Gauge origin independent calculations of nuclear magnetic shieldings in relativistic four-component theory

Abstract

The use of perturbation-dependent London atomic orbitals, also called gauge including atomic orbitals, has proven efficient for calculations of NMR shielding constants and other magnetic properties in the nonrelativistic framework. In this paper, the theory of London atomic orbitals for NMR shieldings is extended to the four-component relativistic framework and our implementation is described. The relevance of London atomic orbitals in four-component calculations as well as computational aspects are illustrated with test calculations on hydrogen iodide. We find that the use of London atomic orbitals is an efficient method for reliable calculations of NMR shielding constants with standard basis sets, also for four-component calculations with spin-orbit coupling effects included in the wave function optimization. Furthermore, we find that it is important that the small component basis functions fulfill the magnetic balance for accurate description of the diamagnetic shielding and that the role of London atomic orbitals in the relativistic domain is to provide atomic magnetic balance even in the molecular case, thus greatly improving basis set convergence. The Sternheim approximation, which calculates the diamagnetic contribution as an expectation value, leads to significant errors and is not recommended.

Four-component relativistic theory for nuclear magnetic shielding: Magnetically balanced gauge-including atomic orbitals

“…͑27͒ with Eq. ͑28͒ shows that the combination of GIAO and MB brings in no complications, contrary to the statement made by Ilias et al 59 Instead, the GIAO-LRT is still very demanding on the RKB basis sets ͑vide post͒ and is thus not recommended for practical applications.…”

“…It will be shown that the calculated NMS tensors are not only independent of the choice of gauge origin but also converge rapidly to the basis set limit. Note in passing that Quiney et al [13][14][15] and Ilias et al 59 also adopted the GIAO method in their uncoupled-DHF or CP-DHF but they did not take the MB into account.…”

Gauge-origin dependence of NMR shielding constants in the Douglas–Kroll–Hess method

“…On the other hand, Iliaš et al stated that the CGO should be placed at atom I in the H NMR calculation for a HI molecule [3]. According to their interpretation [3] and that of Malkina et al [29], the shielding of the hydrogen nucleus is caused by the electronic cloud of iodine only. That is, when the gaugeorigin dependence from the neighboring atoms is negligible, the CGO should be placed at the resonant atom position.…”

“…On the other hand, the DKH2-BP method provides the gauge-origin invariant NMR values and the DKH-BP values agree well with the 4c reference values. Clearly, the CGO should be placed at the X position, as stated by both Iliaš et al [3] and Malkina et al [29]. In addition, unlike the I NMR calculations for HI, the gauge-origin dependence of the H NMR values is eliminated by the DKH2-CGO-WTBS method.…”

“…Recently, four-component (4c) relativistic calculations with gauge-including atomic orbitals (GIAO) [1,2] have been conducted to obtain magnetic properties, such as the nuclear magnetic resonance (NMR) shielding constant [3] and magnetizability [4]. Moreover, by adopting the magnetic balance [5][6][7][8][9][10][11] or restricted magnetic balance (RMB) between the large and small component GIAO basis functions, the converged NMR value with respect to basis set size can be obtained, even in cases of relatively small basis sets [12][13][14][15] (we refer the reader to the review [16,17] for recent 4c NMR theories).…”