Quantum-Chemical Calculations of NMR Parameters

Many approaches ranging from molecular mechanics to electron-correlation second-order Mpller-Plesset (MP2) methods have been used for optimizing the geometry of molecular systems. Here, no attempt is made to cover the technical details of various methods, and the reader is referred to the original literamre for a comprehensive treatment. 

DNA bases can undergo proton shifts while forming various tautomers. Studies of tautomerism in the gas phase can show the relative stabihties of the individual tautomers. However, a bulk solvent and also a microhydrated environment can change the relative stabilities substantially. 

The molecular geometry obtained by experimental methods can be used to calculate the NMR parameters (especially for solid-state smdies). These experimental techniques include diffraction methods (especially X-ray, electron, and neutron). However, specifically in the case of the widely used X-ray diffraction technique, the position of the hydrogen atoms is poorly described and must be corrected or re-optimized before the topology is used to calculate the NMR parameters. The application of the embedded ion method (EIM) as a general approach to efficiently include intermolecular interactions and to optimize the positions of protons has recently been described. 

For optimized or experimentally determined molecular topology, NMR parameters can be calculated at various levels of theory. The tremendous progress in 

The earliest calculations of the chemical-shift tensors for some purine bases employed an IGLO method of the HF type. The general findings agree well with the results obtained recently by a combination of experimental solid-state measurements and GIAO calculations.  

---

In section VII, the value of a combined experimental and theoretical approach, incorporating the ab initio calculation of H chemical shifts, was illustrated. First, in section VIIB, it was stated that the calculation of H chemical shifts for model HBC oligomers allowed the quantitative assignment of the experimental observation of three aromatic resonances in HBC—C12 to a specific packing arrangement. Moreover, in section VIIC, the ability to identify the importance of intra- and intercomplex interactions as well as the role of the separate aromatic moieties was discussed. The advances in computing power as well as the development of methodology means that the use of quantum chemical calculations of NMR parameters in the interpretation of experimental results will become ever more popular. 

Exner and coworkers have used Af-methyl acetamide (NMA) as a test system for amide groups in protein backbones to calculate NMR chemical shifts with the Car-Parrinello MD method with explicit solvent molecules and quantum-chemical calculations of NMR parameters and compare with classical MD simulations. For example the C-P calculations give in general shorter solute-solvent H-bonds which in turn give a... 

Also, recent developments in quantum theoretical calculations of NMR parameters have increased their reliability and usefulness, especially in studying the dynamic processes such as conformational equilibria and tautomerism of aniline derivatives. All the above-mentioned items will be included in the following discussion. However, owing to the huge amount of data about H NMR parameters, the main focus of this review is directed to 13C, 15N and 19F NMR spectral studies of aniline derivatives. Schiff bases are not included in this review although some of them show an amino-imino tautomerism and can thus be considered as anilines. One reason for this is that a search in Chemical Abstracts using key words schiff base and nmr produced more than 1000 hits. 

Recent developments in the quantum chemical treatment of NMR parameters include successful approaches to the calculation of indirect nuclear spin-spin coupling constants. 121,133 includes "/( Si,X) values, at least for nuclei X = H, B,... 

The MS2 (M = Zr, Ti, W, Mo and Ta) was studied by Ti, Zr and Mo solid-state NMR spectroscopies and quantum chemical calculations. The NMR parameters obtained were shown to be sensitive to local geometric and electronic environments. Metal NMR shielding and EFG tensors were examined by quantum-chemical calculations for Ti(iv) complexes and the Ti shielding constants and EFG tensors for a variety of olefin (co)polymerisation catalysts were analysed. A specific dependence of the Ti EFG tensors on the exact arrangement and type of surrounding bonds was also demonstrated. 

The general theory of the quantum mechanical treatment of magnetic properties is far beyond the scope of this book. For details of the fundamental theory as well as on many technical aspects regarding the calculation of NMR parameters in the context of various quantum chemical techniques we refer the interested reader to the clear and competent discussion in the recent review by Helgaker, Jaszunski, and Ruud, 1999. These authors focus mainly on the Hartree-Fock and related correlated methods but briefly touch also on density functional theory. A more introductory exposition of the general aspects can be found in standard text books such as McWeeny, 1992, or Atkins and Friedman, 1997. As mentioned above we will in the following provide just a very general overview of this... 

In this article, we will concentrate on NMR chemical shifts, for which the inportance of spin-free (scalar) relativistic (SFR) and spin-orbit (SO) contributions needs to be better appreciated. Reviews of relativistic calculations of spin-spin coupling constants are available [6,7]. Articles on conten jorary quantum chemical calculations of electronic g-tensors have been published elsewhere [5,8]. Other EPR parameters like zero-field splittings and hyperfine coupling constants are also strongly affected by relativity and are covered. 

Marek et al. have reviewed applications of NMR spectroscopy in the investigation of the structure and the intra- and intermolecular interactions of purine derivatives. NMR methods suitable for studying the purine structure and their application to exploring samples at natural levels of the C and N isotopes using CP MAS were briefly reviewed. In addition, quantum-chemical calculations of the NMR parameters on the DFT level have also been considered. Typical examples of applications were also presented. 

Advances in computing, particularly since 2000, have rendered ah initio quantum chemical calculations extremely useful for understanding the origins and orientations of Zr EFG and CS tensors with respect to the molecular-level structure. Both hybrid DFT and plane-wave DFT calculations have also shown to be well suited for Zr NMR parameter calculations. Rossini et al. showed that metrical parameters such as Zr-ligand distance were important for accurate calculation of NMR parameters [46] a comparison of calculated and measured Zr NMR parameters has also been used to detect inaccuracies in reported crystal structures [36,46,75]. Several criteria were introduced and expanded upon to relate local Zr structural variation to changes in the measured NMR parameters for >6-coordinate Zr complexes these criteria were verified via observed and/or calculated NMR parameters [36,46,55,64]. From these reports, it is clear that even subde distortions in the first coordination sphere of Zr may lead to major differences in reported NMR parameters, while the second and third coordination spheres of Zr also play a role. The appfications of Zr SSNMR have rapidly increased with the passage of time. 

With the advances in experimental solid-state NMR and computational resources (both software and computing power), it is now possible to use both the experimental and computational results (sometimes in a complementary way) to study biologically important macromolecules such as proteins. The quantum-chemical computation (particularly by density functional theory) of NMR parameters in solids has found important application in protein structure determination.30-36 Tesche and Haeberlen37 calculated the proton chemical shift tensor of the methyl groups in dimethyl terephthalate and found the theoretical results were in good agreement with the multiple pulse experiment. 

In this section, the focus is on the analysis of solid-state 170 NMR spectra (CS and EFG tensors) by using a few concrete examples of 170-enriched amino acids. In general, three steps are required in order to obtain information on 170 EFG and CS tensors from the experimental data (1) MAS type experiments are first carried out, and the experimental parameters of <5iso, Cq and r q are extracted (2) The stationary NMR spectra are analysed with the aid of the previous MAS results, so that the 170 CS tensor components can be obtained (3) The results of quantum chemical calculations are used to produce absolute 170 NMR tensor orientations with respect to the molecular frame. In the following, each step is explained. 

Experimental techniques for the measurement of Si nmr spectra (mainly for solutions) are briefly discussed, followed from considerations of the nuclear-spin relaxation mechanisms with emphasis on the Si nucleus. Chemical shifts 5 Si and indirect nuclear spin-spin coupling constants j( Si,x), the most prominent nmr parameters, are discussed in more detail The increasing reliability of quantum chemical methods for the calculation of these parameters is pointed out. The relationship between the electronic structure and the nmr parameters b Si and j( Si,x) is indicated... 

---