SPEC TOP ANAL CHEM
SPEC TOP ANAL CHEM CHEM 729
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NMR Chapter 2 Spectral Content and Interpretation A mAAmnn 7 y JLCL v V i fiftxvlmuntcth whom Lc l n bi An NixM73 spectrum is compriser o described by several observable parammm Prequer acy or clieii39xical shift 2 Mult1p11c1ty due to splnspln coupllng 3 intensity arising from the immaentmtion of the spin Line shape and width arisi l ug from dynamil processes I w Coupling Between Spins NMR active nuclei in a molecule interact with each other For the most common non quadrapolar I 12 nuclei there are two interactions that dominate The first interaction occurs between two nuclei through space This interaction is called Dipole Coupling and is dependent on the orientation of the two nuclei wrt the applied magnetic field Under isotropic conditions ie solution phase samples this effect averages out and the consequences of Dipole Coupling are mostly ignored we will discuss this interaction more when we cover NMR Relaxation The second type of interaction between nuclei is transmitted through the electrons forming the bonds in the molecule This type of interaction is called Scalar Coupling or ICoupling Scalar Coupling is independent of molecule orientation It is also independent from the applied magnetic field so the magnitude will be the same using different instruments 2 Bo The simplistic explanation for H DOYBD2TE scalar coupling this is that the Dcz 7V neighboring spin39s magnetic moment acts to either add to or subtract from the main field The resulting resonance frequency changes due to the change in the effective field at the nucleus For spin 12 nuclei there are two possible orientations for the magnetic moment and the result is two D2 y 30BHV2TE D y BFBHVZE possible frequencies This explanation is rather naive and falls apart for complex cases We will discuss this in detail in a later chapter 02 01 The number of lines for a resonance depends on the number of equivalent neighbors The intensity of each line is the result of the statistical probability of the possible orientation of the magnetic moments T 39 or 39 L of the neighboring spins Neighbor orientation For the case of a single spin 12 lt gt neighbor there are two orientations that the neighbor could be in The population of each state is essentially equal We will see why this is true in a later chapter I Dow2 no 00J2 Frequency The spacing between the lines is called the coupling constant J and is measured in Hz For two equivalent For three equivalent Neighboring spins Neighboring spins N T T i T W TT w W TTT TLT T LN T T NT 1 I 2 I 1 1 I 3 I 3 I 1 owlJ 10 DIDJ ooIIBJZ l 10 l oobJZ Dow2 0042 Spin 12 Multiplet 1 intensities follow Pascal s Triangle l 1 For Equivalent Neighbors l 2 l Inequivalent Spins All neighboring spins may not couple to the same extent In this case the coupling patterns are more complex than the number and intensities predicted by Pascal s Triangle For a spin with more than one in equivalent neighbor each individual coupling will propagate to yield a multiplet Example J12 4 Hz pm J23 12 Hz 12Hz 1 7 4 Hz f CH3 quotdoublet 2 1 doublets 8 4 4 8 H2 0H2 Example Two equivalent plus one non equivalent The coupling pattern can be built up just like the simple doublet of doublets The triple pattern due to the two equivalent protons will have the 121 ratio predicted by Pascal s Triangle H2 J124HZ J H J23 12 Hz 12 Hz F cg 4 Hz CH3 quotdoublet of i 1 I triplets 1O 6 2 2 6 10 Hz E 0H2 Importance of Scalar Coupling Scalar coupling yields information of the number position and type of neighboring spins The splitting line spacing is measured in Hertz Hz and the magnitude is dependent on several factors including 1 2 Type of bonds present between spins 3 Number of intervening bonds between spins 1 6 bonds Bond dihedral angles between spins 4 The magnetic moments of the nuclei ie the nuclei s y The spacing is independent of field strength Coupling constants measured on a compound will be the same on any instrument Examples H H X C C H X CEC H H H H H C H H H C C CC X H Examples Two Bonds Between 1H s H H 2JHH 1215 Hz X C C H X CEC H H H H H C H C C H H gt C C CZC 2JHHO3Hz X c H X H I H Examples Two and Three Bonds between 1H s H H 2JHH 1215 Hz 1 If X C C H X CEC H H H v 3JHH z 7 Hzaverage H C H C C C H 3JHH1218Hz H SJW 6 10 Hz Examples Multiple Bonds Between 1H s H H 2JHH1215Hz X C C H X CEC H H H v 3JHH z 7 Hzaverage Um 12 18 Hz Examples One Bond Between 13C and 1H H H UOHz250Hz l I A X C C H X CEC H JOH z 125 Hzlt I H H IC IT H H C C X JCHz150Hz H US160 Hzlt H W Examples One and Two Bonds Between 13C and 1H 2J9 1 6 HZ H H JOH z 250 Hz l m X C C H X CEC H 1 N JOH N 125 HzCIJI H 21 40 60Hz H 2JCH14Hz I A H C H C C H JCH116 HzH I C C C Q X C H X JOHz 150 Hz H US160 Hzlt H Examples All Bonds Between 13C and 1H 2J9 1 6 HZ H H Us a 250 Hz l m X C CH X CEC H 1 N JOH N 125 HzCIJI H ZJOH 40 60Hz 2JCH116Hz H H C X UGH z150 IE H UGH z 160 Hzlt H Examples Comparing 1H 1H and 13C 1H Coupling 2JCH 1 6 Hz H H 2JHH 1215 Hz JCH 50 Hz ll XC CH X CEC H JCHz125Hz I V H H JCH4O60Hz 3JHH z 7 Hzaverage 3JHH 6 12 Hz TEt 2 C JHHO3H X sz 150 1 H JOH z 160 Hzlt J H 3JH JHH1218Hz K 6 JHH O 1 Hz Karplus Curve The magnitude of three bond coupling between two protons on adjacent aliphatic carbons follow a function first described by Karplus in 1959 The minimum usually zero occurs when the dihedral angle is near 90 The 1800 angle yields the largest coupling The average coupling is about 7 Hz and is observed when rotation I I I about the dihedral angle 0 45 90 135 180 is free and rapid39 Dihedral Angle 6 Degrees First vs Second Order Coupling Multiplet line spacing and intensities given by Pascal s triangle will remain predictable for coupled homonuclear spins ie both 1H only when the chemical shift difference in Hertz between them is large compared to the coupling constant Au gt 10 J This case is considered weakly coupled and the splitting patterns are described as firstordered When the chemical shift difference in Hertz between two coupled homonuclear spins is close to the magnitude of the coupling constant Au S 10 J the system is considered strongly coupled The splitting patterns become skewed from the predicted shapes The individual line intensities and in more complex cases the number of lines are quite different from the firstorder result These patterns are called secondordered Molecular symmetry also plays an important role in determining when a system shows second ordered effects 19 Spin System Nomenclature Spin systems are given a label to indicate the number and type of each spin present The choice of letters depends on the chemical shift difference between them Examples AX This is the label used for the firstordered JAX JAVX case of two coupled spins This includes either two H heteronuclear spins ie 1H BC or two homonuclear spins when the chemical shift I between them in Hz is large compared to the coupling constant U DI A X AB This label is used for two coupled spins that J V J show second ordered skewing The intensity distortion of each doublet is called roofing and is useful because each doublet leans towards its coupling partner Smaller spacing between resonances yields a greater slope in the roofing DA DB AMX Three coupled spins spaced apart from each other are labeled AMX These could consist of three homonuclear spins two homonuclear and one heteronuclear spins ie 1H1H 13C or three 19F heteronuclear spins ie 1H 13 AZX When two spins are chemically and magnetically equivalent the spins system label includes a number The AZX system has two equivalent nuclei and one spin with a different chemical shift An example would be formaldehyde AA XX AA BB Not all chemically equivalent nuclei are magnetically equivalent Such systems are indicated by the or prime symbol Magnetic inequivalence occurs when symmetry allows chemical equivalence but the spins are coupled differently to each other An example of an AA BB system is a parasubstituted benzene ring OQCH H HN HB CI DA UX 3 4 LE to x 8J2 59 A 1 a l 32 a 00 y 1 15 12 mun 0mm mo MHz m1 ukulucd pronm 5pmquot m p chlombenul thyde u Iri llnmnanli laid a z 10 wLvol solution in c A described by several observable 1 r i 3 49 E NMR Chapter 2 Spectral Content and Interpretation n Vilall spedrum is comprised of resc ma39 ces that can be rcnf lnC lr A requer lcv or chemical shift U Mu l ti plicity d Intensity arising from the concentration of the spin Line sl uape and Width arising dynamic 1r0cesses Peak Integration NMR is one of the few analytical technique that yields signal intensity that it directly proportional to the amount of material ie spins present in the sample There is nothing analogous in NMR to an absorptivity coefficient 8 that is common in optical spectroscopy or ionization efficiency that is present in mass spectrometry Therefore relative peak areas can be used as measure of the amount of each spin present in the sample or molecule While more difficult absolute peak intensity can be used in a quantitative fashion when proper sample handling and standards are performed The caveat to this is that few NMR spectra are collect under truly quantitative conditions We will understand this when we discuss NMR relaxation NMR Chapter 2 Spectral Content and Interpretation Em NMR spectrum is comprised of resonances that can be described by 5m 81 observable paran39neters ail 1 Frequency or 39E iemical 5 rift r 21 Multiplicity clue to spinwspin coupLin C1 3 hitensiry arising fro m the concentration the 5p in 4 Line shape and width arising from dynamic processes Chemical Exchange Molecules that undergo dynamic processes like rearrangement or site exchange yield NMR spectra that can be used to measure the frequency of the process The time basis for such experiments are dependent on the chemical shift difference in Hz between the two resonance S E z a n2 Under rapid exchange the spectrum will show a single resonance at the average position between the two sites At slow rates the two resonance can be observed Intermediate rates show broad or partially averaged resonances If you are interested in this topic read Chapter 11 in Friebolin for a good introduction NMR Chapter 7 1D Techniques Interaction between spins can be used for spectral assignments and to obtain structural information The most common techniques exploit scalar J coupling Scalar coupling can be used to identify spin pairs that interact with each other through bonds Resonance splitting can be used for spectral editing Coupling also provides a mechanism for signal enhancements by providing a pathway for magnetization transfer Most of these techniques are classified as double resonance because two nuclei are manipulated and two rf channels are used Ho Crotan01c Ac1d H CH3 CC d5 DMSO HOC H 1quotquotquot T39quotquotquotquotquotquotquotquotquotquotquotquotquotTquotquotT39quotquotquotquotquot 124120ppm II quotquotIquotquot39quot39quotquotquotquot39quot39l39quot39quotquot39quot39quotquotquotquotquotquotquotquot 70 60 50 4 0 30 20 ppm 1 Homonuclear decoupling Low level RF irradiation of a resonance will collapse the splitting on other resonances that normally show coupling with the irradiated resonance The decoupler RF power has to be comparable to the coupling constant yBZ 2 27 I 50 HZ Homo H CH Decouple Crotanoic Acid gtcclt 3 Here H04quot H l H O L Jll ll 7 0 6 0 50 4 0 3 0 20 ppm Why does this happen RF irradiation of a resonance causes rapid conversion of the spin populations of its levels If this conversion is rapid the lifetime of the 0c and 3 states are too short to effect the other spin This causes a collapse of the other multiplet there I DH DH2 UH DH2 UH gun UH Rapid Exchange UA1 3 JHHM39 7 i ampL QB UA Rapid Exchange UX2 2w om I UH UH Pros of Homonuclear decoupling 39Fast and easy to interpret for simple molecules OSmall couplings which 2D correlation techniques sometime miss are easily detected Cons of Homonuclear decoupling 39Setting numerous peaks to decouple for complex molecules is time intensive 2D correlations spectrum yields all correlations with one experiment 39Closely spaced resonances are difficult to selectively decouple OBloch Seigert shifts complicate matters Nuclear Overhauser Difference Spectra Another application of selective irradiation is the N OEDi erence experiment The experiment saturates a single resonance and examines the NOE enhancements on the rest of the spectrum The effects are easily seen when taking the difference between the resulting spectrum and the un saturated ie control spectrum The quotdifferencequot can be taken on the fly Alternating scans being either a control or a saturated acquisition are added to a single experiment FID The presence of a signal indicates an NOE enhancement and thus shows proximity through space to the saturated resonance 90 1H Selective Saturation Crotanoic Acid H CH3 C HOC H 3 Saturate Here i 1H Spectrum j l u l 7 6 5 4 3 2 ppm Crotanoic Acid HCH 3 C A HOC H H Saturate N OE Diff Here Mu J 1H Spectrum 7 3 5 4 3 2 ppm Crotanoic Acid H CH3 C HOC H Saturate 3 Here 1H Spectrum Crotanoic Acid H CH3 xx C gt HOC H Saturate 3 Here NOE Diff l l A H l 1H Spectrum 39 39 39 39 39 7 6 5 4 3 2 PW Pros of NOE Diff 39Fast and easy to interpret for simple molecules OMore immune from instrument instability than 2D NOESY spectra Cons of NOE Diff 39lSetting numerous peaks to saturate for complex molecules is time intensive 2D NOESY spectra yields all correlations with one experiment 39lClosely spaced resonances are difficult to selectively saturate Heteronuclear Decoupling For 13C spectra and other dilute and insensitive spins the coupling to 1H often is eliminated to improve sensitivity Multiplets spread their intensity across several peaks that sometimes also show longer range coupling This loss in signal amplitude makes detection more difficult For congested spectra multiplets often overlap leading to assignment difficulty To gain the benefits of heteronuclear decoupling every proton resonance must be irradiated This is challenging because the power required to excite the whole 1H chemical shift window is quite high Physical limits of the hardware and excessive sample heating make this impossible using simple continuous wave rf irradiation Phase modulation techniques have been developed that increase the effective bandwidth of decoupler fields Decoupled NOE Enhanced Heteronuclear Decoupling and 13C DELAY AQ in EC l A A I DELAY AQ 1H Fully Coupled NOE Enhanced BC A A F DELAY AQ 1H BC Q 1H 1 1 1 Decoupled NOE Suppressed I ll 11 Fully Coupled DELAY l A I 11 ll quotquotquotquotquotquotquotquotIII 180 160 140 Problems with 13C1H decoupled spectra 1 Signals quotcannotquot be integrated 39Because of low sensitivity 13C spectra are usually collected with NOE enhancement conditions The percent each resonance is enhanced by NOE is dependent on the proximity of protons The signal intensity will be stronger for protonated carbons 13 C relaxation times are quite long and usual survey parameters cycle too fast for full relaxation 5T1 2 Resolution of broadband decoupled resonances are not as good as CW decoupling 3 Sidebands are caused by decoupler modulation Typical modulation schemes produce artifacts around the base of peaks Spectral Editing Using sequences of pulses to manipulate resonances based on coupling multiplicities Resulting spectra have intensities and phases depending on their multiplet types These techniques are commonly used for 13C spectra SEPT Spin Echo PT This is the simplest form of editing that uses J modulation spin echo sequence The sequence 90 180 13 C A A 1H l Dwouple SEFT Each scalar multiplet is 1 modulated according to 39msnsw their type C CH CH2 CH3 8 180 J A It is easier to View this 0 development with delay time W H 969 I 1 o 135 180 Angle e I 0c cos 6 I 0c cos2 6 3 I 0c cos 6 l Intenslly 1 NJ Delay Tlme Attached Proton Test APT The main disadvantage of SEFT is the need for the 900 pulse This requires long relaxation delays and therefore slows the data collection The APT sequence is a modification to SEFT that allows an initial pulse of less than 90 The final 180O pulse returns the magnetization back to the z axis where it is ready for the next cycle through the sequence The APT Sequence bx 1 0 180 C l u 7 A A 1H Crotanoic Acid H CH9 CC H 13C APT Spectrum Ho39 O 13C Spectrum 1 60 140 120 100 80 60 40 20 ppm Rotenone Polarization Transfer The fundamental basis of UIW I polarization transfer experiments FTh a exploits the greater Boltzmann population of a more sensitive 5 nuclei 5 like 1H and transfers it to U an insensitive I nucleus like 13C HZX 4i TT u QB 4 aa JHC 4 JLL I I I I 0H1 0H2 001 Dog 0H 0C 400 100 MHz The normal Boltzmann population differences across the two spin 1H13C Um system energy level diagram can be AHAC used to show the expected intensity of each transition Remember yH z 4yc qu Therefore AH 4AC Um JHC A AC lnt 3 I f Ucz ZAH AHAC Int ZAC A I I I I LHl DHZ 0C1 1C2 0H 0C 400 1 00 M Hz If we can selectively invert one of the 1H quot g transitions the population across the 13C OW I transitions will changed AHAC t U H1 The result is an intensity enhancement in the 13C resonance UH2 InveYted Int A AC W 2AH2AC p ZAH A 62 AHAC I LHl HZ DCWD C2 OH Int C 2AH2AC 400 1 00 M Hz 2AH Int Looking at the result carefully shows 2AH2AC that the integrated intensity is unaffected There is no net polarization transferred between proton and carbon The C s magnetic moment has not changed Notes There does not have to be complete inversion of the population for polarization transfer partial transfer Selective population inversion is not generally applicable to solving structural problems not practical to selectively invert each proton for a complex molecule We must think of a way to perform the inversion on all protons at once Insensitive Nuclei Enhancement by Polarization Transfer INEPT The INEPT sequence provides a way of inverting one half of all HC doublets regardless of chemical shift It does this without the need for selective pulses The sequence is an adaptation of the spin echo sequence 90 1802 90 y lt gtLllt gt AZ AZ 1802 90 13C H l l A2 14 J 90 180 90 q The simultaneous 180 INEPT 1H D pulses change the sense M L M of rotation of the vectors 180 90 13C l l I l I W90 quot w m gt Y gt Y gt Y gt Y 90 i H180 1 4 0180 4 X X X X Z 1H Note In this orientation the vectors are in gt gtIlt antiphase H90 y 090 This sequence cannot employ decoupling 1 13C because the antiphase magnetization would cancel The phase of the last proton pulse is reversed to subtract out the residual natural y magnetization of the 13C 25 Hz INEPT gt y gt Y 90 i 4 X X 90quot gt y gt v H180 i mlt CZ 180 r X J Refocused INEPT The inability to decouple with the standard INEPT sequence causes the loss of one half of the maximum intensity The refocused INEPT sequence runs the spins through a second A delay period after polarization transfer The simultaneous 180 pulses centered in the delay allow for refocusing 90 180 90y 180 1H 0 4 gtlt gt A2 A2 A22 A22 180 90 180 13 H H C 1 l 1 JWVVquot mulled dunNed Irme llle MP1 aceum mm 27 Sensitivity Gain Polarization transfer from protons allows INEPT to give significant sensitivity improvement to low y nuclei LNEPT10 IYHvxl Compared to NOE INOE 10 1 1H 2 1 Table 43 Signal intensities for the X spin in lH X pairs arising from polarisation transfer lmgyr and from direct observation with the maximum NOE INQE X 13C ISN 2931 311 57Fe 103Rh 109Ag llgsn 183w 195Pt 207Pb 1mm 398 987 503 247 3095 3177 2150 281 2404 465 478 NOE 299 394 152 224 1648 l489 975 041 1302 333 339 Intensities are given relative to those obtained by direct observation in the absence of the NOE 10 Spectral Editing with INEPT The refocusing delay can be varied to allow spectra editing C J j39 I v 39 umad The center part 1 LIZ Mnqu of the triplet K I X 1 a does not pass I Drnmplr ll u ough the WM gt391Um mg hum mm c INEPT 1 l Cquot i y Y J Inn th x J m 1 l T I 1 T 1 Each scalar multiplet is modulated according to their type CH I 0C sin 6 quotsquotquot CH2 IstinGcosG CHS Ioc3sinGcos26 G 180 J A Note quaternary C s are cancelled out 1 29 Distortionless Enhancement by Polarization Transfer DEPT INEPT s main problem is the loss of the natural multiplicities for the final resonances DEPT was developed to retain the normal doublet triple and quartet patterns Still DEPT is usually run decoupled masking this benefit The editing is controlled with the final pulse angle making it more immune to differences in coupling constants 90 180 e 1 H A 1H AA 90 180 13 C FU AUQ DEPT polarization transfer is similar to INEPT where antiphase vectors for protons are developed However the 90 carbon pulse produces coherent transverse magnetization This state is called multiple quantum coherence MQC which cannot be shown using vector diagrams This is a case where simple models fail and quantum mechanics are necessary The intensity of the multiplets are wens modulated by varying the last CH3 pulse angle by the same function as o INEPTA delay 5 Rotenone DEPT 135a DEPT 900 b l l ll l l i l DEPT 900 a l l l l l l l l M H l 1 l misc HI M H H lll J l i l i l l i i i i i i i l 160 140 120 100 80 60 40 20 ppm 2 Rotenone CH3 o7745 90045 135 CH2 45 135 CH 2900 CH 0 NMR Chapter 5 Instrumentation and Acquisition Parameters NMR Spectrometers have become quite complex There are several vastly different technologies that are incorporated into a pulsed FT system This is a block diagram of the minimum number of components and Z not an actual system u39 39 Pre Arnp Duplexer Receiver Analog to Digital Convertor Magnets Magnets used in early systems were either permanent magnets or electro magnets These magnets had two important limitations They were not very stable and the maximum fields strengths were about 2T 100 MHz 1H Systems today use superconducting solenoidal magnets Most lower field magnets are wound using conductors that are comprised of fine filaments of a niobium titanium NbTi alloy embedded in a copper matrix Magnets above 9 Tesla gt400 MHZ 1H use niobium tin Nb3Sn conductors and some use single filaments of niobium titanium These alloys are super conducting at liquid Helium temperatures 42K For increased stability NMR magnets are run in persistent mode This means that the external power supply is removed and the current ows in a closed solenoid A persistent switch is made from a portion of so wire shunt and a heater that makes this section resistive A power supply can introduce current into the solenoid by putting a voltage across this resistive section When the magnet is at the desired field the heater is shut off and the full solenoid loop becomes superconducting The power supply can then be removed B 0 Heater Power Supply Vacuum Chamber super insulation Liquid N2 Chamber Liquid He Chamber Soleniod Assembly Shim Coils While NMR magnet solenoids are designed for high homogeneity they can only achieve several ppm resolution Built into the magnet are correction coils that increase the resolution These coils called shim coils produce field gradients that offset the imperfections of the main solenoid Like the main solenoid these shims coils are also closed loop superconducting circuits operating in a persistent mode They are commonly referred to as supercon shims Typical resolution of an optimized magnet can be less than a ppm Additional resolution improvement is made through a series of shim coils that are mounted inside the bore of the magnet but not in the cryostat These room temperature shims are optimized for each sample The power supplies for each room temperature shim coils must be low noise and high stability The shims represent Table 1739 x coefflclents of n Function Gradient Inter spherical harmonics Slum Name order action order functions The 20 l 0 0 supercon shims 21 z 1 o enerall onl 22 32 0 W2 2 1 g y y 23 25 3x1 2 3 2 1nc1ude the rst and Z4 325 A30 Uh 31 v52 4 2 second order coils ZS 48 2 5x fgtl 900 2 quot 5 2 x 1 0 Typically the first Y 39 1 0 zx x 2 2 and second order 21 y 2 2 room temperature Xy xy 3 1 shims are adjusted 1242 I 1 x1 3 1 X 14 7lt y3gt1 3 2 for each sample ZwY Wt A 3 3 2 The hlgher order zxr xy 3 2 shims will not vary Z 39 r 30 39yl 3 2 X 13901 v3y 3 I greatly from sample Y vaxz Avg 3 1 to sample Field Frequency Lock NMR magnets are Very stable but they are not perfect A typical magnet requires hundreds of meters of wire to wind a solenoid that can produce its high field strength It is impossible to produce a single length of wire this long Therefore mulh39ple lengths mustbe joined together Thesejaints are a source of Very small resistence in the solenoid This causes a slight decay or drift in the field typical magnet s field decay is much less than a ppm a day There are additional factors that cause instability of the system Temperature and eVen barometric pressure changes can effect stability Thefield frequency lock system compensates for changes in field strength seen by the sample A feed back circuit follows the resonance frequency of a signal present in the sample and makes corrections to the field The most common source of lock signal is deuterium resonance of the solvent Probes Perhaps the most important Match component of an NMR system is the probe Much of the diversity of a system comes from the Variety of probes available Choices include sample size frequency ranges number Tune of channels and placement of coils s an39ruai IN a Typiml pmhe gwmclry employed wim n mgle coil probe in m a xuperwnr dumng magnet and m m m can mgm In my case he rfwil ls marinara in men a my mm H is perpendicular m u Solenoiddl coils are more efficient and sensitive However for ease of sample changes the Helmholtz or saddle coil is used for most liquid probes Solenoids are still used for solidstate and flow cell probes The most recent advancement in probe technology is the development of cryogenically cooled probes These probes use helium gas to cool the coils to 20K while the sample remains at room temperature The sensitivity of the probe can be increased by a factor of four Pre amplifier The preamp is also an important component of the system Much of the sensitivity performance of a system is dependent upon the premap The preamp also acts as a duplexer where the high power excitation rf and small NMR signals are separated Diodes are used to stop noise from the transmitter from reaching the early amplification stage The amplification transistors are protected from the high power RF pulses by both diodes and a quarter wavelength line that puts the transistor at a node of a standing wave Some preamps have active switches for greater isolation Cryogenically cooled probes often have the preamp incorporated into the body of the probe and cooled for lower noise performance Typical preamp circuit diagram block diagram Receiver The receiver takes the output of the preamp and converts it in multiple steps to frequencies less than 100 kHz These audio frequencies are sampled by aualogtodigital convertors ADCs Amplification and filtering are the major functions of the receiver but phase and quadrature detection are also very important The signals high frequencies are converted by mixers which produce sums and differences of two frequencies The net effect of the receiver s mixers converts the NMR signal frequencies into their difference from the reference usually transmitter frequency This frequency conversion in hardware converts the NMR signals to frequencies much like the rotating frame concept allowed us to visualize frequency differences Quadrature detection allows us to discriminate between frequencies that are greater or smaller than the reference transmitter frequency Typical receiver block diagram Gain Setting Care needs to be taken when setting the attenuation Gain through the receiver Each sample will have different signal intensities concentrations that need to be scaled so that over loading does not occur b With the Gain set too high an FID will be Clipped by the ADC The results of an FT on a Clipped data set yields distorted baseline When the Gain is set too low there are a no observed distortions but the dynamic range and sensitivity can be reduced Most systems have provisions for auto scaling of the receiver gain This occurs prior to data collection or has to be explicitly performed Quadrature Detection With the reference in the middle of the spectrum single g channel detection x V y A A cannot discriminate v Hz V t v Hz between a positive V and negative signal To overcome this we detect along both the x and y axis ie 90 out of phase Note the difference in the MX channel a a9 quotWU Quadrature detection actually produces two data sets The Fourier transform of such data produces a complex spectrum These dual data sets are called the real and the imaginary The addition of these data sets produces the final spectrum sill gt l r y A I U my 39 quot V l Hz V0 sz W l v Hz Vo Differences in the amplitude gain between the two channels produces an artifact called a quadrature image It arises from the incomplete cancellation of the mirrored peak These artifacts are quite common but are easily suppressed with phase cycling that is done with multiple scan lPL lrmmniner data sets Malena image Phase cycling makes systematic changes to the phase of the excitation rf and to the paths the data is sent into the two channels This helps eliminate artifacts such as quadrature images that originate from instrumental imperfections Phase cycling is also used in advanced sequences to help remove unwanted NMR transitions The correct signals remain coherent and are added with each element in the phase cycle Artifacts are incoherent and usually are cancelled out The simplest phase cycle for a single pulse sequence is called CYCLOPS It simply changes the rf phase by 90 for each of 4 unique elements before the cycle repeats The observe receiver phase follows the same pattern Scan Pulse Phase Receiver Phase 1 x x 2 y y 3 x x 4 y y 17 a 9 Duadrmm Mommy ham 1 39 WWII When m m 1 Scan Pulse Phase Receiver Phase gt lt quot 1 x x I r x 2 y y ax um 2 3 x x 4 y y b Analog to Digital Converter The quadrature audio signals are processed by either one or two discrete analog to digital converters ADC Systems that have one ADC will process the analog channels sequentially Systems with two ADCs will process each data point simultaneously Sequential OO O C O C C C C Collection 900 Simultaneous 00 O C O O C C C Collection 900 Q Q time gt Sequential acquisition overcomes the differences in gain that two ADC usually have Therefore artifacts from mismatched quadrature channels are minimized However the maximum sampling rate for each point and spectrum bandwidth is half of that which can be achieved with dual ADCs Phase errors with sequential collection can lead to baseline errors 19 ADCs are characterized by their resolution and sampling rate Usually there is a compromise between these values and both are of important for NMR ADC resolution measured in bits 2 sets the dynamic range Sampling rate sets the maximum band width Typical ADCs used in NMR spectrometers have 12 16 bits of resolution and can sample at a maximum rate of 200kHz 1 MHz Because N MR signals have both positive and negative voltages a 16 bit ADC s range of values is i 215 i 32768 Therefore the theoretical maximum dynamic range is one part per 32k In practice the measured dynamic range is usually less 110000 The observed spectral bandwidth is one half the ADC s sampling rate based on the Nyquist Theorem Signals with frequencies greater than 12 the ADC sampling frequency will be aliased and appear in the spectrum at either a folded or wrapped position The Nyquist theorem states that for a regular oscillating wave form sinewave there needs to be at least two points per wavelength for correct sampling Therefore for frequency F the digitizer frequency must be at least 2F For NMR this means that the spectral bandwidth also called spectral width SW is set by the ADC rate SW ADC rate 2 The time interval between collected points is of course the reciprocal of the digitizer rate and called the dwell time Therefore sw 12DW A faxed Correct Correct Resonance frequencies that are greater than half the ADC rate will fall outside the SW These peaks will be aliased and either fold or wrap into an incorrect frequency Simultaneous digitized data will show wrapping while sequentially digitized data will fold 0 ram h man WW 5 5 a a 2 I mm o1sos1osm 155 ADC Pan No 01 50510200 Schematlc sheeq 1 av 5 01805105410 1eaimnc Part No mSDSIaz w Sehematlc5h9211 075 2 3 RF Transmitters The transmitters take RF from a frequency source mixes in the IF reference frequency to create the excitation frequency Gating of the RF pulses are also performed The observe transmitter also passes the reference LO frequency to the receiver Other functions are controlling phase and amplitude The main output of the transmitters are usually near 1 mW This RF is usually attenuated before it is amplified up to 50 1000 W The attenuator controls the exact output power of the rf channel There are usually two to four RF channels in a modern research system 400 390 MHz MHz To Synthesizer Preamp GATE ATTN 10 MHZ Amplifier F 0150215500 L0wBand nansminer 400 Fan No 004392134205 Schematlc5hee1 s 01 s 0130219540 LowBand 39 ansminer 400 Part No 00433284205 Schematic sheet a of 5 Other Options Accessories 4 Variable temperature controller and sample heat exchangers 4 PulsedField Gradient controller single or triaxis 4 Sample changer Flow probe autosampler 4 Solids Sample Spinning Control 4 Choices in Amplifier power output 4 Number of shim channels 01 0521 Mo Sys em Inteyconnen Pan No 01 505111 xw Schumtic Sheet 1 or 12 u1sosz14 w sysiam Intelconneci Part No 01 9501 xw Schematic sheet 1 of 12 Acquisition Parameters We saw how ADC sampling rate sets the spectral width SW 1 2DW The choice of SW is made based on the expected spectral dispersion of the resonances For 1H most resonances fall within 0 14 ppm For a 400 MHZ system a common SW for 1H would be 68 kHz This gives a margin for error for setting the correct width and center For 13C the resonances usually are in a range of 0 240 ppm so a typical SW for 13C is 25 30 kHz The length in time of the data collected by the ADC is set by the number of data points collected AQ DW x TD AQ Acquisition time Varian parameter AT TD Time Domain Points NP There is a circular relationship between AQ SW and DW AQDWxTDTD 28W For older systems that had limited computer memory size TD this forced a compromise between SW and AQ With more recent systems this is only a factor when using very large SW s Why is AQ important The final frequency spectrum will have data points separated by DR 1TD x DW ZSW TD 1AQ We call DR the digital resolution usually expressed in Hz point It is not the true resolution of the instrument Measured resolution in NMR is controlled by field homogeneity probe design T2 relaxation etc DR will control the resolution only when it is worse that the other factors Here is an example of how DR effects the collected a W spectrum m M At long AQ s high DR the peaks are accurately represented As AQ gets shorter lower DR the number of points across each peak becomes less and the shape of the peaks become distorted At low AQ there is not enough DR to resolve the small coupling JW At lower AQ there is not enough DR to resolve the larger coupling Short AQ s also leads to truncation of the FID The truncated data set can be considered a convolution of the normal exponentially decaying signal and a rectangle The FT of a rectangular wave form is a sine function The results of an FT on a truncated data set yields sinc peak shapes on the resonances We call these distortions sinc wiggles Apodizution is an operation that multiplies the FID with an exponential function It is also called linebroadening l because the resulting lines after FT are broader than the natural line widths However upodization can cleanupquot sinc wiggles r 21 humming x Inme Fm Ammvlm Finland m on ad Fm whim has been augudnd by milling muons um wink in the o m w Apodizution linebroadening has two results a 1 The line widths are H increased 2 The noise is reduced increases 8 N b h In the raw FID the signal is exponentially decaying However the noise level is consistent throughout that entire time Therefore the S N is greater in the early portions of the FID The longer data sampling has the ability to resolve similar frequencies The exponential function reduces the noise in the later parts of the FID at the expense of losing resolution information 2 Digital Filtering Apodization is one form of digital filtering that can be applied to an FID before Fourier transformation Since it uses an exponential function the resulting lineshapes remain Lorentzian There are several other wave shapes that can be convoluted with the FID and force lineshape changes Why would we want to makes Changes to the lineshape Larenlziun Iineslmpe Gunman Iineslmpz 33 2 mm Here are a few types of dlgltal lters that are used Some of these are more important b Wm is 51 for mu1t1d1menslona1 data transformatlon W WWW Resultmg 11neshapes are C FT of exp Lorentzian d mm w FT of Gauss Gauss FT of Sine Sine Big FT of Trap 0 WM 2 sum aw 5mm h um v s chlmu av Dill mummy um Resolution Enhancement Besides improving S N for 1D spectra the most common use of digital filtering is resolution enhancement There are a few ways of doing RE A shiftedsine bell is an excellent choice Negative LB combined with Gaussian filtering also gives significant RE The baseline distortions introduced by RE will effect the integration of spectra MNM7 The Wulb lm a mom Rnw no a 3an WW 6 mull I zr m b G llammnmuun wil blb IH h0 2mdlclh Ilz Ind 1b 02 b H JILLn SN Improvement with Signal Averaging When multiple pulses are performed each Fid or transient are added into memory Assuming full relaxation between the pulses the signals that are coherent will add linearly Therefore NS scans added to each other will have NS times N5 5N the intensity of a single scan Noise is random and adds as a function 15 of WNS Therefore 8 N scales with WNS ie SN doubles when NS is increased by a factor of four 711 Computer word size is the ultimate 4 3 limit for NS but for modern systems this is not usually an issue Instrument stability is more likely to limit the number of scans that can be added and still lead to an increase of S N Spectrum Phasing Errors NMR spectra usually show phase errors before correction There are two sources and they each contribute to the total phase error in the spectrum Zero order phase error Phase error that is constant across the frequency spectrum ie frequency independent It is caused by imperfections in the phase between the transmitters and the receiver First order phase error Phase error that changes c7 I A l across the frequency spectrum ie frequency WW dependent It is caused by the time delay between the pulse and the start of rm 1 Manama WWW mm data collection mnpm cm 711 on m m y Since we use the same coil for excitation pulses and signal observation data collection cannot always start at the true initial time A delay DE is introduced to allow ringdownquot of the RF coil in the probe This delay also allows time for the transmitter amplifier to be blanked Another delay is added to allow the turnonquot of the receiver before the digitizer starts collecting These delays cause phase error that is dependent on the precession frequency of the resonance first order First order phase B 319 mm WW error can be shown 39ff quot quot f quot mp maawmm with a vector 21713 MEXHZZL W W v m m m m mum u 2 y mu 1 m unnnu m dnrlap ilgm diagram The longer g f ffmwmmmmm X x the time between the adminquot mamquot pulse and the data collection the greater the phase error m quot dxgmsauun NMR Chapter 4 The Vector Model While energy levels are sufficient to describe most other forms of spectroscopy they tell a limited story for NMR As we saw earlier a collection of like spins ensemble will align themselves either parallel or anti parallel to the orientation of the applied field B0 commonly labeled the z axis The bulk magnetization vector M0 represents the z axis component of the excess lower energy spins at equilibrium conditions Magnetization aligned along the z axis is undetectable so we need a way to perturb the system We will discuss this later but first we need to introduce an important concept Magnetization that is put into the x y plane will precess at the Larmor frequency This precession the FID can be detected by a coil wound along the X or y axis Z Z Z M0 M0 Precession gt gt Relaxation x y x 4 U y x y The precessing frequencies that we normally observe are in the MHz range However we are usually interested in small differences in frequencies ie chemical shifts and coupling splits We need a way to visualize these small frequency differences Hz that are all taking place on the MHz scale 2 The Rotating Frame To visualize the frequency differences that we are interested in the concept of the rotatingfmme is often used In fact most NMR vector diagrams apply the convention without explicitly stating so The precession frequency of 1H in a 939T field is 400 MHZ Our frame of reference for this precession is the static conditions outside the magnetic field An analogy to this is a carousel ride An observer off the ride will see the motion of the riders as it rotates 2 mm w a K i x quotU y We call this frame of reference the lubomtoryfmme If the observer was standing on the ride platform there would not be any perceived motion of the riders 414 41 Likewise if we could move our observation position at the same frequency as a precessing vector it would appear static relative to our axis convention We call this frame of reference the rotating frame The rotating frame frequency is arbitrary but we will see that there is an experimental basis for selection When we use a rotating frame reference at the same frequency of precession we call this condition as being on resonancequot O resonance condition occurs when the reference frequency is different from the Larmor frequency In the rotating frame View the vector would gt appear to rotate at a frequency equal to the difference between the Larmor frequency and the rotation frame frequency DA 00 URF Remember although our reference has changed the spins are always precessing at DA the Larmor frequency in the lab frame Consider two single line resonances Resggme that are separated by 100 Hz AU 100 Hz If we put the rotating frame reference on the lower frequency resonance the vector diagram will look like I I 0H1 UHZ Frequency Z time x y X y u39 100 Hz Again consider two resonances that are separated by 100 Hz If we put the rotating frame reference on the higher frequency resonance the vector diagram will look like Again consider two resonances that are separated by 100 Hz If we put the rotating frame reference between both resonances the vector diagram will look like On Resonance A1 100 Hz I 0H1 lt Frequency 039 100 Hz Rotaton Frame Reference U A1 100 Hz lHz I 0H1 lt Frequency 039 50 Hz We The same approach can be used for Resggnce resonances that are multiplets U Consider a doublet with splitting J 4 D If we put the rotating frame reference at the center of the doublet the vector diagram will look like I oOJ2 lt oOJZ Frequency Z Z o J2 Other multiplets On look like Resonance Resonance I I o3J2 l l o3J2 X oJ2 oJZ How can we move the magnetization off the Zaxis If we could apply a second magnetic field that is perpendicular to the z axis we would perturb the equilibrium by Bl forcing a precession This 031 precession x frequency is directly proportional to the applied B1 field strength How do we physically do this Answer We use the magnetic component of a radio frequency RF wave Remember electro magnetic radiation has a magnetic component This RF irradiation is introduced to a sample by a coil that is wound perpendicular to main field B This RF has to be at or near the resonance frequency to have an e ect If we ignore relaxation the y component of the magnetization will simply oscillate at frequency 031 when 31 is applied along the X axis 21t 031 We can control the final orientation of the magnetization by precisely setting the duration M 03131 of the irradiation field If tp 75203312 90O Pulse Width X y Other orientations are possible Z NIo DB1 If tp 75 031 E 1800 Pulse Width gt x V V Z Am 0131 If tp 27 031 E 3600 Pulse Width x y Note We are not limited to pulse Widths at 900 multiples What do pulses do to 2M the populations of the A amp 3 energy levels Equilibrium State X y TTTTT a Note Energy levels 2MB 03m llll B cannot prov1de any P 1 t insight to the gt Ilsp1aati1orr11 magnetization in the xy X plane JANA l3 gt Population x y Inversion TTT Why do we need RF at or near the Larmor Frequency RF irradiation is produced by an oscillating voltage Run into a coil it actually produces a field that also oscillates To Visualizes this we can represented this oscillating field by two oppositely rotating fields that are in the xy plane The resulting field is 4 69 Sillating along the x r l aaaa If we View the resulting field v in a rotating frame x lt gt lt l gt g gt referenced to the Larmor a 1 frequency we can see that it will stay aligned along the x 9x E B X 7 axis if the RF oscillation is quot the same frequency mg M p Therefore when the RF irradiation is at the Larmor frequency the full B1 field strength is seen by the spins The vector trajectory shows pulmabovlmu lnxm Nnmmo posmmalllm l mam anallnu 16 Off resonance pulses do have an effect on the magnetization vector The effective field strength Em of the applied RF can be determined by the vector sum of the applied B1 and the residual of the main field B0 that the spins still see AB We can define AB AB2nAoy The net effect of off resonance pulses are the introduction of phase errors and pulse angle errors c nlh394lh suenglh gammy m enema eld inventions are labelled c and n 17 Consequence of Using Rectangular Pulse Excitation The resulting envelope of a RF pulse is 4W7 usually rectangular The excitation profile across the spectral frequency caused by a pulse is defined by the Fourier transform of the pulse H shape The excitation bandwidth is controlled by the pulse width The excitation profile follows a sine function sinc x sin x x The profile is not J L uniform across the t frequency spectrum p Egt mo Therefore the H frequency spectrum H H is not excited t 110 equally 9 Time a e Frequency gt 1g Rectangular pulse Excitation profile sinc function Range with Uniform Excitation H u N 1ft 0 Frequency gt The general rule for uniform excitation is to have the spectral window of interest fall within 20 of the excitation width determined by pulse length 1 tp A 13C spectrum of 200 ppm on a 939T magnet c0D 100 MHZ would need a spectrum width of 20000 Hz uniformly excited When the pulse is positioned in the center of the spectrum the full excitation band width 1 needed is 5 x 10000 Hz 50000 Hz The maximum pulse width would be The shape of a pulse can be tailored to give excitation profiles that are selective Some researchers have dedicated much of their careers producing and studying these shaped 1 or selective pulses Here are a few examples tP 1 50000 Hz 20 as is Gaussian Half Gaussian 53 A V n 5 Gaussian Cascade IBURPZ AVA Q3 Gaussian Casoa de REBURP V V V A h x t 225 395 s g EEEE m 452 1 a z a 3233 45 5 n H m 1 2 b 65 8 8 OJ H z z 3 1 6 gt 3 5 a a a a 2 so 5 5 a E u m 8 E 3 E m s an I I 398 an 6 7 a a ii in39 E 022 a g 5 g WU 5 E g E e 5 a G E lt an We now have the basis for the Fourier Transform NMR Experiment 2 Mn 90 X Y X A wire coil that is used to perform the pulse also acts as a detector 2 Mn Pressman Relaxation x The magnetization of the sample My induces an oscillating voltage W CPD that is multiplied digitized and transformed We MY Exponential will look at f Decay instrument details W I next Frequency Lorentzian Line Shape Frequency NMR Chapter 6 Relaxation E2 For all forms of spectroscopy the excited state has a limited life time This transition in higher energy spectroscopy is usually accompanied by 39 ho the emission of a photon of energy E1 The most common mechanism for this loss of energy is called spontaneous emission Typical life times for optical spectroscopy are in the nano pico second timescale If we use the theory describing spontaneous emission for NMR and its small energy differences the rate of decay would be 10 25 sec 1which would predict a lifetime in centuries NMR relaxation rates are typical in the seconds to 1039s of second range so there must be another form of induced emission that causes higher energy spins to revert back into the lower energy form Recall that the Bloch equations describe two separate relaxation rates dMZdt yM BZ MZ M0T1 dMXdt yM BX MXT2 dMYdt yM BY MYT2 T1 is the SpinLattice relaxation time constant It is also called longitudinal relaxation It is characterized as energy released into the surrounding environment Tzis the SpinSpin relaxation time constant It is also called transverse relaxation It is characterized by transfer of energy to other spins It dictates the line widths 0 1 7 T2 In 1948 Bloembergen Purcell and Pound Phys Rev 737 679 produced the first theory describing NMR relaxation It remains the frame work for our current understanding BPI Theory Summary 1 Relaxation is a magnetic phenomenon 2 T1 for liquids is in the seconds range 3 T1 for liquids small molecules is independent of field strength 4 T1 is inversely proportional to viscosity Implies slower molecular motion aids relaxation 5 For solids usually T2 lt T1 and T2 increases as mobility increases 6 Increasing concentration of paramagnetic ions decreases T1 Remember this was all observed before the chemical shift was known What is the mechanism for relaxation BPP showed that the process of relaxation was a magnetic phenomenon The spin needs to interact with surrounding molecules for energy to be released For relaxation to occur the spin must interact with a uctuating or moving magnetic field that is on the molecular level The most dominant source of moving fields are from neighboring spins These dipoledipole interactions are the primary mechanism for most small molecules spin 12 quot 1939 I Molecular motion and tumbling f w causes the field fluctuations 1 v m x x J l J iy This a through space Interactlon Since NMR energies are quantized the oscillating field must match the resonance frequency 030 yBO for relaxation energy transfer to occur Molecular motion and tumbling are random and incoherent giving them a wide range of frequencies However Fourier analysis can show the distribution of motion present The spectral density function J shows the distribution of motions present for molecules with a specific correlation time TC 2 average time for molecule to change orientation by 1 radian Derivation of spectra density function yields J D A Cn 1 0 1 where A is a constant derived for specific mechanisms of relaxation and o is the frequency of molecular reorientation CC for small molecules in non viscous solvents are about 10 12 sec For macro molecules EC can be several orders of magnitude higher 5 For three relative motion regimes Tc Slow Molecular Motion EC gtgt 10 Kw A TC Macro molecules 1 0213 Jo DO Logw 5 Larmor Frequency 6 For three relative motion regimes Tc Slow Molecular Motion EC gtgt 1 0 Km A TC Macro molecules 1 021 EC z 1 00 Intermediate Molecular J 03 Motion DO Logw Larmor Frequency 5 For three relative motion regimes Tc Slow Molecular Motion EC gtgt 1 0 Km A TC Macro molecules 1 0213 EC z 1 00 Intermediate Molecular J 03 Motion EC z 1 00 Tc Fast Molecular Motion ltlt 1 Small Molecules TC w Logw Do 5 Larmor Frequency 8 The intermediate case shows a greater number of molecules moving at a frequency of 00 From this we can predict that this case will have the fastest relaxation rate J 0 smallest T1 The two other cases have a Tc z 1030 lower number of molecules moving at TC ltlt 1030 the 00 frequency and should have longer Tls Tcgtgt103 JwA 1 oft DO Logw 5 Larmor Frequency 9 Log T1 11 Ejy jajayjH Lo EC 100 gm If we plot these points as T1 versus ECWE can see that there is a minimum when the correlation time is at the resonance frequency Molecules fall into three motion regions Fast Small molecules in non Viscous solvents Intermediate Moderate size molecules or smaller molecules in Viscous solvents Slow Macro molecules polymers and solid state samples Molecules in the extreme narrowing limit have T2 T1 Their relaxation is controlled by motion There are no contributions of static mechanisms In all cases T2 S T1 Remember natural line width cx 1T2 Log T1 Log T2 Log T1 Motion Fast Intermediate Slow L EC 100 Ogm Extreme Narrowing Limit Details of T1 Mechanisms The mechanism for relaxation has several components that contribute to the actual rate that a spin relaxes They all involve fluctuating fields The measured T1 is the reciprocal sum of these individual mechanisms 111i111 III1 TIDD TIPAR TIQ TISR T16A TISC T1DD Dipole Dipole Relaxation T1PAR Paramagnetic Relaxation T1Q Quadrupolar Relaxation Tf R Spin Rotation Relaxation Tfsquot Chemical Shift Anisotropy Relaxation T1SC Scalar Coupling Relaxation 13 DipoleDipole Relaxation Most common mechanism for spin 12 nuclei It involves motion or rotation of two spins that are close to each other This form of relaxation leads to the Nuclear Overhauser E ect 1 N Y vi Ich DD 6 T1 2 7c r12 Paramagnetic Relaxation The unpaired electron of paramagnetic ions generate very large fluctuating fields and greatly increase the relaxation rate The relaxation occurs as the paramagnetic species come into contact to the relaxing spin It is common for a chemist to add paramagnetic species to a sample to accelerate relaxation of slowly relaxing species and allow more rapid data collection 1 472 N v2 is TlPAR kT NP number of paramagnetic ions present um effective magnetic moment of the paramagnetic ion 14 Quadrupolar Relaxation The unsymmetric electric field surrounding a quadrupolar nuclei causes large magnetic fields that accelerate the relaxation of the nucleus This mechanism is controlled by molecular motion rotation 1 T1Q 0C QZTC Q the Quadrupole Moment Spin Rotation Relaxation A molecule in a fluid medium is a charged system and therefore generates a magnetic moment apart from the nuclear moment Collisions change the rotation rate and causes the field to fluctuate which aids in relaxation 1 2 72 I k T C2 15R SR 2 T1 h C average spin rotation coupling tensor 15R spin rotation correlation time I moment of inertia 15 Chemical Shift Anisotropy Relaxation Chemical shift is a directional quantity and depends on the orientation of the molecule with respect to the magnetic field In liquid systems the motion is fast enough to average the shielding and give the isotropic chemical shift This fluctuation of the local field does aids in relaxation c 1 2 y2 B on of E Tfsquot 15 1 m3 1 o amp2 0 are the shielding tensors for each orientation Scalar Coupling Relaxation Quadrupolar nuclei can accelerate the relaxation of the neighboring through bond non quadrupolar nuclei by a process similar to the one which it relaxes This mechanism is also controlled by molecular motion rotation 1 2 sc 0C JO Tc 1 The Nuclear Overhauser Effect A spin 12 nucleus that has dipoledipole relaxation can have its equilibrium population altered from the normal Boltzmann distribution when the other spin s population is perturbed This population change affects the observed signal intensity The definition of the measurable effect is called the Nuclear Overhuuser Effect NOE and signal intensity change is mathematically 1 ID m S I D x 100 where nIS is the enhancement of spin labeled 1 when the other spin s we will call it S population is saturated Saturation of spin S can be done with a low power rfexcitation or a selective 90 pulse 900 1H Selective Saturation of Spin S 17 Saturation of spin S will equilibrate the populations of levels that are connected through the S transitions The spins will attempt to relax 1 back to the equilibrium population through a T1 process The new populations will give rise to either a more intense or weaker signal for I mun mmmwmu NA 4 m Wimm Mm I m 1 5 mm dupoiv The relaxation paths WD and W2 compete with E each other to give the NOE for a dipoledipole W s w spin system The Solomon equations show how an w2 up both rate processes leads to the NOE Wu Vs W2 WD Vs 015 k 5 nx Y1 VVD l39VVi l39VV2 71 915 s 1 an mums m m puma mnim in n Iwospin sysmm GS cross relaxation rate and pIS dipolar longitudinal relaxation rate 1 T1DD These processes are dependent on the distance between the dipole pair and the correlation time W1 rx yz yz 31C 39 r61wiri 21C r6 1 oI 7 c032 121C m 01 of 3 19 W0 06 M W DC Y Y From this approach we can MOIECUIal Motion predict that molecules FaSt Interme ate 810W tumbling faster will favor o nm the higher energy W2 m process and have positive a n1 m 100 mm NOEs Slower molecules a will favor the WD process quot5 and have negative NOEs n u Extreme Narrowing Limit 1 z 2 3 1 W1 0C Y1 Y5 C Under extreme narrowmg r 39 39 V 21 conditions one ltlt 1 WD 0C 7 y C W 0c 7 V T1 Measurement by Inverse Recovery T1 is the process of relaxation of the magnetization along the z axis It seems we need a way to follow the intensity of magnetization buildup along the z axis However remember we can only observe magnetization that is in the xy plane The Inversion Recovery sequence first puts all the magnetization onto the negative z axis with the 1800 pulse After a period of time T the 900 pulse puts the residual z axis magnetization into the xy plane for immediate observation T1 IR Pulse Sequence 1 80 90 L I Equilibration Data Dday Collection Precessmn Data Collection Z Relaxation r gt E FT T IR 180 90 1 W i 1 Relaxation Precession Data Collection Ma 5 r gt ygtlt y180 y y 90 y T IR 180 90 1 W b I Precession Relaxation Data Collection Z Z Z Z Ma 5 gt gt gt y180 y y 90 y T1 IR T1 IR Precession Precession Relaxation Data Collection Relaxation Data Collection 39c0 39c0 Z Z Z Z Z Z M T M T gtlltgtllt gtgtllt gt lt gtlltgtllt gtgtllt gt lt y180 y y 90 y y180 y y 90 y IzQSTl TZ25T1 Z Z Z Z Z Z M Ma r 39c gt gt gt gt gt gt y180 y y 90 y y180 y y 90 ITlan EITlan Z Z Z Z Z Z M Ma 395 39C y180 y y 90 y y180 y y 90 y 39c z 2 T1 1 z 2 T1 Z Z Z M 39C lt gt gt gt lt y y180 y y 90 y y y Tgt5T1 The zcomponent of the magnetization MD exponentially recovers to its equilibrium state as predicted by the Bloch Equations MZ M0 2 ellT MD 74 3 2 Cquot 15 W 80 W L l 40 Quick Estimate l 2300 16 T1 13mm 1112 Measurement of T2 The Bloch equations told us that the FWHH line D 1 width oi2 was inversely proportional to T2 A 1 T2 However measured line widths are usually 1 limited by other factors including field 012 TC 2 inhomogeneity and we can only estimate the apparent relaxation time 2 So we need a way of overcoming field inhomogeneity and other factors that cause signal dephasing of the magnetization in the xy plane time Q y 2 The effects of spin de phasing can be overcome with a Hahn Spin Echo experiment The 900 pulse puts the magnetization onto the y aXis Both T2 and de phasing occur during the delay The 1800 pulse flips the magnetization along the X axis The de phasing continues but now this process brings the vectors back into ocus forming a spin echo 90 180 l 1 MW I r r V Equilibration Echo Delay Formation Z Z Z Z Z MEl T T gt gt gt i gt y 90 y F y 180 y y Looking at just the xy plane gt y gt y gt y gt y 90 E 180 E X X X X After refocusing any loss in the magnetization is due to T2 The echo intensity can be measured at different E values and the resulting curve follows an exponential decay It turns out that this is not the best way to do the experiment Diffusion during long t s causes additional intensity loss M M em Y 0 Carr Purcell Meiboom amp Gill modified the Hahn experiment by changing the phase of the 180 pulse to the y axis This refinement allows the refocusing to occur along the yaxis The second refinement is to keep 5 short so that diffusion is not a problem Instead of lengthening the echo time multiple echos are collected to increase the relaxation effect The CPMG Sequence 900 Looking at just the xyplane gt Y gt Y gt Y gt Y 90 C 180 T x x x x 1391 After refocusing any loss in the magnetization is due to T2 Intensity of the echo is measured after n l cycles through the sequence The time for relaxation is given by 2nr The resulting curve follows an exponentlal decay I All Wm lflft um mu m m m NMR Chapter 8 2D Techniques The previous chapter covered techniques that collected individual time domain data sets FIDs that produced a single frequency scale spectrum after an FT 2D techniques introduce a second frequency axis that most commonly provides correlations between resonances This second frequency axis arises from a second time domain FT relationship Where do we get a second time domain We saw with our discussion on the refocused INEPT that varying a delay between pulses caused a modulation in the amplitude of a coupled resonance This concept is used with 2D pulse sequences to develop the second time domain Everything we discussed about sampling bandwidth resolution and processing of 1D NMR signals also applies to this second domain The general form of any 2D NMR sequence is Detection Evolution Preparation lt gt Mixing t1 t2 The Preparation and Mixing periods are a pulse or series of pulses and fixed delays The Evolution period is the varying delay time t1 where chemical shift or I modulation occurs The Detection period t2 is similar to the collection of 1D FIDs Taken further nD NMR can have three or more time domains in the general form Detection Evolutlon 1 Evolutlon 2 Preparation 4 Mixing 1 4 Mixing 2 t1 t2 t 3 Let s consider the simplest 90 903 case of two pulses 1 separated by a varying H delay f1 P E M D A single spin that is off resonance will evolve or precess during the t1 period The second 90 pulse will convert the xy magnetization into xz magnetization Z Z Z 90 t10 90 a a a X y X y X J I Z Z 90 t1gt0 90 a a a X y X L U y X 1 As the time t1 is increased the x and z component of the magnetization follows a specific function Remember this zcomponent MX M0 sin 360 9 t1 MZ M0 cos 360 9 t1 For our simple example we are only interested in the x component because data collection happens immediately after the second pulse The FIDs at the different tl s give spectra like this To achieve reasonable resolution and f1 bandwidths there are many 504000 t1 increments taken The longer t1 lengths show considerable T2 T3 relaxation Plotting the resulting peak amplitude versus t1 yields a wave form that looks exactly like a FID It is commonly called an interferogmm domain data points in a process called transposing Every data point across f2 is included not just the peak centers Because of this requirement the f2 The f2 spectra are converted to t1 39 l domain is collected with a minimum number of points short AQ and t1 narrow SW FT ing the complete transposed data set yields a series of 1D spectra Aligning the resulting f1 frequency domain spectra yields a 2D stacked spectrum with a single peak at the shift frequency v in both dimensions The data can also be represented by using a topography map style contour plot The outer ring of a contour plot represents the width of the peak at lower heights The inner rings show how the pear narrows at higher slices If we have two uncoupled resonances both off resonance the vector diagram will look like MX M0 sin 3600 t1 90 t1gt0 90 gt gt gt X y X z y X y 0 02 The resulting 2D transformation would give two resonances that fall on the diagonal This concept is called chemical shift evolution Almost all 2D sequences have evolution based on chemical shifts Two coupled resonances A AX are a little y gt y y more 90 i complicated X 2 X and we 90 Coherence ShOW their X Transfer evolution on two separate y gt y y vector 90 i diagrams 2 X X X When the coupled spins are in the antiphase orientation coherence transfer can occur during the second 90 pulse Remember the x component of the magnetization was a function of the precessing frequency The coherence transfer acts to modulate spin A with the chemical shift of spin X X is modulated by A The result gives cross peaks or correlations in the 2D spectrum 8 The technique we just described is called Correlation Spectroscopy COSY The COSY contour plot of an AX spin system is below The diagonal still represents the chemical shift information 00 00 9 co 0 0 0 of o 0 diagonal lt9 0 0 is o o 0 VA The off diagonal peaks are the cross peaks or correlation peaks For COSY spectra crosspeaks are symmetric about the diagonal The cross peaks Connect the two resonances that couple each other diagonal 00 oo cross peaks VA VA Coherence Selection In reality our simple COSY sequence produces multiple coherence paths that produce different signals or phases These signals are similar to the negative frequency quadrature image signal that we saw earlier Just like the image signal these different coherences can be added into or subtracted out of the final data by phase cycling The t2 domain is always collected by quadrature detection 2 data sets CYCLOPS or some other from of quad image suppression must be included in the phase cycling The t1 domain is usually also acquired with quadrature detection ie 4 data sets Phase cycling to remove the t1 quad images must also be incorporated This type of data retains phase information and we call it phase sensitive detection These data have superior resolution to absolute value spectra which are collected without the second phase t1 set Another method of coherence selection is the used of pulsed field gradients PFGs PFGs place a strong field gradient across the sample typically along the zaxis The intensity of the PFC can quickly defocus the coherent spins based on their physical location The spins can be refocused if a gradient of equal but opposite strength is applied RF pulses between these PFG pulses can cause only selective refocusing based on the coherence path chosen law 0 mom Iquot PFG COSY sequence 903 903 General advantages of PFC over phase cycling 1 Greater selectivity In most cases PFG coherence selection is better than phase cycling PFG selection can be performed in a single scan while some phase cycling schemes require 16 or 32 transients on each t2 increment While the time savings are enormous with PFG the quality of the coherence selection is superior to the phase cycling less artifacts Dynamic range is also improved since only the desired coherence is passed to the ADC 2 Calibration of PFC not as stringent as rf pulses 15 Disavantages of PFC 1 PFC sequences are less sensitive than the phase cycle variants Different coherence paths can be added together with phase cycling PFG only lets one pass and be added 2 Phase errors that arise from chemical shift evolution during the gradient pulse msecs often force absolute value detection 3 Diffusion can lead to signal loss The PFG Spin Echo is actually used to measure diffusion 4 Many sequences often still require some phase cycling ie f2 quad image suppression 5 Requires special probes and PFG amplifiers that older systems might not have Still PFG sequences usually preferred over non PFG methods Most new instruments should have PFG options Classifications of 2D NMR Experiments 2D NMR experiments can be broken down into groups based on a couple of criteria Homonuclear Heteronulcear Both Axis are the Different nucleus on same nulceus each axis Directly Detected IS thcorre gon COSY TOCSY HETCOR COLOC roug on S 13 13 coupled INADEQUATE C C Indirectly Detected SI HSQC HMQC HMBC Correlations NOESY through Space ROESY HETERONOESY NOE Variants ISpectroscopy Homo2D amp Hetero2D EXSY Chemical Exchange DOSY Diffusion Correlation Spectroscopy COSY Most common of the homonuclear throughbond correlation techniques Usually refers to the 1H lH correlation experiments There are many variants that yield either the same or similar information Some examples COSY simplest experiment usually collected in magnitude mode COSY90 COSY45 signifies last pulse angle DQF COSY DQCOSY double quantum filtered variant Relay COSY multiple bond connectivity ECOSY PECOSY zCOSY zzCOSY COSY RCOSY Double Quantum Filtered COSY PFGDQFCOSY Preferred by me at least COSY sequence It is a phase sensitive experiment that utilizes pulsed field gradients Phase sensitive experiments have better resolution due to narrower line shapes but take twice as long to collect due to the phase sensitive detection The gradients reduce data collection time by eliminating phase cycling for artifact suppression iCOSYi DQ Filter 90 9p x180 X90 X i i 1 I IAHAIAI H ITI u I g i 5 64g Crotanoic Acid 1 l C CHa ppm HOI39IJ H 2 n O I gt 3 I 4L 5 6 I 39 I gDQCOSY 1i 39 39 39 MercuryVX 400 MHz 39 20mM in d6 dmso 1 scan 256 PS inc 14 mins 1 s 5 4 a 2 Crotanoic Acid CH gDQCOSY MercuryVX 400 MHz 20mM in d6 dmso 1scan256PSinc 14 mins 1 s 5 4 a 2 Heteronuclear Shift Correlation HETCOR Single bond correlations J coupling observed directly from the low y nuclei usually 13C The directly observed nucleus axis usually has higher resolution and the 1H axis poorly resolved Since observation is on the low y nucleus sensitivity is a problem These type of experiments have been mostly replaced with variants that detect low y information through the more sensitive 1H indirect detection HETCOR 900 900 Crotanoic Acid H CH Cc Ho O H F2 HETCOR 92 Mercury VX 400 MHZ 40 10 M in d6dmso 4 scans 128 inc oo 19 mins F1 PM 2 3 Crotanoic Acid H 3Ha 1H Projection cc Hoc H HETCOR wag Mercury VX 400 MHZ 40 10 M in d6dmso 4 scans 128 inc oo 19 mins 1D Spectra Crotanoic Acid H CH 1H Projection Cc HO H 0 r2 HETCOR ppm Mercu VX 400 an 13937 MHZ E 40 10 M in d6dmso 4 scans 128 inc oo 19 mins 1D Spectra 0ng H1 ILOK PM Mercury VX 400 8v m MHZ 4D 4D 200 mM in d6dmso a 16 scans 128 inc 3Om1 2a w 125 hrs 6D 6D 2OMe 6a so 5 1 39 10 4 y S 1 J7 syn 1D pectra 12 39 7 anti 14o 1oo ll A A1 1 1 1 1 u A 1 39 39 39 39 39 1 s 5 4 3 2 1 Indirect Detection HETCOR uses Jcoupling between 13C and 1H to allow polarization of the attached 1H to transfer to the observed 13C signal This produces the correlations in the 2D experiment However heteronuclear Jcoupling is bidirectional ie both nuclei are split to the same extent So we could reverse the concept and observe 1H with the transferred 13C chemical shifts This method is called Indirect Detection ID The main advantage of ID is that the higher frequency 1H is observed and this gives an significant sensitive advantage The 1H axis will have higher resolution than the 13C axis but this is usually limited by hardware considerations Challenges of ID experiments For 13C and other low natural abundance isotopes the actual component of the sample that is observed is a minor fraction Coupling between these nuclei shows up as satellite splitting that are on the baseline of 1H resonances Removal of the resonance of the more abundant signal which does not lead to correlations is very important Phase cycling schemes are far from perfect Additional suppression by saturation methods ie bilinear rotation decoupling BIRD can improve the suppresion However gradient coherence selection is the preferred method 13C Satellites Typi al PS Improved Gradient Cancellation at baseline cancellation Selection with BIRD 2 n c d 2 Challenges of ID experiments c0nt The resulting peaks for single bond correlation ID experiments are doublets Sensitivity is enhanced by decoupling the low y 13C during data acquisition However the spectral dispersion of carbon and other low y nuclei are quite large and the power needed to cover the full window can be quite high Probe design and the use of modern broadband modulation to cover the 13C have helped reduce the amount of power required for effective decoupling However sample heating and hardware failure issues arching still limit the duty cycle and the length of the FID t2 While the limit of pulse repetition is usually controlled by relaxation the 1H resolution is limited by these power handling factors Heteronuclear Single Quantum Correlation HSQC One of the more common ID experiments that yields single bond correlations Jcoupling The sequence has a gradient coherence selection version not shown that greatly improves the selectivity and reduces artifacts Polarization of the 1H is passed to 13C via an INEPT sequence where it is allowed to evolve chemical shift After the evolution period t1 it is passed back to the 1H reverse INEPT for detection The HSQC is the basis for many sequences that were developed for bio molecular analysis 90 180 90 180 90 180 H I H I H I H L 4 gtI U A2 A2 m2 m2 A 12J 180 90 90 180 13C H I I H U l tll U 3n Heternoclear Multiple Quantum Correlation HMQC Another common ID experiment that yields single bond correlations The main benefit of HMQC over HSQC is that HMQC is more robust against mis calibrations in pulse Widths and delay times Also HMQC has a simple modification that allows for long range correlations There are both gradient and non gradient versions of the sequence 180 gHMQC 90 T U T 90 90 BC I I I Decouple I a G A 1 21 Crotanoic Acid gHMQC CH Mercury VX 400 MHZ HCc 20 mM in d6dmso Hoc H 8 scans 256 inc H 45 mms 0 F1 99 n 40 so so 100 120 140 O 160 I I 39 I 39 39 39 I I I 1 a 5 4 a 2 Crotanoic Acid gHMQC H CH Mercury VX 400 MHZ Cc 20 mM in d6dmso Hoc H 8 scaos 256 inc H 45 mms 0 F1 pug W 1H Projection 1 D Spectra Crotanoic Acid gHMQC H CH Mercury VX 400 MHZ Cc 39 20 mM in d6dmso Hoc H 8 scaos 256 inc H 45 mms O 1H Projection F1 ppm 20 1D Spectra q a on 5 u M gHMQC 2 Mercury VX 400 MHZ 20 mM in d6dmso H Projection 8 scans 256 inc i 12 a M 45 mins LL IM AJJLWM 5 8 0 4n 4n 39 o 12a 39 30MB 80 o 6D a 6G 39 6a a ao 5 o 10 10 a 4 y l 1 7 syn 1D Spectra 12 7 anti 11 I 14o 39 I 100 m l I I39ll I ImlhlIll IMI lll Ill In l I J II 1 e s 4 a 2 1 Hm Heteronuclear Multiple Bond Corrrelation HMBC The HMBC sequence is a variation on the HMQC experiment The gradient HMBC has perhaps the greatest improvement over its non gradient sequence than any other experiment The suppression of artifacts using the gradient selection has made these experiments much more useful It was very difficult to get successful data using the non gradient sequence The sequence utilizes fixed delays that are longer to match the smaller multiple bond coupling constants The gradients are set to a different coherence pathway Long range coupling allows resonance structural assignments through small and moderately sized molecules Crotanoic Acid gHMBC Mercur VX 400 y H CH3 MHz c39c 20 mM in d6dmso Ho39 H 192 scans 256 inc 0 16 hrs 11 F1 5 ppm 39 m 5 4o oo 39 E 90 I 100 I 120 o 14o O 1oo I I I I I 5 4 2 1 37 Crotanoic Acid deMBC VX 400 ercur H 35 MHz y c39c 20 mM in d6dmso Ho H H 192 scans 256 inc 0 16 hrs 11 H i 3 ppm I I I I 20 5 I I J 40 J 60 39 l 50 I I 100 3 i l 140 mi Crotanoic Acid gHMBC K Mercury VX 400 Hg 3 H3 MHz cc39c 20 mM in d6dmso Ho39 H 192 scans 256 inc 0 16 hrs ll F1 5 39 2 a l 4o 0 i E f 30 I I m z 5 120 I i s r i 100 3 a 39 up 39 39 39l 39 1 6 5 4 39 F203Wquot Crotanoic Acid gHMBC Mercury VX 400 H CH3 MHz cfc 3 20 mM in d6dmso FloNH 192 scans 256 inc 0 16 hrs Jll 11 F1 39 5 Wang E i l w i 00 i f I i 39 I 100 i i 120 quot IJ I m i 3 1w 3 W 2D Nuclear Overhauser Effect Spectroscopy NOESY The 2D NOESY produces cross peaks between resonances that interact through space dipolar coupled Intensity of NOESY cross peaks can be used as a molecular ruler to measure distances between two atoms This makes NOESY an important tool for the determination of 3D structures bio molecules Remember when we examined the COSY sequence we saw that the two pulses produced z axis magnetization that was modulated by their chemical shifts This z axis magnetization can quottransferquot to neighboring spins during the fixed mixing time tm Via the NOE mechanism relaxation The final pulse allows detection of the signals NOESY Crotanoic Acid I n HOC H F2 NOESY I quotE h Mercury VX 400 MHZ 7 20 mM in d6dmso 4 scans 256 PS incs 133hrs 2D Spectroscopy 2D methods that show coupling multiplets versus chemical shift There are both homonuclear and heteronuclear versions Both methods are useful for resolving overlapping multiplets They are also used to measure coupling constants HOMOZD HETEROZD 90 1250 90 1 OZ 13CAI J 1 ll 22quot 22 H 180 HOMOZD crotanolc ACId Mercury VX 400 MHZ H CH 20 mM in d6dmso C 4 scans 128 inc HOC H 22 mins 0 F1 E H I 15 3 v 3910 l o 6 I HOMOZD crotanolc ACId Mercury VX 400 MHZ H a 20 mM in d6dmso 1H ProjeCtion C I 4 scans 128 inc HoE H 221m i H HOMOZDI Mercury VX 400 MHZ 20 mM in d6dmso 1H Projection 4 scans 128 inc 22 mins M MA A A A CHQ 7 39 I 15 m 2 l lilhll39 n J l u H 3 J 439 Crotanoic Acid HETEROZD H CH1 MerFuryVX 400 MHz CC 1M 1n d6dmso 2 scans 128 inc HO H 24 mins 0 F1 quot1 39 40 4 40 2 o 2 4 0 so 100 I I I I I I I I l I I I I 160 140 120 100 so
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