NMR shielding tensor calculations

The combination of the SOS-DFPT and IGLO approaches leads to the following working equations for the shielding tensor calculations. 

The original paper concerning SOS-DFPT [28] contains a description of the theory and a wide range of applications to different types of systems. In this Chapter we will include the most illustrative material. Here we will present the comparison between Zero-order and Loc.l approximations, and experimental data discuss the influence of the choice of the exchange-correlational functional on the results of the chemical shift calculations and compare our SOS-DFPT results with the results of HF and post-HF approaches for cyclic organic compounds and for the ozone molecule. 

A comparison between shielding constants calculated using Zero order and Loc.l approximations (basis set IGLO-III and PW91 exchange-correlation potential) versus their experimental counterparts is presented visually in Fig. 1. 

Influence of the exchange-correlation functional on the results of the shielding constant calculations (IGLO-III Loci) for non-hydrogen nuclei. All values are in ppm. 

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NMR shielding tensors calculated using Hartree-Fock method the 6-... 

J. Autschbach. Analyzing NMR shielding tensors calculated with two-component relativistic methods using spin-free localized molecular orbitals. /. Chem. Phys., 128 (2008) 164112. 

Certain physical properties, such as NMR shielding tensor calculations directly involve the nuclear cusp and correct treatment of radial nodes, which indicates that basis sets such as Coulomb Sturmians are better suited to their evaluation than gaussians [4,16,33]. 

Since HF calculations have a tendency to underestimate the N—N and the C—N bond lengths in triazoles [98JPC(A)620, 98JPC(A) 10348], the structural parameters should be computed at least at the DFT or MP2 levels. This is particularly true if electron-donating substituents are attached to the ring. Nitrogen NMR shielding tensors were computed for a set of methylated triazoles and tetrazoles but will be discussed in the context of tetrazoles (cf. Section IV,B). 

Schreckenbach, G., Ziegler, T., 1997a, Calculation of NMR Shielding Tensors Based on Density Functional Theory and a Scalar Relativistic Pauli-Type Hamiltonian. Application to Transition Metal Complexes , Int. J. 

A more complete list of early applications of QM/MM methods to enzymatic reactions can be found elsewhere [18, 35, 83, 84], Gao [85] has reviewed QM/MM studies of a variety of solution phenomena. QM/MM methods have also been used to study the spectra of small molecules in different solvents [86] and electrochemical properties of photosynthetic reaction centers within a protein environment [87-89], An approach has also been developed for calculation of NMR shielding tensors by use of a QM/ MM method [90]. 

The calculation of NMR shielding tensors based on DFT and the GIAO approach has been implemented into the Amsterdam Density Functional code ADF (27,25-27). The non-relativistic as well as scalar relativistic (Pauli) implementations are the work of Schreckenbach and Ziegler (5-7) whereas the spin-orbit (Pauli) and ZORA NMR approaches were implemented by Wolff et al. (9,10). For the mathematical and technical details, the reader is referred to the literature. 

NMR shielding tensors were calculated using the Gauge-Independent Atomic Orbital (GIAO) method as implemented in Gaussian 98 (44-46). The basis sets and level of theory are the same as used in the geometry optimizations and frequency calculations mentioned above. 

Given the huge volume of work on the calculation of molecular properties in MO theory, it is surprising that there is so little effort in this direction within the VB area. The fact that the orbitals used in VB approaches are, as a mle, well-localised, suggests that these approaches would be very suitable for the calculation and interpretation of local properties, such as NMR shielding tensors and nuclear spin-spin coupling constants. 

T. D. Bouman and A. E. Hansen, Int. J. Quantum Chem. Symp., 23, 381 (1989). Linear Response Calculations of Molecular Optical and Magnetic Properties Using Program RPAC NMR Shielding Tensors of Pyridine and n-Azines. 

Gas-phase DFT NMR calculations using the GIAO cluster approach for determining NMR shielding tensors, the hybrid B3LYP DFT functional and the... 

Si NMR shielding tensors of a series of triphenylsilanes PhsSiR with R = Ph, Me, F, Cl, Br, OH, OMe, SH, NHz, SiPhs, C = CPh were determined from Si CPMAS spectra recorded at low spinning rates. In addition the principal components of the shielding tensor were calculated employing the DFT-IGLO method. ... 

Tjandra N, Bax A (1997) Solution NMR measurement of amide proton chemical shift anisotropy in N-ebmiched proteins. Corrrelation with hydrogen bond length. J Am Chem Soc 119 8076-8082 Tossell JA (1984) Correlation of Si NMR chemical shifts in sihcates with orbital energy differences obtained from x-ray spectra. Phys Chem Mineral 10 137-141 Tossell JA (1992) Calculation of the Si NMR shielding tensor in forsterite. Phys Chem Mineral 19 338-342... 

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