Paramagnetism in Experimental Biomolecular NMR

Claudio Luchinat, Giacomo Parigi, Enrico Ravera, Claudio Luchinat, Giacomo Parigi, Enrico Ravera

• Publisher: Royal Society of Chemistry
• Year: 2018
• ISBN:
  9781788014960
• Edition: 1
• Topic: Sciences physiques
• Subtopic: Chimie analytique

Paramagnetic NMR is a growing technique that represents an increasingly important tool for the investigation of biomolecules. This book presents an update and overview of the paramagnetic NMR phenomena and effects as well as guidelines for practical implementation of state-of-the-art experiments. All experiments are supported by a solid theoretical foundation. Areas mentioned are the development of solid state NMR, the use of paramagnetic tags providing information on the structure and mobility of the investigated systems, and dynamic nuclear polarization to increase sensitivity.

Compiled by experts in the field, this book has international appeal for researchers as well as students interested in magnetic resonance and structural biology who require experimental support and accessible information.

CHAPTER 1

NMR Consequences of the Nucleus–Electron Spin Interactions

GIACOMO PARIGI^a,b AND CLAUDIO LUCHINAT*^a,b

^a Magnetic Resonance Center (CERM), via L. Sacconi 6, Sesto Fiorentino 50019, Italy;

^b Department of Chemistry “Ugo Schiff”, University of Florence, via della Lastruccia 3, Sesto Fiorentino 50019, Italy
*Email: [email protected]

1.1 The Effect of Paramagnetism on NMR Spectra

The presence of unpaired electrons in molecules makes them paramagnetic and largely affects their NMR spectra. The main effects related to the presence of a paramagnetic center, i.e., of atoms or ions with unpaired electrons, are (see Figure 1.1):¹

(1) the NMR shifts are perturbed, so that the shifts measured for the paramagnetic molecule (δ) and for a diamagnetic analogue (δ^dia) (i.e., for the same molecule without the paramagnetic center or with the paramagnetic metal ion substituted by a diamagnetic one) differ. These differences are called hyperfine shifts (δ^hs):

(1.1)

(2) the nuclear relaxation rates of the paramagnetic molecule (R₁, longitudinal; R₂, transverse) are increased with respect to those of a diamagnetic analogue (R^dia₁ and R^dia₂). This difference is called paramagnetic relaxation enhancement (R_1M and R_2M):

(1.2)

(3) the probabilities for the different orientations of the paramagnetic molecule in a magnetic field are not the same, so a partial self-orientation occurs. This partial self-orientation is responsible for the occurrence of residual dipolar couplings (Δν^rdc), analogously to what happens when partial molecular orientation is driven by external devices. The presence of paramagnetic residual dipolar couplings affects the J-coupling between nuclei:

(1.3)

This chapter deals with the description of these effects, and of their physical origin, which is related to the so-called hyperfine coupling. In eqn (1.1)–(1.3) other minor effects, namely residual anisotropic chemical shifts, cross relaxation terms, and dynamic frequency shifts, respectively, have been neglected (see later).

Figure 1.1 The presence of a paramagnetic center affects NMR shifts (a), relaxation rates (b) and ¹J splitting (c).

1.1.1 The Hyperfine Coupling

The interaction between the magnetic moment associated to a nuclear spin I and the magnetic moment associated to an unpaired electron spin S is called hyperfine coupling and is traditionally described by the Hamiltonian

(1.4)

The energy corresponding to this interaction fluctuates with time (and thus this interaction represents a source of relaxation for the nuclear spin, see Section 1.4) as a result of the molecular motions and of changes in the electron spin state. The other terms describing the contributions to the energy of the system are:

(i) the Zeeman interaction between the applied magnetic field B₀ and the nuclear magnetic moment μ_I=ħγ_II, where ħ is Planck's constant divided by 2π and γ_I is the nuclear magnetogyric ratio,

(ii) the Zeeman interaction between B₀ and an ‘effective’ electron magnetic moment taking into account both the electron spin and the orbital magnetic moments. This is parameterised using the g tensor, with the effective electron magnetic moment given by μ_S=−μ_Bg · S, where μ_B is the electron Bohr magneton. Therefore, the g tensor couples the ‘effective’ electron spin to B₀, thus accounting for the presence of the anisotropic orbital contributions to the electron ma...