Calculation of nuclear magnetic shieldings: infinite-order Foldy–Wouthuysen transformation

A scheme for calculating nuclear magnetic shieldings using the infinite-order Foldy–Wouthuysen (FW) transformation proposed by Barysz and Sadlej (BS) is presented. The nuclear magnetic shieldings of hydrogen halides are calculated by three variant BS schemes; a double finite perturbation method for the external magnetic flux density (B 0) and the nuclear magnetic dipole moment (  μ M ) (BS/FPT-2), a single finite perturbation method for B 0 with analytical differentiation of energy with respect to (  μ M ) (BS/FPT-1), and an approximate analytical differentiation method with respect to both B 0 and μ M (BS/CHF). Although the BS/FPT-2 method is exact theoretically, the actual computation for heavy nuclei includes large error due to reduction of the number of significant figures. The BS/FPT-1 and BS/CHF approaches, on the other hand, yield reasonable values for all of the shieldings. Although several results could not be obtained by the BS/FPT-2 method, no serious contradictions were recognized among these ...