Introduction

Diorganozincs (ZnR2)1,2 have a special place in chemical history; diethylzinc (ZnEt2) was amongst the first organometallics (Frankland C19th)3. ZnR2 can range in reactivity from Lewis basic/nucleophilic (i.e. electron donating) in e.g. transmetalation4 or nucleophilic substitution reactions5,6,7,8,9,10,11,12 through to Lewis acidic/electrophilic9,11,12,13,14,15,16,17,18,19,20 (i.e. electron acceptor). This diversity of reactivity has led to considerable liquid-phase applications in synthetic chemistry: the Nobel Prize-recognised Negishi cross-coupling reaction21,22,23,24,25; asymmetric autocatalysis of the Soai reaction26; Lewis acid catalysis27; frustrated Lewis pair catalysts (FLPs)15; insertion chemistries (CO2 and SO2)28,29; transfer reagents30,31,32,33; and in nanomaterial preparation13,14.

These significant advances in ZnR2 chemistry have been driven mainly by empirical, iterative synthetic experimentation, as liquid-phase ZnR2 species are spectroscopically quiet (Fig. 1)34,35. In a telling approach, the enzymatic community at times have substituted Zn2+ for other metal cations (e.g. Co2+, Cu2+, Cd2+ etc.) that were easier to observe spectroscopically in model systems34. This spectroscopic near-silence has led to a dearth of descriptors for ZnR2, severely limiting the interpretation, prediction and fine-tuning of ZnR2 reactivity. Liquid-phase EPR and UV-Vis spectroscopies are ineffective for producing descriptors for closed-shell d10 Zn2+. One quantitative Lewis acidity descriptor, the electron acceptor number measured using 31P NMR spectroscopy, has been used for three ZnR2 compounds11. This method investigates the interaction of ZnR2 with triethylphosphine oxide. However, it is unsatisfactory because the phosphorus atom is positioned at a distance from the zinc centre36, which is the site of ZnR2 reactivity e.g. electron acceptance for Lewis acidic ZnR2.

Fig. 1: Current diorganozinc analysis methods, their limitations, and our liquid-phase X-ray spectroscopy approach.
figure 1

Overview of current methods for studying ZnR2 complexes and their shortcomings and our work here using an advanced X-ray spectroscopy toolkit for studying liquid-phase ZnR2 complexes.

Experimental or calculated electronic structure data is often used to produce Lewis basicity/acidity descriptors37,38,39,40. Advantageously, these intrinsic descriptors capture Lewis basicity/acidity independent of any probe molecule. However, liquid-phase experimental electronic structure spectroscopy has been severely limited by experimental challenges. Due to the vacuum conditions required, liquid-phase photoelectron spectroscopy studies are very challenging even for simple aqueous solutions41, let alone very reactive ZnR2 solutions. Gas-phase photoelectron spectroscopy has been used to produce a Lewis basicity descriptor, the highest occupied molecular orbital (HOMO) energy, for four ZnR2 (R = alkyl)38; however, this descriptor is not representative of liquid-phase ZnR2, leaving a huge unanswered question over solvent influence. Therefore, for liquid-phase ZnR2 the frontier orbitals (e.g. the HOMO and the lowest unoccupied molecular orbital, LUMO) have never been experimentally investigated let alone quantified.

In this article we use zinc-specific X-ray spectroscopies to produce zinc-specific, intrinsic descriptors, as hard X-ray spectroscopies overcome experimental challenges for liquid-phase studies as vacuum conditions are not required42,43. The zinc-specificity of these X-ray spectroscopy-derived descriptors give direct insight into the zinc centre, where ZnR2 reactivity occurs, e.g. electron donation for Lewis basic/nucleophilic ZnR2. Zn 1s X-ray absorption near edge structure (XANES) spectroscopy has been used widely for liquid-phase zinc compounds but sparingly for organozinc compounds44,45,46. Only two liquid-phase studies of Zn 1s non-resonant valence-to-core X-ray emission spectroscopy (NR-VtC-XES) are known, both for ZnCl2-based samples47,48, and none for Zn 1s resonant VtC-XES (R-VtC-XES), highlighting the novelty of our approach. For metals, the main usage of XANES, NR-VtC-XES and R-VtC-XES has been fourth period (i.e. first row) transition metals42,43,49,50,51,52.

In part one of our article, we determine speciation and geometric structure for 14 ZnR2 using a combination of synchrotron-based Zn 1s high-energy-resolution fluorescence detected (HERFD)-XANES spectroscopy (Fig. 2a), density functional theory (DFT) and time-dependent DFT (TDDFT) calculations. To produce intrinsic descriptors, the structure of ZnR2 must be known, so the influence on reactivity of steric factors relative to electronic structure factors can be considered. Synthetic chemists are in the very unusual position where the starting geometric structures of ZnR2 in toluene/hexane9,10,11,12 are poorly understood; indeed, the geometric structures of ZnR2reagents in non-coordinating solvents remain scattered and elusive53. The 67Zn nucleus (spin 5/2) possesses low NMR sensitivity and gives very broad features so geometric structural conclusions cannot be drawn. Other NMR active nuclei (e.g. 1H and 13C) are distant from the reactive Zn centre and, coupled with the nature of NMR (through-bond and through-space effects), makes relating chemical shift with geometric structure unreliable. Linearity (i.e. C-Zn-C angle of 180°) has been inferred for some ZnR2 using indirect methods, e.g. melting points, boiling points, solubility, and dipole moment determination54,55. In contrast, diffusion-ordered spectroscopy (DOSY) NMR studies in [D8]toluene suggested that ZnPh2 can form dinuclear (ZnPh2)29, although the relatively high atomic weight of zinc and elongated shape of ZnPh2 make this interpretation very uncertain9,56,57. Furthermore, in the solid-phase, ZnPh2 displayed dinuclear three-coordinate bridging (ZnPh2)254. XANES spectroscopy showed that ZnEt2 is linear in toluene (i.e. C-Zn-C angle of 180°), but no other R substituents were studied45.

Fig. 2: Probing electronic transitions in diorganozinc complexes.
figure 2

A new spectroscopic approach for ZnR2. Electronic transition schematic of ZnR2 complexes studied: a Zn 1s HERFD-XANES, b Zn 1s NR-VtC-XES, c Zn 1s R-VtC-XES, d final-states of Zn 1s R-VtC-XES and UV-Vis spectroscopy.

In part two of our article, we use a combination of NR-VtC-XES (Fig. 2b) and Zn 1s HERFD-XANES spectroscopy (Fig. 2a) to identify the zinc-containing occupied molecular orbitals (OMOs) and unoccupied molecular orbitals (UMOs). This identification is essential for producing zinc-specific descriptors, and also allows us to highlight the OMOs and UMOs that give ZnR2 their remarkable reactivity compared to other common zinc-containing species such as [Zn(OH2)6]2+ and ZnCl2(THF)2.

In part three of our article, we describe a new approach using zinc-specific X-ray spectroscopy experiments and calculations to produce three zinc-specific (i.e. local), intrinsic36 descriptors: zinc-specific hardness (ηZn), zinc-specific absolute electronegativity (χZn, the negative of the zinc-specific electronic chemical potential, μZn) and zinc-specific global electrophilicity index (ωZn). To obtain ηZn, χZn and ωZn, we combine our knowledge on experimental R-VtC-XES (Fig. 2c), zinc-containing OMOs and UMOs, and DFT calculations (underpinned by the theories of Pearson37,39,40).

Results and discussion

Speciation and geometry

All ZnR2 compounds (typically 0.1 M) in toluene studied here have a linear C-Zn-C structure, i.e. a C-Zn-C angle of 180°. The Zn 1s HERFD-XANES spectra for all ZnR2 in toluene (Figs. 3a, 4a and Supplementary Fig. 1) and ZnEt2 in hexane (Supplementary Fig. 2) gave a single sharp, intense peak at a low incident energy of ~9661 eV. This common motif for linear two-coordinate complexes, e.g. copper complexes58, has previously been observed for ZnEt2 in toluene using standard resolution XANES spectroscopy45, and is due to two absorption transitions; Zn 1s to two degenerate UMOs with very strong Zn p contributions (discussed further below). In contrast to linear ZnR2, the Zn 1s HERFD-XANES spectra for octahedral [Zn(NCMe)6]2+ and [Zn(OH2)6]2+ and tetrahedral ZnCl2(THF)2 gave broader, lower intensity peaks at higher incident absorption energy (Fig. 3a). The excellent visual match of experimental Zn 1s HERFD-XANES spectra (Figs. 3a, 4a) and calculated XANES spectra (Figs. 3b, 4b), give high confidence that we have captured the speciation and geometric structure correctly in our calculations. These linear structures in relatively non-coordinating solvents are analogous to gas- and solid-state linear structures for ZnR2, i.e. in the absence of any solvent molecules38,59.

Fig. 3: Zn 1s HERFD-XANES, NR-/R-VtC-XES, and DFT calculated spectra of ZnEt2 and common zinc-containing compounds.
figure 3

0.1 M ZnEt2 in toluene, ZnCl2(THF)2 (0.1 M ZnCl2 in THF), [Zn(NCMe)6]2+ (0.1 M Zn(OTf)2 in MeCN) and [Zn(OH2)6]2+ (0.1 M ZnCl2 in H2O): a Zn 1s HERFD-XANES spectra (y intensities normalised), b TDDFT calculations of Zn 1s HERFD-XANES (shifted by –8.90 eV to visually match experimental Zn 1s HERFD-XANES spectra69), c Zn 1s NR-VtC-XE spectra, d KS-DFT calculations of Zn 1s NR-VtC-XE spectra (shifted by −8.90 eV to visually match experimental Zn 1s NR-VtC-XE spectra). e R-VtC-XE spectra. f Visual representations for key Zn p-based OMOs and UMOs; for ZnEt2 the LUMO + 2 is degenerate (or near-degenerate) with another UMO (Supplementary Fig. 8).

Fig. 4: Zn 1s HERFD-XANES, NR-/R-VtC-XES, and DFT calculated spectra of ZnR2 (R = Me, Et, i-Pr, C6F5) complexes.
figure 4

Experimental and calculated X-ray spectra for the diorganozinc compounds ZnR2 (R = Me, Et, i-Pr, Ph, C6F5, concentration 0.1 M for all apart from C6F5 which was 0.033 M); calculated C6F5 shown here is the staggered conformer. a Zn 1s HERFD-XANES spectra (y intensities normalised), b TDDFT calculations of Zn 1s XANES spectra (shifted by −8.90 eV to visually match experimental Zn 1s HERFD-XANES spectra69), c Zn 1s NR-VtC-XE spectra, d KS-DFT calculations of Zn 1s NR-VtC-XE spectra (shifted by −8.90 eV to visually match experimental Zn 1s NR-VtC-XE spectra), e Zn 1s R-VtC-XE spectra, f Visual representations for key Zn p-based OMOs and UMOs; for ZnR2 the UMO shown here is degenerate (or near-degenerate) with another UMO (Supplementary Fig. 8).

There is the potential for liquid-phase flex in the C-Zn-C linear bonds for ZnR2 away from a C-Zn-C angle of 180°. Using calculated total energies for ZnEt2, the structure at 180° is the most stable; decreasing the C-Zn-C angle decreases the structure stability (Supplementary Table 1 and Supplementary Fig. 3). However, when the C-Zn-C angle is greater than 160° the calculated XANES spectra are very similar to that for the structure with C-Zn-C angle at 180° (Supplementary Fig. 3); our experimental data cannot distinguish between structures with a C-Zn-C angle of between 180° and 160°. Furthermore, the calculated total energies for structures with a C-Zn-C angle greater than 160° are within 10 kJ mol−1; therefore, whilst the structure at C-Zn-C angle of 180° is the most stable, we cannot rule out slight flexing of the C-Zn-C angle away from 180° (i.e. linear) in the liquid-phase. The dihedral angles (eclipsed 0° or staggered 90°) between the two R substituents gave, within calculated uncertainty, the same total energies (Supplementary Figs. 4,5 and Supplementary Table 24). Therefore, both conformers are very likely to be present in the solution for ZnR2.

No evidence for the existence of bimetallic bridging structures was found. The calculated XANES spectrum for dimeric (ZnPh2)2, based on a solid-state structure54, shows a clear loss of the sharp, intense peak at low incident energy (Supplementary Fig. 6). This is as expected for a three-coordinate, non-linear zinc centre, as the UMO degeneracy is lifted compared to two-coordinate linear ZnPh258. Furthermore, all ZnR2 compounds studied here gave very similar experimental and calculated Zn 1s HERFD-XANES spectra with relatively sharp absorption features at low incident energy, showing that bridging species were not present in significant concentration.

Electronic-structure-based descriptors will explain the reactivity of two-coordinate, linear ZnR2 because the zinc centre is sterically accessible. The vdW space filling structures for ZnR2 studied here, even Zn(C6F5)2 and Zn(t-Bu)2 with their relatively bulky ligands, all have a clearly visible zinc centre (Figs. 3, 4, right-hand side, Supplementary Fig. 7). In contrast, for the four- and six-coordinate species, the zinc centre is shielded by the ligands and is not visible in the vdW space filling structures (Fig. 3, right-hand side). Therefore, steric hindrance by the R substituents on ZnR2 is unlikely to be a factor in deciding reactivity at the zinc, especially when the zinc centre is acting as an electron acceptor. Furthermore, all ZnR2 in non-coordinating solvents are coordinatively unsaturated. Hence, all ZnR2 can form a bond to an electron donor ligand without the need to first break a Zn-ligand bond, e.g. ZnMe2 + THF to form ZnMe2(THF)260. Furthermore, binding of a chiral Lewis donor substrate/ligand to the coordinatively unsaturated zinc centre has been shown to allow a range of stereoselective reactions to be performed26,61.

Molecular orbital identification—Why are ZnR2 so remarkable?

Given the importance of the sterically accessible zinc centre in all ZnR2, it is vital to build a picture of the frontier molecular orbitals with significant zinc contributions, as these MOs will control reactivity instead of stereochemical factors. We will demonstrate why the remarkable reactivity of ZnR2 occurs relative to other common zinc-containing species.

For all ZnR2 where R = alkyl the only MO with a significant Zn p contribution ( ~ 16% Zn p, Supplementary Table 5) is the HOMO (Fig. 4f and Supplementary Figs. 914). This is a remarkable result given that the formal oxidation state is Zn2+, with the expectation being that electron density of frontier OMOs would reside mainly on the ligands. For R = aryl the OMO,Zn p is the HOMO-4 (with the HOMO to HOMO-3 from the aryl substituents, Fig. 4f, Supplementary Table 5 and Supplementary Figs. 1524). These identifications are based on the intense, narrow, high energy peak observed for all ZnR2 in both the experimental (Fig. 3c, Fig. 4c) and calculated (Fig. 3d, Fig. 4d) Zn 1s NR-VtC-XE spectra (the selection rules for Zn 1s NR-VtC-XES are OMO,Zn p to Zn 1s35,47,48), along with a visual analysis of the MO, which shows a clear sigma bond along the axis of the linear C-Zn-C bonds (Fig. 3f, 4f). In contrast, for the 4/6-coordinate zinc-containing species, the main zinc contributions were for multiple OMOs far deeper than the HOMO, captured by the broader and lower energy peaks in Zn 1s NR-VtC-XE spectra (Fig. 3c), e.g. for [Zn(OH2)6]2+ the HOMO-8 to HOMO-10 each had ~6% Zn p contribution (Supplementary Table 6). The OMO,Zn p is very likely to be more influential on reactivity than OMO, Zn s, as the only OMO with a strong Zn s contribution is HOMO-1 for ZnR2 (where R = alkyl) and HOMO-5 for ZnR2 (where R = aryl) (Supplementary Figs. 2528 and Supplementary Table 5), which are ~1.5 eV deeper than the single Zn p OMO.

The three lowest energy UMOs (LUMO, LUMO + 1 and LUMO + 2) for almost all ZnR2, and also the common zinc-containing species, were composed of two Zn p-based UMOs and one Zn s-based UMO (Figs. 3f, 4f, Supplementary Figs. 924 and Supplementary Table 5). This identification is based on a combination experimental and calculated Zn 1s HERFD-XANES spectra plus ground state DFT calculations. All three of these UMOs for ZnR2 are similar in energy (Supplementary Figs. 2528). The two degenerate (or near-degenerate) Zn p-containing UMOs have Zn p contributions of ~75% (R = alkyl) and ~40% (R = aryl), all perpendicular to C-Zn-C bond (Figs. 3f, 4f and Supplementary Table 5).

Our results demonstrate that Zn p orbitals contribute strongly to both OMOs and UMOs that are key in bond breaking and forming, contradicting theoretical findings which suggested that Zn p contributions could be neglected for zinc-containing species, including ZnR262,63. Furthermore, previous reports utilising a simplified hypervalent scheme, with no Zn p orbital contributions for ZnMe263, were clearly too much of a simplification.

Overall, the UMOs for ZnR2 are unremarkable compared to common zinc-containing species, highlighting that the electronically unusual states for ZnR2 are the OMOs. Therefore, the strong reactivity of ZnR2 compared to common zinc-containing species comes mainly from a combination of the OMOs and the two-coordinate structure.

Quantifying the effect of R on ZnR2 reactivity: three new descriptors

To capture the zinc-specific, intrinsic hardness, ηZn, our first new descriptor, we use the experimental Zn 1s R-VtC-XES peak energy (Fig. 2c), which represents the experimental energy gap between OMO,Zn p and UMO,Zn p, E(gap,exp). E(gap,exp) captures the Zn p-specific energy gap ηZn = E(OMO,Zn p)—E(UMO,Zn p), where E(OMO,Zn p) and E(UMO,Zn p) represent the energies of the OMO and UMO with strongest Zn p contribution, respectively. Very importantly, the final-state electronic structure of R-VtC-XES is analogous to UV-Vis spectroscopy (Fig. 2d)42, i.e. one electron in an UMO bound state and a hole in a valence OMO, but R-VtC-XES is an overall two-photon process which can bypass the dipole selection rules of UV-Vis spectroscopy to effectively access the optically dark Zn p to Zn p transitions. Therefore, our energy gap is essentially a zinc-specific, experimental version of the Pearson η (which is η = (E(HOMO) − E(LUMO))/2)37). A small zinc-specific ηZn means relatively strong Zn-reactant molecule covalent interactions; large zinc-specific ηZn means relatively strong Zn-reactant molecule electrostatic interactions, i.e. more ionic. In addition, we have used both DFT and multiconfigurational, multistate-restricted active space second-order perturbation theory (MS-RASPT2) calculations to guide our approach.

The experimental R-VtC-XES-derived descriptor ηZn was: Zn(C6F5)2 ZnMe2 > ZnPh2 > ZnEt2 > Zn(i-Pr)2 (Fig. 4e and Supplementary Fig. 29). Based on a combination of experimental and calculated data, the zinc-based ηZn for ZnR2 is: Zn(C6F5)2 > Zn(2,6-F2C6H3)2 > Zn(3,5-F2C6H3)2 > ZnMe2 > ZnPh2 > ZnEt2 ≈ Zn(n-Pr)2 ≈ Zn(n-Bu)2 > Zn(i-Pr)2 > Zn(t-Bu)2 (Fig. 5a). This experimental ηZn can only be measured using R-VtC-XES as the experimental energy gaps for ZnR2 correspond to ~175 nm to ~250 nm respectively (Fig. 4e), which cannot be measured using standard UV-Vis spectroscopy due to the energy gap being too large (for peaks up to ~200 nm) and the peaks being overwhelmed by the toluene solvent (for peaks up to ~285 nm)64. Furthermore, this experimental R-VtC-XES-derived ηZn effectively captures a Zn p to Zn p transition, rather than the classic E(OMO) – E(UMO) energy gap measured using UV-Vis spectroscopy (Fig. 2d). MS-RASPT2 R-VtC-XES calculations, where the valence hole is included, match both the experimental R-VtC-XES energy gap order and absolute energy gap values for ZnR2 (Fig. 6), demonstrating that the R-VtC-XES calculations capture the same physical effect as the experiments. Whilst an excellent match, these MS-RASPT2 calculations are time intensive and technically challenging. The ground state Zn p-specific ηZn = E(OMO,Zn p) – E(UMO,Zn p) energy gap order (but not the absolute energies) is the same as observed using both experimental R-VtC-XES (Fig. 7a, R2 = 0.98, Supplementary Fig. 32), demonstrating that the much cheaper and simpler ground state calculations capture ηZn.

Fig. 5: Computed Zn-specific electronic structure descriptors: ηZn, χZn, ωZn, E(OMO,Zn p), and E(UMO,Zn p).
figure 5

Electronic structure properties for ZnR2: a zinc-specific hardness (ηZn), b zinc-specific absolute electronegativity (χZn), c zinc-specific global electrophilicity index (ωZn), E(OMO,Zn p), e E(UMO,Zn p). Tabulated values available in Supplementary Table 7.

Fig. 6: Experimental and calculated spectra of ZnR2 (R = Me, Et, i-Pr, C6F5) and [ZnCl4]2-.
figure 6

Comparison of experimental and calculated R-VtC-XE spectra: a experimental spectra for ZnR2 (R = Me, Et, i-Pr and C6F5; concentration 0.1 M for all except C6F5, which was 0.03 M) and x = 0.33 ZnCl2 in [C8C1Im]Cl (which gives only [ZnCl4]2- in solution47,69); b Calculated RASPT2 (MS-RASPT2(12,1,1;1,5,3) ANO-RCC-VTZP) spectra for ZnR2 (R = Et, i-Pr and C6F5; the staggered conformer of C6F5 was used) and [ZnCl4]2-. All calculated spectra include Gaussian broadening with a full width at half maximum (FWHM) of 2.5 eV.

Fig. 7: Computed Zn-specific descriptor correlations with experimental R-VtC-XES gap.
figure 7

Linear correlation fits for calculated descriptors against experimental R-VtC-XES energy gap (E(gap,exp)): a zinc-specific hardness (ηZn) versus E(gap,exp); b zinc-specific absolute electronegativity (χZn) versus E(gap,exp); c zinc-specific global electrophilicity index (ωZn) versus E(gap,exp) and E(OMO,Zn p) versus E(gap,exp).

We calculate a zinc-specific, intrinsic absolute electronegativity, χZn = (E(OMO,Zn p) + E(UMO,Zn p)) / 2, our second new descriptor. These DFT calculations are validated against data from both Zn 1s HERFD-XANES spectroscopy and NR-VtC-XES (Fig. 3b, 3d); we have high confidence in given the excellent matches of our experimental and calculated spectra (Fig. 3 and Fig. 4). A large (or small) zinc-specific χZn corresponds to a strong Lewis acidic (or Lewis basic) zinc centre.

Using both ηZn and χZn, a zinc-specific version of the global electrophilicity index (ω)39,40, where ωZn = (χZn)2 / (2 × ηZn), was calculated, our third new descriptor. A large (or small) zinc-specific ωZn corresponds to a strong Lewis acidic (or Lewis basic) zinc centre.

The zinc-specific descriptors χZn and ωZn for ZnR2 are: Zn(C6F5)2 > Zn(2,6-F2C6H3)2 > Zn(3,5-F2C6H3)2 > ZnPh2 > ZnMe2 > ZnEt2 ≈ Zn(n-Pr)2 ≈ Zn(n-Bu)2 > Zn(i-Pr)2 > Zn(t-Bu)2 (Fig. 5b, Fig. 5c, Supplementary Fig. 29 and Supplementary Table 7). χZn and ωZn correlate linearly (R2 = 0.99, Supplementary Fig. 33c), demonstrating that either can be used for quantifying Lewis acidity/basicity strength. Our results match quantitative reports on ZnR2 and SacNacZnR Lewis acidity of Zn(C6F5)2 > ZnPh231,65. Our results also match qualitative reports from empirical patterns of reactivity; ZnEt2 as a relatively weak/mild Lewis acid65 compared to ZnPh2 and Zn(C6F5)210,19, and Zn(C6F5)2 as a strong Lewis acid9,12. Results from DFT calculations suggest that ZnMe2 can act as a nucleophile4; our results show that any other ZnR2 (where R = alkyl) would be a better nucleophile than ZnMe2 (ignoring steric constraints).

Using zinc-specific ηZn, χZn and ωZn descriptors means we directly capture the electronic structure of the location where both electron acceptance (controlling Lewis acidity) and electron donation (controlling Lewis basicity4) occur for ZnR2, i.e. the zinc centre. This approach removes the problem of ligand electronic contributions clouding production of the descriptors, ensuring that comparable and consistent values for different R substituents are produced. Furthermore, our zinc-specific approach means that the zinc spectroscopic contributions are not overwhelmed by solvent/ligand contributions.

The ηZn, χZn and ωZn descriptors show that strong Lewis acids are hard, and strong Lewis bases are soft. Zn(C6F5)2 is a hard, strong Lewis acid/electrophile and Zn(t-Bu)2 is a soft, strong Lewis base/nucleophile.

χZn and ωZn descriptors exhibit a strong correlation with the R Taft inductive substituent constant, IR, for ZnR₂; as evidenced by a high R² value. (Supplementary Fig. 34 and Supplementary Table 7). The ability of substituent R to donate/withdraw electron density to/from the zinc centre explains ZnR2 reactivity. The alkyl chain length makes very little difference for n-alkyl from Et onwards. This finding matches to results from gas-phase photoelectron spectroscopy of four ZnR2 (R = alkyl)38. For the partially fluorinated Ph, χZn increased fairly consistently with the increasing number of F substituents, e.g. Zn(4-FC6H4)2 has a smaller χZn than Zn(3,5-F2C6H3)2; the positioning of the fluorine on aryl matters: ortho has the largest effect relative to ZnPh2, with a weaker effect for meta (Supplementary Fig. 29).

ηZn, χZn and ωZn descriptors have almost the same order (Fig. 5a-c, Supplementary Fig. 33), and correlate well with E(gap,exp) (Fig. 7). Therefore, our experimentally measured R-VtC-XES Zn p-specific energy gap E(gap,exp), i.e. ηZn, can be used with a good level of confidence as a single experimental descriptor to quantify the effect of substituent R on ZnR2 reactivity. Furthermore, ηZn, χZn and ωZn descriptors are influenced strongly by E(OMO,Zn p) (Fig. 5 and Supplementary Fig. 35). Therefore, E(OMO,Zn p) can be used as a single descriptor to quantify the effect of substituent R on ZnR2 reactivity; E(OMO,Zn p) can be readily calculated—a ground state DFT calculation, then straightforward visual identification of OMO Zn p for ZnR2—allowing accessible in silico screening of ZnR2 species. Even simpler, χZn and ωZn can be predicted if the induction ability of the R substituent is known (Supplementary Fig. 34).

Conclusions and future work

Our combination of three synchrotron-based, solution-phase, zinc-specific X-ray spectroscopies coupled with calculations allows the comprehensive, systematic and quantitative elucidation of the electronic properties that define the reactivity of synthetically-relevant ZnR2. We have unambiguously and directly demonstrated that a range of ZnR2 reagents, in the solvents toluene and hexane, adopt a linear two-coordinate geometry, which establishes that electronic structure will be the primary controller of reactivity. We provide new, intrinsic, quantitative Lewis acidity/basicity descriptors for liquid-phase ZnR2 compounds, which opens up the possibility of fine-tuning ZnR2 reactivity and greatly reduces the need for empirical, iterative synthetic experimentation. Zinc-specific hardness, equivalent to the experimental energy gap between OMO,Zn p and UMO,Zn p, quantifies the chances of forming a more covalent or electrostatic bond with a reactant molecule. Zinc-specific absolute electronegativity and zinc-specific global electrophilicity index both quantify electron acceptor (i.e. Lewis acidity/electrophilicity) and electron donor (i.e. nucleophilicity/nucleophilicity) abilities. For rapid screening, both the induction strength of the R substituents of ZnR2 and the energy of the calculated OMO,Zn p, E(OMO,Zn p), are excellent descriptors for quantification of both zinc-specific hardness and absolute electronegativity, of potential use within the wider catalysis and FLP communities. These new empirical zinc-specific descriptors also provide excellent inputs for quantitative structure-property relationships (QSAR) or for reaction discovery/development using automated synthesis machines.

A combination of factors give rise to the remarkable reactivity of ZnR2 over common zinc-containing species. Firstly, the easily ionised Zn p-containing OMO; secondly, ZnR2 electronic softness; thirdly, the sterically accessible Zn p-containing UMOs due to the linear ZnR2 geometric structure.

Our liquid-phase and zinc-specific suite of X-ray spectroscopy techniques allow us to side-step many common spectroscopic issues for zinc in solution. Zn 1s R-VtC-XES, which we demonstrate the use of for the first time here, is incredibly powerful for studying zinc as we can exclusively focus on the electronic structure associated with the zinc centre rather than that of the associated ligands. R-VtC-XES effectively provides a zinc-specific version (with different selection rules) of UV-Vis spectroscopy that avoids the classic problems of solvent windows or ligand absorption. Therefore, R-VtC-XES is suitable for a vast range of functional zinc species, from enzymes through to batteries and under the diverse conditions they would encounter. In the area of organometallics, future work could focus on donor/coordinating solvents60, potentially intramolecularly coordinating R substituents (e.g. Zn[(CH2)3X]2 where X = SCH3, N(CH3)2)66, zincates/dinuclear complexes67, and zinc bis-amides68.

Our liquid-phase and element-specific suite of X-ray spectroscopy techniques offers exceptional opportunities for capturing geometric and electronic structure and producing descriptors for interpreting and predicting reactivity, for the first time for many elements. Plenty of XANES, NR-VtC-XES and R-VtC-XES studies exist for fourth period (i.e. first row) transition metals42,43,49,50,51,52, but studies for other elements are limited. Elements for which this approach is particularly attractive are those with oxidation states that give closed-shell d10, where p orbitals are crucial for bonding, i.e. main-group elements in the latter part of the fourth period and the start of the fifth period: Ga, Ge, As, Se, Br, Rb, Sr.

Methods

Sample preparation

All samples were prepared in a glove box, under inert conditions (nitrogen, H2O < 0.1 ppm, O2 < 0.5 ppm). 1 M diethylzinc (ZnEt2) in hexanes, 2 M dimethylzinc (ZnMe2) in toluene, 1 M diisopropylzinc (Zn(i-Pr)2) in toluene, diphenylzinc (ZnPh2) (98%), bis(pentafluorophenyl)zinc (Zn(C6F5)2) (98%), anhydrous zinc trifluoromethanesulfonate (Zn(TfO)2) (98%), and anhydrous zinc chloride (ZnCl2) (99%) were obtained from Sigma-Aldrich. 1-octyl-3-methylimidazolium chloride ([C8C1Im]Cl) (99%) was obtained from Iolitec. Neat solvents toluene, tetrahydrofuran and acetonitrile were obtained from Sigma-Aldrich. To avoid self-absorption, solutions were made/diluted to 0.1 M. Zn(C6F5)2 was prepared at 0.033 M due to the presence of insoluble matter at 0.1 M. Zinc tetrachloride, [ZnCl4]2-, was prepared from a mixture of ZnCl2 (0.838 g, 6.15 mmol) in [C8C1Im]Cl (2.882 g, 12.49 mmol) to the desired mole fraction x = 0.33, i.e. 2 × [C8C1Im]Cl + ZnCl2 → [C8C1Im]2[ZnCl4], following literature procedures47,69. The samples were prepared within plastic centrifuge vials (ca. 0.5 ml to 1.0 ml), sealed, and transported to the I20-Scanning experimental hutch. The samples were held in front of the X-ray beam either in a small plastic vice at the top and bottom; or the centrifuge vial was held with a small ring (Supplementary Fig. 36).

HERFD-XAS experiments

X-ray absorption (XA) spectra were collected at Diamond Light source I20-Scanning70. A Si(111) four-bounce monochromator (energy range: Si(111): incident energy, Ei = 4 eV to 20 keV; energy resolution: δE/E = 1.3×10-4) was used to scan from Ei = 9600 eV to 9900 eV. XA spectra were collected using an X-ray emission spectrometer71, and by fixing the emission energy to monitor the relaxation of the Kβ1,3 emission line at emission energy, Ee = 9572 eV. Scanning parameters were as follows: the pre-edge region (Ei = 9600 eV to 9650 eV) in 5.0 eV steps, the edge region Ei = 9650 eV to 9675 eV) in 0.3 eV steps, and the post-edge region (Ei = 9675 eV to 9698 eV) in 0.6 eV steps, and the post-XANES region (Ei = 9698 eV to 9750 eV in 1.6 eV steps; Ei = 9750 eV to 9900 eV in 2.0 eV steps, respectively). Samples were orientated at a 90° angle with respect to the incident beam at ambient temperature and pressure. Incident beam flux was lowered through attenuation (aluminium 0.2 mm, carbon 2.0 mm) to minimise radiation damage. XANES spectra were monitored throughout all scans to determine any degradation or damage to the sample over time. The energy of the monochromator was calibrated to the Zn K-edge of a Zn foil (9659.0 eV) (Supplementary Fig. 37).

XES experiments

X-ray emission (XE) spectra were collected using the X-ray emission spectrometer at Diamond Light source I20-Scanning using three Ge(555) crystal to record the Kβ2,5 emission line, i.e. valence-to-core (VtC). For NR-VtC-XE spectra, the incident energy was set to Ei = 9800 eV, significantly above resonant conditions. For the R-VtC-XE experiments, the incident energy was set to the white-line intensity (near-edge region absorption maxima). Resonant and non-resonant VtC XE spectra were recorded over the emission energy range, Ee = 9630 eV to 9700 eV.

Data processing

Experimental XA spectra were averaged and normalised using the Demeter software package, Athena72. NR-VtC-XES and R-VtC-XES data processing were performed using Igor Pro 8.0. The recorded emission spectra were adjusted to account for the incident beam energy calibration, ensuring accurate emission energy alignment. This was achieved by fitting a Gaussian distribution to the recorded elastic peak and adjusting so that the emission energy subtracted from incident energy equals zero. This shift was applied to all recorded emission spectra, assuming the spectrometer remained stable during the measurement of each solution studied (Supplementary Table 8).

Calculations

Geometry optimisations

All calculations were performed using the ORCA 5.0.3 electronic structure program73. Cartesian coordinates for all complexes were built using Avogadro74. Geometry optimisations were performed with tight convergence, an ultrafine grid (defgrid3) and without symmetry constraints using a range-separated hybrid functional, ωB97X-D3BJ75, with a modified ZORA-def2-TZVPP basis set76, paired with a decontracted SARC/J auxiliary basis set77. The RIJCOSX approximation was used to speed up optimisations. Scalar relativistic effects were introduced using the zeroth-order regular approximation (ZORA)78. Dispersion effects were taken into account using the atom-pairwise dispersion correction with the Becke-Jonson damping scheme. The solvent environment was modelled using the Conductor-like Polarisable Continuum Model (CPCM)79,80, via the PCM implicit solvent models for toluene, hexane, water, acetonitrile (MeCN), tetrahydrofuran (THF) and ionic liquid (relative permittivity = 11.40)81, respectively. Frequency analysis was carried out for all optimised structures, which are confirmed as minima by the absence of imaginary modes. Avogadro was used as an aid in the quantitative analysis of ORCA output files and the visualisation of molecular orbitals.

XAS and XES calculations

All calculations were performed using the ORCA 5.0.3 electronic structure program73. Single point calculations utilising a larger basis set to better capture the electronic structure were performed with time-dependent DFT for XAS and Kohn-Sham DFT for XES, using the ωB97X-D3BJ functional, with a ZORA-def2-QZVPP basis set76 and SARC/J auxiliary basis set77. In all cases, electric-dipole, magnetic-dipole, and quadrupole contributions were allowed in spectral calculations. Time-dependent DFT calculations were performed with the Tamm-Dancoff approximation (TDA) applied. The solvent environment was modelled using the Conductor-like Polarisable Continuum Model (CPCM)79,80, via the PCM implicit solvent models for toluene, hexane, water, acetonitrile (MeCN), tetrahydrofuran (THF) and ionic liquid (relative permittivity = 11.40)81, respectively. For the XAS calculation, the Zn 1s orbital was excited into all virtual UMOs to mimic the Zn 1s K-edge XAS. Calculated XAS spectra were shifted by −8.90 eV to align with the experimental energies (Supplementary Fig. 38). Ground-state KS-DFT VtC-XES calculations were performed. A single relative shift of −8.90 eV was applied from the difference between the most intense VtC peak in the experiment and the calculation (Supplementary Fig. 39). All computational spectra were generated by convoluting the computed energies and oscillator strengths with Gaussian functions with a full width at half maximum (FWHM) of 2.50 eV.

MS-RASPT2 calculations

RXES spectra were calculated with the state-averaged restricted active space self-consistent field (SA- RASSCF)82,83 method with multi-state restricted active space second-order perturbation theory (MS-RASPT2)84,85. Calculations were performed in OpenMolcas86, where the core-hole states are generated using the highly excited state scheme (HEXS)87 and the transition energies and dipole vectors between states are calculated across a set of biorthonormal orbitals using the restricted active space state interaction method88. All calculations use the ANO-RCC-VTZP basis set, which includes relativistic effects89,90,91,92, and an imaginary shift of 0.1 a.u. was applied to the MS-RASPT2 calculation to remove intruder states. Solvent effects were included using the implicit PCM solvent model for toluene and ionic liquid (relative permittivity = 11.40)81. To maintain a consistent level of theory, the RXES calculations of the different zinc complexes use the same active space size. The Zn 1s orbital was placed into RAS1 (maximum number of holes restricted to 1), the highest 5 occupied orbitals were placed into RAS2 (full CI space) and the lowest three unoccupied orbitals were placed into RAS3 (maximum number of electrons restricted to 1). 3 core excited and 15 valence excited states were included in each calculation and approximate relative RIXS intensities were calculated using a previously used simplified formalism of the Kramer-Heisenberg equation which assumes resonant conditions and a constant lifetime-broadening broadening93,94,95.

Calculation processing

MOAnalyzer was employed to determine the percentage contribution of Zn s/p character within key molecular orbitals involved in both XAS and XES calculations using Löwdin population analysis96. MultiWFN was used to visualise the molecular orbitals constituting the occupied valence states97; this was achieved by analysing the total density-of-states (tDoS) and partial density-of-states (pDoS), specifically fragmenting both the Zn s/p orbitals.