Self-consistent perturbation theory of diamagnetism

TLDR

The study develops an ab initio gauge‑invariant molecular orbital theory for nuclear magnetic shielding. The authors construct gauge‑invariant molecular orbitals as linear combinations of gauge‑invariant atomic orbitals, determine the wavefunctions under a uniform magnetic field via self‑consistent field perturbation theory, decompose the shielding into electronic‑structure contributions, and compute constants using three sets of contracted Gaussian atomic orbitals, including minimal and slightly extended bases. The method accurately reproduces shielding for first‑row and hydrogen atoms, and the extended basis yields carbon and hydrogen chemical shifts that agree excellently with experiment.

Abstract

An ab initio gauge-invariant molecular orbital theory is developed for nuclear magnetic shielding. The molecular orbitals are written as linear combinations of gauge-invariant atomic orbitals, the wavefunctions in the presence of a uniform external magnetic field being determined by self-consistent field perturbation theory. The final magnetic shielding result is broken up into contributions which can be related to various features of electronic structure. Calculated magnetic shielding constants are presented using three sets of atomic orbitals, all of which are taken as contracted gaussian-type functions. The first two sets are minimal and the third is slightly extended. All three levels of theory give good descriptions of shielding at first row and hydrogen atoms. Carbon and hydrogen chemical shifts calculated at the extended level are in excellent agreement with experimental values.