Parametri NMR: Chemical shift

Mario PiccioliMagnetic Resonance Center

CERMDepartment of Chemistry

University of Florence, Italy

Ringraziamenti

M.Levitt Spin DynamicsJ. Keeler Understanding NMR Spectroscopy

H.Gunther NMR Spectroscopy

Stefano MammiStefano ChimichiAlessandro BagnoDaniel CiceroPaola Turano

Different Isotopes Absorb at Different Frequencies

low frequency high frequency

15N 2H 13C 19F 1H

50 MHz 77 MHz 125 MHz 200 MHz 470 MHz 500 MHz

31P

Resonance Frequencies Depends on Magnetic Field

low field high field

1H

200 MHz 400 MHz 600 MHz 700 MHz 800 MHz 950 MHz

1H 1H 1H 1H 1H

Rapporto giromagneticoE= = −−−− ħ γ γ γ γ m B ∆E= = ħ γ γ γ γ B

La separazione in energia dipende dal valore del rapporto giromagnetico

La frequenza di precessione di un determinato nucleo ad un determinato campo magnetico è detta FREQUENZA DI PRECESSIONE DI LARMOR

Frequenza di precessione

ν0 = - γ B0 /2π

Se cosi fosse, ogni nucleo attivo entrerebbe in risonanza con il campo esterno alla sua frequenza e tutti gli isotopi uguali si comporterebbero allo stesso modo (un unico segnale).

Es: al campo magnetico di 11.7 T, La FREQUENZA DI PRECESSIONE DI LARMOR del nuclide 1H è 500 MHz.

La costante di schermo

ν= γ/2π Β0 (1−σ)Dipende dall’intorno elettronico

Campi magnetici elevati determinano un aumento della risoluzione e della sensibilità

Chemical shift

(ν−νref/νref)∗106 = δ (ppm)

Es: ω1= 500.131 MHzω0=500.13 MHz

ω1-ω0=1000 Hz

δ= 1000/500.13x106

δ(ppm)= 2.0

TMS (Tetramethylsilane)

chemical shift δ

Si

CH3

CH3CH3

CH3

δ = 0

Un po’ di Storia…..

ν= γ/2π Β0 (1−σ)

Upfield Downfield

Spettro 1H NMR di Vanillina

750 MHz 1H NMR Spettro di Tyrosine Kinase

1H NMR Spettro di vari solventi

13C NMR del Fullerene (C60)

1H Chemical Shift Table

σtot= σlocal + σmagn+ σrc + σel + σsolvPople, 1960

Fattori che influenzano il chemical shift

Caratteristiche funzionaliEffetti induttiviEffetti mesomeri

Effetti attraverso lo spazioEffetti paramagnetici

Effetti induttivi

Effetto della Sostituzione sul Chemical Shift

CHCl3 CH2Cl2 CH3Cl 7.26 5.32 3.05 ppm

-CH2-Br -CH2-CH2Br -CH2-CH2CH2Br 3.30 1.69 1.25 ppm

Shoolery Equation

Il chemical shift dipende dalla sommatoria degli effetti di tutti I sostituenti

Effetti Mesomeri

Effetti Mesomeri

ortho +0.64 meta +0.09 para +0.30

ortho -0.50 meta -0.14 para -0.40

Competizione traeffetto mesomero ed effetto induttivo

3.74

3.93

Effetto dei sostituenti

Composti olefinici

Fattori che influenzano il chemical shift

Caratteristiche funzionaliEffetti attraverso lo spazioCorrenti d’anello Anisotropia magneticaEffetti sterici

Effetti paramagnetici∆δ= ∆δel +∆δanis+∆δst

Correnti d’anello

Correnti d’anello

Modelling 1H NMR Spectra of Organic Compounds: Theory, Applications and NMR prediction Software Di Raymond Abraham,Mehdi Mobli

Pople -Dipole model

0.42

Anisotropia di schermo indotta dai legami chimici

Anisotropia

Equazione di Mc Connell

∆χ C-H 90

∆χ C-C 140

∆χ C≡C -340

x 1036 m-3mol-1

∆χ = χ|| −χ ⊥

∆σ = ∆χ (1−3cos2θ)/12πR3

∆δ (Heq-Hax)= ca. 0.50 ppm

Ibridizzazione vs Anisotropia

C2H6C2H4C2H2

sp3sp2sp

C2H6C2H4 C2H2

sp3sp2 sp

0.88 ppm1.48 ppm5.29 ppm

Effetti Long range∆δ= ∆δsterico+∆δel+∆δanisotropia

sterico

X=OH0.46

-0.20

0.510.16

elettrico

L’effetto di F- non puo’ essere sterico perché F- ha raggio ionico simile a 1H. E’ un effetto dovuto al campo elettrico perturbato da F-

Effetti sterici vs Effetti induttivi

La sostituzione dell’alogeno va in senso opposto all’effetto induttivo

CH3 CH2 X

Legami a idrogeno

CH3OH

5.34 ppm

CH3OHDiluito in CDCl3

1.1 ppm

C6H5OH C6H5OHDiluito in CDCl3

7.45 ppm 4.60 ppm

12.1 ppm

pH dipendenza

Catena polipeptidica

Water

Benzene(d6) 0.5

CCl4 1.1CDCl3 1.5THF 2.5

Ac(d6) 2.8DMSO 3.3H2O 4.7

EtOD 5.3Pyr(d5) 5.0

Solvent Shift (ppm)

CH3

HγHβHα (helices)Hα (sheets)

H2O

aromatic

NH sidechains

NH backbone

The amount of shielding the nucleus experiences will vary with the density of the surrounding electron cloud

If a 1H nucleus is bound to a more electronegative atome.g. N or O as opposed to C, the density of the electron cloud will be lower and it will be less shielded or “deshielded”. These considerations extend beyond what is directly bonded to the H atom as well.

Simple shielding effects--electronegativity

N

H

C

H

more electronwithdrawing--less shielded

less electronwithdrawing--more shielded

less shieldedhigher resonance frequency

more shieldedlower resonance frequency

amides (HN) aliphatic/alpha/beta etc.(HC)

most HN nuclei come between 6-11 ppm while mostHC nuclei come between -1 and 6 ppm.

Simple shielding effects-electronegativity

One consequence of these effects is that aromatic protons, which are attached to aromatic rings, are deshielded relative to other HC protons. In fact, aromatic ring protons overlap with the amide (HN) region.

aromatic region (6-8 ppm)

amide region (7-10 ppm)

More complex shielding effects:Aromatic protons

Questo lo hai già visto nella descrizione delle molecole organiche

Example: shielding by aromatic side chains in folded proteins

Picture shows the side chain packing in the hydrophobic core of a protein--the side chains are packed in a very specificmanner, somewhat like a jigsaw puzzle

a consequence of this packing is that some protons may be positioned within the shielding cone of an aromatic ring such as Phe 51. Such protons will exhibit unusually low resonance frequencies (see picture at left). Note that such effects depend upon precise positioning of side chains within folded proteins

++

shielded methylgroup

methyl regionof protein spectrum

It should now be apparent to you that different types of proton ina protein will resonate at different frequencies based on simple chemical considerations. For instance, Hα protons will resonate in a region centered around the relatively high shift of 4.4 ppm, based on the fact that they are adjacent to a carbonyl and an amine group, both of which withdraw electron density. But not all Hα protons resonate at 4.4 ppm: They are dispersed as low as ~3 and as high as ~5.5. Why?

“Hα region”

“Average” or “random coil” chemical shifts in protein s

“Average” or “random coil” chemical shifts in protein s

One reason for this dispersion is that the side chains of the 20 aminoacids are different, and these differences will have some effect on the Hα shift.

The table at right shows “typical” values observed for different protons in the 20 amino acids. These were measured in unstructured peptides to mimic the environment experienced by the proton averaged over essentially all possible conformations. These are sometimes called “random coil” shift values.

Note that the Hα shifts range from ~4-4.8, but Hα shifts in proteins range from ~3 to 5.5. So this cannot entirely explain the observed dispersion.

Regions of the 1H NMR Spectrumare Further Dispersed by the 3D Fold

What would the unfo lded prote in look like?

Regions of the 1H NMR Spectrum are Further Dispersed by the 3D Fold

A simple reason for the increased shift dispersion is that the environment experienced by 1H nuclei in a folded protein (B) is not the same as in a unfolded, extended protein or “random coil” (A).

shift of particular proton in foldedprotein influenced by groups nearby in space, conformation of the backbone, etc. Not averaged among many structures because there is only one folded structure.

So, some protons in folded proteins will experience very particular environments and will stray far from the average.

shift of particular proton in unfolded protein is averaged over many fluctuating structures

will be nearrandom coilvalue

“Average” or “random coil” chemical shifts in protein s

Linewidths in 1D spectra: aggregation andconformational flexibility

Linewidths get broader with larger particle size, due to faster transverse relaxation rates. We’ll learn the physical basis for the faster relaxation later. Broader than expected linewidths can indicate that the protein is aggregated. It can also indicate that the protein has conformational flexibility, i.e. that its structure is fluctuating between several slightly different forms. We’ll learn why this is when we cover the effect of protein dynamics on NMR spectra. Conformational flexibility also tends to reduce dispersion by averaging the environment experienced by a nucleus.

poorlydispersed amides

poorlydispersed aromatics

poorlydispersed alphas

poorlydispersed methyls

very shielded methyl

unfoldedubiquitin

foldedubiquitin

You can tell if your protein is folded or not by lo oking at the 1D spectrum...

An example of analyzing linewidths and dispersion:

Hill & DeGrado used measurements of chemical shift dispersion and line broadening in the methyl region of 1D spectra to gauge the effect of mutations at position 7 on the conformational flexibility of α2D protein

leucine and valine mutants have poordispersion and broad lines, despite being very stably foldedand not aggregated (circular dichroism and analytical ultra-centrifugation measurements). These mutants are folded but flexible.

Hill & DeGrado (2000) Structure 8: 471-9.

13C NMR

The rules discussed for 1H spins, (shielding and deshielding effects) hold also for 13C spins.

Some general features of 13C should be pointed out:

Unlike 1H atoms, 13C atoms may form a different number and type of chemical bonds. Therefore, the so calle d paramagnetic contributions (see later) are much mor e effective for deshielding. The chemical shift range of 13C spins spans more than 200 ppm

Range of observed shifts for 13C

A protein 13C NMR spectrum (low resolution)

Backbone CO and side chain COO- signals

Aromatic signals

Aliphatic

13C NMR

The rules discussed for 1H spins, (shielding and deshielding effects) hold also for 13C spins.

Some general features of 13C should be pointed out:

The amino acid dependence of chemical shift values is stronger for 13C atoms than in 1H atoms. Therefore, each amino acid has an almost u nique

pattern of 13C chemical shifts

13C chemical shifts are residue-specific

13C NMR and Secondary Structure

The chemical shift from secondary structure can be used to get the secondary structure arrangement directly from 13C shifts of Ca, Cb and C’ spins

Fig. 1. Simulated 13C chemical-shift distribution of (a) Ala and (b) Met. (•) Strand; ( ) coil; ( ) helix.

13C

Use of chemical shifts as source of structural information

•CSI

•Molecular fragement replacement (3 to 9 aa)

BMRB – Biological Magnetic Resonance Bank

A Repository for Data from NMR Spectroscopy on Proteins, Peptides,

Nucleic Acids, and other Biomolecules

http://www.bmrb.wisc.edu/

BMRB – Biological Magnetic Resonance Bank

A Repository for Data from NMR Spectroscopy on Proteins, Peptides,

Nucleic Acids, and other Biomolecules

http://www.bmrb.wisc.edu/

HH HeHe

LiLi BeBe BB CC NN OO FF NeNe

NaNa MgMg AlAl SiSi PP SS ClCl ArAr

KK CaCa ScSc TiTi VV CrCr MnMn FeFe CoCo NiNi CuCu ZnZn GaGa GeGe AsAs SeSe BrBr KrKr

RbRb SrSr YY ZrZr NbNb MoMo TcTc RuRu RhRh PdPd AgAg CdCd InIn SnSn SbSb TeTe II XeXe

CsCs BaBa LuLu HfHf TaTa WW ReRe OsOs IrIr PtPt AuAu HgHg TlTl PbPb BiBi PoPo AtAt RnRn

The NMR periodic table

Common

Fairly common

Rarely studied

Difficult or unfavorable chemistry, rarely studied

Very difficult or unfavorable chemistry, hardly studied

Quadrupolar nuclei I ≥ 1

Relevant Properties of NMR-Active Nuclei

Only the natural abundance can be changed

•Nuclear spin quantum number I•Magnetogyric ratio γ•Nuclear quadrupole moment Q (if I > 1/2)•Natural abundance

Sensitivity ∝ γ3

Proton NMR vs. Heteronuclear MR

Very small chemical shift range (< 12 ppm)

Line widths: < 0.5 Hz

Relaxation time: 1-5 s

A single set of acquisition parameters will suffice for

most purposes

Wide chemical shift range (up to 10000 ppm)

Line widths: 0.5 Hz – 104 Hz

Relaxation time: 0.1 ms - 102 s

Acquisition parameters have to be tailored to the system

An estimate of chemical shift range, T1 or line width is generally essential

NMR of transition metal nucleiTransition metal nuclei with natural abundance below 5% that may be usefully studied with enrichment are 57Fe (I=1/2), 61Ni =(I=3/2), 67Zn (I=5/2) and 187Os (I=1/2).

Another severe hindrance to the development of transition metal NMR spectroscopy is caused by the fact that some nuclei in specific oxidation states, such as high spin Fe(II), Fe(III), Co(II), Ni(II), Cu(II) and Ru(III), are paramagnetic.

Paramagnetic compounds contain unpaired electrons, and the unpaired electron density has a drastic effect on both the chemical shift and the linewidths of signals in the NMR spectra of molecules containing one or more paramagnetic transition metals.

Unusual I=1/2 nuclei

NMR PARAMETERS• 57Fe chemical shifts cover a range of 9000 ppm

myoglobin derivatives (+7200/+8200ppm).

57Fe NMR spectroscopy has limited application due to its very low sensitivity

199Hg

Utschig, Bryson, O’Halloran, Science 1995

MeR 3coord

MeR+DNA 3coord

Gal4 Zinc finger 4coord

MeR Mercuric ion Receptor

Hg2+ substituted Plastocyanin

Quadrupoles

Quadrupolar nuclei

Quadrupolar nuclides account for nearly 75% of the stable magnetic nuclides in the periodic table

BUT

due to sensitivity and resolution problems, the NMR of quadrupolar nuclei is not so widely explored as for I=1/2 nuclei.

The most characterized is 2H.

Quadrupolar nuclei

The effect of shape and size of the molecule can be demonstrated with 14N-NMR.

NH4+ is small and highly

symmetric yielding a line-width of 0.8 Hz

NH3 is also small but asymmetric giving a line-width of 16 Hz

Urea is larger and even less symmetric yielding a line-width of 982 Hz.

For a given nucleus, line-widths are minimized for smallmolecules in low-viscosity samples (τc small), with highly symmetrical environments of the metal nucleus (q small).

Quadrupolar nuclei

In the liquid phase, rapid and isotropic molecular tumbling averages the quadrupolar (as well as the dipolar) interactions.But the relaxation of the electric quadrupole with fluctuations of the electric field gradient (e.g. in molecular collisions) relaxes the nuclear spin as well, and fast relaxation leads to quadrupolar broadening.

The quadrupolar relaxation rate and the line-width are proportional to the square of the the asymmetry parameter of the electric field gradient, and also to the rotational correlation time for isotropic tumbling.

The NMR signals of quadrupolar nuclei are usually broader than those of spin-½ nuclei due to rapid quadrupolar relaxation.

Exchange process:a dynamic process that exposes a nucleus to at least two distinct chemical environments

Two-site exchange

kex=∆ω/23/2=∆νπ/21/2

kex=2.21 ∆ν

Equal population of exchange sites

Exchange process:a dynamic process that exposes a nucleus to at least two distinct chemical environments

Two-site exchange

δobs= fAδA + fBδB = 0.75 δA + 0.25 δB

Ix ∝ Px

kex=∆ω/23/2=∆νπ/21/2

kex=2.21 ∆ν

Unequal population of exchange sites

The exchange regime is determined by the chemical shift separation (in Hz).

Can be modulated by T(affecting kex)and B0 (affecting ∆ν) .

Factors Affecting Chemical Exchange Rates

Special case:ligand binding to a protein

Reaction scheme:

The exchanging sites are the free (P) and the complexed form (PL) of the protein.

The exchange rate is given by:

Line shapes simulated for the one-step binding mechanism for increasing populations of the complex (from blue to red).

∆ν = 250 Hzkex = 2000 Hz.

kex = koff

Slow exchange

If the exchange rate is << R2, then the exchange event has little or no effect on the linewidth.

But, if the exchange rate is > R1 it may be possible to measure the rate constants by detecting the exchange of magnetization between the nuclei in the two environments.

EXchange SpectroscopY (EXSY), also known as the zz-exchange experiment.τex≈10–5000 ms; k ex ≈0.2−100 s-1

Fe(III)Cytc + Fe(II)Cytc Fe(II)Cytc + Fe(III)Cytc

Electron self exchange rate

EXSY experiments(a)

(b)

(c)

Here τm is the mixing time!!!

heteronulcear

Slow exchange with respect to the chemical shift time scale, but fast with respect to T1

Zeeman interaction with the static magnetic field B 0

This interaction is modified by the chemical shielding.

Generally the chemical shit is weak with respect to B0, which is parallel to the z-axis.

The interaction with the radiofrequency field has the same form as the Zeeman interaction.

Internal spin Hamiltonian-1

Indirect magnetic interaction of the external magnetic field with the nuclear spinsThrough the involvement of electrons

Free Rotation in Solution

If rotational averaging of the spin Hamiltonian is taken into account,

where the nuclear shielding constants M is associated with the corresponding tensor

Shielding tensor

Physical application of a magnetic field to a molecule produces a shielding field at each nucleus which is due to the diamagnetic current of the electrons and which is proportional to the external field.

The shielding field of the electrons can be either in the same or in the opposite direction of the external field .

The shielding constant σA of a nucleus A consists of a diamagnetic (opposed to the magnetic field) and a second-order paramagnetic (paralel to the magnetic field) part:

σA = σd + σp

Shielding in molecules

In molecules, the circulation of electronic currents around the target nucleus is hindered due to the presence of other nuclei and electrons revolving about them and this deviation from the spherical symmetry leads to emergence of an additional contribution to the total nuclear shielding,

which is known as the paramagnetic term, σp,A.

Because the paramagnetic contribution opposes the diamagnetic shielding, this results in deshielding (an increase in the resonance frequency) of the target nucleus as compared to an isolated atom. The paramagnetic term involves the mixing between ground and excited states of the molecule due to the magnetic field, and it is rather sensitive to the molecular electronic structure.

Diamagnetic and paramagnetic terms

The diamagnetic shielding, which depends only on the electronic ground state of the molecule, described the behavior of the innermost electron density distribution.

The paramagnetic term arises from the perturbation of the ground state wave function due to the coupling between the electronic orbital momentum and the external magnetic field.

Diamagnetic and paramagnetic terms

While 1H chemical shift is usually dominated by diamagnetic contributions, heavy nuclei (13C, 19F, 31P, for example) are severely affected by the paramagnetic contributions.

Approximately, the paramagnetic term is given by

Carbon chemical shifts depend on the hybridization of the 13C atom

With the availability of powerful workstations, it is now customary for NMR laboratories to have the capability of calculating NMR chemical shifts. The methods currently employed are ab initio (from first principles) Hartree-Fock or density functional calculations. One first solves the electronic Schroedinger equation in the absence of a magnetic field.

The density matrix is then allowed to change with the application of a magnetic moment and a static external magnetic field.

The zero order and first order density matrices are then used to give the diamagnetic and paramagnetic terms, respectively.

Ab Initio Calculations

In quantum mechanics, the quantity that is normally encountered is NMR shielding. This quantity is directly related to NMR chemical shifts.

The shielding is defined as the mixed second derivative of the energy with respect to magnetic moment of the nucleus and the strength of the applied magnetic field.

It is solved through second-order perturbation theory with the Zeeman Hamiltonian treated as a perturbing term.

The first-order contribution is called diamagnetic while the second-order (which requires knowledge of excited electronic states) is termed paramagnetic.

Nuclear Magnetic Shielding

The quality of these calculations depend on the lev el of theory employed, the basis set used and the quality of the structure of the molecule.

Gaussians are normally employed as basis functions to fit the electronic orbitals in a molecule.

The quality of the results depend on the number of Gaussians employed.

Calculation times, however, increase dramatically w ith the number of Gaussians.

These ab initio packages also require that the molecular geometry be specified.

Ab Initio Calculations

The s term is the short range contribution (dependencies upon bond lenghts,bond angles, torsion angles, short H-bonds, …); it is calculated ab initio. One need take into account only the local geometry, so that only a small number of atoms require basis functions.

The l term is a long range electrostatic. In proteins it’s a perturbation derived from multipoles in the vicinity of the nucleus of interest. Partial atomic charges can be used to replect the protein’s electrostatic field in SCF calculations.

The o term derives from ring current and magnetic anisotropy contributions such as those arising from aromatic rings and carbonyl groups. They are considerent only for protons using classical theory

Ab Initio Calculations