Hirshfeld/Generalized Atom Refinement (HAR/GAR) [1] allows to calculate individually tailored aspherical scattering factors (pseudoatoms) by using Olex2 [2] and NoSpherA2 [3] software together with quantum chemical packages like Orca [4] or Tonto [5]. However, the choice of the electron density calculation method is usually experience based. With a high-quality data, using a large basis set with the functionals from the top of the “Jacob’s Ladder” [6] can be meaningful. In [7] and [8], we did some benchmarking of HAR methods using Orca version 4.2.1 and 5.0.3 with the NH4[Zn(cma)(H2O)2]·H2O data suffering from suboptimal absorption correction. This work is dedicated to the HAR refinement of relativistic systems by ECP based methods using Orca 5.0.4.
As a starting point for HAR, the results of the IAM refinement of selected compounds using proper constraints with X–H distances free to refine were used. The refinements for all combinations of selected LDA (PWLDA), GGA (BLYP, PBE), meta-GGA (TPSS, R2SCAN), hybrid GGA (B3LYP, PBE0), hybrid meta-GGA (M06-2X) and range separated hybrid (wB97X) functionals with ECP-def2-SVP – def2-TZVPP basis sets were performed by Olex2 1.5 in combination with NoSpherA2 and Orca 5.0.3. For the comparison, calculations using all-electron x2c-def2-TZVP basis set with R2SCAN functional with ZORA approximation were also performed. The results were compared with previous results in [8] and with the values obtained from neutron diffraction [9].
Regarding the time of calculation, the functionals were divided into two groups. LDA, GGA and meta-GGA functionals were significantly faster than hybrids, with meta-GGA hybrids and range separated hybrids being slower than GGA hybrids.
Similarly to [8], if the data were influenced by strong absorption effect, PWLDA is best all-round performer (except of ECP-def2-TZVP/R2SCAN combination), followed by R2SCAN and M06–2X and PBE0 being on par, with the best results using ECP-def2-TZVP basis set. Otherwise, the results are better when using larger basis sets and the best performer is PBE0 functional followed by PBE and wB97X or R2SCAN. Residuals (R, wR, S) were practically identical for all refinement methods.
For individual bond types, there are often best performing basis set/functional combinations. Agreement between obtained distances and neutron defaults was exceptionally good for C–Csp3–H3 and Car–H distances. Although there is no reference for (Car)2–Nsp3–H (N pyramidal) distance based on neutron data, but we found Car–N–H2 (N pyramidal) distance [9] being in a good agreement with refined distance.
Non-empirical GGA and GGA hybrid functionals (PBE, PBE0) outperformed empirical (BLYP, B3LYP) GGA and GGA hybrids by a small margin. Using all-electron x2c-TZVP/R2SCAN method using ZORA approximation didn’t led to significantly different results with approximately the same calculation times.
This work was supported by the Operation Program of Integrated Infrastructure for the project, UpScale of Comenius University Capacities and Competence in Research, Development and Innovation, ITMS2014+: 313021BUZ3, co-financed by the European Regional Development Fund.