shieldingconstant

The shielding constant, denoted σ, is a dimensionless quantity in nuclear magnetic resonance (NMR) that describes how electron density around a nucleus reduces the local magnetic field experienced by that nucleus when placed in an external field. In general, shielding is described by a tensor σ with components along three axes; the isotropic shielding σ_iso is the average of the three diagonal elements and often used as a scalar descriptor of the environment.

The observed resonance frequency ν of a nucleus in a strong magnetic field B0 is proportional to the effective field B_eff = B0(1 − σ). The chemical shift δ is defined relative to a reference compound, most commonly tetramethylsilane (TMS) for 1H and 13C spectra, and is approximately δ ≈ σ_ref − σ_sample in parts per million. Values and trends in σ reflect local electronic structure: greater shielding corresponds to smaller chemical shifts.

Shielding constants can be determined experimentally from high-resolution NMR spectra and are also calculated computationally. The shielding tensor is commonly evaluated via ab initio quantum chemical methods, especially gauge-including atomic orbital (GIAO) approaches, using standard basis sets; results are often reported as σ_iso along with the anisotropy and principal components of the tensor.

Applications include structural elucidation and interpretation of NMR spectra, calibration of chemical shifts, and testing computational models of electronic structure. Limitations include dependence on molecular conformation, solvent effects, and reference standard choices, all of which can influence calculated and observed shieldings.