Nuclear shielding tensors

Solid-state high-resolution NMR spectroscopy, combined with quantum chemistry, is able to provide detailed information on the electronic and stereochemical structures of molecules[l]. Quantum-chemical calculations produce three principal values of the nuclear shielding tensor. These principal values have more detailed information about structure of molecules as compared with isotropic chemical shifts. Comparison of the observed chemical shift and chemical shift tensor with the calculated shieldings, produced by quantum-chemical calculations, permits deep insight into the structures of the molecules under investigation. 

The presence of magnetic moments /lia, b, of nuclei A,B,... in a molecule are responsible for the two observables of the NMR experiment that are most frequently utilized in chemical applications. They are physically observed in form of quantized energy differences AE that can be measured very precisely. These two observables are the nuclear shielding tensor cr for nucleus A and the so-called indirect reduced coupling tensor KAB for a pair of nuclei A,B. Both crA and Kab are second-rank tensors that are defined via the phenomenological Hamiltonians... 

The expression for the nuclear shielding tensor a a does not depend on any particular value of ha- Though the spin magnetic moment of the nucleus must not be zero in order for magnetic resonance to occur at all in an experiment, in the theoretical formalism the nuclear shielding can be calculated anyway. In consequence, an explicit expression for <7 depends only on the position of the... 

Table 1-3. Diagonal components, and the corresponding isotropic value, of the nitrogen nuclear shielding tensor in pyrimidine calculated using either DPM or PCM. All calculations are at B3LYP/6-311++G(2d,2p) level. Results are in ppm...

This theory was first formulated by Stephens (1985). In his approach to go beyond the Bom-Oppenheimer approximation, Stephens mixed excited electronic states with the ground state. Though that approach seemed to call for the difficult calculation of excited electronic states, he finally arrived at expressions, that only involve ground state properties. As an example to the application of the theory Jalkanen et al. (1989b) report nuclear shielding tensors, atomic polar and axial tensors, as well as IR and VCD intensities of the ammonia isotopomer N H (NHDT) using different basis sets. 

Some of the nuclear shielding tensors are related to spectroscopic parameters. The static electric shielding can be experimentally obtained via infrared (IR) intensities [12], and the static electromagnetic shielding is available from the intensities of vibrational circular dichroism spectra [16-20]. 

There are different parameters that can provide insights into the hydrogen bond interaction in the solid state. Solid state 13C-NMR studies of protonated and deprotonated carboxylates in amino acids have shown that the values of the principal elements of the nuclear shielding tensor change significantly with the protonation state of the carboxylic groups [54—59]. The orientation of the three CSA tensors for the COOH and COO" groups in a peptide is depicted in Fig. 3.2.21. 

Fig. 22.13. Plots of the observed principal values of nuclear shielding tensor (a) S,i (b)...

There are a number of spectroscopic parameters that can be formulated as the second derivative of the total energy with respect to two perturbations [88]. One such parameter is the nuclear shielding tensor [104]... 

Frequencies and intensities of bands in the IR spectra of 1,2,4-triazines have been calculated by the 4-31G method50 and by ab initio Hartree-Fock level with 6-31G, 6-31G, U-9 and 3-21G methods.51 The shifts for the protons in the parent 1,2,4-triazine have been predicted and are in reasonable agreement with the observed values.52 The shifts of the 13C NMR signals for 3,5,6-trichloro-l, 2,4-triazine have been calculated by the first and second order SCS method and compared with the experimental values.53 The nature of lone pair effects of heteroatoms on direct 13C — H spin coupling constants has been calculated by the AMI method54 and the nuclear shielding tensors of 15N and 1 C nuclei by the SOLO (second-order corrected localized orbital-local origin method) ab initio method.55 14N Shifts have been predicted.75 The electron distribution of 1,2,4-triazines has been estimated from the observed NMR shifts.76... 

A similar procedure yields the one-electron integrals for the GIAO evaluation of the nuclear shielding tensor [3-6]... 

Let us deal with the nuclear shielding tensor. This is a sum of two terms. The diamagnetic term is... 

This expression is free of the gauge origin. The formula for the total nuclear shielding tensor is... 

Direct ab initio calculations of magnetic parameters are usually restricted to the magnetic susceptibility and the nuclear shielding tensors. Only recently have calculations of the g-tensor appeared. 

Both APTs and AATs depend on the wave function derivatives with respect to nuclear displacements the computation of these terms for a molecule in solution has been already treated above. AATs depend also on the derivative of the wave function with respect to an external magnetic field. This derivatives is already known as it enters in the general definition of the nuclear shielding tensors discussed in the previous section. Once again, for its evaluation its possible to exploit the GIAO method. 

In NMR experiments one can only measure the CSs in a limited set of points in space (the nuclei positions r ). However, the induced field and, consequently, the nuclear shielding tensor, are defined and can be computed for aU points in space such that one can drop the index i from Equation 12.4 and calculate the shielding tensor at any arbitrary position r, yielding the so-called nucleus-independent chemical shifts (NICS) [24]. NICS values are, thus, not referenced with respect to any nucleus and that is why they are nucleus independent. Also, and similarly to site-specific shieldings, rather than dealing with the shielding itself, one frequently reports the isotropic NICS shift (5j, j,5) defined as follows ... 

Linear Response (2nd rank tensor) Electric dipole polarizability, a, magnetic dipole susceptibihty, optical rotatory power, k, nuclear shielding tensor at... 

Vaara J, Lotmilla J, Ruud K, Helg er T (1998) Rovibiational effects, temperature dependence, and isotrop effects on the nuclear shielding tensors of water a new 0 absolute shielding scale. J Chem Phys 109 8388-8397... 

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