Two-Dimensional Nuclear Magnetic Resonance: Principle and Applications Guangjin Hou 0.07.008
Outlines Histories of Multi-Dimensional NMR The general scheme for D NMR The classes of D NMR experiments -D J-Resolved NMR spectroscopy -D Correlated NMR spectroscopy Summary of D NMR methods
Histories of Multi-Dimensional NMR Some histories in NMR Spectroscopy Reasons for developing MD NMR. Spread spectrum out resolve peaks remove overlap. Supply more information 946 Bloch and Purcell - First NMR experiment 967 Richard Ernst - Fourier transformations 97 Jean Jeener - Two dimensional NMR - COSY 976 Richard Ernst - First two dimensional NMR experiment 987 Griesinger et al. - Advent of three dimensional NMR 990 Ad Bax et al. - Four dimensional NMR J. Jeener R. Rrnst
The general scheme for D NMR Basics of ANY D NMR Experiment Evolution t Acquisition t Preparation Mixing Preparation period: some kind of coherence is obtained. Generally consists of a single pulse, but may also have complicated set of pulses and delays. Evolution period: Incrementable delay; no observation is made. Mixing period: Time during which through-bond or through-space couplings are allowed to interact; coherence is manipulated into observable signal. Acquisition period: Normal FID
The general scheme for D NMR The acquisition process for two-dimensional NMR The first t increment The second t increment The third t increment The fourth t increment.
The general scheme for D NMR Two-dimensional Fourier Transform Considering the spin magnetization evolves with resonant frequency Ω in the t period, evolves with Ω as well as spin-spin splitting of strength a in t domain, then ic0 iω t iω t iat / iat M () ( / I t = e e e + e ) f ( t, t) Taking its Fourier transform with respect to the two time variables t and t, g + iω, ) t iωt ω e e f ( t, t) dt (π ) dt ( ω ic 0 = δω Ω δω Ω+ a + δω Ω Here δ function is expressed as, ( )[ ( /) ( a/)] δ ( x ) = / π exp( ixt) dt ω Ω Ω -a/ Ω +a/ω If there are a second chemical shift and a second spin-spin spliting, then ic0a g( ω, ω) = δω ( Ω)[ δω ( Ω a/) + δω ( Ω+ a/)] ic0b + δω ( Ω)[ δω ( Ω b/) + δω ( Ω + b/)] ω Ω Ω Ω -a/ Ω +a/ ω
The general scheme for D NMR t 400 500 f 0 00 400 600 800 000 t pts t 500 600 700 800 900 f pts t f f f pts
The general scheme for D NMR Visualization of D NMR Spectra v v v stacked plot contour plot
The general scheme for D NMR The line shapes in two-dimensional FT spectra For one-dimensional case f ( t) = g Ae ( iω α ) t iω ( ) t A α + i Ω ω ω) = ( ) π e f t dt = π α 0 + ( Ω ω For two-dimensional case ( f( t, t ) = Ae e ( iω α ) t ( iω α ) t ) g ω ω = dt dt e e f t t iω t iωt (, ) (, ) ( π ) 0 0 = Re{ g( ω, ω )} = ( π ) [ α i( Ω ω)][ α i( Ω ω)] A α + i( Ω ω ) α + i( Ω ω ) = ( π) α ( ω ) α ( ω ) + Ω + Ω α α ( Ω ω )( Ω ω ) A [ ( ) )][ ( ) ] α + Ω ω α + Ω ω A mixture of absorption and dispersion. A Re Im
The general scheme for D NMR Basics of D NMR Four periods in D experiments: preparation, evolution, mixing and detection. All D experiments are a simple series of D experiments collected with different timing. The D methods are based on the couplings between nuclear spins. A D frequency correlation map is produced after a Fourier transform in both dimensions (t and t ).
The classes of D NMR experiments I. Two-dimensional J-resolved spectrum: chemical shift is plotted along one of the frequency axes, and coupling constants along the other. II. Two-dimensional correlated spectrum: chemical shift is plotted along both frequency axes. Coherence transfer is accomplished in the mixing period, based on through-bond or through-space couplings. a. shift correlated spectrum b. multi-quantum transition spectrum c. chemical exchange/noe spectrum
The classes of D NMR experiments D J-Resolved NMR spectroscopy BB Rotating frame at Larmor frequency of v c v c (Hα) =v c -/ J CH v c (Hβ) =v c +/ J CH +/J -/J F F v c FT with respect to t gives a series of 3 C spectra, the amplitude depends on t, modulated by J(C,H) FT with respect to t yields two peaks with a separation J(C,H)
The classes of D NMR experiments D COrrelation SpectroscopY(COSY) H,H-COSY -Two-dimensional homonuclear (H,H)-correlated NMR DQFCOSY -Double Quantum Filtered COSY; Cross peaks occur only for spin systems that contain at least two different spins (e.g. AB or AX). HETCOR -HETeronuclear CORrelation ( 3 C- H COSY, carbon detected) Only J couplings are resolved. HMQC -Heteronuclear Multiple Quantum Correlation; H- 3 C, proton detected and, therefore, more sensitive. Cross peaks are usually seen only for protons directly attached to the carbon. HMBC -Heteronuclear Multiple Bond Coherence; Proton detected H- 3 C COSY with long range heteronuclear correlation. Cross peaks of HMQC plus peaks for - 4 J CH. INADEQUATE Incredible Natural Abundance DoublE QUAntum Transfer Experiment.
The classes of D NMR experiments D Heteronuclear Correlated NMR spectroscopy (HETCOR or C,H-COSY) COSY) ω 3C J CH ω H f J CH f ω 3C J CH ω H f ω 3C ω H f f
The classes of D NMR experiments D Homonuclear Correlated NMR spectroscopy (H,H-COSY) v S F β I β S J (Hz) α I β S I S βi α S v I S I α I α S I S v I F v S
The classes of D NMR experiments D D INADEQUATE spectroscopy Evolution in the t period: sin( πjδ)[cos([ Ω sin([ Ω A + Ω B ] t A + Ω ) DQ x ] B ] t ) DQ y I z 90x I sin( πjδ)i sin( πjδ)i x y S x y πjδi zsz S z cos( πjδ) I 90x cos( πjδ) I z y + I x S y + + + + = ( I S I S I S + I S 4i ) When Δ/ is set to /4J IS, the maximum efficiency of Double Quantum transition is achieved.
The classes of D NMR experiments D D Exchange NMR Spectroscopy (D NOESY, EXSY) Transfer of magnetization can also be driven by dipole-dipole coupling, chemical exchange process. The magnetization component transfer during the mixing time t m and dipolar coupled spins will undergo NOE. The D NOESYspectrum will have chemical shifts in f and f. The intensity of the cross peak often quantifies the interaction. The cross peaks are for nuclei that are dipolar coupled. COSY: gives information on through-bond coupling (chemical structure). NOESY: gives information on through-space coupling (stereochemistry and configuration).
Summary of Two-Dimensional techniques Experiment Nuclides observed Types of information and applications Heteronuclear J-resolved 3 C NMR spectroscopy Homonuclear J-resolved H NMR spectroscopy H,H-COSY Long-range COSY H,C-COSY Heteronuclear multiple bond correlations HMBC D-TOCSY NOESY, ROESY EXSY D-INADEQUATE 3 C H H H H/ 3 C H/ 3 C H H H 3 C C,H coupling constant, number of directly bonded hydrogen atoms. Determining δ-values in complicated spectra, idendifying the peaks of a multiplet. Assigning signals in complicated spectra. Assigning signals of protons separated by 4 or more bonds where the coupling are small. Assigning signals in the H and 3 C spectra, starting from known signals. Assigning H and 3 C signals on the basis of J(C,H) and +n J(C,H)-values. Allows one to identify all the protons belonging to a common coupled spin system. Gives evidence for spatial proximity of nuclei. Qualitative evidence of exchange processes. Assigning signals by detecting coupling between adjacent 3 C
References:. Basic one- and two-dimensional NMR spectroscopy, Horst Friebolin. Understanding NMR spectroscopy, James Keeler 3. Principles of Magnetic Resonance, Charles P. Slichter
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