Cameron F.
Baker
a,
John A.
Seed
a,
Ralph W.
Adams
a,
Daniel
Lee
*b and
Stephen T.
Liddle
*a
aDepartment of Chemistry, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK. E-mail: daniel.lee@manchester.ac.uk; steve.liddle@manchester.ac.uk
bDepartment of Chemical Engineering, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
First published on 6th December 2023
Diphosphonioalkylidene dianions have emerged as highly effective ligands for lanthanide and actinide ions, and the resulting formal metal–carbon double bonds have challenged and developed conventional thinking about f-element bond multiplicity and covalency. However, f-element–diphosphonioalkylidene complexes can be represented by several resonance forms that render their metal–carbon double bond status unclear. Here, we report an experimentally-validated 13C Nuclear Magnetic Resonance computational assessment of two cerium(IV)–diphosphonioalkylidene complexes, [Ce(BIPMTMS)(ODipp)2] (1, BIPMTMS = {C(PPh2NSiMe3)2}2−; Dipp = 2,6-diisopropylphenyl) and [Ce(BIPMTMS)2] (2). Decomposing the experimental alkylidene chemical shifts into their corresponding calculated shielding (σ) tensor components verifies that these complexes exhibit CeC double bonds. Strong magnetic coupling of Ce
C σ/π* and π/σ* orbitals produces strongly deshielded σ11 values, a characteristic hallmark of alkylidenes, and the largest 13C chemical shift tensor spans of any alkylidene complex to date (1, 801 ppm; 2, 810 ppm). In contrast, the phosphonium-substituent shielding contributions are much smaller than the Ce
C σ- and π-bond components. This study confirms significant Ce 4f-orbital contributions to the Ce
C bonding, provides further support for a previously proposed inverse-trans-influence in 2, and reveals variance in the 4f spin–orbit contributions that relate to the alkylidene hybridisation. This work thus confirms the metal–carbon double bond credentials of f-element–diphosphonioalkylidenes, providing quantified benchmarks for understanding diphosphonioalkylidene bonding generally.
In recent years, 13C NMR spectroscopic studies of transition metal alkylidenes have delivered a comprehensive understanding of MCR2 double bonds.31–35 In particular, the isotropic chemical shift (δiso) is intimately dependent on the shielding (σ) tensors, and a signature feature of alkylidene complexes which has emerged is that the σ11 tensor component, which is in the M
CR2 plane and orthogonal to the M
C σ- and π-bond principal axes, is substantially deshielded due to strong magnetic coupling of the M
C σ/π* and π/σ* orbitals.31 When considering applying that approach to diamagnetic lanthanide- and actinide-BIPM complexes, where data are available they exhibit a wide range of 13C NMR Ccarbene chemical shifts4,7,8,10 implying a varied range of bonding scenarios where the more deshielded the Ccarbeneδiso value is the more multiple bond character it will likely have to the metal, if not disproportionately shifted by spin orbit effects. However, in contrast to transition metal alkylidenes31–36 a detailed dissection of the shielding tensors beyond calculated δiso values has remained largely untested for f-element–BIPM complexes.30,37,38
In recent years NMR spectroscopy has emerged as a powerful tool for quantifying f-element chemical bonding when the individual contributions to the shielding tensors are analysed in detail,39 because the chemical shifts of a wide range of nuclei have proven to be very sensitive to the nature of their interactions with f-block ions.30,37,38,40–62 Recently some of us,56,58,62 and others,53,54 demonstrated that 15N, 29Si, and 31P NMR spectroscopies combined with computational analysis of chemical shielding tensor properties provides powerful probes of f-element–ligand covalency, so our attention turned to examining BIPM–f-element complexes using 13C NMR spectroscopy. We focus on two cerium(IV)-carbene complexes [Ce(BIPMTMS)(ODipp)2] (1, BIPMTMS = {C(PPh2NSiMe3)2}2−; Dipp = 2,6-diisopropylphenyl)15,18 and [Ce(BIPMTMS)2] (2) (Fig. 2).19 Using 13C–31P 2D solution NMR spectroscopy the 13C δiso of the carbene centres in 1 and 2 were previously determined to be 324.6 (JPC = 149 Hz) and 343.5 (JPC = 170 Hz) ppm, respectively. These downfield δiso values are unusually highly deshielded and well into the usual range (200–400 ppm) of alkylidenes,36 and a range of spectroscopic, magnetic, and computational methods consistently describe 1 and 2 as having no appreciable temperature independent paramagnetism (TIP) and being closed-shell singlet (i.e. not multi-reference) formulations.18,19 These two complexes therefore represent ideal benchmarks from which to quantify the nature of the CeCBIPM bonds and so inform the debate that surrounds the multiple bonding aspect of BIPM complexes generally.
![]() | ||
Fig. 2 Cerium-carbene complexes 1 and 2. These complexes are the two subject molecules of this study. Dipp = diisopropylphenyl. |
Here, we report an assessment of the shielding tensors that underpin the δiso values for 1 and 2. This work confirms that CeC double bond interactions are indeed present in 1 and 2, revealing dominant σ11 data that are the hallmark of alkylidenes, and the largest tensor spans of any metal-alkylidene complex. The data quantifies the relative extent of Ce
C σ- and π-bond stabilisation with respect to the smaller phosphonium-substituent contributions, provides further support for the previously proposed inverse-trans-influence (ITI) in 2, and reveals variance in the spin–orbit-induced spin-polarisation of the Ccarbene that can be related to the σ- and π-components and their variable levels of 2s vs. 2p character. Overall, this work confirms the M
C double bond credentials of these diphosphonioalkylidene complexes and provides quantified benchmarks for diphosphonioalkylidene bonding more generally.
In order to provide a chemically localised and hence more instructive model than the delocalised MO description, the Natural Bond Orbitals (NBOs) of 1 and 2 were examined using the B3LYP-HF20 and -HF30 functionals, respectively. In both cases NBO identifies clear-cut σ- and π-bonding interactions constituting CeC double bonding interactions (Fig. 4 and 5). For 1, the Ce
C σ-bond is found to be 13% Ce (6s/6p/5d/4f: 1/0/32/67%) and 87% Ccarbene (2s/2p: 15/85%) character. The Ce
C π-bond in 1 is similarly polarised being composed of 11% Ce (6s/6p/5d/4f: 1/1/31/67%) and 89% Ccarbene (2s/2p: 2/98%). For 2, the Ce
C σ-bond is 15% Ce (6s/6p/5d/4f: 3/0/47/50%) and 85% Ccarbene (2s/2p: 11/89%) but the π-bonds are more polarised at 7% Ce (6s/6p/5fd/4f: 0/0/53/47%) and 93% Ccarbene (2s/2p: 0/100%) character. We note in passing that these NBO data are in good agreement with the previously reported BP86-NBO data (see Tables S5 and S6† for BP86–B3LYP comparisons).15,18,19 Given that these calculations satisfactorily reproduce the experimentally determined δiso spectroscopic data, they: (i) quantify significant contributions of 5d- and 4f-orbital bonding character for Ce; (ii) acknowledging that the bonding is polarised, support the Ce
C double bonding interaction description.
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Fig. 4 Natural Bond Orbitals (NBOs) of 1 at the B3LYPHF20 level. (a) The Ce![]() ![]() |
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Fig. 5 Natural Bond Orbitals (NBOs) of 2 at the B3LYPHF30 level. (a and b) The two Ce![]() ![]() |
Ramsey's formalism, eqn (1), relates NMR interactions to a quantum-mechanical perspective by decomposing magnetic shielding contributions into σd and σp components. These parameters are dependent on electron orbital angular momenta,64–66 and whilst this does not directly translate to the MO approach of hybrid DFT (B3LYP), it provides a framework with which to rationalise NMR magnetic shielding calculations when σso contributions are included,67eqn (2).
σiso = σd + σp | (1) |
σiso = σd + σp + σso | (2) |
The 13Ccarbeneσd values for 1 and 2 are 268.6 and 258.9 ppm, respectively. As expected, there is relatively little variation for these values, since σd derives principally from tightly-bound core electron densities that respond little to valence-level perturbations.67 The ∼10 ppm variance within the 13Ccarbeneδiso values of >320 ppm can be considered to be minor and thus negligible to the discussion.
Turning to the 13Ccarbeneσso data, the values for 1 and 2 are −23.6 and −79.7 ppm, respectively, which is consistent with σso contributions in other CeIV–C complexes,55 but in passing a σso of close to −80 ppm is indicative of significant 4f-orbital character in the bonding, which is notable given the usual ‘core-like’ description of 4f-orbitals. This likely reflects the strong CeC σ-bonding in 2, see below. These are clearly not insignificant contributions to the 13Ccarbeneσiso values of 1 and 2, but given the observed 13Ccarbeneδiso values of >320 ppm, which would be >280 ppm in the absence of spin–orbit effects it is clear that whilst the σso data should not be ignored they can be considered to be secondary to the primary determinant of the 13Ccarbeneδiso values, which is the σp values.
The σp term can be presented in reduced form as:
![]() | (3) |
The σp term is inversely proportional to the energy gap between the occupied and virtual orbitals that become magnetically coupled in the presence of an externally applied magnetic field, so smaller ΔE gaps produce larger σp values. However, examination of the HOMO–LUMO gaps of 1 and 2 shows that they are unremarkable (2.846–4.218 eV in B3LYP calculations) and so a disproportionate effect on σp from ΔE can be discounted.
Field-induced magnetic mixing of the ground state with low-lying, thermally inaccessible, paramagnetic states in 1 and 2, that is TIP, has been previously found to be negligible18,19 and multi-reference calculations on 1 and 2 showed little multi-reference character.18,19 This suggests that any TIP effects on the σp term will be modest,52,58 and thus the term will, like the ΔE term, not introduce a disproportionate effect on σp.
Turning to the remaining r3 term, σp is inversely proportional to r3. This is because as a nucleus (M) withdraws charge from the NMR nucleus (C) the C valence orbitals contract due to the increased electron deficiency at C. Thus, the 1/r3 term becomes larger (i.e. the NMR nucleus is more deshielded) resulting in a larger σp term. Put another way, the larger the bond order of, so more covalent, the bond involving the NMR nucleus the larger σp becomes.46 In this context, recalling the δiso values of 1 and 2, the σp values of −382.1 and −333.1 ppm are large, and hence significant, and consistent with the presence of CeC double bond interactions.
The shielding effects can be understood in terms of the rotated orbital model,31,68–71 which considers the action of the angular momentum operator on magnetically coupled occupied and virtual orbitals, which can be visualised as a 90° rotation of an idealised occupied C p-orbital to mix with an orthogonal vacant orbital. This has been comprehensively described elsewhere for alkylidenes,31 but of pertinence to the results here in brief the computed orientations of the 13C σ11, σ22, and σ33 shielding tensor principal components of 1 and 2 are shown in Fig. 6, where it can be seen that they align closely to the principal axes (x, y, and z). Thus, magnetic coupling of the σ and π* and π and σ* orbitals will correspond to rotation about the x axis resulting in σ11 deshielding along the x axis. The results of the MO analysis are presented in Fig. 7 and 8. For 1 and 2, for a given BIPMTMS ligand the occupied CeC σ-bond mixes with unoccupied Ce
C π*- and 4f-orbitals and the Ce
C π-bond mixes with unoccupied Ce
C σ*- and f-orbitals. In all cases, the dominant individual σ contribution to the σiso is σ11, which is deshielded due to strong σ/π* and π/σ* magnetic couplings that are orthogonal to the σ11 direction (x axis), and this is a signature feature of alkylidene complexes. Thus, for both 1 and 2 the principal magnetic coupling of orbitals that is responsible for the shielding tensors at the carbene centres derives from orbitals associated with the Ce
C linkage as found analogously in transition metal alkylidenes.31–35
Compound | SR | SOR | Δ so | % NBO | Occ. | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
NLMOa | Lb | NLc | L + NL | Lb | NLc | L + NL | Lb | NLc | L + NL | |||
a B3LYP calculations (HF = 20%, 1; 30% 2), all shielding parameters are in ppm. b Lewis contribution of the NLMO. c Non-Lewis contribution of the NLMO. d Defined as σ(SOR) − σ(SR) to isolate the SO component. e Essentially isotropic so only the average values provided. f Minor component so only average values provided. g Multiple NLMOs, but % NBOs all >85%. h Multiple NLMOs, but all occupancies >1.71 electrons per NLMO. i Data given for one carbene only since the data for both are identical. | ||||||||||||
1 | ||||||||||||
σ-Ce![]() |
σ iso | −135 | 4 | −131 | −186 | 3 | −183 | −51 | −1 | −52 | 89 | 1.78 |
σ 11 | −432 | 20 | −412 | −495 | 18 | −477 | −63 | −2 | −65 | |||
σ 22 | 3 | −11 | −8 | −76 | −13 | −89 | −79 | −2 | −81 | |||
σ 33 | 25 | 3 | 28 | 13 | 3 | 16 | −12 | 0 | −12 | |||
π-Ce![]() |
σ iso | −123 | 15 | −108 | −121 | 16 | −105 | 2 | 1 | 3 | 85 | 1.70 |
σ 11 | −405 | 35 | −370 | −400 | 32 | −368 | 5 | −3 | 2 | |||
σ 22 | −5 | 4 | −1 | 2 | 9 | 11 | 7 | 5 | 12 | |||
σ 33 | 42 | 8 | 50 | 35 | 7 | 42 | −7 | −1 | −8 | |||
2 × C–P | σ iso | −57 | −5 | −62 | −40 | −5 | −45 | 17 | 0 | 17 | 98 | 1.96 |
σ 11 | −9 | 2 | −7 | 14 | 1 | 15 | 23 | −1 | 22 | |||
σ 22 | −88 | −12 | −100 | −60 | −12 | −72 | 28 | 0 | 28 | |||
σ 33 | −75 | −5 | −80 | −73 | −5 | −78 | 2 | 0 | 2 | |||
1score-Ce | σ iso | 200 | 0 | 200 | 204 | 0 | 204 | 4 | 0 | 4 | 100 | 2.00 |
Σ other | σ iso | −9 | 7 | −2 | −4 | 5 | 1 | 5 | −2 | 3 | ||
![]() |
||||||||||||
2 | ||||||||||||
σ-Ce![]() |
σ iso | −101 | −11 | −112 | −227 | −5 | −232 | −126 | 6 | −120 | 89 | 1.79 |
σ 11 | −386 | −4 | −390 | −563 | 4 | −559 | −177 | 8 | −169 | |||
σ 22 | 71 | −30 | 41 | −126 | −20 | −146 | −197 | 10 | −45 | |||
σ 33 | 13 | 1 | 14 | 7 | 1 | 8 | −6 | 0 | −6 | |||
π-Ce![]() |
σ iso | −100 | 13 | −87 | −101 | 13 | −88 | −1 | 0 | −1 | 85 | 1.71 |
σ 11 | −394 | 35 | −359 | −390 | 35 | −355 | 4 | 0 | 4 | |||
σ 22 | 13 | 0 | 13 | 7 | 0 | 7 | −6 | 0 | −6 | |||
σ 33 | 82 | 5 | 87 | 81 | 5 | 86 | −1 | 0 | −1 | |||
2 × C–P | σ iso | −65 | −10 | −75 | −24 | −12 | −36 | 41 | −2 | 39 | 98 | 1.96 |
σ 11 | 4 | −2 | 2 | 54 | −4 | 50 | 50 | −2 | 48 | |||
σ 22 | −100 | −23 | −123 | −27 | −26 | −53 | 73 | −3 | 70 | |||
σ 33 | −99 | −5 | −104 | −99 | −5 | −104 | 0 | 0 | 0 | |||
1score-Ce | σ iso | 201 | 0 | 201 | 207 | 0 | 207 | 6 | 0 | 6 | 100 | 2.00 |
Σ other | σ iso | −11 | 10 | −1 | 2 | −1 | 1 | 13 | −11 | 2 |
Inspection of the data in Table 1 reveals that the principal shielding contributions to the δiso values of 1 and 2 are dominated by the CeC σ- and π-bond components supplemented by smaller C–P bond contributions. These contributions are in essence counter-balanced only by the σd contribution from the 1s core Ccarbene orbital since various Lewis and Non-Lewis contributions from the Ce ions and other minor contributions tend to cancel out. Thus, like any other M
CR2 bond, the Ccarbene centres in 1 and 2 exhibit δiso values that reflect stabilisation of the Ccarbene by the metal- and R-substituents (where here R = the phosphonium groups).
Focussing on the SOR-NLMO-NMR aspects of Table 1, the data clearly show a dominance of the CeC bonds in total (1: −288 ppm; 2, −320 ppm) over the total two C–P bonds (1: −45 ppm; 2, −36 ppm) to the shielding. Thus, for 1 and 2 the M (here Ce) is performing the dominant stabilising role with the C–P constituting a much smaller stabilising role.
Where the split of σ- vs. π-bonding of the CeC bonds in 1 and 2 are concerned, in both cases the former component dominates over the latter, being ∼2
:
1 and ∼3
:
1, respectively. This confirms that the σ-components are strongest, but it is also the case that for 1 and 2 in each case the π-components are over twice that of the two C–P bonds combined. The Ce
C π-bonds are thus clearly far from being negligible, and weaker π-bonds compared to σ-bonds would anyway be anticipated from basic σ- and π-orbital overlap efficiency arguments. The presence of Ce
C π-bonds from this analysis is also consistent with the QTAIM data that consistently present non-zero ellipticity parameters consistent with the presence of double bonds rather than the zero ellipticity parameters that are associated with single and triple bonds.
Whilst the NLMO analysis does not report which virtual orbitals the NLMO orbitals are magnetically coupled to, the MO analysis provides the necessary framework to rationalise the NLMO shielding data. In particular, echoing the MO analysis the CeC σ- and π-bonds all exhibit large deshielded σ11 values, that are consistently the largest components of the breakdown of σiso, resulting from σ/π* and π/σ* magnetic coupling that can be visualised as rotation of the relevant C p-orbitals about the x axis. Interestingly, for both complexes the C–P bonds show not insignificant deshielded σ22 and σ33 values, reflecting magnetic coupling that can be visualised as rotation of the C p-orbital aligned along the P–C–P bond (x axis) into the σ* (z axis, rotation about the y axis) and π* (y axis, rotation about the z axis), respectively. These contributions are facilitated by the T-shaped nature of the Ce
CP2 linkages in 1 and 2,31 but are still far smaller than the main Ce
C σ- and π-bond contributions to the shielding.
The NLMO analysis also reveals another interesting feature, which is that the σ-component is larger for 2 than for 1 even though in 2 there are two mutually trans-carbene donors; these strong σ-donors would ordinarily be anticipated to result in mutually weaker, not stronger, trans bonding. Thus, the shielding and bond order data presented here further support the presence of an ITI, which had previously been proposed for 2 on the basis of structural data and 5p-orbital in- and out-of-core calculations.19 This situation for 2 is accompanied by the π-bonding component still being present, but weaker than the π-bonding component in 1, which is in-line with the flexible nature of the bonding of these carbenes. This also likely reflects the dominance of the σ-bonding leaving the Ce ion with a diminished requirement for additional π-bonding compared to the situation in 1.
Since increased stabilisation is another way of articulating stronger bonding in covalent interactions, then given the relationship between shielding and σp and the NBO (and NLMO) bonding descriptions, these data support the presence of CeC double bonding interactions in 1 and 2.
The data in Table 1 also permits an analysis of the spin–orbit contributions by subtraction of the SR-NLMO values from the SOR-NLMO data. Notably, for 1 and 2 the dominant spin–orbit contributions are mediated by the CeC σ-bonds rather than the π-bonds. This can be rationalised by recalling that the 4f-orbitals will likely mediate the majority of the spin–orbit contributions from the Ce ion, and that transfer of spin–orbit-induced spin-polarisation to the NMR-nucleus (Ccarbene) will be via the C 2s orbital (Fermi contact). The NBO (and NLMO) data consistently show significant 4f contributions to the Ce-bonding, but variable 2s C-character. The Ce
C σ-bonds consistently show ∼11–15% C 2s character, which is evidently sufficient to mediate the spin-polarisation by Fermi contact, whereas the Ce
C π-bonds exhibit ≥98% 2p character and thus they have little 2s character to mediate spin–orbit contributions. Notably, the NLMO spin–orbit contribution for 2 is large, as it was for the σso value from the shielding analysis, for the Ce
C σ-bond. This further supports the presence of significant 4f-orbital character in the Ce
C bond, even though 4f-orbitals are normally regarded as being ‘core-like’, which is also consistent with the presence of ITI bonding in 2.
Having identified DFT functionals that reproduce the 13Ccarbeneδiso values to within 2 ppm, there can be confidence in the resulting computational benchmarking descriptions. It is interesting to note that whilst the BP86 functional does not reproduce the δiso values as well as B3LYP functionals, the MO, bond order, NBO, and NLMO analysis from either functional for 1 and 2 are, like-for-like, very similar. So whilst BP86 does not fare as well as B3LYP in the fine detail of reproducing shielding tensors, which are exceedingly sensitive to the computed wavefunction and spin–orbit effects, any differences recede with the arguably coarser orbital and bond order metrics. The tentative implication is that BP86 is adequate for ‘generic’ orbital and bond order analysis, but a hybrid functional really is needed for ‘specific’ sensitive spectroscopic parameters, a situation that was also found in modelling a terminal uranium(VI)-nitride.58
The consistent picture that emerges from the computational analysis is that the highly deshielded experimentally observed 13Ccarbeneδiso values are predominantly due to large, negative σp values, which in themselves directly reflect strong CeC multiple bonds and external field-induced magnetic coupling of occupied and vacant orbitals associated with that linkage. Indeed, complexes 1 and 2 exhibit the largest 13C chemical shift tensor spans of any metal-alkylidene to date.31–35 The NLMO-NMR analysis reveals a dominance of Ce
C σ- over π-bond contributions, but these combined are far greater than the contributions from the phosphonium-substituents. The Ce
C π-bonds, perhaps the most debatable component of the bonding, are hence shown to be far more substantial than the two phosphonium-substituents combined, which together reaffirms the notion that the Ce
C bond is principally stabilised by the Ce ion, with the two phosphonium-substituents providing much weaker stabilisation. These data are all consistent with prior QTAIM data, whose ellipticity parameters were consistent only with the presence of Ce
C double bonds in 1 and 2. Indeed, the consistent picture that emerges from the MO and NLMO analysis is the dominance of the strongly deshielded σ11 component, which is a signature of alkylidenes.31
The NLMO analysis also clearly shows that the two CeC σ-bonds in 2 are evidently strong, which given they are mutually trans is notable and provides further support for the prior suggestion of the presence of an ITI in 2.19 The NLMO analysis also shows variable transmittance of spin–orbit-coupling, which can be related to the hybridisation of the alkylidene centres, i.e. greater 2s character facilitates greater σso. That there are substantial spin–orbit contributions that likely originate from the Ce 4f-orbitals, which are usually described as ‘core-like’ and hence interacting little with ligand frontier orbitals, is notable and in-line with the overall description of 1 and 2 as exhibiting significant Ce
C double bonds. Lastly, the clearly larger spin–orbit contributions for 2 compared to 1 reflects the strong Ce
C σ-bonding, which again emphasises the presence of an ITI in this tetravalent complex.
Restricted calculations were performed using the Amsterdam Density Functional (ADF) suite version 2017 with standard convergence criteria.74,75 Geometry optimisations were performed using coordinates derived from the respective crystal structures as the starting points. The H-atom positions were optimised, but the non-H-atom positions were constrained as a block. The DFT geometry optimisations employed Slater type orbital (STO) TZ2P polarisation all-electron basis sets (from the Dirac and ZORA/TZ2P database of the ADF suite). Scalar relativistic approaches (spin–orbit neglected) were used within the ZORA Hamiltonian76–78 for the inclusion of relativistic effects and the local density approximation (LDA) with the correlation potential due to Vosko et al. was used in all of the calculations.79 Generalised gradient approximation corrections were performed using the functionals of Becke and Perdew.80,81
Scalar and spin–orbit relativistic (ZORA-TZ2P-all-electron) single point energy calculations were then run on the geometry optimised coordinates. The conductor-like screening model (COSMO) was used to simulate benzene solvent effects. The functionals screened included BP86, PBE0-HF25, PBE0-HF40, B3LYP-HF20, B3LYP-HF30, B3LYP-HF35, and B3LYP-HF40, with B3LYP-HF20 and B3LYP-HF30 giving the closest agreement of computed NMR properties compared to experiment for 1 and 2, respectively. Nalewajski-Mrozek values were computed within the ADF program. NBO and NLMO analyses were carried out on the respective B3LYP data using NBO6.82 These calculations used the Hartree–Fock RI scheme to suspend the dependency key and overcome numerical issues. The MOs and NBOs were visualised using ADFView.
NMR shielding calculations were carried out using the NMR program within ADF.72,73,83–87 Calculated nuclear shieldings were converted to chemical shifts by subtraction from the calculated nuclear shielding of CH4 calculated at the same SR or SOR functional level in each case (HF20 SR/SOR = 191.3/192.1; HF30 SR/SOR = 191.4/192.2). MO contributions to the nuclear shieldings were calculated at the scalar and spin–orbit levels, the former with the FAKESO key. Scalar and spin–orbit NLMO calculations of the computed nuclear shieldings were carried out using NBO6 and ADF. These calculations used the Hartree–Fock RI scheme to suspend the dependency key and avoid numerical issues. Shielding tensors were visualised using TensorView.88
Footnote |
† Electronic supplementary information (ESI) available: Computational details. See DOI: https://doi.org/10.1039/d3sc04449a |
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