Solution of a Puzzle: High-Level Quantum-Chemical Treatment of Pseudocontact Chemical Shifts Confirms Classic Semiempirical Theory

A recently popularized
approach for the calculation of pseudocontact
shifts (PCSs) based on first-principles quantum chemistry (QC) leads
to different results than the classic “semiempirical”
equation involving the susceptibility tensor. Studies that attempted
a comparison of theory and experiment led to conflicting conclusions
with respect to the preferred theoretical approach. In this Letter,
we show that after inclusion of previously neglected terms in the
full Hamiltonian, one can deduce the semiempirical equations from
a rigorous QC-based treatment. It also turns out that in the long-distance
limit, one can approximate the complete A tensor in terms
of the g tensor. By means of Kohn–Sham density
functional theory calculations, we numerically confirm the long-distance
expression for the A tensor and the theoretically predicted
scaling behavior of the different terms. Our derivation suggests a
computational strategy in which one calculates the susceptibility
tensor and inserts it into the classic equation for the PCS.