Jan
Vícha‡
^{ab},
Jan
Novotný‡
^{a},
Michal
Straka
^{ac},
Michal
Repisky
^{d},
Kenneth
Ruud
^{d},
Stanislav
Komorovsky
*^{d} and
Radek
Marek
*^{ae}
^{a}CEITEC – Central European Institute of Technology, Masaryk University, Kamenice 5/A4, CZ-62500 Brno, Czech Republic. E-mail: radek.marek@ceitec.muni.cz
^{b}Centre of Polymer Systems, University Institute, Tomas Bata University in Zlin, Trida T. Bati 5678, CZ-76001 Zlin, Czech Republic
^{c}Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo nám. 2, CZ-16610 Prague, Czech Republic
^{d}Centre for Theoretical and Computational Chemistry, Department of Chemistry, UiT – The Arctic University of Norway, N-9037 Tromsø, Norway. E-mail: stanislav.komorovsky@uit.no
^{e}Department of Chemistry, Faculty of Science, Masaryk University, Kamenice 5, CZ-62500 Brno, Czech Republic
First published on 25th August 2015
The role of various factors (structure, solvent, and relativistic treatment) was evaluated for square-planar 4d and 5d transition-metal complexes. The DFT method for calculating the structures was calibrated using a cluster approach and compared to X-ray geometries, with the PBE0 functional (def2-TZVPP basis set) providing the best results, followed closely by the hybrid TPSSH and the MN12SX functionals. Calculations of the NMR chemical shifts using the two-component (2c, Zeroth-Order Regular Approximation as implemented in the ADF package) and four-component (4c, Dirac–Coulomb as implemented in the ReSpect code) relativistic approaches were performed to analyze and demonstrate the importance of solvent corrections (2c) as well as a proper treatment of relativistic effects (4c). The importance of increased exact-exchange admixture in the functional (here PBE0) for reproducing the experimental data using the current implementation of the 2c approach is partly rationalized as a compensation for the missing exchange–correlation response kernel. The kernel contribution was identified to be about 15–20% of the spin–orbit-induced NMR chemical shift, Δδ_{SO}, which roughly corresponds to an increase in Δδ_{SO} introduced by the artificially increased exact-exchange admixture in the functional. Finally, the role of individual effects (geometry, solvent, relativity) in the NMR chemical shift is discussed in selected complexes. Although a fully relativistic DFT approach is still awaiting the implementation of GIAOs for hybrid functionals and an implicit solvent model, it nevertheless provides reliable NMR chemical shift data at an affordable computational cost. It is expected to outperform the 2c approach, in particular for the calculation of NMR parameters in heavy-element compounds.
Calculated relativistic effects in the vicinity of the heavy metal are generally very sensitive to (i) the character of metal–ligand bonding,^{8,9} requiring the use of correct and accurate structures, (ii) the inclusion of environmental effects (e.g., solvent),^{10} and (iii) reliable methods for treating the relativistic effects.^{11}
(i) Density functional theory (DFT) is nowadays the most commonly used method for optimizing the structures and calculating various properties of molecules and molecular systems, mainly due to its favorable scaling with system size and the rather good accuracy that can be achieved. A large number of density functionals have been developed over the years for calculating the molecular structures and/or molecular properties. The performance of individual functionals differs dramatically for various properties and systems, and careful evaluation/calibration of the functional behavior must be performed before production DFT calculation can be used for interpreting any chemical problem.
Nice examples of such assessments are the calibration studies by Bühl and coworkers,^{8,12} which focused on the optimization of structures of transition-metal complexes, with DFT structures optimized in vacuo and referenced to structural parameters obtained in the gas phase. However, the geometries obtained in vacuo (or in an implicit solvent) are frequently inappropriately referenced to the structures determined by X-ray diffraction, neglecting any crystal effects. This approximation can lead to substantial errors and even to incorrect conclusions.^{13,14}
To achieve the best available precision in the geometry optimizations, either molecular clusters based on experimental X-ray structures or periodic-boundary calculations should be used for calibrating the methods for solid-state structure optimization. In this work we focus on the cluster approach to assess the performance of the DFT functionals in optimizing the molecular geometry.
Recently, we applied this approach to a very limited number of complexes (mainly octahedral),^{10,15} but a wider selection of compounds and new functionals are required in order to draw more general conclusions. Therefore, the cluster-based comparison of ten DFT functionals (with or without D3 dispersion corrections) for structure optimization is presented in this work for seven square-planar complexes with various ligands and central metal atoms (Pt, Pd, Au, Rh, Fig. 1). These complexes were selected primarily based on the availability of high-quality X-ray structures and the availability of complete NMR data and variability of central metals.
Fig. 1 Structures of selected square-planar complexes. The transition-metal centers are shown in blue and the ligand spectator NMR atoms (LA) are shown in green. |
(ii) The solvent effects can be simulated using explicit solvent molecules or implicit solvent models. Whereas implicit solvent models in general are limited to accounting for electrostatic effects of the solvent environment (continuum) on the NMR parameters of the solute,^{16} an explicit solvent model accounts also for specific weak interactions (hydrogen bonding, stacking),^{17} which can significantly alter the NMR chemical shifts of atoms involved in these interactions. This applies in particular to the hydrogen atoms and the easily polarizable heavy element.^{18} The application of an explicit solvent model is, however, beyond the scope of everyday calculations due to its complexity. For a proper determination of the NMR chemical shifts, classical molecular dynamic (MD) or QM/MD simulations must be performed to determine the positions of the solvent molecules relative to the solute and to calculate NMR chemical shifts averaged over individual snapshots, which can be very time and resource consuming, although great advances are being made for NMR parameters of molecules containing light elements.^{19,20} Furthermore, computationally demanding QM/MD simulations are limited by the size of the model that can be evaluated in a reasonable period of time, whereas specialized force-field parameters for MD simulations must be developed for each structurally different molecule or non-standard solvent.^{21} Therefore, the explicit solvent model is used predominantly in detailed studies of individual systems, whereas the implicit solvent model is adopted more generally, being usually sufficient for calculations of many properties, including NMR chemical shifts of HALA-influenced light atoms as we demonstrate in this work.
(iii) The relativistic effects can be treated in several ways at various levels of theory. A majority of the current computational codes operate with an approximate treatment of relativity. One of the most widely used approaches is the Zeroth-Order Regular Approximation. The ZORA Hamiltonian can be defined as:^{22}
(1) |
The SO-ZORA approach provides a good description of the valence-shell orbitals, often comparable with that of four-component methods.^{23} Because the NMR chemical shifts of the light atoms (e.g., ^{1}H, ^{13}C, ^{15}N) are significantly influenced by the type of chemical bonding, determined by the valence orbitals, the performance of the SO-ZORA approach for NMR chemical shift calculations of light atoms is good.^{4,7,25,26} However, it has been demonstrated^{10,11,15,27} that increasing the admixture of exact exchange in the functional is required to obtain correct NMR chemical shifts of atoms strongly affected by HALA effects. Recently, the role of the missing self-consistent first-order response of the DFT exchange–correlation (XC) potential to the external magnetic-field perturbation, the so-called XC response kernel (f_{xc}), has been highlighted in NMR chemical shift calculations using the SO-ZORA approach.^{28} The missing terms arising from f_{xc} were found to be quite sizable for hydrogen and mercury NMR chemical shifts. However, to the best of our knowledge, these effects have not been evaluated for light, non-hydrogen NMR atoms (^{13}C, ^{15}N).
For a more complete inclusion of relativistic effects, the Dirac Hamiltonian must be considered:^{29}
Ĥ^{D} = cα· + βmc^{2} + | (2) |
Therefore, in addition to the two-component (2c) SO-ZORA approach, we employed four-component (4c) calculations in the Dirac–Coulomb framework. The fully relativistic NMR calculations (ReSpect program) use restricted magnetically balanced basis sets for the small-component wave function.^{32} To further improve basis-set convergence, gauge-including atomic orbitals (GIAO) are employed for the pure DFT functionals.^{33} In the case of the hybrid functionals, only the common gauge origin (CGO) methodology is implemented in the ReSpect program, and thus special attention must be paid to errors arising from basis-set incompleteness in these calculations. In contrast, the implementation of the state-of-the-art non-collinear DFT kernel for GGA (generalized gradient approximation) functionals is used.^{34}
Here we evaluate the influence of structure, solvent, spin–orbit contribution, exact-exchange admixture, role of f_{xc}, and CGO approximation for hybrid functionals on relativistic NMR chemical shift calculations (2c and 4c) of light atoms in the vicinity of a heavy element for a series of square-planar transitional-metal complexes.
Acronym | Formula | R-factor (%) | CSD code | NMR chemical shift^{a} | NMR solvent | Ref. |
---|---|---|---|---|---|---|
a All ^{15}N NMR chemical shifts are reported relative to liquid NH_{3}. b This work. | ||||||
Pt1 | trans(S,N)-[Pt(2-ppy*)(DMSO)Cl] | 1.8 | JISPAD01 | ^{15}N 220.6 | DMSO-d_{6} | 35 and 36 |
^{13}C 140.2 | ||||||
Pt2 | [Pt(oxalato)(1R,2R-cyclohexanediamine)] | 1.9 | CUHKEV | ^{15}N 9.1^{b} | DMSO-d_{6} | 37 |
Pd1 | [Pd(2,2′-biquinoline)Cl_{2}] | 2.7 | YASPAK | ^{15}N 224.0 | CDCl_{3} | 38 and 39 |
Pd2 | [Pd(4,4-di-tert-butylbipyridine)Cl_{2}] | 4.8 | MOYWIG01 | ^{15}N 211.1 | DMSO-d_{6} | 40 and 41 |
Au1 | [Au(2-benzoylpyridine)Cl_{2}] | 2.9 | PUKYAV | ^{15}N 215.2 | DMSO-d_{6} | 42 and 43 |
^{13}C 136.7 | ||||||
Au2 | [Au(2-phenylpyridine)Cl_{3}] | 2.2 | YIDMAA | ^{15}N 227.7 | CDCl_{3} | 44 and 45 |
Rh | [Rh(dipyrrolylphoshinoxylene) CO] | 3.3 | SOWDUE | ^{31}P 119.8 | THF-d_{8} | 46 |
^{13}C 172.2 |
The geometries of the central molecules in the clusters were optimized using the def2-TZVPP basis set^{51} for all atoms, with corresponding relativistic effective core potentials (def2-ECPs)^{52} for the metal center (ECP substituting 60 electrons for Pt and Au and 28 electrons for Rh and Pd). The packing molecules with fixed coordinates were treated using the def2-SVP basis set^{51} for all atoms, with corresponding ECP for the metal center.
Each cluster was optimized using ten selected density functionals. The LYP-based^{53} functionals BLYP,^{54} B3LYP,^{55} and BHLYP^{56} were selected to map the effect of exact-exchange admixture on the structural parameters. Due to the known unbalanced performance of the B3LYP functional in calculations involving transition metals,^{57} the CAM-B3LYP,^{58} the B3LYP functional with corrected long-range exchange, was included in the test set. From the GGA family, PBE^{59} and BP86^{54,60} are present because they are known to perform reasonably well for transition-metal complexes.^{12} The TPSSH^{61,62} functional is an example of a successful meta-GGA hybrid functional, and it was shown to be a very good choice for optimizing transition-metal complexes.^{8,12} The PBE0,^{63,64} the hybrid version of the “parameter-free” PBE functional, has demonstrated superb performance for geometry optimization of heavy transition-metal compounds.^{10,12,15} Advanced long-range corrected hybrid functional with empirical dispersion corrections, ωB97XD,^{65,66} was recently tested with good results in structure optimizations of transition-metal complexes.^{67} Furthermore, a recent addition to the family of “Minnesota functionals”, the so-called screened-exchange density functional, MN12SX,^{68} which was reported to offer very good performance in calculating various properties,^{68} is included. The effect of the D3 dispersion correction^{69} on the geometry was tested in several cases, see Fig. S1 (ESI†). The observed effect was found negligible for the PBE0 functional (it even deteriorates the results by 0.2 pm for PBE and BP86), and the D3 correction is thus not further considered in this work.
A convergence of the basis set was estimated in the series def2-SVP → def2-QZVPP using the PBE0 functional, see Fig. 3. The def2-TZVPP basis provides results almost identical (difference <1 pm) to those of much larger (and computationally demanding) QZ bases, confirming our previous results.^{10}
Fig. 3 Basis-set effects on the M–L distance in the optimization of compound Au1 using the PBE0 functional with def2-ECP. |
Based on the performance of individual functionals (vide infra), the basis-set effects (Fig. 3), computational costs, and the marginal effects of dispersion correction, the PBE0/def2-TZVPP/ECP approach was used to optimize molecular geometries in the production calculations. For all the in-solution optimizations discussed below, the COSMO (COnductor-like Screening MOdel)^{16} solvent model was used, see Section 2.3.
To determine the importance of f_{xc}, 4c calculations using the ReSpect code were performed also without f_{xc}, and the corresponding correction to the NMR chemical shift, Δδ^{XC}_{kernel}, was obtained as a difference between the NMR chemical shift calculated with and without kernel contribution at a given level of theory. With Δδ^{XC}_{kernel} being unaffected by the gauge origin (GIAO vs. CGO), (tested using GIAO/CGO calculations at the 4c-PBE level, data not shown) we assume its additivity for the 2c SO-ZORA results (vide infra).
δ_{i} = σ_{ref} − σ_{i} + δ_{ref} |
Poor results are obtained by using the BLYP functional, which greatly overestimates the M–L bonds (RMSD_{28} = 5.2 pm) and thus should not be used for structure optimizations of transition-metal complexes.^{10} Increasing the exact-exchange admixture in the LYP-based functionals improves the correlation with experimental data for M–L bonds [BLYP (0%, 5.2 pm) → B3LYP (20%, 3.3 pm) → BHLYP (50%, 2.4 pm)] notably. When all bond lengths are considered, both B3LYP and BHLYP are performing with the same level of accuracy (RMSD_{161} ∼ 2 pm), which is due to the fact that the impact of non-metal ligand bonds (mostly organics, in which B3LYP is known to perform excellently) compensates for the inaccuracy in describing the M–L bonds. The best of the LYP-based functionals, BHLYP, produced moderately accurate results (RMSD_{28} = 2.4 pm, RMSD_{161} = 1.9 pm) compared to the rest of the functionals. However, almost identical performance was observed for PBE and BP86, at notably lower computational costs. Both of these GGA functionals can be recommended for geometry optimization of transition-metal complexes in cases where the use of hybrid GGAs is inconvenient, e.g. for very large molecules or molecular clusters.
The ωB97XD functional produces good overall results (RMSD_{161} = 1.7 pm), whereas the description of the M–L bonding is comparable to BHLYP, BP86, and PBE.
The importance of corrected long-range exchange in the CAM-B3LYP functional to optimize the geometry of the transition-metal complexes is obvious from a comparison of the B3LYP and CAM-B3LYP results. The CAM version improves the results of B3LYP by 40% for M–L bonds (RMSD_{28} is 2.0 pm vs. 3.3 pm for B3LYP) and by about 20% for all non-hydrogen bonds (RMSD_{161} is 1.7 pm vs. 2.1), see Fig. 5.
The best results for the tested set were produced by three functionals – MN12SX (RMSD_{28} = 1.7 pm and RMSD_{161} = 1.6 pm), TPSSH (with RMSD_{28} = RMSD_{161} = 1.6 pm), and PBE0, which performs excellently in describing the M–L bonds (RMSD_{28} = 1.2 pm, RMSD_{161} = 1.5 pm). For a more detailed analysis of the results according to the atom type (Fig. S2 and S3, ESI†) and for a comparison between the cluster approach and the in vacuo results (Fig. S4), see ESI.†
To estimate the magnitude of the structural effects on the NMR chemical shifts (NMR CS) separately from all the other factors, we calculated the NMR CS of metal-bonded light atoms (highlighted in green in Fig. 1) using non-relativistic and SO-ZORA approaches at the PBE-40/TZP level in vacuo for BLYP, B3LYP, PBE0, and MN12SX geometries (def2-TZVPP/def2-ECP basis set) optimized in vacuo (see Table 2). The difference between the NMR CS calculated using BLYP and MN12SX functionals (Δδ_{geom}, see Table 2) ranges between 5–14 ppm at the non-relativistic level, and 2–22 ppm at the 2c SO-ZORA level. Also, the deficiency of the popular B3LYP functional in describing the M–L bond length can result in a 19 ppm difference in the relativistic ^{13}C NMR chemical shift (e.g., ^{13}C in Au1 calculated at the 2c SO-ZORA level). We conclude that the inaccurate geometry can be reflected in the ^{13}C and ^{15}N NMR CS deviations, amounting easily to as much as 10–20 ppm. These deviations are more pronounced for the NMR chemical shifts calculated at the relativistic level (SO-ZORA) compared to those calculated using the non-relativistic approach (Table 2). This relativistic effect is particularly evident for the ^{13}C NMR CS in Au1 due to the more covalent character of the M–C bond compared to that of the M–N bond (Table 2).^{11,82} As expected, the PBE0, TPSSH, and MN12SX functionals, producing the most reliable geometries in the test set, give very similar calculated NMR CS.
Non-relativistic | SO-ZORA | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
BLYP | B3LYP | PBE0 | MN12SX | Δδ_{geom}^{a} | BLYP | B3LYP | PBE0 | MN12SX | Δδ_{geom}^{a} | |
a Δδ_{geom} calculated as δ(BLYP) – δ(MN12SX); note that δ(BLYP) – δ(PBE0) would result in almost identical numbers. | ||||||||||
Pt1 | ||||||||||
^{13}C | 182.8 | 179.1 | 177.0 | 177.0 | 5.8 | 141.6 | 141.1 | 143.2 | 143.4 | −1.8 |
^{15}N | 270.0 | 261.6 | 257.1 | 256.6 | 13.4 | 234.8 | 229.3 | 228.8 | 228.2 | 6.6 |
Au1 | ||||||||||
^{13}C | 176.6 | 172.1 | 168.9 | 168.6 | 8.0 | 147.0 | 144.6 | 125.6 | 125.3 | 21.7 |
^{15}N | 250.4 | 242.3 | 237.2 | 236.8 | 13.6 | 244.2 | 236.0 | 230.5 | 230.2 | 14.0 |
In this work, the PBE0/def2-TZVPP/def2-ECP approach was selected for all further geometry optimizations in Sections 3.2–3.5.
Generally, increasing the EE admixture in the functional increases the nuclear magnetic shielding of the light atoms bound to the metal center in platinum and gold compounds considerably.^{10,82} However, this effect is marginal for palladium and even reversed for ^{31}P in the rhodium complex. The increased EE admixture improves the results for some cases already in vacuo, particularly for ^{13}C NMR CS, where the solvent effects obviously play a less significant role compared to ^{15}N NMR CS.^{80,83–85} For instance, the PBE functional results in Δδ(^{13}C) = 21.4 ppm for Pt1-C, whereas PBE-40 gives Δδ(^{13}C) = 1.5 ppm (see Fig. 6). Conversely, the improvement is small or negligible for ^{15}N NMR CS, where solvent effects are known to play a significant role and the effects of the EE admixture are less important (see the palladium and gold complexes in Fig. 6).
Δδ_{solv} | |||
---|---|---|---|
Atom | PBE | PBE0 | PBE-40 |
Pt1-N | −5.0 | −5.7 | −6.1 |
Pt2-N | −1.3 | −4.4 | −6.3 |
Pd1-N | −4.6 | −14.6 | −20.4 |
Pd2-N | −6.0 | −16.8 | −22.2 |
Au1-N | −12.3 | −15.7 | −17.5 |
Au2-N | −14.5 | −17.9 | −20.1 |
Pt1-C | −4.1 | −4.4 | −4.5 |
Au1-C | −2.5 | −3.4 | −4.1 |
Rh-C | −0.2 | −0.3 | −0.2 |
Rh-P | +2.7 | +2.2 | +2.0 |
The implicit solvent improved the RMSD^{SO-ZORA}_{PBE} from 21.5 ppm in vacuo to 14 ppm with COSMO (for RMSD^{mDKS}_{PBE}, 18.6 ppm in vacuo and 11.4 ppm including Δδ_{solv}). In parallel, the RMSD^{SO-ZORA}_{PBE0} was reduced from 16.5 ppm to 4.4 ppm (RMSD^{mDKS}_{PBE0} from 17.5 ppm to 5.1) and the RMSD^{SO-ZORA}_{PBE-40} from 14.6 ppm to 4.5 ppm (RMSD^{mDKS}_{PBE-40} 15.1 ppm to 5.2 ppm).
Note that the magnitude of Δδ_{solv} is increasing considerably with increasing exact-exchange admixture in the functional; the more exact exchange in the functional, the more important the solvent correction is, which is partially reflected in the decrease of the RSMD for the individual approaches. Whereas PBE results for both the 2c SO-ZORA and 4c mDKS approaches still deviate significantly from the experimental values, which is partially due to the differences in the description of Δδ_{SO} by the individual functionals (see Table 4), PBE0 and PBE-40 results are considerably closer to the experimental data. For the differences between calculated (PBE, PBE0, or PBE-40 functional using implicit solvent) and experimental NMR CS, see Fig. 7.
Atom | Δδ_{SO} (ZORA) | Δδ_{SO} (mDKS) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
PBE | PBE0 | PBE-40 | ΔΔδ_{SO}^{a} | ΔΔδ_{total}^{b} | PBE | PBE0 | PBE-40 | ΔΔδ_{SO}^{a} | ΔΔδ_{total}^{b} | |
a Calculated as ΔΔδ_{SO} = Δδ^{SO}_{PBE-40} − Δδ^{SO}_{PBE}. b Calculated as ΔΔδ_{total} = Δδ^{total}_{PBE-40} − Δδ^{total}_{PBE}. | ||||||||||
Pt1-N | −9.3 | −15.2 | −19.1 | −9.8 | −14.4 | −10.7 | −15.7 | −19.0 | −8.3 | −9.0 |
Pt2-N | −24.5 | −27.5 | −30.3 | −5.8 | −27.2 | −24.7 | −27.5 | −29.6 | −4.0 | −23.3 |
Pd1-N | −5.1 | −9.3 | −12.4 | −7.3 | +2.4 | −5.6 | −9.5 | −12.6 | −7.0 | +5.7 |
Pd2-N | −7.1 | −11.5 | −15.1 | −8.0 | −2.7 | −8.6 | −13.8 | −17.6 | −9.0 | −1.0 |
Au1-N | −2.7 | −3.5 | −4.5 | −1.8 | −4.6 | 0.6 | −1.5 | −3.0 | −3.6 | −1.9 |
Au2-N | 6.0 | 5.6 | 5.0 | −1.0 | −3.6 | 9.9 | 7.3 | 6.3 | −3.6 | −3.9 |
Pt1-C | −14.0 | −23.2 | −29.1 | −15.1 | −19.9 | −18.3 | −28.1 | −29.5 | −11.2 | −14.1 |
Au1-C | −8.0 | −12.1 | −16.2 | −8.2 | −14.9 | −9.0 | −14.3 | −18.4 | −9.4 | −16.8 |
Rh-C | −3.1 | −4.3 | −5.9 | −2.8 | −5.5 | −2.5 | −4.5 | −5.8 | −3.3 | −4.8 |
Rh-P | −17.0 | −22.0 | −24.9 | −7.9 | +14.9 | −5.1 | −10.3 | −12.7 | −7.6 | +15.3 |
Although at the SO-ZORA relativistic level with solvent correction, the PBE0 and PBE-40 calculations result in almost identical averaged RMSD values (RMSD^{SO-ZORA}_{PBE0} = 4.4 ppm and RMSD^{SO-ZORA}_{PBE-40} = 4.5 ppm), the PBE-40 provides better results in 7 out of 10 systems, which is in agreement with previous studies.^{10,11} The better average RMSD achieved by the PBE0 functional can be ascribed to quite poor results of the PBE-40 approach for Pt2-N, NH_{2} group in oxaliplatin, which is probably involved in protonation equilibria affecting its experimental ^{15}N NMR CS, and overestimated ^{31}P NMR chemical shift for Rh-P. When the two abovementioned problematic Pt2-N and Rh-P cases are excluded, RMSD^{SO-ZORA}_{PBE-40} decreases to 2.4 ppm, whereas RMSD^{SO-ZORA}_{PBE0} = 4.7 ppm.
Similar results were achieved by the 4c mDKS approach, where slightly better RMSD was obtained by using PBE0 (RMSD^{mDKS}_{PBE0} = 5.1 ppm) than by PBE-40 (RMSD^{mDKS}_{PBE-40} = 5.2 ppm), however, one should keep in mind that this was achieved by applying several external corrections (solvent, CGO).
Given the good results obtained for PBE0 and PBE-40 with an implicit solvent correction, the use of explicit solvent models would not bring any considerable improvement at reasonable costs for routine NMR applications; therefore, we use the COSMO implicit solvent model for calculating the NMR CS in subsequent sections.
The increase in the shielding character of Δδ_{SO} is an important factor for explaining the differences between the values calculated at the PBE, PBE0, and PBE-40 levels (vide infra). Comparing Δδ_{SO} calculated at these three levels of theory with total NMR chemical shift differences (in vacuo, Table S1, ESI†) indicates that ΔΔδ_{SO} (Table 4) induced by altering the exact-exchange admixture (40 → 0%) can represent a significant portion of the ΔΔδ_{total}.
The Δδ_{SO} values in Table 4 calculated using the ZORA and mDKS methods are of a comparable magnitude. Generally, the Δδ_{SO} values vary between +5 ppm for Au2 (deshielding) and −30 ppm for Pt2 (strong shielding contribution). It should be noted that the electronic factors responsible for the SO deshielding (Au2-N) or small Δδ_{SO} (Au1-N) in the gold complexes compared to their platinum counterparts were interpreted very recently by our group as a result of the involvement of 6p orbitals in Au–N bonding^{82} caused by the electrostatic potential of Au^{3+} and large scalar-relativistic effects^{90} found in the gold complexes.
To illustrate the role of the missing f_{xc} terms, appropriate Δδ^{XC}_{kernel} values were added to the 2c SO-ZORA NMR chemical shifts calculated at the PBE0 and PBE-40 levels, see Fig. 8.
Upon addition of Δδ^{XC}_{kernel}, the majority of the PBE0 results were improved, with the RMSD^{SO-ZORA}_{PBE0} reduced to 3.4 ppm, whereas the PBE-40 results are uniformly deteriorated (RMSD^{SO-ZORA}_{PBE-40} = 5.8 ppm). The most important fact is revealed, however, when the differences in Δδ_{SO} caused by the increase of the EE admixture from 25% to 40% are compared with the Δδ^{XC}_{kernel} calculated at the PBE0 level, see Table 5. Our observations suggest that the absence of the response f_{xc} term in the current SO-ZORA implementation (ADF2014) results in Δδ^{XC}_{kernel} deviations that are almost perfectly counterbalanced by the artificial Δδ_{SO} rise introduced by increasing the EE admixture in the functional (25 → 40% in PBE0), ΔΔδ_{SO} in Table 5.
Atom | ΔΔδ_{SO}^{a} | Δδ^{XC}_{kernel}^{b} |
---|---|---|
a Calculated at the SO-ZORA level as ΔΔδ_{SO} = Δδ^{SO}_{PBE0} − Δδ^{SO}_{PBE-40}. b Δδ^{XC}_{kernel} estimated at the mDKS level by using the PBE0 functional. | ||
Pt1-N | −3.9 | −3.0 |
Pt2-N | −2.8 | −3.2 |
Pd1-N | −3.1 | −0.8 |
Pd2-N | −3.6 | −1.6 |
Au1-N | −1.0 | 0.9 |
Au2-N | −0.6 | 2.7 |
Pt1-C | −5.9 | −5.6 |
Au1-C | −4.1 | −3.6 |
Rh-C | −1.6 | −1.3 |
Rh-P | −2.9 | −2.4 |
Although individual factors play different roles in ^{13}C and ^{15}N NMR CS of different compounds, the EE admixture seems to be crucial and one of the most important factors for reproducing the experimental NMR values. However, as demonstrated here, when the correct geometry and the treatment of solvent effects is combined with the proper description of relativity (including terms arising from f_{xc}), standard 25% exact-exchange admixture in the PBE0 functional (instead of somewhat artificial 40%) seems to be sufficient for the NMR CS calculations in square-planar transition-metal complexes.
The role of an implicit solvent was found to be of considerable importance for the NMR chemical shifts in the square-planar complexes, mainly for ^{15}N, with an average 13 ppm contribution to the total NMR chemical shifts (estimated at the SO-ZORA level using the PBE0 functional).
The most important relativistic NMR CS contribution is the Δδ_{SO}, with its size varying between +5 ppm and −30 ppm (for both 2c SO-ZORA and 4c mDKS), which was also demonstrated to be highly dependent on the amount of exact-exchange admixture in the functional.
The importance of increased exact-exchange admixture to 40% in the PBE0 functional for the 2c SO-ZORA approach was confirmed for the light spectator atoms (^{13}C, ^{15}N, and ^{31}P), and rationalized as a compensation for the missing Δδ^{XC}_{kernel} contribution. Therefore, with the current implementation of the SO-ZORA approach used in this work, the PBE-40 functional slightly outperforms PBE0. However, accounting for the effect of the response exchange–correlation kernel, the standard PBE0 functional provides somewhat better agreement with the experiment. Undoubtedly, the effect of the XC kernel should not be neglected for systems with a large HALA effect, such as actinides.^{7}
Finally, the relative importance of individual effects (geometry, solvent, relativistic approximation, DFT functional) to the total NMR CS is demonstrated by stepwise calculations. Currently, the use of hybrid GGA functionals (with the DFT functionals used) is mandatory for reproducing the experimental NMR data in heavy-element compounds.
In the fully relativistic mDKS approach using restricted magnetically balanced basis sets, an implementation of GIAOs for hybrid functionals as well as an implicit solvent model is still missing. However, using simple empirical corrections estimated at the 2c SO-ZORA level provides reliable NMR CS data at affordable computational costs. Undoubtedly, the four-component mDKS method would outperform 2c approaches in calculating heavy-element NMR parameters.^{91} Our efforts in this direction will be reported elsewhere.
Footnotes |
† Electronic supplementary information (ESI) available. Fig. S1: role of dispersion (empirical D3 correction) in cluster-based geometry optimizations; Fig. S2: the RMSDs (pm) for the interatomic distances according to the type of central metal; Fig. S3: the RMSDs (pm) for the interatomic distances according to the type of the light spectator atom; Fig. S4: comparison of total RMSDs (in pm) for interatomic distances calculated in vacuo and in cluster; Fig. S5: the 4c mDKS NMR chemical shifts with and without empirical “CGO corrections”. Table S1: the Δδ (ppm), in vacuo; Table S2: the Δδ (ppm), COSMO; Table S3: the Δδ^{XC}_{kernel} values (ppm). See DOI: 10.1039/c5cp04214c |
‡ These two authors contributed equally. |
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