CAPITULO VII PROYECTO ARQUITECTONICO
2. Localización
59Co was one the first nuclides to be measured using NMR spectroscopy.226 It has one
of the largest chemical shift ranges of all nuclides, spanning 20 000 ppm and generally favourable NMR properties. It additionally has a rather large quadrupole moment making the 59Co chemical shift and EFG tensors excellent probes for
electronic structure and molecular geometries of cobalt complexes. Computational
59Co NMR spectroscopy has been studied by Bühl and coworkers.105,227 B3LYP
calculations can be recommended (mean absolute errors of 500-‐760 ppm for complexes from almost the entire chemical shift range of 59Co), and in some cases
accounting for solvation and zero-‐point and thermal effects is necessary. 59Co
chemical shifts remain a challenge, however, and better functionals are most likely needed for improved predictions.
Cobaloxime complexes are popular model compounds of the biomolecule vitamin B12
where the dimethylglyoxime (DMG) ligands mimic the complex corrin system of vitamin B12 and other cobalamines.
A combined 59Co solid-‐state and solution-‐state NMR study of selected cobalamines
and cobaloximes with differing axial ligands afforded a set of anisotropic chemical shift and quadrupole coupling data.228 When the cobaloxime solid-‐state data are
compared to solution data for the isotropic chemical shifts, only small liquid-‐to-‐solid shifts are noticeable, 0-‐70 ppm. As the 59Co chemical shift range is 20000 ppm this
suggests very small environmental effects on the chemical shift tensor.
Modelling the anisotropic parameters, however, is a challenge on its own and we were interested in seeing how simple gas-‐phase calculations of the anisotropic parameters for the cobaloxime compounds would compare to the experimental solid-‐ state NMR data. Initial test calculations revealed unusually large deviations between gas-‐phase computational results (B3LYP) for the [CoDMG2(NH3)2]+ complex (28) and
the experimental [CoDMG2(NH3)2]Cl results. While the isotropic chemical shift was in
good agreement (~300ppm), the reduced anisotropy deviated by 1000 ppm and the quadrupole coupling constant was off by ~50 MHz. Although the anisotropy, not benefitting from as much error cancellation is more challenging to compute than isotropic chemical shifts, a 1000 ppm error is massive. The quadrupole coupling constant deviation of 50 MHz is also surprising since an 11 MHz B3LYP error is expected based on the benchmark study in Chapter 3.3.
These deviations thus pointed towards significant solid-‐state effects on the chemical shift and EFG tensors in the [CoDMG2(NH3)2]Cl crystal. We were thus curious to see if
our QM/MM protocol would be capable of accounting for these effects. Unfortunately, a crystal structure was only available with Br-‐ as the counterion instead of Cl-‐ . While
Cl-‐ and Br-‐ would be modelled identically in our QM/MM scheme (as a fixed point
charge with value -‐1 ), the different counterion could mean that the crystal structures are slightly different as the ionic radii are different. While the molecular structure of the complex might not change very much, the unit cell volume could be different. Nonetheless we decided to proceed using the [CoDMG2(NH3)2]Br structure.
A classical cluster with radius ~37 Å was built and subjected to the QM/MM protocol. BP86-‐D calculations with the mixed def2-‐TZVPP/def2-‐SVP basis set were used for both charge calculations and geometry optimisations. NMR calculations were
performed using a decontracted def2-‐QZVPP basis set on Co and the 6-‐31G* basis set on ligand atoms and using three different functionals: TPSS, TPSSh and B3LYP. The isotropic shieldings were converted into chemical shifts by referencing to the Co(CN)63-‐ anion.
As the experimental reference is the 1M aqueous K3[Co(CN)6] and it has been shown
by CPMD simulations that there is a substantial gas-‐to-‐liquid shift105 we here add a
(δCPMDave, liq – δCPMDave,gas ) = +1205 ppm gas-‐to-‐liquid correction for the standard to all
our isotropic chemical shifts. This correction is evaluated as the difference between the average isotropic shielding at the B3LYP level using geometries from
BP86/CPMD/D2O MD simulations (Co(CN)63-‐ in periodic box of D2O liquid) and the
average isotropic shielding at the B3LYP level using geometries from BP86 MD simulation in the gas phase.105,227 We note, however, that geometries and shieldings
used to calculate this correction were evaluated using different basis sets than used in our work. It is not known how reliable this correction is but we use it here as it is more likely to improve predictions rather than introduce artifacts.
Table 18 shows the results of chemical shift and EFG calculations of the
[CoDMG2(NH3)2]+ cation in the gas-‐phase and the QM/MM solid with and without
embedded point charges. Results for the gas-‐optimised cation show that the isotropic chemical shift is in good agreement with experiment (after the gas-‐liquid shift for the standard is taken into account), while the computed reduced anisotropy and the NQCC are in strong disagreement with experiment. Using the X-‐ray geometry instead, results in even worse agreement, particularly for the NQCC. Interestingly, however, embedding the cation in self-‐consistent NPA charges results in a dramatic
improvement in the reduced anisotropy and especially in the quadrupole coupling constant (a shift of 35.2 MHz) with the isotropic shift being barely affected. The chemical shift and EFG tensors of compound 5 are thus influenced unusually strongly by the surrounding environment.
Some properties change unexpectedly upon QM/MM geometry optimisations. A much lower NQCC is predicted (very close to to experiment) but both the reduced
anisotropy and the isotropic chemical shift are now severely underestimated.
Table 18 Anisotropic chemical shift and EFG parameters of the cobaloxime complex (28) using different computational models.a
Experimentb
Cation
Gas opt. //Xray Cation Embedded cation //Xray QM/MM opt. Cation Embedded cation QM/MM opt
δiso 5320 ± 100 5733 5022 4964 4116 4127
δσ -‐1570 ± 50 -‐2502 -‐2625 -‐2022 -‐1427 -‐876
ησ 0.2 ± 0.2 0.31 0.05 0.03 0.23 0.46
CQ ±30.7 ± 0.4 81.4 99 63.2 -‐56.2 33.6
ηQ 0.6 ± 0.2 0.76 0.53 0.73 0.7 0.94 a Evaluated at the B3LYP/QZVPPdecon/6-‐31G* level on BP86-‐D geometries (basis set: def2-‐TZVPP/def2-‐SVP).
+1205 ppm gas-‐to-‐liquid shift correction added to isotropic chemical shifts. b From Ref.228
Figure 14 [CoDMG2(NH3)2]+ (28) structures from different sources. a) X-‐ray b) Cation QM/MM optimisation c)
Large cluster full optimisation d) Large cluster, partial optimisation.
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The reason for these dramatic changes in the tensor properties becomes obvious by comparing the new QM/MM optimised geometry with the X-‐ray geometry, as
illustrated in Figure 14 (a vs. b) and shown by bond lengths in Table 19. Curiously, the QM/MM optimised structure is dramatically distorted when compared to the X-‐ ray structure where the DMG ligand framework deviates significantly from planarity and the calculated Co-‐Nax bond lengths in Table 19 (see “Small cluster QM/MM Opt”)
are significantly shorter than both the X-‐ray and the gas structure.
Table 19. Co-‐N bond lengths (Å) of the different geometry optimisations of 28 compared to the X-‐ray structure.
Bond lengths X-‐ray Gas
Small cluster QM/MM Opt Large cluster QM/MM Opt: Partial Large cluster QM/MM
Opt: Full Periodic Co-‐Nax 1.96 1.98 1.90 1.99 1.97 1.99
Co-‐Neq 1.89 1.92 1.90 1.91 1.90 1.92
As the [CoDMG2(NH3)2]Br X-‐ray structure shows an almost planar DMG framework
and the gas-‐phase optimised structure is both planar and has Co-‐N bond lengths closer to the X-‐ray structure, this geometry distortion would appear to be an artifact of the QM/MM protocol we employ. The most likely explanation would be
overpolarisation of the QM region (specifically the ammine groups) by nearby point charges (mimicking hydrogen-‐bond accepting oxygen atoms), leading to shorter Co-‐N bond lengths that distort the whole complex or the inability of the L-‐J parameters to describe the intermolecular interactions between QM and MM regions sufficiently well. It is hard to distinguish between the two effects but it is possible to test if either of these effects are the reason, by increasing the QM region.
Figure 15 The large cluster of 28 that was calculated.
QM/MM geometry optimisations (using already converged charges) employing a larger -‐1 charged 5-‐unit cobaloxime cluster were thus performed. Two different geometry optimisations were tried: one in which the full cluster was optimised and another in which only the central unit was optimised while all other atoms were fixed. The structures from these optimisations can be seen in Figure 14 (c and d). Curiously, optimising the full cluster still results in distortion (of all units), although not as strong as before, while optimising only the central unit (keeping the others fixed but still in the QM region) leads to a structure that looks less distorted. The Co-‐N bond lengths in Table 19 reveal that the Co-‐Nax bond lengths for the partially
optimised structure are much longer now (presumably preventing most the distortion) but are slightly larger than the X-‐ray structure. The fully optimised structure on the other hand has bond lengths much closer to the X-‐ray structure but all units are quite distorted. These optimisations thus demonstrate the sensitivity of the central molecule to neighbouring interactions (specifically the Co-‐Nax bonds) and
suggest the QM-‐MM interaction term to be at least partly to blame. The reason for why the full cluster optimisation results in distortion might be due to a domino effect where the units near the QM-‐MM boundary are distorted by point charges which results in distortion of the other units, including the central one.
The NMR results for these large cluster optimisations are shown in Table 20. The results for the fully optimised structure show similar effects due to distortion as the results for the single QM/MM optimised cation before. However, the results for the partially optimised structure (which has almost almost planar DMG ligands) are in remarkable agreement with experiment for essentially all solid-‐state NMR
parameters. The NQCC is slightly larger than experiment, yet an ~8 MHz deviation is to be expected since DFT errors for NQCC can be even larger according to our EFG benchmarking study (see Table 8).
Table 20 Anisotropic chemical shift and EFG parameters of the cobaloxime 28 using the large cluster models.a
Experiment Large cluster Opt: partial Emb. Large cluster Opt: partial Large cluster Opt: Full Emb. Large cluster Opt: Full
δiso 5320 ± 100 5776.5 5689.7 5153.1 5070.6
δσ -‐1570 ± 50 -‐1680.0 -‐1629.4 1237.3 -‐1171.7
ησ 0.2 ± 0.2 0.32 0.29 0.45 0.40
CQ ±30.7 ± 0.4 -‐36.4 -‐38.5 25.7 27.4
ηQ 0.6 ± 0.2 0.58 0.58 0.96 0.99 a Evaluated at the B3LYP/QZVPPdecon/6-‐31G* level on BP86-‐D geometries (basis set: def2-‐TZVPP/def2-‐SVP).
+1205 ppm gas-‐to-‐liquid shift correction added to isotropic shifts.
Additionally, in order to get a more reliable geometry for NMR calculations, we carried out periodic DFT optimisations (using the CPMD code) at the BP86-‐D level with a planewave cutoff of 80 Ry starting from the X-‐ray crystal with Br-‐ exchanged
for Cl-‐ . This structure is much closer to the original crystal structure going by
planarity of the DMG framework and the bond lengths are very similar to the partial QM/MM large cluster optimised structure. This demonstrates that the distorted structure obtained from the small cluster QM/MM optimisations are artifacts
involving the QM-‐MM interaction term and not related to the crystal structure having a different counterion (which was another possibility).
Using the periodic structure, the single-‐point part of the QM/MM protocol was
then performed for a single cation and a larger cluster with and without embedded point charges. The results, presented in Table 21 show very good agreement with experiment although the reduced anisotropy is slightly underestimated. Again, dramatic changes in the solid-‐state NMR parameters upon inclusion of the point charges are seen, an effect that is reduced significantly as the QM region is increased.
Table 21 Anisotropic chemical shift and EFG parameters of the cobaloxime 28 using a periodic-‐DFT optimised geometry.a
Experiment Cation Emb. Cation Large Cluster Emb. Large Cluster
δiso 5320 ± 100 5826.3 5734.6 5821.5 5718.7
δσ -‐1570 ± 50 -‐2582.0 -‐1336.2 -‐1401.1 -‐1291.5
ησ 0.2 ± 0.2 0.09 0.08 0.23 0.19
CQ ±30.7 ± 0.4 85.0 -‐28.8 -‐27.6 -‐29.2
ηQ 0.6 ± 0.2 0.63 0.42 0.31 0.36 a Evaluated at the B3LYP/QZVPPdecon/6-‐31G* level. +1205 ppm gas-‐to-‐liquid shift correction added to isotropic
shifts.
We note that the solid-‐state NMR parameters obtained from these computations are strongly dependent on the DFT method used. We chose the B3LYP functional for most of these calculations as it has been used for 59Co NMR parameters in many other
studies but we also wanted to test the TPSS and TPSSh functionals, especially as they were among the best performers in the EFG study in Chapter 3.3. We thus repeated the NMR calculations on the periodic DFT geometry with the TPSS and TPSSh functionals. The results in Table 22 reveal that the obtained chemical shift tensor parameters are worse with TPSS and TPSSh than with B3LYP and that the computed NQCC is closer to experiment with TPSSh (and B3LYP) than TPSS. It may thus be that there is a slight advantage of hybrid functionals for transition metal EFG tensors after all, even though TPSS and TPSSh resulted in almost identical mean absolute errors in the EFG benchmarking in Chapter 3.3.
Table 22 Embedded large cluster of 28 (CPMD geometry) with different functionals.a
Experiment TPSS TPSSh B3LYP δiso 5320 ± 100 4504.6 4912.5 5718.7 δσ -‐1570 ± 50 -‐1033.3 -‐1119.3 -‐1291.5 ησ 0.2 ± 0.2 0.06 0.11 0.19 CQ ±30.7 ± 0.4 -‐41.3 -‐33.3 -‐29.2 ηQ 0.6 ± 0.2 0.24 0.21 0.36 a Evaluated at the DFT/QZVPPdecon/6-‐31G* level. +1205 ppm gas-‐to-‐liquid shift correction added to isotropic
shifts.
Solid 28 is thus a very interesting and difficult system for computational solid-‐state NMR spectroscopy. The system exhibits an unusually strong electronic effect of the environment on the wavefunction/electron density that affects the chemical shift anisotropy and especially the EFG tensor. Additionally, modelling the system by QM/MM approaches presents unusual difficulties for geometry optimisation that have not been encountered before.
We have demonstrated that these solid-‐state effects can be accounted for, resulting in much improved agreement with experiment, but at a rather high computational cost (large clusters and periodic DFT optimisations). This system should be very valuable as a test system to further explore QM/MM and other embedding approaches in order
to better account for solid-‐state effects on molecules. It may well be that slightly larger clusters like the one in Figure 15 may always be required for the NMR
calculation (which could be made computationally tractable by using CEP-‐basis sets as discussed before), however, one would ideally like to be able to perform the geometry optimisation with a small QM region (single molecule in this case). It is clear that a more accurate QM-‐MM interaction term will be required for this to be possible. Finally, we note that the validity of our gas-‐to-‐liquid correction deserves further scrutiny.
3.5.7 Test case: Towards larger crystals, 59Co solid-‐state NMR properties of vitamin B