The GIAO-B3LYP method was employed to calculate the isotropic NMR shielding increments of a diatomic hydrogen probe above the tetrafluoroborate (BF4 −) and tetrachloroborate (BCl4 −) anions in tetrahedral (Td) symmetrical structure. The covalently bonded hydrogen nuclei are held in various positions over the anion to obtain the isotropic shielding increment. The NMR chemical shift shielding increments experienced by the proximal proton of diatomic hydrogen have been mapped as a function of their position X, Y, and Z in Cartesian coordinates relative to the center of the anion. A mathematical function was fit to this 3D shielding increment surface at each of the four distances from the plane of the anion, and also, a single mathematical equation was used for predicting the shielding caused by the anion. This equation could be integrated into a molecular mechanics-chemical shift prediction program which could help in the structural determination of structures having these features. In addition, the effect of shielding/deshielding of various probes such as H-atom, H2 molecule, He atom, proximal hydrogen of CH4 molecule, and ghost atom was also studied through their calculated shielding increments (∆σ) with respect to their distance above the center of the both anions. Also, natural bond orbital (NBO) and highest occupied molecular orbital-lowest unoccupied molecular orbital analysis calculations were carried out for both the anions along with the H2 probe placed above the center of the anions in order to investigate the most stable interactions, atomic charges, chemical reactivity, and kinetic stability. [Figure not available: see fulltext.]. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.