Structure Determination by NMR

Transcription

1 Analtische Chemie IV Structure Determination b NMR Prof. Bernhard Jaun Office: ETH Hönggerberg HCI E317 Phone: jaun@org.chem.ethz.ch home page:

2 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 2 Contents 1. Practical aspects of pulse Fourier transform NMR spectroscop 1.1 The basic NMR eperiment: phsical description 1.2 Ecitation b RF pulses 1.3 Digitization, window functions and fourier transform 1.4 Quadrature detection 1.5 Phase ccles and Z-gradients 1.6 Dnamic range and solvent suppression 1.7 The principal components of an NMR spectrometer 2. The principle of 2D-NMR 2.1 The basic idea 2.2 A meaningless eperiment 2.3 Quadrature detection in ω 1 3. Homonuclear shift correlation through scalar couplings 3.1 COSY. 3.2 Determination of coupling constants from COSY cross peaks. 3.3 TOCSY 3.4 INADEQUATE: homonuclear 13 C- 13 C double quantum spectroscop. 4. Spectral editing 4.1 Spin echo building blocks 4.2 Heteronuclear J-modulation 4.3 Polarisation transfer: INEPT and DEPT 5. Heteronuclear shift correlation through one bond and long range couplings 5.1 Proton detected methods 5.2 Proton detected H,X-COSY 5.3 HSQC and HMQC 5.4 HMBC

3 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 3 6. Relaation, dipole-dipole couplings and NOE 6.1 Longitudinal and transversal relaation 6.2 NOE in a two spin sstem without scalar coupling 6.3 The mechanism of dipolar relaation 7. Homonuclear 1D-NOE difference spectroscop 7.1 The stead state NOE in homonuclear multi-spin sstems 7.2 Practice of 1D-NOE difference spectroscop 8. Kinetic NOE-spectroscop 8.1 NOESY 8.2 NOE in the rotating frame: ROESY 9. On the influence of dnamic processes on NOE spectra 9.1 Overall molecular tumbling, internal rotation (conformational changes) und chemical echange 9.2 How to proceed with molecules with ω 0 τ c near Combined application of several methods 10.1 Tpical structure problems with organic molecules and suitable strategies 11. References and additional reading 11.1 Tetbooks 11.2 Homonuclear correlation through scalar coupling 11.3 Heteronucleare correlation through scalar coupling 11.4 NOE 11.5 Coupling constants und Karplus relationships 11.6 Abbreviations and Acronms 11.7 On the presentation of 2D-NMR data in the eperimental part of a thesis or publication.

4 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 4 What we would like to achieve with this course: - The student knows which method ields which tpe of structural information. - The student is able to choose the most promising combination of methods for the solution of a given structural problem. Since spectrometer capacit is epensive, the selection of an optimal strateg depends on technical (feasibilit) as well as on economical (fast and simple) factors. - The student knows how to interpret each tpe of spectrum and how to etract the pertinent data. - The student is aware of the possible artifacts and errors of interpretation for each method. - The student knows the NMR vocabular and is able to correctl describe NMR data in publications. Subjects that are not part of this course: - Comprehensive treatment of the underling theor (quantum mechanics of NMR) (-> courses b Prof. Schweiger and Meier). - Solid state NMR - Practical "nuts and bolts" of carring out the measurements on the spectrometer. (-> Praktikum Analtische Chemie) - Application to large biopolmers such as proteins and nucleic acids (-> course b Prof. Wüthrich) and calculation methods (simulated annealing, distance geometr etc.) used to derive solution structures of biopolmers from NMR data. Shorter oligopeptides, oligonucleotides und oligosaccharides, however, will be discussed as eamples or problems. Outline of the course: - Lectures on the individual methods with discussion of eample spectra. - Problems (real life spectra) for each of the discussed methods. - Problems on structure elucidation of medium to comple organic molecules with combined methods (in the last ca. 1/3) of the course.

5 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV Practical aspects of pulse Fourier transform NMR spectroscop 1.1 The basic NMR eperiment: phsical description Spin Component of the angular momentum of nuclei, electrons (and other elementar particles) that cannot be described as orbital momentum. Its origin is onl understandable in terms of relativistic quantum mechanics. The magnetic moment The magnetic moment (µ) associated with the orbital angular momentum (L) of a charged particle is given b: µ L = r p L p µ = γ L r e- The spin angular momentum J is associated with a magnetic moment as well: µ = γ J γ, the gromagnetic ratio is a fundamental propert of each nuclear isotope with non-zero spin Interaction between the magnetic moment und an eternal magnetic field Classical phsics: The torque T acts on µ. In response, µ z precesses around the direction of B 0 (analogous to a spinning top under the force of gravit) with B 0 the circular frequenc ω 0 [rad/s], which is called the Larmor frequenc. µ T = µ B0 ω 0 T ω 0 = γ B 0 E pot = - µ. B 0

6 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.2 Quantum mechanics: Quantum mechanical description of the spin angular momentum J : J ˆ = h ˆ I ˆ I : nuclear spin operator I : spin quantum number of the nucleus, a propert of each isotope (I = 1/2. n; n=0,1,2 ). a) The z-component (parallel to the eternal field) of the spin angular momentum can onl assume certain values governed b the magnetic quantum number m I : J z = h m I m I = - I, - I + 1,..,0,, I - 1, I m I magnetic quantum number This leads to 2I+1 allowed states. For nuclei with I = 1/2, which are of predominant interest in organic chemistr, onl the two states with m I = -1/2 and m I = +1/2 are possible. The interaction energ for each state with a static eternal magnetic field along the z-ais is E = - µ. z B 0 = - γ J z B 0 E = - γ h m I B 0 The energ difference between the two states is: E = - γ (1/2 - (- 1/2)) B 0 = - γ B 0 In order to achieve resonance, the energ of the irradiated radio frequenc has to match the energ difference between the two states: E = hν = ω = - γ B 0 The Larmor (circular) frequenc is: ω i = - γ (1-σi)B 0z With ω I = resonance frequenc (rad/s) of spin i with shielding constant σ i The resonance frequenc for a given isotope is proportional to the gromagnetic ratio and to the eternal magnetic field. a) The spin quantum numbers of nuclei follow the rules: A = Z + N A = mass number Z = number of protons (nuclear charge) N = number of neutrons A even -> I = integer Z even, N even -> I=0 Z odd, N odd -> I=1,2,3... A odd -> I= 1/2, 3/2, 5/2...

7 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.3 Macroscopic magnetization M Eperimentall, onl the total magnetization M of the sample inside the RF coil can be detected. corresponds to the vector sum of the magnetic moments of all spins. M = i µ i sum over total sample volume inside the coil M For I = 1/2, γ > 0 (e.g. 1 H): m I = + 1/2 z B 0 z B 0 M m I = - 1/2 Because the magnetic moments are distributed statisticall in the plane, there is no net transverse magnetization. In the Boltzmann equilibrium and for γ > 0, the population of the α (m I = +1/2) state is slightl larger than that of the β (m I = 1/2) state. This leads to a small residual magnetization in the direction of the eternal field B 0. The energ difference between the two states (α: m I = +1/2; β: m I = 1/2) is ver small. For 1 H at 14.1 Tesla (600 MHz) the ratio of the two populations is onl: N +1/2 / N -1/2 = Because ω 0 is proportional to γ and B 0, nuclei with high γ are more sensitive than those with low γ, and higher magnetic fields increase the sensitivit dramaticall. In practice, the sensitivit of NMR spectrometers increases approimatel according to B 3/ Ecitation b radio frequenc pulses Rotating coordinate frame: The Larmor frequencies in modern NMR spectrometers are in the order of MHz. On the other hand, the differences between the individual spins of the observed nucleus (chemical shifts and scalar couplings) are tpicall in the 1 Hz to 20 khz range. In order to make the description of the dnamics of the magnetization both mathematicall and visuall easier, it is usual to use a coordinate frame which rotates around the B 0 = z-ais with the circular frequenc ω 0.

8 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.4 The resulting "stroboscope" effect allows to describe the precession in terms of frequenc differences Ω = ω - ω 0. In the following, we will use the rotating frame for all vector diagrams. In modern NMR spectrometers with superconducting magnet coils, the magnetic field is parallel to the ais of the sample tube. The radiofrequenc coil, which transmits the ecitation pulses and the induced signal to and from the sample to transmitter and detector, respectivel, is a saddle coil that generates and detects RF fields having their magnetic component B 1 (t) orthogonal to the constant eternal field B 0. The relative orientation of B 1 vectors in the plane can be controlled b changing the relative phase of the irradiating RF. Irradiation of radiofrequenc corresponding to the Larmor frequenc of a given nucleus for a short time (an RF pulse of frequenc ν = ω 0 /2π and duration τ) induces a complicated "spiral" movement of the macroscopic magnetization M awa from the z-ais towards the plane. In the rotating coordinate frame this process, which is called nutation, is a simple rotation of M around the ais of the field B 1. The nutation angle (ξ) is a function of both, the RF field strength B 1 and of the pulse duration (it is proportional to the integral of the RF pulse): ξ = γb 1 τ [rad]. In practical work, the amplitude of the RF field is usuall given as γb 1 /2π [Hz]. It can be calculated if the duration necessar for a nutation of ξ =90 is known: γb 1 /2π = 1/(4. τ(90 )). Note: The spectrometer software uses parameters in the unit decibel (db) attenuation from the maimal output in order to control the amplitude of RF pulses. Since these values are different for each instrument/amplifier/probe head combination, one should alwas use the absolute RF amplitude γb 1 /2π [Hz] in publications. z z M z0 B 1 M 0 π 2 -

9 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.5 Dependence of the ecitation band width on the duration of the pulse Because the nutational angle is proportional to the integral of the RF pulse, the same nutation can be achieved either with a long weak pulse or with a short intense one. However, this holds onl for spins, which resonate eactl at the frequenc of the transmitter (Ω = 0). The bandwidth of ecitation ( the frequenc region in which spins are more or less equall ecited) is directl dependent on the intensit of the pulse (peak to peak voltage, B 1 amplitude). The first zero crossing of the ecitation function occurs at ω 0 /2π± γb 1 /2π Hz. Short intense pulses (so called hard pulses) are unselective and ecite a broad region of the spectrum, long weak pulses (so called soft pulses) are selective and ecite onl a narrow region around the transmitter frequenc. Continuous wave irradiation with ver weak amplitude during 0.5-5s allows to irradiate a single line and is used for homodecoupling and presaturation of solvent signals. Phase and amplitude of ecitation B 1 τ ω 0 Phase and amplitude of ecitation B 1 τ ω 0 Offset Effects Spins resonating at frequencies different from the transmitter frequenc eperience an effective RF field B 1 eff that is the vector sum of B 1 and of a component along B 0 : tan θ = 2π(ν-ν o )/γb 1 Nutation around B 1 eff with τ(90 ) no longer follows a grand circle. For 90 pulses, the longer path and slightl stronger field B 1eff compensate each other. Therefore, 90 pulses are much less sensitive to offset effects than 180 pulses. Pulse sequences are usuall based on the assumption that offset effects are negligible. In realit, offset effects lead to artifacts and loss of signal in pulse sequences such as DEPT and heteronuclear shift

10 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.6 correlation, which depend on accurate 180 pulses. In order to minimize offset effects, high amplitude pulses for unselective ecitation are standard in modern instruments. In practice, probe heads and amplifiers (tpicall 300W for X-nuclei) on a modern high resolution spectrometer can deliver 90 pulses as short as ca. 7 µs (γb 1 /2π = 35 khz). Higher power would lead to arcing in the probe and could destro the probe head or amplifier. Practical eample: 11.7 T (125 MHz for 13 C / 500 MHz for 1 H): chemical shift range 13 C: -10 to 240 ppm = ±15.6 khz. Offset of a carbonl signal: 13.5 khz.-> With γb 1 /2π = 35 khz and transmitter frequenc at 110 ppm -> θ = 21. Offset effect z z M M 0 B eff θ B eff θ B 1 tanθ = 2π (ν - ν 0 ) / γ B 1 Evolution of magnetization in the plane after ecitation b an RF pulse If equilibrium magnetization M z is ecited with an RF pulse, transverse magnetization (with components along and ) is created. This corresponds to promotion of α spins to the β state and therefore to the generation of single quantum coherence (ecitation of a m I = 1 transition). After the pulse, the magnetization in the plane evolves due to the chemical shift and the scalar coupling between spins as shown below:

11 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.7 Evolution of transverse magnetization under chemical shifts and scalar couplings M = M 0 sin(-πjt) M = M 0 sin(ωt) M = M 0 cos(-πjt) Ω < 0 M = M 0 cos(ωt) M = M 0 cos(πjt) Ω > 0 Evolution of scalar coupling in the plane: shown is the A-part of an AX sstem with J AX > 0 and ΩA = 0 Evolution of chemical shifts Ω in the plane In the coil of the probe head, the precession of magnetization in the plane induces a ver weak RF signal (µv), the so called free induction deca (FID), which is amplified and recorded during the acquisition time t 2 (tpicall 0.1s to 5 s). For practical reasons, the frequenc of the transmitter and a so-called intermediate frequenc are subtracted from the original signal such that the final signal entering the digitizer is in the khz range (for details see 1.7). The FID decas with time due to the transverse (T 2 ) and longitudinal (T 1 ) relaation processes. T 1 is the characteristic time for recover of z-magnetization (return to Boltzmann equilibrium), whereas T 2 is the characteristic time b which the coherence of transverse magnetization is lost because of dephasing of the individual spin vectors (for details see chapter 7.1). T 2 is correlated with the line width of a signal in the NMR spectrum. The time domain signal (S(t), FID) is an interferogram of all frequencies corresponding to the individual lines of the NMR spectrum. The spectrum S(ω) has to be calculated from the time domain signal b the mathematical operation of a Fourier transform. Since computers can onl do discrete Fourier transforms, the analog time domain signal has to be converted into a series of discrete numbers S(t 0 + t) equidistant in time b the analog to digital converter (ADC, digitizer).

12 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV Analog to digital conversion und Fourier transform In order to allow reconstruction of a periodic signal such as a sine or cosine function from discrete data points, one has to digitize with at least twice the frequenc of the periodic signal (Nquist theorem). Therefore, the time interval between two data points, called dwell time (t dw ), has to be t dw 1/(2F) [s] when the signal most distant from the transmitter has a frequenc 2π(ω-ω o ) = F. Because single channel detection cannot distinguish between positive and negative frequencies, the transmitter has to be set at one of the edges of the spectrum. Practical eample: 1 H at 500 MHz. Transmitter at 16 ppm, TMS at 0 ppm. F = 8000 Hz, t dw < 62.5 µs. With quadrature detection (standard nowadas), the transmitter can be set in the center of the spectrum which reduces the spectral with b half: F' = F/2 and t' dw 1/(2F') = 1/(F). However, because two data points have to be collected for each time increment (the ADC alternatel digitizes the signals of the two channels), the dwell time allowed for each channel is again 1/(2F). Eample: 1 H at 500 MHz. Transmitter at 8 ppm, TMS at 0 ppm. F =4000 Hz, t dw < 125 => 62.5 µs per channel. With the availabilit of faster digitizers, modern high-end instruments allow to digitize much faster then dictated b the Nquist theorem (so called oversampling). The redundant data points are used for digital filtering, giving much sharper cutoffs than with analog filters. Folding (Aliasing): Illustration of the Nquist theorem: Acquisition time (ms) Solid line: cos(2πνt) with ν=300 Hz; broken line: cos(2π(ν ν)t) with N = 1000 Hz, ν = 300 Hz. The dwell time is t dw =1ms, corresponding to a Nquist frequenc (2F) of 1000 Hz. Both signals give identical digitized data and the signal from the broken line would be folded into the spectrum after FT. Under these conditions, the highest correctl digitized frequenc would be ± 500 Hz.

13 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.9 Signals that are outside the limits given b the Nquist theorem ( ν ν o > 1/(2t dw )) will be folded around the edges of the spectrum. Not onl signals, but also noise is folded into the spectrum from regions outside the spectral width. This makes it necessar to use computer settable analog cutoff filters that are set to ca. ±(1.25*SW/2). For real FT, folding occurs around the nearer edge of the spectrum, for comple FT around the far edge ( see quadrature detection). Because no analog filters act in the artificial time domain t 1 of 2D spectra, folding is of particular importance in the ω 1 dimension of 2D spectra. Folding after a real Fourier transform (cos-transform) signal with ν 1 < N 2N ν 2 N (ν 2 ) folded ν 1 0 Hz - N Folding after a comple Fourier transform signal with ν 1 < N 2N ν 2 N ν 1 0 Hz - N (ν 2 ) folded

14 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.10 Fourier transform After single channel detection, the time domain arra of data points is transformed b a discrete real FT (cos-transform). With quadrature detection the data in the two channels are used as the imaginar and real part of a comple FT. The algorithm used is FFT, which, using precompiled sine tables and coefficient swapping instead of multiplications is ver fast on toda s computers. Comple analtical FT: + s(ω) = { f (t) + if (t)} e iωt dt Comple discrete FT S(ωi) = N 1 k = 0 { SA(k t) + isb(k t) }ep( i2πlk / N) Phase correction After the Fourier transform, the real and imaginar parts both contain the spectrum but with a phase difference of 90, in other words, orthogonal linear combinations of the absorption A and the dispersion spectrum D. During the process of zero order phase correction, a miing coefficient θ is determined interactivel such that the "real" part of the spectrum (the one displaed on the screen), contains the pure absorption spectrum. R = A cos φ + D sin φ A = R cos θ + I sin θ Frequenc dependent phase errors are approimatel corrected according to θ=θ 0 + cν in the 1 st order phase correction. Frequenc dependent phase errors are tpicall the result of delaed acquisition after the end of the pulse sequence. Digital resolution The acquisition time corresponds to the dwell time multiplied b the number of data points acquired in the time domain ( t aq = t. dw n t2 ). After the Fourier transform, the number of data points of the real spectrum is half the acquired points (n ω2 =n t2 / 2), evenl distributed over the spectral width (sw). Therefore, the digital resolution in the frequenc domain is 2sw/n t2 [Hz/Pt]. Because t dw = 1/(2sw) the digital resolution is 1/t aq. In order to correctl digitize a well-resolved spectrum with natural line widths of 0.2 Hz, one has to acquire for 10s (at least 2-3 data points per line).

15 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.11 Zero filling Etension of the measured time domain signal b an arbitrar number of zero data points before Fourier transformation leads to an interpolation of data points in the frequenc spectrum. This gives smoother data but can not recover resolution that was lost b too short an acquisition. Since, in 2D eperiments, the number of acquired points in the time domain t 1 is directl proportional to the eperiment time, zero filling b at least a factor of two is standard in the t 1 / ω 1 dimension. Convolution and window functions The natural envelope of a (strictl: single spin) FID is an eponential function according to: I( t) = I o e iωt e t /T 2 The effective line width 1/T 2 * is the sum of the natural line width 1/T 2 and the instrumental line broadening 1/T* (e.g. due to a non homogeneous magnetic field) 1/T 2 * = 1/T 2 + 1/T* Fourier transformation of an eponential function gives a Lorentz function, the natural line shape of a single spin NMR signal. Multiplication of the time domain signal with another eponential function before the FT does not change the Lorentz nature of the frequenc domain signal but changes the apparent line width: multiplication with e -t/a leads to line broadening concomitant with improved S/N whereas multiplication with e +t/a narrows the lines and drasticall deteriorates the S/N. Multiplication of the time domain signal with a Gaussian (e t2 /a ) leads to Gaussian instead of Lorentzian line shapes in the spectrum. Since Gaussians have a much more narrow base than Lorentz lines, this improves the apparent resolution of multiplets without serious costs in S/N. Stopping the acquisition before the analog signal has full decaed into the noise is equivalent to multiplication of a step function into the FID. After the FT, this gives spectra with wiggles on both sides of each signal (the FT of a step function is a sinc (sin / ) function). This can be avoided if the end of such an FID is multiplied with a half Gaussian function (apodization).

16 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV Quadrature detection after (π/2) - sinωt ω > 0 f (t) ω < 0 - sinωt f (t) = cosωt Simultaneous acquisition of the signal b two detectors that are 90 out of phase allows to distinguish between positive and negative frequencies. The signals from the two channels are combined as the real and imaginar part of the integrand in the FT. + s(ω) = f (t) + if (t) e iωt dt comple FT { }

17 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.13 Illustration of the principle: cos(-ωt) = cos(ωt) + SW/2 +ν 1 0 Hz ν 1 - SW/2 sin(-ωt) = -sin(ωt) ν 1 + SW/2 +ν 1 0 Hz - SW/2 sum ν 1 +ν + SW/2 1 0 Hz - SW/2

18 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.14 Redfield method of quadrature detection transmitter frequenc largest absolute frequenc to be digitized single channel detection mirror images for all signals + SW + SW/2 0 - SW/2 - SW dwell = 1/ (2 SW/2) = 1/ SW SW* = 2 SW -> dwell = 1/ 2 SW A shift of the receiver phase b 90 from one data point to the net one leads to an apparent shift of the spectrum b 1/(4SW*): the mirror images no longer overlap + SW + SW/2 0 - SW/2 - SW After the FT, the two mirror images are folded on top of each other and the reference is shifted back b SW*/4 = SW/2 Redfield method: the digitizer rate is doubled: t dw = 1/(2. SW) This gives the same number of data points as with true two channel detection but in a single file. The time domain signal is the integrand of a real (cos) Fourier transform: + s(ω) = f (t) e iωt dt This method is also called TPPI (time proportional phase increments), in particular, if used in the t 1 dimension of a 2D spectrum.

19 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV Phase ccles Cclops pulse # transmitter phase FID channels A, B memor B A A: B: A B A: B: B A A: B: A B A: B: total: 1 2 A-B-A+B = 4 cos ω t B+A-B-A = 4 sin ω t channels A and B are full equalized

20 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.16 Phase ccles are not onl used to balance the contributions of the two detector channels but also in order to select desired coherence transfer pathwas and to eliminate undesired contributions to the signal. This is possible because zero- and multi-quantum coherence respond differentl to a phase shift than single quantum coherence. A phase shift of 90 leaves zero quantum coherence unshifted, shifts single quantum coherence b 90 and double quantum coherence b 180. That allows constructing phase ccles that lead to coherent addition of the desired signal but eliminate the undesired components b subtraction (a 180 phase shift on alternate scans is equivalent to a difference spectrum). Disadvantage of phase ccles: 1. The undesired components are eliminated b subtraction. Therefore, the full signal, including the unwanted components, is entering the receiver and the receiver gain has to be set to accommodate the full signal. Good subtraction requires ver high spectrometer stabilit over the length of the eperiment; otherwise, non-perfect subtraction of large unwanted signals gives residual artifacts in the spectrum. 2. Suppression of unwanted coherence transfer pathwas requires a certain minimal length of the phase ccle (e.g. 16 or 32 scans per FID). This imposes a lower limit on the eperiment time even if the signal to noise ratio of a sample would allow recording the spectrum with onl one or two scans per FID. Gradients volume sensed b the RF coil z + A A B B C 0 B 0 + B(z) C E D B 0 D E The disadvantages of phase ccling mentioned above can be avoided if coherence transfer pathwas are selected using z-gradients. A gradient coil in the probe head generates a linear field gradient along the z-ais that adds itself to the main field B 0. If such a gradient of amplitude g (usuall given in Gauss/cm) is applied for the time t g, the frequenc of precession of -magnetization depends not onl on Ω and J but also on the location of the spin along the z-ais of the sample. If the gradient is strong

21 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.17 and long enough (it is the integral under the gradient pulse that counts), the frequencies of individual spins will be spread according to their z-coordinate and the net -magnetization is no longer detectable. Application of a gradient in the opposite direction with equal length and amplitude reverses the dephasing process and leads to a gradient echo when the spins in all volume elements reach the original phase coherence. π/2 echo acquisition RF gradients t g dephased t g in phase refocussed As with phase shifts, coherences of different order respond to gradients in a different wa. Zero quantum coherence precesses with the difference of the frequencies, double quantum coherence with the sum. Accordingl, magnetization that was dephased b a gradient as single quantum coherence, and then transformed into double quantum coherence b a pulse, will not be refocused b a gradient of opposite sign and equal amplitude and length. Application of gradients at suitable places in the pulse sequence is therefore an alternative method for selection of desired coherence transfer pathwas. t g 0 θ tg = γp B z (t)dt p = coherence order; ±1 for SQC, ±2 for DQC, 0 for ZQC; θ tg = dephasing angle Advantages of gradients for coherence transfer pathwa selection Since the unwanted magnetization is not refocused, the receiver does not detect it at all. This allows setting the receiver gain according to the desired signals onl and eliminates the necessit for subtraction and the artifacts related to it. Since phase ccling is no longer mandator, samples with a good S/N ratio can be measured with onl one or two scans per FID, which reduces the eperiment time dramaticall.

22 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.18 Disadvantages of gradients Because the refocusing of magnetization that was dephased b a gradient depends on the z- coordinate of a given molecule to remain constant during the eperiment, diffusion leads to a loss of refocusable signal. This imposes an upper limit on the duration of the pulse sequence. Gradient spectroscop requires additional hardware: the probe head has to be equipped with a gradient coil and a gradient amplifier that can deliver stable and high currents (tpicall 10A) is needed. Because of the enormous advantage of using gradients, this equipment is now standard for high end spectrometers. 1.6 Dnamic range and solvent suppression +volt Receiver most significant bit least significant bit ADC 12 Bit or 16 Bit - volt analog signal The receiver gain is set to give correct digitization of the highest voltage b the ADC. Dnamic range = ratio between the strongest signal and the weakest signal to be digitized. Eample: 1 mm protein in H 2 O; (110 M in protons) dnamic range = 110/0.001 = 10 5

23 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.19 Accumulation: Modern instruments have 16Bit ADCs for high resolution work and 32 or 64 Bit computer words. This corresponds to a dnamic range of ±32768 : ±1. The signal is accumulated according to S(N) = N. S(1).Correctl digitized noise will accumulate as N= N 1/2. N(1). Therefore, S/N improves with the square root of the number of accumulations. However, this requires that the noise be digitized correctl. Because, in samples of ver high dnamic range, the receiver must be set to accommodate the largest signal, there is a risk that the smallest signals (including noise) are no longer correctl digitized because the corresponding voltage is below the least significant bit of the ADC. In this situation, accumulation does not improve the S/N. Solvent suppression If the molecules to be analzed have echangeable protons (NH, OH) and have to be measured in protic solvents such as water or methanol, the echangeable protons are replaced b 2 H of the deuterated solvent (D 2 O or CD 3 OD) and are no longer detectable. In particular with oligopeptides and oligonucleotides, the NH protons are ver important for the structure analsis. Therefore, one usuall measures the spectra in H 2 O / D 2 O 9:1 or in CD 3 OH, which makes it necessar to suppress the etremel intense solvent proton signal in order to be able to measure the analte signals correctl. Depending on the echange rate of the NH (OH) protons, two strategies are used: RF π/2 π π 2 - selective π 2 - selective AQ gradients z z If the echange is relativel slow on the time scale of T 1 (ca < 0.01 s -1 ), the solvent signal is saturated b a highl selective cw-irradiation of 1-5s duration at the beginning of the pulse sequence. This so called presaturation method can be used successfull for most amide NH in oligopeptides. The iminoand amino-nh protons in oligonucleotides, however, echange too fast for this method: presaturation of the solvent signal leads to transferred saturation of all NH signals as well. In this situation, one has to use a method that does not ecite the solvent signal, but all other signals as uniforml as possible. The corresponding methods include jump-return, WATERGATE and ecitation sculpting. The last two methods use pulsed z-field gradients and are among the best water suppression techniques available toda.

24 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV NMR spectrometer hardware Block diagram of a modern high resolution liquids NMR spectrometer Host Computer usuall a UNIX Workstation Acquisition Computer: Pulseprogrammer ADC RF-Unit Lock( 2 H)-RF channel 1 H-RF channel X-RF channel field-frequenc stabilization main coil Magnet Sample Hard-Disks Buffer memor Y-RF channel(option) MO Disks Tape Gradient unit (Option) Temperature controller Temperature sensor cooling gas N 2 / air Probehead Radio frequenc unit sum to memor real imaginar Dwell clock Digitizer ω φ =0 φ = 90 audio signal probehead Receiver ω preamplifier phase IF ω ω ο + ω Snthesizer ω transmitter pin diode tuning matching ω

25 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 1.21 Magnet and probe head upper barrel pneumatic sample injection, ejection vacuum sample tube spinner N 2 He shim coils (RT) and Z 0 supraconductor coil (B 0 ) and croshim coils isolated gas inlet (Dewar) RT-shimcoils RF connectors cooling gas heater Further reading T.D.W.Claridge, High Resolution NMR Techniques in Organic Chemistr, Pergamon, 1999, Chapters 2 and 3. J. Sanders, B. Hunter, "Modern NMR-Spectroscop", Oford Universit Press, 2nd Edition, 1992, chapter 1. H. Günther, "NMR-Spektroskopie", Thieme, 3. Auflage, H. Günther, "NMR spectroscop : basic principles, concepts, and applications in chemistr^", 2 nd edition Wile, 1996 H. Friebolin, "Ein- und zweidimensionale NMR-Spektroskopie", 3. Auflage, Wile-VCH, F. K. Kneubühl, "Repetitorium der Phsik", Teubner, 5. Auflage, 1994.

26 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV The principle of 2D-NMR spectroscop 2.1 The basic idea Preparation Evolution Miing Detection t 1 t m t 2 Acquire a series of FIDs: t 1 Starting with t1=0, the evolution time t1 is incremented b t1 (the "dwell time" in t1) from one FID to the net one. t 2 FT in t2 / ω2 t 1 A series of spectra in ω 2, an interferogram ("FID") in the orthogonal direction (t 1 ). Ω FT in t1 / ω1 A 2D NMR spectrum: diagonal peaks (Ω1=Ω2) and cross peaks (Ω1 Ω2) Ω Ω

27 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV A meaningless eperiment: Labeling the t 2 -signal with chemical shifts during t 1 COSY spectrum of an AX sstem without scalar coupling (J AX = 0) t 1 t 2 (π/2) - (π/2) - AQ z z (π/2) - t 1 sinω A t 1 sinω X t 1 z sinω A t 1 sinω X t 1 cosωx t 1 z cosω X t 1 X X (π/2) - A cosω A t 1 cosω A t 1 A The final amplitude of the signal depends on t 1 and on the chemical shift during the evolution time. In a 2D-eperiment, t 1 is incremented from FID to FID. signal amplitude after the second pulse. t 1

28 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 2.3 Because there is no coherence transfer without coupling between A and X, all signals have the same frequenc during t 1 and t 2 and the 2D spectrum contains onl diagonal peaks. The actual acquisition during t 2 is done with quadrature detection, which eliminates the mirror image. In the "artificial" t1 dimension, all signals will be mirrored around the ω 1 = 0 ais: Result: ω ω In order to eliminate the mirror images in ω 1, the equivalent of quadrature detection has to be constructed in t 1 As for 1D spectra, there are two methods: 1. Hpercomple (Ruben, States, Haberkorn, RSH) 2. Redfield (Time Proportional Phase Increments, TPPI) 2.3 Quadrature detection in ω The hpercomple method (RSH) For each t 1 -value, two FIDs with a phase difference of 90 with regard to modulation in t 1 have to be acquired. This can be achieved b changing the phase of the 2nd pulse b 90.

29 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 2.4 z z z FID 1 t 1 (π/2) - z z sin ωt 1 z FID 2 t 1 (π/2) - cos ωt 1 For each t 1 value, FID1 and FID2 are stored in separate memor blocks. Together with the two quadrature signals from channels A and B in t 2, one obtains four memor blocks. Comple FT in both, ω 1 and ω 2, gives a 2D spectrum that is a matri of four blocks: rr, ri, ir, and ii. Phase correction in each direction mies the two blocks in the corresponding dimension such that in the end, the rr block (the one that is usuall displaed and plotted) contains the 2D spectrum with absorption line shapes in both dimensions. quadrature detection in t2 FID 2 FID 2 FT(ω 2 ) 0 90 FID 1 FID 1 comple 0 90 quadrature detection in t1 FID R 2 I 2 FT(ω 1 ) R 1 I 1 comple spectrum RI RR II IR TPPI Onl one FID is acquired per t1 value, but the t1 increment is half of that used with RSH. This gives a single block with twice as man FIDs as in the hpercomple mode. Each time t1 is incremented, the phase of the 1 st pulse is shifted b 90. The spectrum obtained after a real FT in t 1 can be folded around ω 1 =0 and the reference is shifted back into the middle of the ω 1 -domain (see Redfield method).

30 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 2.5 Result: ω 2 0 -SW 1 /2 +SW 1 /2 ω 1 ω 2 TPPI and RSH are equivalent with regard to eperiment time, S/N and digital resolution. Certain artifacts, in particular so called aial peaks, appear at the center of the ω 1 domain for RSH but at the edge of the spectrum with TPPI. Folding in ω 1 is also different in the two cases (see folding with real and comple transforms).

31 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV Homonuclear shift correlation based on scalar coupling 3.1 COSY AX ββ AX sstem (1st order) with JAX > 0 AX SQ A 1 X 1 SQ AX J AX J AX αβ ZQ βα A 1 A 2 X 1 X 2 DQ X 2 A 2 SQ SQ ω A ω X αα AX Coherence: Coherence is a generalization of the concept of magnetization. In the quantum mechanical treatment coherence corresponds to off-diagonal matri elements of the densit matri. Single quantum coherence (SQC) corresponds to ecitation of an allowed ( m I = ±1) transition and is either equivalent to observable transverse magnetization or evolves into observable transverse magnetization under chemical shift and/or scalar coupling. In the eample of an AX sstem given above, the transitions A 1, A 2, X 1, X 2 are SQCs. Double quantum coherence (DQC) correlates two states differing b m I = ±2 and connected b two transitions originating at a common energ level of coupled spins (e.g. A 1 and X 2 via αβ or A 2 X 1 via βα). Zero quantum coherence (ZQC) correlates two states differing b m I = 0 which are connected b two transitions originating at an energ level common to two coupled spins (e.g. A 1 and X 1 via ββ or A 2 and X 2 via αα). In general, a sstem of p mutuall coupled spins can develop coherence of order 0 to ±p (p-quantum coherence, multi quantum coherence = MQC). Coherences other than SQC (DQC, ZQC, MQC) are not directl observable. Starting from equilibrium z-magnetization, a single pulse can onl generate SQC (A 1, A 2, X 1 or X 2 ). Further pulses acting on SQC of one of the coupling spins can generate SQC of the coupling partner(s) as well as DQC and SQC of the pair(s).

32 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 3.2 SQC(A 1 ) SQC(A 1 ) SQC(A 2 ) SQC(X 1 ) SQC(X 1 ) DQC(A 1 X 2 ) DQC(A 2 X 1 ) ZQC(A 1 X 1 ) ZQC(A 2 X 2 ) This process, brought about b the second (miing) pulse, is called coherence transfer. One wa to illustrate the coherence transfer pathwas in a pulse sequence is to use a sstem of horizontal lines as in musical notation. 2 π /2 π /2 t 1 t Onl SQC (usuall -1) is detected during t2 In addition to SQC, the second pulse generates DQC and ZQC, which are not detectable. In order to obtain pure absorption lineshapes in both dimensions, the magnetisation that was SQC of order 1 and -1 during t1 has to pass the phase ccle. 2-spin sstem AX: COSY pulse sequence Absolute value COSY (magnitude COSY) In the earl das of 2D spectroscop (COSY was the first 2D eperiment proposed), quadrature detection in t 1 was not et implemented. In order to avoid mirror signals in ω 1, a phase ccle that selects either for -1 SQC or for +1 SQC in t 1 was used (so called echo or anti-echo selection). This eliminates the quadrature images in ω 1 but leads to line shapes that are mitures of dispersion and absorption (phase instead of amplitude modulation of the signal in t 1 ). In order to get reasonable contour plots of such 2D-spectra, one has to calculate the absolute value s = (r 2 +i 2 ) 1/2 of each data point (magnitude spectrum). The dispersive contributions to the line shape lead to long tails in both ω 1 and ω 2. When two such tails (star shaped ridges in the contour plot) cross each other, artificial cross peaks appear although no coupling eists between the two spins. The star-shaped cross- and diagonal peaks can be changed into bo-shaped ones if a "pseudo-echo" (e.g. sin 2 -function) window function is applied. However, this deteriorates the S/N and the fine structure of cross peaks is lost. Therefore, magnitude COSY has been replaced largel b methods giving pure absorptive line shapes such as DQF-COSY.

33 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 3.3 Magnitude COSY of an AX sstem (without pseudo echo filter) Pseudo-Echo Filter

34 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 3.4 Resulting 2D-spectrum t 1 -noise and smmetrization: Instabilities of the spectrometer and environmental influences such as temperature and pressure changes in the lab, acoustic noise from walking around or magnetic disturbances of street cars (Zurich Tram), elevators etc. lead to variations of the intensities of strong signals from one FID to the net one in addition to the (wanted) amplitude modulation. After the FT, this transforms into noise bands parallel to ω 1 at the chemical shifts (in ω 2 ) of strong signals. Because, in principle, a 2D COSY spectrum is smmetrical around the diagonal, whereas the t 1 -noise is not, so-called smmetrization can be used to eliminate t 1 -noise. The operation of smmetrization consists of setting the intensit values of the two points that are smmetric to the diagonal to the smaller of the two values. In practice, however, the two dimensions of 2D spectra are commonl measured with different digital resolutions (e.g data points in t 2 but onl 512 data points in t 1 ). Even if identical numbers of points are used for FT in both dimensions (e.g. b zero filling in t 1 ), the resulting 2D spectrum is no longer trul smmetrical around the diagonal. While quite popular for a while (man eamples in the literature), smmetrization is no longer used in modern practice.

35 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV Phase sensitive detection of COSY (PS-COSY) If COSY spectra are acquired with quadrature detection (RSH or TPPI) in t 1, the cross peaks can be phased to give true antiphase absorption line shapes. However, the diagonal peaks are 90 out of phase with regard to cross peaks and therefore have dispersion line shape. The star-shaped form of the diagonal peaks often covers cross peaks close to the diagonal. In contrast to magnitude COSY, the fine structure of cross peaks is well resolved in PS-COSY and can be used to qualitativel judge the size of the coupling constants. For protons with more than one coupling, the active coupling (the coupling that causes the cross peak) can be identified, because the cross peak is in antiphase with regard to the active coupling, but in phase with regard to all other couplings (passive couplings) 1D-spectrum cross peak antiphase in ω 1 and ω 2 X diagonal peak in-phase dispersive in ω 1 and ω 2 ω 1 ω 2 cross section at ω 1 = X J AX

36 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 3.6 PS-COSY of multi spin-sstems: active and passive couplings Eample: phase sensitive COSY of an AMX sstem with J AX = 0, J AM > 0, J MX > 0: trace A A B trace B Double quantum filter A third 90 pulse, immediatel after the 2 nd one, reconverts some of the DQC generated b the second pulse back into observable SQC. Since DQC is twice as sensitive to phase shifts as SQC, it is possible to construct phase ccles that let onl pass magnetization that was present as DQC between pulses 2 and 3. Because DQC is onl possible for at least two mutuall coupled spins, the double quantum filter eliminates all signals (including the diagonal peaks) of singlets. Furthermore, the cross peaks and the diagonal peaks can be phased into pure absorption in both dimensions in DQF-COSY spectra. This gives a much narrower diagonal and allows seeing cross peaks ver close to the diagonal. Although the sensitivit of DQF-COSY is onl half of that of magnitude or PS-COSY, the advantages predominate and make DQF-COSY the method of choice in toda's practice.

37 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV π /2 π /2 π /2 t 1 t The 2 nd pulse generates DQC (and ZQC), the 3 rd pulse converts it partiall back into SQC. The phase ccle or gradients select magnetisation that was present as DQC during. 2-spin sstem AX: DQF-COSY Multiquantum filters In analog to the double quantum filter, phase ccles that act as n-quantum filters can be constructed. The onl let pass magnetization that was present as n-quantum coherence during. n-quantum coherence requires n mutuall coupled spins (each of the n spins couples with all others). In practice, sstems with more than three mutuall coupled spins are rare. In addition, the sensitivit of the eperiments rapidl diminishes with higher coherence order n of the filter. A triple quantum filter, e.g., ma allow distinguishing between the following three-spin sstems: H A H B H A H B H C H C J AB, J AC, J BC all 0 J AC often = 0 cross peaks in TQF-COSY no cross peaks in TQF-COSY

38 Prof. Dr. B. Jaun: Structure determination b NMR/Analtische Chemie IV Eamples for COSY variants Menthol CH 3 OH H 3 C CH 3 Menthol in acetone-d6 300 MHz magnitude COSY processed with cos 2 -Filter ppm ppm

39 Menthol in acetone-d6 300 MHz magnitude COSY processed with pseudo-echo filter ppm ppm Menthol in acetone-d6 300 MHz PS-COSY ppm ppm

40 Menthol in acetone-d6 300 MHz DQF-COSY ppm ppm Menthol in acetone-d6 300 MHz DQF-COSY epansion ppm ppm 1.2

41 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV Determination of 1 H- 1 H coupling constants from COSY spectra 1 H- 1 H three-bond (vicinal) coupling constants depend on the dihedral angle around the central bond according to the Karplus relationship. If suitable parameters for the Karplus equation are known, possible dihedral angles (in general, there are several solutions for a given 3 J HH ) can be deduced from accuratel measured coupling constants. If the signals are well dispersed, the J-values can be determined with the highest precision from 1D spectra. If sstems of higher order occur, the chemical shifts and coupling constants can be determined b iterative fitting with a simulation program (e.g. SWAN-MR, MESTRE-C, VNMR, g-nmr, NMRSIM). However, if the signals overlap in the 1D spectrum, one has to etract the coupling constants from the fine structure of cross peaks in appropriate 2D spectra. Qualitative (large, medium, small) coupling constants can be estimated based on the antiphase / in phase properties and the intensities of cross peaks in DQF-COSY spectra. The antiphase nature of the cross peaks with regard to the active coupling leads to a new, "antiphase Pascal triangle" for the line intensities in multiplets of protons coupling with several magneticall equivalent spins. In contrast to in phase spectra, central lines of multiplets with an odd number of lines can actuall disappear. In an antiphase triplet, e.g., onl the two outer sub-lines are seen in antiphase, whereas the central line vanishes. The distance between the two visible lines is twice the coupling constant etc. The precise determination of numerical J-values from antiphase cross peaks in DQF-COSY spectra is difficult for the following reasons: 1. The digital resolution in the ω 2 dimension of the 2D spectrum is usuall much lower than in the 1 H- 1D spectrum (and even worse in the ω 1 dimension). 2. Lorentz lines in antiphase partiall cancel each other, if the linewidth is comparable to the splitting. The distance between the maima of such strongl attenuated residual lines is larger than the coupling constant. In-phase lines with splittings not much larger than the linewidth are not baseline resolved and will have their maima closer than the coupling constant. Thus, active coupling constants will be overestimated and passive coupling constants will be underestimated.

42 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV δν /LW = δν /LW = δν / LW = δν /LW = 1 δν /LW =.5 δν /LW =.25 in Phase δν /LW = δν /LW =.1

43 Prof. B. Jaun: Structure determination b NMR / Analtische Chemie IV 3.10 E.COSY The best wa to determine coupling constants from cross peaks is to measure the distance between two in-phase sub-lines that are not affected b antiphase cancellations. E.COSY is one method that produces cross peaks with onl half of the sub-lines present in DQF-COSY. E-COSY is a weighted linear combination of nqf-cosy spectra with n = 2,3,4 i (coherence order of the nq-filter, in practice, one stops the series at n=3 or 4). The cross peaks in nqf-spectra with different n have different smmetr properties. Therefore, summation cancels half of the sub-lines. The measurement of true E.COSY spectra with good S/N is ver time consuming. An alternate pulse sequence that gives E.COSY tpe cross peaks but with improved sensitivit is PE.COSY. E.COSY of an AMX 3-spin sstem TQF-COSY DQF-COSY + = E.COSY The basic element of an E.COSY cross peak is an antiphase square which represents the active coupling. Each spin that passivel couples with one or both of the activel coupled nuclei generates a displaced set of squares. The displacement vectors connecting identical corners of the squares have