NMR Computational Spectroscopy

NMR spectroscopy is a technique extremely sensible to the chemical environment of spin-active nuclei, so an exhaustive interpretation of experimental data paves the way for the study of the structure and dynamics of many complex systems difficult to study only with diffractometric techniques such as amorphous solids ( polymers and multi-component inorganic glasses), disordered crystals where particular cations may be distributed in different ways in the sites at their disposition, molecular crystals having a rich polymorphism and biomolecules.

NMR spectra emerge from the transitions between nuclear spin levels. The transition frequencies and intensities can be understood and predicted by inspecting the nuclear spin hamiltonian. This is composed of various terms that accounts for the Zeeman, chemical shift, dipolar and quadrupolar and other interactions.

Some of these interactions are described by anisotropic properties that lead to a very large bandwidth in solid state and thus to a very difficult if not impossible interpretation in some cases. The work of various researchers has led to the development of various techniques that can mediate the various interactions to zero by manipulating the sample like in MAS and DOR experiments or by manipulating both the sample and the spins using different pulse sequences like in DAS and MQMAS experiments for example.

By using these techniques it is possible to achieve high resolution in crystalline materials but very large spectra are still obtained for amorphous solids because of the topological and chemical disorders present.

Two-dimensional experiments have led to considerable progress in the structural resolution but  their interpretation is extremely complicated also because it is necessary to know the correlations between the local structure and the NMR parameters.

Fortunately, several methods have been developed in recent years to calculate NMR parameters from first principles. The first approach used was the cluster approach in which a periodic system is approximated (reduced) to a large molecule. This is therefore a molecular approach widely used by chemists where the shieldings tensor is calculated as a mixed energy derivative with respect to the magnetic field and at the magnetic moment of thenucleous.

The advantages of this method are that it is possible to calculate the NMR parameters at different levels of theory: HF, DFT and post-HF even though these latter methods are very costly from the computational point of view.  Therefore, DFT methods are usually used and one can use all the functionals available from LDA, GGA, hybrids, etc ...

The disadvantages of this approach in the simulation of periodic systems are related to the size of the cluster which must be small enough to reduce the computational cost but big enough to get converged parameters not affected by the size of the cluster.

Care must be taken to terminate the cluster because it is possible to introduce instability in the wave function and moreover it is necessary to account for the long-range electrostatic forces. In addition, when a chemical species is present in inequivalent sites, it is necessary to create a cluster for each site with all the issues described above.

For these reasons, the cluster approach is very good and usable for molecular systems but not for ionic crystals.

In the case of condensed-phase systems, more efficient methods are based on periodic conditions utilizing DFT calculations in the framework of plane-waves and pseudopotentials.

In these methods, the shielding tensor is calculated as a constant of proportionality between applied and induced magnetic field and the latter is calculated by the current density induced by Biot-Savat's law. The induced current is calculated using perturbative theory and the problem of gauge invariance is solved by the GIPAW method developed by Pickard and Mauri in 2001.  The main disadvantage of this method is that so far only the functional PBE can be used.

Several papers have shown that NMR parameters calculated using NMR-GIPAW are in great agreement with the experimental data available. Discrepancies depend on the nucleus studied but are a few ppm.

Often the only calculation of NMR parameters is not enough to interpret experimental spectra or to validate structural models and it is useful to make a direct comparison between the experimental and the theoretical spectrum calculated on the basis of the proposed structural model.

To do this in the last few years we have written (owner and main developer is Alfonso Pedone, contributors: Davide Presti) a computing code that we called SoSNMR that allows, utilizing spin-effective Hamiltonians and the chemical shifts tensors calculated with various quantum computing programs like Gaussian, CASTEP and QE to simulate 1D and 2D solid state spectra for quadrupolar nuclei.

For example, Static Spectra, Variable Angle Spinning, Magic Angle Spinning, between an isotropic dimension and anisotropic, MQMAS and DAS. The SoSNMR code can be downloaded here.

The SoSNMR module has been included in the VMS-Draw graphical user interface developed at the ScuolaNormale of Pisa for the very user-friendly simulation of NMR spectra.

To get the VMSDraw GUI ask to professor Vincenzo Barone.

NMR spectroscopy is very useful in the study of the structure of multi-component oxide glasses that being disordered systems are difficult to investigate with only diffractometric techniques.

To get detailed information on the structure of these systems, together with Dr. Thibault Charpentier we have developed a synergistic, computational-experimental approach schemitized in the following:

The first step consists in synthesis of glass and in the generation of a structural model through  molecular dynamics simulations. On the glass structure, the NMR parameters of the different atomic sites are calculated using DFT calculations, and the NMR spectra of interest are computed through the the SoSNMR (or the fpNMR code developed by Charpentier) that is based on spin-effective Hamiltonians. At the same time from the experimental side NMR spectra are collected and NMR parameters extracted.

Once this information is obtained, a comparison is made between theory and experiment. In this step the experiment is useful to test the theory and the latter is used to interpret the experiment. If the agreement is not good the structural model is refined.

Once a satisfactory agreement is reached, it is possible to study the relationships between NMR parameters and structural parameters using the theory and finally exploit these relationships to obtain information on the real structure of the glass by mapping the parameter distributions obtained from the experiment on structural parameters. This method, developed by Charpentier is called a structural inversion method.

This approach has been used to investigate several glass compositions. Among these we recall aluminosilicateglasses. In the following figures we show the 17O MAS and 3QMAS NMR spectra and the 29Si MAS spectra of a sodium aluminosilicate (NAS), a calcium aluminosilicate (CAS) and a sodium-calcium aluminosilicate (CASN)glasses.

This approach has been also applied to investigate the structure of magnesium silicate hydrate binding phase of Mg-based cements, disordered crystals and molecular crystals.