The Intermolecular NOE Depends on Isotope Selection: Short Range vs Long Range Behavior

The nuclear Overhauser effect (NOE) is a powerful tool in molecular structure elucidation, combining the subtle chemical shift of NMR and three-dimensional information independent of chemical connectivity. Its usage for intermolecular studies, however, is fundamentally limited by an unspecific long-ranged interaction behavior. This joint experimental and computational work shows that proper selection of interacting isotopes can overcome these limitations: Isotopes with strongly differing gyromagnetic ratios give rise to short-ranged intermolecular NOEs. In this light, existing NOE experiments need to be re-evaluated and future ones can be designed accordingly. Thus, a new chapter on intermolecular structure elucidation is opened.


Theory
The nuclear Overhauser effect describes a magnetization transfer between two different nuclei with spins I and S via a dipole-coupled mechanism. Its dynamics can be described by the first-order differential equations, 1 a special case of Redfields relaxation theory 2 where I z and S z represent the longitudinal magnetization of spins I and S. The structural information of the system studied is contained in the self-and cross-relaxation rates ρ and σ modulating the transfer rate, sometimes referred to as the 'lattice' or, more descriptively, 'chemical environment'. These relaxation rates can be measured experimentally. They depend on the spectrometer frequency ν and the isotopespecific Larmor frequencies ν I = ν · γ I and ν S = ν · γ S : where σ NOESY L and σ ROESY R refer to the laboratory-and the rotation frame cross relaxation rate. J(ν) is the spectral density function (SDF) which contains the information of the dipole-coupled system. It can be obtained via real-part Fourier transform as with ρ IS as the number density of particles in a volume and g IS (r IS ) as the radial pair distribution function (RDF) of spins I and S. In essence, this is analogous to the calculation of a coordination number, but weighed by a decay term 1/r 6 . From this, we can infer that the SDF at ν = 0 is the product of the amplitude G IS (0) (structural information) and the relaxation time τ IS (dynamics information): Experimentally, we have neither access to the TCF amplitude G(0) nor the zero-frequency SDF J(0). Instead, spectrometer frequency ν (e.g. 500 MHz for 1 H) determines the part of the SDF J(ν) and of the correlation function G(t) obtainable by experiment, inherently influenced by the dynamics of the sample.
The range for the mixing time was 20 ms -4 s for 1 H-19 F experiments and 50 ms -6 s for the 1 H-7 Li experiments. All HOESY data sets were processed by applying a sine squared window function in both dimensions (SSB = 2) and zero-filling to 2048 (t 2 ) × 512 (t 1 ) prior to the Fourier transform. The cross-peak integrals were measured using the Bruker software.
For a semi-quantitative interpretation of the data, the peak volume of each cross-peak has been corrected by dividing the original integral by a correction factor taking into account the contribution of the number of spins, N I N S /(N I + N S ), with N I the equivalent spins I ( 1 H) and N S the equivalent spin S ( 19 F or 7 Li). 6-12

Molecules and force field
In contrast to our preceding IL-NOE study, 4 the molecules (C 2 MIm + , Li + and OTf − ) are modeled as fully atomistic to accurately represent the internuclear distances of spin-bearing The non-hydrogen atoms and their attached Drude particle form an atomic dipole and account for induced dipole-induced dipole attraction. Hence the Lennard-Jones attraction of the polarizable atoms had to be reduced. We used a λ-scaling correction introduced by Vlugt et al. 20 and chose a scaling factor of λ = 0.4 in accordance to previous C 2 MIm + -based IL MD studies which accurately reproduced experimental dielectric spectra 16 and NMR field cycling dispersion curves. 21 Similar scaling approaches are reported by Pádua and co-workers. 22

Equilibration and simulation
All subsequent fully atomistic, polarizable MD simulations were carried out with CHARMM. 23 The system comprises 900 molecules of C 2 MIm + , 100 ions of Li + and 1000 molecules of OTf − .
The initial intermolecular geometry of the simulation box was generated using PACK-MOL 24 followed by energy minimization via 1000 steps of a steepest-descent algorithm. The system was then equilibrated as an isothermal-isobaric N pT ensemble (T = 300K, p = 1 atm) with periodic boundary conditions until the simulation box length converged to its equilibrium extent.
The trajectory was produced as an isothermal-isochoric N V T ensemble with periodic boundary conditions and a dual Nose-Hoover thermostat 25,26 to keep the temperature of the atoms at 300 K and the temperature of the Drude particles at 1 K. The SHAKE algorithm was applied to covalent bonds involving hydrogen atoms to constrain high-frequency vibrations.
This allowed for a time step of 0.5 fs, a write frequency of 50 fs, and a total trajectory length of 20 ns. Electrostatic interactions were calculated using the Particle-Mesh Ewald method 27,28 with conducting boundary conditions (κ = 0.41 Å −1 ).

Post-production analysis
The spectral features of the simulation were calculated using a Python3 program introduced in ref. 21. The CHARMM trajectory was read into the program with the MDAnalysis module. 29,30 The first 5000 ps of the trajectory were discarded to exclude possible slow equilibration artifacts.
The trajectory was unfolded to remove toroidal coordinate jumps and allow for the nat- The RDFs g(r) were obtained by MDAnalysis based python scripts. Their respective decomposition into first, second and bulk solvation shell (see Fig. 1) was done by Voronoi tesselation which was performed using the Voro++ library. 31

Structure
The RDF between two particle sets is defined as: with N i and N j as the particle counts, ρ j = N j /V as the number density and δ as the Dirac delta function. Fig. 1 presents the RDF g(r ij ) of all C 2 MIm + -Li and C 2 MIm + -F pairs, further divided into shells via Voronoi tesselation, 32 a purely geometrical, parameter-free procedure. [33][34][35] The first shell, often referred to as the contact shell, is of particular interest to the structure. The second shell is characterized by the transition to the bulk formed by the third and subsequent shells. Voronoi tesselation is a more reliable descriptor of particle neighborhood for anisotropic molecules than radial shells. 36     (r, ν) of the C 2 MIm + -F spin pairs (left-hand side) and the C 2 MIm + -Li spin pairs (right-hand side). Note that σ L converges faster for 1 H-7 Li spin pairs than 1 H-19 F spin pairs.