th 90 puls? d) Sktch th ffct of th 90 -puls in th rotating fram using a vctor diagram. What is th rotation frqunc of th rotating fram? 0. Sktch in a vctor diagram (rotating fram, on rsonanc) th ffct on th magntiation of a crtain proton for th following cass. a) Start with quilibrium (+ ) magntiation. Appl a 90 -puls. b) Rpat th sam for a 90 -puls. c) and a 80 -puls d) and a 90 -puls ) and a 270 -puls. What is th diffrnc compard with d)? What if th puls is slightl miscalibratd (.g. if it is slightl too short)? f ) Start with + magntiation. Appl a 90 -puls. g) Start with +. Appl a 90 -puls. h) Start with +. Appl a 90 -puls. i) Start with +. Appl a 90 -puls.. You want to cit quilibrium magntiation. Unfortunatl our citation puls is miscalibratd and is onl an 80 puls instad of a 90 puls. How much of th quilibrium magntiation will b in th transvrs plan? B2. Us th quation-of-motion (radr q. 2.) to calculat th ffct of a 90 -puls. h magntic momnt μ for a singl spin can b rplacd b th nt magntisation vctor combining all spins of th nsmbl. B3. Considr rcis 9 again. Suppos ou us a B -puls with a frqunc of 400 H. o amin th ffct of this puls, w nd to us a rotating fram with a rotation frqunc of 400 H.

5 a) Sktch in a vctor diagram th nt-magntiation vctor in quilibrium in this rotating fram. b) Sktch in a vctor diagram th magntiation vctor of an individual spin in this rotating fram. What is th prcssion frqunc of th spin in this rotating fild? c) What is thn th ffctiv B 0 fild in this rotating fild? Us H as th unit for magntic fild strngth. d) What is th total ffctiv B-fild in this rotating fild, so B 0 + B? Assum a B strngth of 25 kh. ) Prdict th rsult of a 0 μs B -puls. Chaptr 4. Spin rlaation 4. Assum magntiation. Appl a 90 -puls. a) Draw th path that th nt-magntiation vctor follows back to quilibrium, onc in th laborator and onc in th rotating fram. b) Sam as a) but now onl considr 2 -rlaation. c) Rpat this for an 80 -puls. B5. Vrif that radr q. 4.2 and 4.3 ar valid solutions of q. 4.. Chaptr 5. Fourir ransform NR 6. What is th lin wih at half hight (us radr q. 5.8) of a signal with a 2 of: a).0 s? b) 0 ms? c) 0 μs? d) Associat th 2 s of a), b) and c) with ithr a solid protin, chloroform, or a protin in solution. Eplain using th graph on radr p. 20. ) Sktch th D spctra of compounds containing onl two protons, with 2 simliar to thos of a dissolvd protin, dichloromthan and a solid protin. h diffrnc in th Larmor frquncis of th two protons is 00 H. 7. Sktch roughl th Fourir transforms of th following FIDs (on th lft th part of th FID, on th right th part). a) 5

6 b) c) d) B8. h of a crtain sampl dcrass with incrasing tmpratur. At 20 C it is ncssar to lav 0 sconds btwn succssiv scans, whil at 40 C onl 5 sconds ar rquird. Suppos that 3 hours of spctromtr tim ar availabl and that th instrumnt is st up for opration at 20 C. It taks hour to warm th sampl to 40 C and to stabili th tmpratur. Assum that th NR signals ar idntical at th two tmpraturs. What is th bst stratg for rcording th NR spctrum: running for 3 hours at 20 C or warming th sampl and running for 2 hours at 40 C? Us q Chaptr 6. Spctromtr hardwar 9. a) What is mant b rsolution? b) What ar th possibilitis to rais th signal-to-nois-ratio (S/N) for a H primnt? c) Compar th S/N in an NR primnt using 3 C nucli at natural abundanc with th S/N of H. 20. You want to rcord a spctrum of compound which has svral signals in th rang of -2 kh to +5 kh. o what valu must th dwll-tim b st?

7 B2. If th magntic fild varid b ± 0 n btwn th dgs of th sampl, what lvl of rror would this introduc in th rsonanc frqunc of H nucli at a magntic fild strngth of.7 (500 H)? Compar this rror to th tpical lin wih of a H signal of H. Chaptr 7. NR paramtrs 22. Considr a compound containing two H spins that giv signals at 2.0 and 7.0 ppm, rspctivl. You prform a D primnt at a 500 H spctromtr. Calculat th prcssion-frquncis in th rotating fram for th two signals, assuming a carrirfrqunc (th ro-frqunc of th rotating fram) which is at 4.7 ppm. 23. h chmical shift of two quivalnt mthln protons is 3.57 ppm. hir NR signal is split in two lins du to th scalar coupling (J-coupling) to th attachd 3 C nuclar spin. h valu of th scalar coupling constant is 32.5 H. h magntic fild strngth is 0.5. What is th diffrnc whn th magntic fild is 0? a) Calculat th chmical shift diffrnc btwn th two mthln signals. b) Calculat th frqunc diffrnc btwn ach mthln signals and th rfrnc signal of S at 0 ppm. c) What is th chmical shift diffrnc whn th fild is tn tims strongr? Chaptr 8. Nuclar Ovrhausr ffct 24. h following NOEs ar obsrvd involving th aromatic protons of a trosin (s appndi p.0 for th atom nomnclatur): atom pair η-intnsit R (Å) H δ2 - H ε H ε5 - H δ H δ2 - H β 0.05? H δ2 - H α 0.02? H δ2 - H? 0.0? H δ2 - H? 0.005? h distancs btwn th δ and ε protons ar known. Calculat th rmaining distancs and idntif th two unassignd protons. B25. Estimat th molcular wight whr th NOE vanishs on a 500 H spctromtr (s radr p. 46). Chaptr 9. Rlaation masurmnts 26. Driv radr q. 9. from quation 4.2 and prov that at τ = ln(2) no signal will b obsrvd in a invrsion-rcovr primnt. 7

8 27. Assum magntiation. What happns in th following squnc, whr th dla is a crtain fid waiting tim: 90 dla 80 dla. Giv a vctorial rprsntation of th volution of th magntiation for two spins of unqual frqunc (rlaation can b nglctd). Us th rotating fram to draw th vctor diagrams. Assum that th th ro-frqunc of this fram (th carrir-frqunc) is th avrag of th frquncis of th two spins. Rpat this for th squnc: 90 dla 80 dla. What is th diffrnc? 28. You masur th 2 of th 5 N-spins in two 5 N-labld protins undr th act sam conditions. h avrag 2 of protin A is 20 ms, whil th avrag 2 of protin B is 60 ms. Giv an planation for this diffrnc. Chaptr 0 wo-dimnsional NR 29. h structur of compound A undrgos a complt chang b irradiating with light and is transformd to compound B: A B. his raction can b masurd in th SCOCH 2D primnt (radr p. 56). h light puls is short nough that w can assum that in th tim of th puls no prcssion of th spins occurs. a) A proton A with a rsonanc ω A has a frqunc ω B aftr th light puls. Sktch th 2D-spctrum. b) What is th diffrnc if th raction is not complt? Sktch th 2D-spctrum again. 30. h following Figur shows th NR spctrum of th amino acid trptophan (W) acquird in D 2 O. Figur. H NR spctrum of structur of rp

9 a) Sktch th COSY spctrum without fin structur of th cross-paks. b) Sktch th OCSY spctrum. c) In th NOESY th β-protons hav cross-paks to just two of th ring protons. o which of thm? Sktch th NOESY spctrum. 3. h following Figur shows th NR spctrum of th nuclotid adnosinmonofosfaat (AP, s radr p. 8) acquird in H 2 O. Figur 2. H NR spctrum of AP ( a) Sktch th COSY spctrum without fin structur of th cross-paks. b) Sktch th OCSY spctrum. c) Sktch th NOESY spctrum. B32. h thr mthl-protons in thanal ar quivalnt and ar 2.55, 2.78 n 2.88 Å from th aldhd proton. a) Calculat th NOE intnsit for ach of ths distancs assuming a calibration constant of b) How man cross-paks will b visibl in th 2D NOESY spctrum? c) Calculat th intnsit of on of ths cross-paks. d) Calculat th distanc corrsponding to this cross-pak. Chaptr h assignmnt problm 33. Sktch and plain th H-NR spctrum of th following compounds (tak onl coupling ovr -3 bonds into account): a),2-dichloorbnn b),3-dichloorbnn c),4-dichloorbnn 34. How man signals and what multiplicit do ou pct in th H spctrum for th following compounds (tak onl coupling ovr -3 bonds into account): a) mthanol b) -bromo-2,2-dimthl-propan c) 2-chloro--mtho-propan 9

10 35. Assign th proton spctra blonging to propanal (Fig. 3). Pak data (ppm-valu, intnsit): Figur 3. H NR spctrum of propanal. (SDBSWb : (National Institut of Advancd Industrial Scinc and chnolog, )) 36. wo proton spctra is shown togthr with th formulas of th corrsponding compounds (Fig. 4). Dtrmin th structur. Figur 4. H NR spctra of som organic compounds.

11 B37. Figur 5 shows th NR spctrum of th amino acid prolin (P) acquird in D 2 O. Figur 5. H NR spctrum and structur of Pro. a) Draw th COSY spctrum without fin structur of th cross-paks. b) Sktch th OCSY spctrum. c) Sktch th NOESY spctrum. Chaptr 2 Biomolcular NR 38. h following pptid sgmnt is part of a protin squnc:... YVGLSA... Fig. 6A shows th corrsponding OCSY spctrum of this part. Assign th sgmnt. What is th origin of th paks around 7 ppm? 39. Assum this sgmnt has an β-sht conformation. Add th charactristic paks ou would pct in th NOESY spctrum in Fig. 6B. Us Fig. 2.4 in th radr. 40. Now th sgmnt is locatd in an α-hli. Add th pctd paks in Fig. 6C (us Fig. 2.4).

12 Figur 6A. H, H OCSY spctrum of -YVGLSA-

13 Figur 6B. H, H OCSY spctrum of -YVGLSA- 3

14 Figur 6C. H, H OCSY spctrum of -YVGLSA-

15 B4. Considr again th pptid fragmnt YVGLSA of rciss Construct th NOE-pattrn for a tp-i turn starting at Gl in Fig. 7 (us Radr Fig. 2.4). B42. W prform an chang primnt, rplacing H 2 O with D 2 O. Indicat for Figs. 6B-C (qustions 39 and 40) th paks that ar still visibl in this solvnt (dirctl aftr th chang of solvnt). For 6B, assum that th HN of th rosin is in a H-bond with an opposit β-strand, and th β-strand is th outr strand of a β -sht. For 6C, first assum that th sgmnt is locatd in th middl of a long α-hli. What would b diffrnt if th hli starts with th trosin(y) of th sgmnt? 5

16 Figur 7. H, H OCSY spctrum of -YVGLSA-

17 Answrs Chaptr. Introduction B. h tp of magntism of prmannt magnts and magntiabl matrials is calld frromagntism and is causd b a vr strong intraction btwn th magntic momnts of th lctron spin. h magntic momnt of th lctron spin is roughl 650 tims as larg as that of a proton. A nuclar vrsion of frromagntism can thrfor onl ist at tmpraturs clos to 0 K. Chaptr 2. Basic NR hor 2. a) h nrg diagram consists of two nrg lvls (both ar spin I = /2 nucli), not that for nucli with a positiv gromagntic ratio th α-stat (m = /2) has th lowst nrg and th β-stat th highst nrg. h nrg sparation btwn th two lvls is largr for th 3 H spin sinc it has a highr gromagntic ratio and Δ E=hγB. b) h rsonanc frqunc can b calculatd using radr q. 2.0a ν 0 = γ 2π B 0. hus, th rsonanc frqunc of 3 H quals ( s).5 / 2π = s = H = 68. H. Likwis, th rsonanc frqunc of 3 Cd is / 2π = s = 4.2 H. Clinical RI scannrs tpicall oprat at.5. h protons in our brain will thn rsonat at 63 H. c) h prcssion has th sam frqunc as th rsonanc frqunc. h corrsponding angular frquncis ar obtaind b multipling b 2π giving s ( 3 H) and s ( 3 Cd) (NOE: th unit has to b s and not H). 3. Radr q. 2.0a shows that th rsonanc frqunc dpnds linarl ( rcht vnrdig ) on th strngth of th magntic fild. hus, th fild should b raisd to.7 / = Radr q. 2.6 dnots th dot-product ( in-produkt ) of th magntic momnt and th static magntic fild (two vctors), rsulting in th scalar nrg: E = r μ B r. h orintation r of th magntic fild is normall takn to b paralll with th -ais, thus B = ( 0,0,B 0 ). h magntic momnt will hav non-ro -projctions. hus: 7

18 E = r μ B r 0 = μ ( μ μ ) 0 = ( μ 0 + μ 0 + μ B 0 ) = μ B 0 5. Us radr q. 2.0a: th rsonanc frqunc (= Larmor frqunc) of th 3 C spins is ν 3C = γ 3C 2π B. For th 0 H spins ν H = γ H 2π B 0. h diffrnc in th Larmor frqunc is thus: ν H ν 3C = γ H 2π B 0 γ 3C 2π B 0 = ( γ H γ 3C ) B 0 2π B 0 = 2π ν H ν 3C. hus, th γ H γ 3C fild strngth is 2π H / ( ( s) ) = H / ( s) = 2.8. h Larmor frqunc of th protons is ν H = γ H 2π B 0 = ( s) 2.8 / 2π = 90.7 H. 6. Radr q. 2. dnots th cross-product ( uit-produkt ) of th magntic momnt and th magntic fild. h cross-product quals th rminant of th matri shown on th right-hand sid of radr q. 2.. h rminant is calculatd b pansion b minors ( ontwikkling naar d rst rij ): dμ B B B B B B = γ B B B = γ { + } μ μ μ μ μ μ μ μ μ = γ = γ B 0 { ( B μ B μ ) ( B μ B μ ) + ( B μ B μ ) } { B μ B μ } 0 + Not that is th unit vctor (,0,0). Similarl, =(0,,0) and =(0,0,). hat mans that th trm shows th chang of dμ/ in th -dirction, tc. In th last lin, it was usd that B r = ( 0,0,B 0 ). hus, dμ = γb 0 μ dμ = γ ( B0μ + B0μ ) dμ or = γb 0 μ = γb0μ γb0μ dμ = 0 Not that th orintation of th rsulting vctor is givn b th right-hand rul (s Figur on radr p. 0). Now to vrif that radr q. 2.3 is a corrct solution, w back substitut th solution in th diffrntial quation and diffrntiat: 0

19 dμ dμ ( μ (0)cos(γB t)+ μ (0)sin(γB t) ) = d = μ (0)γB sin(γb t)+ μ (0)γB cos(γb t) = γb ( μ (0)sin(γB t)+ μ (0)cos(γB t) )= γb μ ( μ (0)sin(γB t)+ μ (0)cos(γB t) ) = d = μ (0)γB cos(γb t) μ (0)γB sin(γb t) = γb ( μ (0)cos(γB t)+ μ (0)sin(γB t) )= γb μ dμ = d μ (0) = 0 Hr ou hav to us th chain-rul ( ktting-rgl ): d/ (f(g(t)) = d/dg f d/ g. Not that ou hav to assum that th answr is corrct to stablish th corrctnss of th answr! B7. h rsonanc frqunc can b calculatd using radr q. 2.0a ν 0 = γ 2π B. hus, th rsonanc frqunc of H quals ( s) / 2π = 96.0 s =.92 kh. h corrsponding wavlngth can b calculatd using λ = c ν (c = 2, m/s), rsulting in a wavlngth of m = km. Chaptr 3. An nsmbl of Nuclar Spins 8. a) Using th Boltmann quation (radr q. 3.), and radr q. 2.9 and 2.0 to rlat th magntic fild strngth to an nrg diffrnc and k = J/K, on finds: b) n β n α = ΔE k = γhb k = γhb 2πk = s Js π JK 298 K = π = = = = = n β = ( n α ) n α n α n α = n α n α = = hus, for an nsmbl of 0 6 spins thr ar = spins in th α-stat and = spins in th β-stat. h population diffrnc for a ral sampl, prssd as a fraction of 0 6 spins, is thus 8.06 spins. c) For 3 C spins, this is 2.02 spins. 9

20 9. a) h nt-magntiation vctor is alignd with static B 0 -fild undr quilibrium conditions: b) h frqunc of th B -puls should match th nrg-diffrnc btwn th two nrg-lvls, which mans that it should b idntical to th Larmor-frqunc (s radr q. 2.9 and 2.0). hus, th frqunc should b 500 H. γ c) h magntiation vctor prcsss around th B -fild with ν = 2π B (s radr q. 3.2). h rotation frqunc is: ( s) / 2π = H. A 90 -puls corrsponds to a quartr of a rotation. hus, th lngth should b ¼ /25546 = 9.79 μs. d) o dscrib th ffct of th 90 -puls, th rotating fram must hav th sam frqunc as th B -puls, 500 H. 0. a) + b) c) d)

21 ) h magntiation vctor now travls in th opposit dirction to nd up at th sam point. If th puls is slightl too short, a 90 -puls will rotat th magntiation vctor to som point abov th -plan, whras a 270 -puls will rotat th vctor to som point undr th -plan. Not that bcaus of th thr tims longr puls, this mismatch will b thric as larg, i.. th ffcts of miscalibration ar mor pronouncd for longr pulss. f) + g) + h) i) +. Not that all rotations ar clock-wis.. h projction of th magntiation vctor onto th -ais is givn b sin(α), whr α is th flip-angl. hus, 98.5 % is in th transvrs plan. 2

22 B2. Again w us th quation of motion, radr q. 2.. In th rotating fram B = (0,B,0): B B B B B B B B B B B B B B B = + = + = + = hus, ( ) B B B B d γ γ γ + = =, or: B d d B d 0 γ γ = = = h solution of th diffrntial quation is analogous to radr q. 2.3 (just swap th,, indics): 0 (0) ) ( ) (0) cos( ) (0) sin( ) ( ) (0) sin( ) (0) cos( ) ( = = + = + = t B t B t t B t B t t γ γ γ γ Which simplifis to: 0 ) ( ) sin( ) ( ) cos( ) ( 0 0 = = = t B t t B t t γ γ whn starting from quilibrium magntiation. hus w s a simpl rotation around th -ais going from + to. B3. a). h nt-magntiation is alignd with th B 0 -fild, sam as in 9a). b) h magntic momnt of an individual spin will mak an angl with -ais and prcsss around th B 0 -fild with 500 H in th laborator fram. Whn transforming into th rotating fram, th nw prcssion frqunc is Ω = ω - ω rt, whr ω is th lab-fram Larmor frqunc and ω rt th rotation frqunc of th rotating fram. h spin thus prcsss with = 00 H.

23 c) As th spin still prcsss in this rotating fild, it must still fl a B 0 -fild. his fild is now much smallr as th prcssion frqunc is also smallr. Whn w prss th strngth of th B 0 -fild in H, th strngth is 500 H in th lab-fram and 00 H in th rotating fram. d) h total ffctiv fild is th vctor-sum of th rducd B 0 and B. So th strngth is: B ff = B 2 0,rducd + B 2 = ( ) 2 + ( ) 2 00 H. h angl of this ffctiv fild with th -ais is: B α = arctan = arctan = arctan( ) 0. B 0,rducd ) Sinc th frqunc of th B -puls (400 H) is much lowr than th rsonanc frqunc of th spins (500 H), th spins ar not affctd b th puls. So th orintation of th nt-magntisation vctor will not chang. Chaptr 4. Spin rlaation 4. a) In th laborator fram: th magntiation vctor starts som whr in th -plan and prcsss around th -ais. Du to 2 -rlaation, th componnt in th -plan will shrink. Simultanousl, th vctor starts moving back to th positiv -ais du to -rlaation. In th rotating fram: now thr is no prcssion around -ais sinc th spin is on rsonanc. So aftr th puls, th vctor is along th +-ais and th vctor rotats around th -ais back towards th -ais. Chck for ourslf that th Figur is onl corrct if = 2. What dos it look lik if 2 <? b) In th laborator fram: th magntiation vctor starts som whr in th -plan and prcsss around th -ais. Simultanousl, th lngth of th vctor bcoms smallr du to 2 -rlation. In th rotating fram, th magntiation starts at th +-ais and simpl shrinks to vntuall vanish. 23

24 c) Aftr a 80 puls th magntiation is along. As thr is no - or -componnt, thr is no 2 -rlaation, onl rlaation. h magntiation vctor starts at, will shrink, at som point b ro, and thn start growing again to bcom +. h dscription in th lab and rotating fram ar th sam sinc thr will b no prcssion sinc thr is no transvrs magntiation, onl longitudinal magntiation. B5. d = = d d = 0 + = q q + d [ (0) ] (0) [ (0) ] + (0) t q and t t q q d t = t q ( t) t q d = d = = (0) 2 (0) 2 t 2 (0) t 2 t 2 ( t) = 2 Chaptr 5. Fourir ransform NR 6. h lin wih (l.w. or Δν ½ ) is rlatd to th 2 via: l.w. = π 2. a) 0.38 H; b) 3.8 H; c) 3.8 kh; d) chloroform = a, dissolvd protin = b, solid protin = c. h 2 bcoms shortr as th tumbling tim of a molcul bcoms longr (= slowr tumbling). Chloroform is a vr small molcul so tumbls vr rapidl, rsulting in vr slow 2

25 rlaation = larg 2 valus. A solid protin dos not tumbl at all, rsulting in vr fast 2 rlaation = small 2 valus. ) 7 Rali that in th obsrvd FID th prsnt frqunc is Ω = ω j ω rf (radr pag 23). Ω 0 ωhn ω j ω rf, so whn ν j ν rf. In a), transvrs magntisation starts at +, thn turns to +, so turns fastr than th rotating fram. hrfor in th spctrum th frqunc will hav a positiv valu. Also, whn in and FID intnsit gos to ro, 2 rlaation occurs and lin-wihs ar not ro (radr q. 5.8). In th FID shown in b) th visibl wavlngth is longr, so th visibl frqunc Ω is smallr than in a). h dirction of rotation is th sam as for a), so frqunc is positiv. h signal dcas with similar spd as in a), so th 2 and lin wih is th sam. In c) th frqunc and sign of th FID ar th sam as in b), but th signal dcas to ro fastr. hat mans that 2 is shortr and th signal gts broadnd. In d), th magntisation starts at + and thn turns to. his mans that is rotats slowr than th rotating fram and givs a ngativ frqunc. a) b) (H) (H) +25 ν j ν rf c) d) ν j ν rf (H) (H) +25 ν j ν rf ν j ν rf 25

26 B8. At 40 C ou can rcord twic as man scans within a th sam tim as at 20 C. In 2 hours, ou thus rcord 2 2/3 = 4/3 as much scans at 40 o C as in 3 hours at 20 C. h 4 signal-to-nois is thus bttr at 40 C. 3 Chaptr 6. Spctromtr hardwar 9. a) In th contt of NR rsolution is usd to rfr to th rsolving powr of th NR spctrum, i.. th dgr to which paks with small diffrncs in rsonanc frqunc can b distinguishd. b) According to radr q. 6. on can: rais th numbr of spins (highr concntration), rais th fild, incras th numbr of scans, lngthn th rlaation tim (highr tmpratur, lowr viscosit mdium) or lowr th tmpratur (notabl of th ction circuit, not of th sampl) c) h S/N of a 3 C primnt will b much lowr du to th lowr numbr of spins and th lowr gromagntic ratio. In most cass thr will b slightl mor favorabl 2 for th 3 C spins than th H spin. Disrgarding this last ffct, th rlativ S/N is: 5 2 N 3C γ 3C =. N H γ H = = = So th H primnt is roughl 3000 tims as snsitiv! 20. h dwll-tim has b st according to th Nquist-quation (s radr q. 6.2). h largst absolut valu of frquncis is 2 kh. his frqunc has to b sampld twic pr priod, so th dwll-tim must b 0.5 /2000 = ms. B2. h rlativ rror in th rsonanc frqunc will b qual to th rlativ rror in th magntic fild, which is 0 n / his crats an absolut rror of H 0-9 = 0.5 H, roughl half of th natural lin wih. his is unaccptabl and must b improvd b shimming. Chaptr 7. NR paramtrs 22. h prcssion-frqunc in th rotating fram (Ω) is givn b: Ω = ω - ω rt, whr ω is th frqunc of th signal of intrst and ω rt th rotation frqunc of th rotating fram (in H this would b ν - ν rt ). In this cas it is as to calculat th frquncis with rspct to an rfrnc signal at 0 ppm. hus, w nd to translat ppm to H: at 500 H, ppm corrsponds to millionth of 500 H is 500 H. hus, th frqunc ν of signal at 2 ppm is = 000 H (with rspct to a signal at 0 ppm), th frqunc ν of th signal at 7 ppm is = 3500 H (with rspct to a signal at 0 ppm) and th frqunc ν rt of th rotating fram is = 2350 H.

27 hus, th frqunc diffrnc for th signal at 2 ppm is = -350 H (a countr clockwis rotation) and for th signal at 7 ppm is = +50 H (a clockwis rotation). 2 ppm = 350 H ' 7 ppm = +50 H ' 23. a) h frqunc diffrnc btwn th componnts of th doublt is rmind b th scalar coupling constant and is not influncd b th magntic fild strngth. h frqunc diffrnc is thus 32.5 H. At 0.5, th rsonanc frqunc of H quals ( s) 0.5 / 2π = 2.3 H, ppm is thus about 2.3 H, and 32.5 H = ppm (dus ). b) h rfrnc signal of S is at 0 ppm. h diffrnc to th cntr of th mthln doublt is thus 3.57 ppm. At 0.5, th rsonanc frqunc of H quals ( s) 0.5 / 2π = 2.3 H ppm thus quals H = H = 67.2 H. h two lins ar thus at /- 32.5/2 H from 0 ppm, which maks th shortst frqunc distanc qual to.3 H. c) n tims smallr, i ppm. hrfor th signals appar much closr to ach othr in th spctrum ( and ). So, th J-coupling constant is in H indpndnt of th fild strngth, but lads to signals at diffrnt positions whn th ppm-scal is considrd. Chaptr 8. Nuclar Ovrhausr ffct 24. H δ2 - H β r = r rf (V rf /V) /6 = 2.45 (0.25/0.05)**(/6) = 2.85 Å. H δ2 - H α 2.45 (0.25/0.02)**(/6) = 3.32 Å. H δ2 - H? = 3.73 Å. H δ2 - H? = 4.9 Å. h distanc btwn th δ2 and ε5 proton is 2 cos(60) = 4.9 Å. h distanc btwn th δ2 and δ6 proton is 2 cos(30) 2.45 = 4.24 Å. So th first distanc, must b to th β2-proton, and th scond is to th δ6 proton. (Us th molcular structur on radr p. 0 to prov ths rlations). 27

28 B25. h NOE vanishs for ω τ c =.8. hus, τ c =.8 / (500 2 π 0 6 ) = s. his corrsponds to a molcular wight of τ c = 900 Dalton. Chaptr 9. Rlaation masurmnts 26. For th invrsion-rcovr primnt (0) = - q, thus: t = q + [ (0) q ] t = q + [ q q ] t = q 2 q t = q 2 and ln 2 ( ln(2) )= q 2 = q( 2 ln 2 )= q 2 ln 2 ( )= q ( 2 2)= 0. (Using th rul that ln() = ln ( - ) = ln(/)) prcssion crats an componnt 80 puls rotats th + componnt to but th lavs th -componnt unaffctd: ffctivl th vctor is rflctd in th plan prcssion rotats th vctor along th sam angl as in th first part and in th sam dirction, thus laving th vctor alignd th -ais. his squnc is calld a spin-cho (not that th last thr Figurs show projctions on th -plan). Using a 80 puls th -componnt is unaffctd but th componnt is rotatd to +: a rflction in th -plan. Now th sam prcssion-angl nds up at h 2 rlaation tim dpnds on th rotational corrlation tim which is a masur for th tumbling tim of th molcul. Larg molculs hav long tumbling tims (tumbl vr slowl) and hav vr short 2 s (s radr Figur p. 20). hus protin B must b largr than protin A.

29 Chaptr 0 wo-dimnsional NR 29. a) a pak at coordinat (t,t 2 ) (ω A, ω B ). b) two paks: on at (ω A, ω A ) and on at (ω A, ω B ). hir rlativ intnsitis will rflct thir rlativ concntrations. 30. Diagonal paks ar prsnt, but not shown hr! h β-protons onl s th H4 and H2. Not that th H2 is mor than 5 Å from th H4 or H7. 3. a) COSY: cross paks btwn H H2 ; H2 H3 ; H3 H4 ; H4 H5 /H5 b) OCSY: cross paks btwn all sugar protons. No cross pak btwn H2 and H8 29

30 c) NOESY: cross paks btwn all sugar protons. H H2; H H8; H2 H8; H3 H8, H4 H8; H5 /H5 H8, tc. Signal intnsitis btwn sugar and bas dpnd on th bas orintation. B32. a) V = C r -6. Substituting th valus rsults in , and , rspctivl. b) Onl sinc th mthl protons ar dnamicall avragd to quivalnc. c) It will b th sum of th volums abov, so d) h corrsponding singl distanc is 2.25 Å, shortr than th thr actual distancs! Whn calculating protin structurs from NOESY cross-pak volums this ffct must b takn into account to prvnt distortd structurs. Chaptr h assignmnt problm 33. h chmical shift of th protons in ths compounds will b roughl th sam, around 6-7 ppm. h numbr of signals and th splitting will diffr. a),2-dichloorbnn has two sts of chmicall quivalnt protons, H3/H6 and H4/H5. Within th H3 is coupld to th H4 and th H6 to th H5, thus th hav th sam coupling pattrn and th ar magnticall quivalnt. For th H4/H5 is th sam thing. So on pcts two signals, ach split in a doublt (:). b),3-dichloorbnn has thr diffrnt sts of protons: th H2, th H4/H6 and th H5. h H5 is coupld to th H4 and th H6 so will b a triplt (intgral /4:/2:/4). h H4 and H6 ar split in a doublt (:). h H3 is a singlt (). c),4-dichloorbnn is full smmtric, so all 4 protons princ th sam chmical nvironmnt. h protons ar onl coupld to th adjacnt proton and both hav th sam coupling pattrn, so th ar also magnticall quivalnt, so on signal without splitting is obsrvd (intgral 4). 34. a) CH 3 OH -CH 3 doublt (:); -OH: quartt(:3:3:) b) (CH 3 ) 3 C CH 2 Br -CH 3 s singlt; -CH2 singlt c) CH 3 CHCl CH 2 O CH 3 -CH 3 doublt; -CH quartt of triplts (:2:) in cas J CH3-CH >> J CH2-CH or a triplt of quartts in cas J CH3-CH << J CH2-CH. If th two J s ar qual, thn a stt rsults with rlativ intnsitis :5:0:0:5:; -CH 2 doublt; -OCH 3 singlt. 35. h triplt at 9.7 ppm COH; th quartt of doublts at 2.4 ppm CH 2, th triplt at.ppm CH a) 2-chloro-propan; c) dithl-para-bnndicarbolat.

31 B37. Chaptr 2 Biomolcular NR 38. s Figur blow. h paks around 7 ppm ar th aromatic δ,ε protons of Y. 39. add d αn (i,i+) strong pak and d NN (i,i+) wak pak. Not that th d NN (i,i+) contacts should b smmtrical wth rspct to th diagonal. 3

32 40. add d αn (i,i+) wak pak, d NN (i,i+) strong pak, d NN (i,i+2) wak pak, d αn (i,i+3) mdium pak, d αn (i,i+4) wak pak, B4.

33 B42. If th β-strand is on th outsid of a β-sht, th amid proton of vr scond rsidu is posd to th solvnt. E.g. if Y s HN is in a H-bond, th amid protons of V,L,S will b unprotctd and will chang rapidl disappar from th spctrum. If th sgmnt is in th middl of a long hli, all paks rmain visibl bcaus th amid protons ar protctd b hdrogn bonds (at last initiall, th will b changd onl vr slowl). If th hli starts at Y, th amid protons Y,V,G will b unprotctd and will chang rapidl and disappar from th spctrum. 33