Analytic high-order Douglas-Kroll-Hess electric field gradients

Abstract

In this work we present a comprehensive study of analytical electric field gradients in hydrogen halides calculated within the high-order Douglas-Kroll-Hess ͑DKH͒ scalar-relativistic approach taking picture-change effects analytically into account. We demonstrate the technical feasibility and reliability of a high-order DKH unitary transformation for the property integrals. The convergence behavior of the DKH property expansion is discussed close to the basis set limit and conditions ensuring picture-change-corrected results are determined. Numerical results are presented, which show that the DKH property expansion converges rapidly toward the reference values provided by four-component methods. This shows that in closed-shell cases, the scalar-relativistic DKH͑2,2͒ approach which is of second order in the external potential for both orbitals and property operator yields a remarkable accuracy. As a parameter-dependence-free high-order DKH model, we recommend DKH͑4,3͒. Moreover, the effect of a finite-nucleus model, different parametrization schemes for the unitary matrices, and the reliability of standard basis sets are investigated.

Perspective: Relativistic effects

“…For properties such as electric field gradients (EFGs) which depend on polarizations not only in the valence but also in (outer) atomic core shells, picture-change effects can be pronounced. [68][69][70] Additional examples are discussed in Sec. III.…”

Relativistic calculations of magnetic resonance parameters: background and some recent developments

“…Correspondingly, PC effects can be large for the EFG [77][78][79][80][81]. Selected examples are discussed in §8.…”

“…Relativistic and PC effects of the EFG at the X nucleus grow rapidly as X becomes heavier. Mastalerz et al have studied relativistic and PC effects on EFGs in molecules using DKH transformations of increasing order in a scalar relativistic (spin-free, SF) framework [81]. Results for the HX series are provided in table 1.…”

“…a NR data, and relativistic SF data for direct relativistic perturbation theory of order c −2 (DPT), X2C with (*) and without electric field contributions to the decoupling transformation of the EFG operator, SF DC (4c) [82]. b Seventh-order SF DKH with PC corrections (DKH (7,7)) and DC (4c) with SO coupling and finite-nucleus model [81]. c SF NESC data [169].…”

Exact decoupling of the relativistic Fock operator

“…If the transformation of the property operator is neglected, a picture change error [89,90] is introduced, whose magnitude depends on the type of property considered [91][92][93][94][95][96][97]. In general, the picture change error is large for core properties.…”