The role of the exchange-correlation response kernel and scaling corrections in relativistic density functional nuclear magnetic shielding calculations with the zeroth-order regular approximation

Abstract

To cite this article: Jochen Autschbach (2013) The role of the exchange-correlation response kernel and scaling corrections in relativistic density functional nuclear magnetic shielding calculations with the zeroth-order regular approximation,The relativistic NMR module of the Amsterdam Density Functional (ADF) package, which is frequently utilised in studies of heavy atom NMR chemical shifts, is extended to calculate a hitherto neglected term from the response of the exchangecorrelation (XC) potential. The term vanishes in the absence of spin-orbit coupling. Further, corrections to the shielding arising from scaling factors in the zeroth-order regular approximation (ZORA) relativistic framework are investigated. The XC response markedly improves calculated proton chemical shifts for hydrogen halides. Mercury chemical shifts for mercury dihalides are also noticeably altered. Contributions from density-gradient dependent terms in the response kernel contribute about 30-40%. New fully relativistic density functional theory (DFT) benchmark data are compared with ZORA and literature reference values. In line with previous work, it is found that absolute shielding constants for Hg are not accurately predicted with ZORA. However, chemical shifts agree well with fully relativistic calculations. The application of 'scaled-ZORA' scaling factors deteriorates the shielding constants and is therefore not recommended. The scaling hardly affects chemical shifts. ZORA calculations are not suitable for absolute shielding of heavy atoms but they can be used safely for chemical shifts in most application scenarios. IntroductionFirst-principles calculations of structure, thermochemistry, and spectroscopic properties of molecules with heavy elements require a relativistic quantum chemistry framework [1][2][3][4][5][6][7]. This is particularly true for molecular properties for which the relevant quantum mechanical operators predominantly sample the electronic structure close to a nucleus. NMR parameters are prime examples of such properties. The zeroth-order regular approximation (ZORA) [8-10] is a variationally stable approximate (quasirelativistic) twocomponent (2c) all-electron relativistic framework. In conjunction with density functional theory (DFT), ZORA is widely applied to calculations of NMR parameters. For a small selection of recent applications to a variety of problems in chemistry see, for instance [11][12][13][14][15][16]. A ZORA module for NMR shielding tensors has been part of the Amsterdam Density Functional (ADF) [17] package since 1999 [18,19], followed by an implementation of a module for calculations of indirect nuclear spin-spin coupling (J-coupling) tensors in the year 2000 [20,21]. Among the reasons for the early development of ZORA-based magnetic property modules have been the ease by which magnetic perturbation operators can be derived and the rather straightforward way of calculating matrix elements with the help of numerical integration techniques. Extensions for hybrid DFT calculations have been

Calculation of chemical-shift tensors of heavy nuclei: a DFT/ZORA investigation of 199Hg chemical-shift tensors in solids, and the effects of cluster size and electronic-state approximations

“…Autschbach shows that the valence-shell properties such as chemical shift and J coupling are well described in the ZORA formalism. 67,68 This observation is supported by our findings that calculations using ZORA produce results in agreement with experiment.…”

Insights into trans‐Ligand and Spin‐Orbit Effects on Electronic Structure and Ligand NMR Shifts in Transition‐Metal Complexes

“…The calculations used gauge‐including atomic orbitals (GIAOs) . ZORA calculations of NMR chemical shifts were performed with the previously neglected terms from the exchange‐correlation (XC) response kernel . The calculated 1 H and 13 C nuclear shieldings σ were converted into chemical shifts δ =σ(TMS)–σ (in ppm) relative to the shielding of tetramethylsilane (TMS; σ(TMS)=31.6 ppm).…”

“…[32] ZORA calculations of NMR chemical shifts were performed with thep reviously neglectedt erms from the exchange-correlation (XC) response kernel. [33] The calculated 1 H and 13 Cn uclear shieldings s were converted into chemical shifts d = s(TMS)-s (in ppm) relative to the shielding of tetramethylsilane (TMS; s(TMS) = 31.6 ppm). This computational level reproduces excellently the available experimental 1 HNMR shifts for trans-[HOsL(dhpe) 2 ]( L = Cl, CN), trans-[HPtL(PMe 3 ) 2 ] (L = NO 3 ,C l, CH 3 ,B H 2 ), and HAuNHC (NHC = 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene); see Ta ble S1 in the Supporting Information.…”

Giant spin–orbit effects on 1H and 13C NMR shifts for uranium(vi) complexes revisited: role of the exchange–correlation response kernel, bonding analyses, and new predictions

“…37 The ZORA calculations of NMR chemical shifts are done with and without the previously neglected terms from the exchangecorrelation (XC) response kernel. 20 We note in passing that the implementation of the PBE functional used here without and with XC kernel differs slightly, as the former uses PW92 29 for the LDA part and the latter VWN. 38 The latter goes back to the initial implementation of PBE in ADF by S. Patchkovskii.…”

“…21 Employing a modified pilot implementation, Autschbach demonstrated significant changes between the standard implementation in ADF and the modified one for 1 H shifts in hydrogen halides and for 199 Hg shifts in mercury halides were demonstrated. 20 Notable differences between two-and four-component results in a recent study of carbon and nitrogen shifts in transition-metal cyanide complexes also pointed to possible inaccuracies with the previous ZORA implementation in ADF due to the lack of the XC-kernel SO effects on the nuclear magnetic shielding 22 (see also ref. 15 and 23 for other two-vs. four-component comparisons).…”