Magnetic properties with multiwavelets and DFT: the complete basis set limit achieved

Abstract

Multiwavelets are emerging as an attractive alternative to traditional basis sets such as Gaussian-type orbitals and plane waves. One of their distinctive properties is the ability to reach the basis set limit (often a chimera for traditional approaches) reliably and consistently by fixing the desired precision ε. We present our multiwavelet implementation of the linear response formalism, applied to static magnetic properties, at the self-consistent field level of theory (both for Hartree-Fock and density functional theories). We demonstrate that the multiwavelets consistently improve the accuracy of the results when increasing the desired precision, yielding results that have four to five digits precision, thus providing a very useful benchmark which could otherwise only be estimated by extrapolation methods. Our results show that magnetizabilities obtained with the augmented quadruple-ζ basis (aug-cc-pCVQZ) are practically at the basis set limit, whereas absolute nuclear magnetic resonance shielding tensors are more challenging: even by making use of a standard extrapolation method, the accuracy is not substantially improved. In contrast, our results provide a benchmark that: (1) confirms the validity of the extrapolation ansatz; (2) can be used as a reference to achieve a property-specific extrapolation scheme, thus providing a means to obtain much better extrapolated results; (3) allows us to separate functional-specific errors from basis-set ones and thus to assess the level of cancellation between basis set and functional errors often exploited in density functional theory.

NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations

“…As the shielding can be calculated as a second-order energy derivative, the same extrapolation has also been used for shieldings. [34][35][36] This extrapolation appears to work quite well for our DALTON results (Table S5 of the supplementary material). The maximal absolute deviation of the XY = Q5 extrapolation from the X = 5 results occurs for F 2 and is 0.4 ppm.…”

“…36, for the specific extrapolation (XY = TQ) that closely (albeit not perfectly) approximates the complete basis set shieldings that were calculated using a multi-wavelet approach in Ref. 36. For our DALTON numbers, this exponent appears to work less well (Table S5 of the supplementary material), yielding substantially larger differences between the XY = TQ and XY = Q5 extrapolations.…”

“…α = 1.05 is used in Ref. 36, for the specific extrapolation (XY = TQ) that closely (albeit not perfectly) approximates the complete basis set shieldings that were calculated using a multi-wavelet approach in Ref. 36.…”

Gauge-origin independent calculations of electric-field-induced second-harmonic generation circular intensity difference using London atomic orbitals

“…In the recent study by Rizzo and Ågren, fairly large basis sets were used in order to obtain results close to the basisset limit, and thus reduce the dependence of their calculated results on the choice of gauge origin. [18] Nevertheless, for many magnetic properties, even fairly large basis sets may not suffice in order to reach the basis-set limit, [29,31] making it highly desirable to develop methods that improve basis set convergence and ensure gauge-origin independent results.…”

“…Although rather obvious, we note that the problem of origin independence remains challenging for the frequency-dependent magnetizabilities as well as the material constants. [25][26][27][28]] Secondly, at the computational level, origin-independent properties involving magnetic-field perturbations can only be achieved for variational wave functions in the complete basis set limit, as can for instance be achieved through the use of multiwavelets, [29] or using local gauge-origin approaches (vide infra). List et al have proposed to avoid the multipole expansion altogether to achieve origin independence, [30] but this approach has not yet been applied to the study of nondominant contributions to the induced dipole moment, as for instance is the case in optical rotation where it is not the total induced dipole moment that is needed, but rather that arising from the magnetic component of the electromagnetic wave.…”