Benchmarking Magnetizabilities with Recent Density Functionals

Abstract

We have assessed the accuracy of the magnetic properties of a set of 51 density functional approximations, including both recently published and already established functionals. The accuracy assessment considers a series of 27 small molecules and is based on comparing the predicted magnetizabilities to literature reference values calculated using coupled-cluster theory with full singles and doubles and perturbative triples [CCSD(T)] employing large basis sets. The most accurate magnetizabilities, defined as the smallest mean absolute error, are obtained with the BHandHLYP functional. Three of the six studied Berkeley functionals and the three range-separated Florida functionals also yield accurate magnetizabilities. Also, some older functionals like CAM-B3LYP, KT1, BHLYP (BHandH), B3LYP, and PBE0 perform rather well. In contrast, unsatisfactory performance is generally obtained with Minnesota functionals, which are therefore not recommended for calculations of magnetically induced current density susceptibilities and related magnetic properties such as magnetizabilities and nuclear magnetic shieldings. We also demonstrate that magnetizabilities can be calculated by numerical integration of magnetizability density; we have implemented this approach as a new feature in the gauge-including magnetically induced current (GIMIC) method. Magnetizabilities can be calculated from magnetically induced current density susceptibilities within this approach even when analytical approaches for magnetizabilities as the second derivative of the energy have not been implemented. The magnetizability density can also be visualized, providing additional information that is not otherwise easily accessible on the spatial origin of magnetizabilities.

Magnetically Induced Ring-Current Strengths of Planar and Nonplanar Molecules: New Insights from the Pseudo-π Model

“…A better agreement, with values obtained at the MP2 level, is achieved when the functional includes at least 50% of Hartree-Fock exchange. 17,18,[36][37][38]…”

Spatial Contributions to 1H NMR Chemical Shifts of Free-Base Porphyrinoids

“…This approach has been employed in other studies [39,40], however it has not been considered in this work. Even though the NMR shieldings obtained with the gradient theory and the integration approaches are the same, the integration method can provide information about orbital and spatial contributions to a given NMR chemical shift [36,37,41]. When a numerical representation of the current density is gauge-origin independent, the calculated NMR chemical shifts obtained with the integration approach are also independent of the gauge origin.…”

“…The NMR shielding constants were calculated with Turbomole at the BHandHLYP (LIBXC ID 436) [53,58,59] level of theory using gauge-including atomic orbitals (GIAO) [20,[60][61][62]. The BHandHLYP functional that has 50% Hartree-Fock exchange yielded accurate magnetizabilities in a recent benchmark study [41]. For all NMR calculations the pcseg-3 basis set has been employed which has been optimized for the calculation of NMR parameters [63].…”

“…Contributions to NMR shieldings can be calculated by integrating the Biot-Savart expression in Equation ( 7) numerically using the CDT calculated in the integration points. We have implemented a numerical integration scheme into the GIMIC program for calculating spatial contributions to nuclear magnetic shieldings and magnetizabilities [5,34,41]. Atomic contributions can be obtained by integrating atomic domains generated by the NUMGRID library [69] using Becke's multicenter scheme [70].…”

Correction to “Benchmarking Magnetizabilities with Recent Density Functionals”

“…It has been brought to our attention that our recent study 1 erroneously employed a vanishing Hartree–Fock (HF) magnetizability for the SO 2 molecule. The reason was a Turbomole input error for this calculation.…”