Optical, third order non-linear optical and electrochemical properties of dipolar, centrosymmetric and C 2v organoimido polyoxometalate derivatives

A family comprising seven arylimido-polyoxometalate (POM) hybrid chromophores (three of which are new), with linear dipolar, C 2v and linear centrosymmetric geometries have been synthesised and studied by electronic absorption spectroscopy, electrochemistry, Z-scans (two photon absorption, TPA) and computation (DFT/TD-DFT). These reveal that POM acceptor units are an eﬀective basis for TPA materials: the centrosymmetric bis-POM chromophores produce significant cross sections ( d up to 82 GM) from a single aryl bridge, a similar performance to larger dipolar p -systems combining carbazole or diphenylamino donors with the imido-POM acceptor. DFT/TD-DFT calculations indicate strong communication between POM and organic components is responsible for the linear and non-linear optical behaviour of these compounds, while electrochemical measurements reveal class II mixed valence behaviour resulting from an interplay of through-bond and through-space eﬀects.


Introduction
Polyoxometalates (POMs) -a vast family of well-defined, nanoor sub-nanosized molecular metal oxide clusters 1 -are attractive functional building blocks for use in materials and devices. 1,2his is because of the wide range of properties obtained by incorporating transition metal heteroatoms or organic moieties into their structures, and the ability of many POMs to reversibly accept one or more electrons without degradation or structural change. 3These features have made POMs a focus of attention in oxidation catalysis for many years, 4 and because of their oxygento-metal charge transfer bands, POMs are also strong UV chromophores and UV photocatalysts. 5More recently, there has been a growing interest in the interaction of POMs and POM hybrid materials with visible light, 6 and the resulting optical, photophysical and photochemical properties. 7on-linear optical effects are a particular focus because of their relevance to many current, emerging and future technologies -for example terahertz generation, telecommunications (electro-optic modulators), imaging, optical limiting, and optical and electro-optical switching and computing. 8We recently demonstrated that in donor-functionalised arylimidopolyoxometalates, strong electronic coupling between the organic and POM sub-units results in strong charge transfer transitions and strong second order optical nonlinearities (relevant to laser frequency doubling). 9In many examples, static first hyperpolarizabilities b 0 significantly exceed those obtained for comparable structures with organic acceptors.Meanwhile, several other groups have demonstrated that POMs can offer third order NLO properties (e.g.laser frequency tripling, two-photon absorption (TPA) and reverse saturable absorption (RSA)), finding that incorporation of POMs in films of organic chromophores (such as porphyrins) can enhance third order NLO susceptibility 10 and adjust saturable/reverse saturable absorption.Coordination of Keggin ([XM 12 O 40 ] nÀ , X = B, P, Si; M = Mo, W) POMs and their lacunary derivatives to first row transition metal complexes of pyridines and other conjugated organic ligands has produced materials with high TPA cross sections, 11 while covalent molecular POM-porphyrin materials show similar enhancements of non-linear absorption (vs.porphyrins alone) to those found in films. 12However, so far third order NLO properties have mostly only been studied in POM hybrid systems where POM-organic electronic communication is intrinsically weak, as there is either no covalent linkage, or an aliphatic bridge.The only prior study of an arylimido-POM This journal is © the Owner Societies 2021 investigated overall non-linear absorption of a porphyrinderivatised arylimido-Lindqvist ([ArNMo 6 O 18 ] 2À ) system with a nanosecond laser source, 12b thus including longer time-domain effects such as excited state absorption as well as simultaneous TPA.
Here, we present the synthesis and TPA cross sections of several centrosymmetric and C 2v aryl bis-[imido Lindqvist] hexamolybdate derivatives, along with those of previously published dipolar derivatives featuring carbazole and diphenylamino groups.These first TPA measurements on arylimidopolyoxometalates show that the imido-POM acceptor unit is effective for use in 3rd order, as well as second order NLO, yielding p-electron normalised TPA cross sections in dipolar D-p-A and centrosymmetric A-p-A structures that are comparable to efficient organic materials.DFT/TD-DFT calculations suggest this is consequence of strong electronic communication between the POMs and organic groups, which also leads to electrochemically-observed Class II mixed valence behaviour, while methylation ortho to the imido-groups reveals a subtle interplay of through-space and through-bond communication effects.

Materials and procedures
Acetonitrile (MeCN) was freshly distilled under nitrogen from calcium hydride. 13Dry (sure seal) dimethyl sulfoxide (DMSO) was purchased from Sigma Aldrich.All other reagents and solvents were obtained as ACS grade from Sigma Aldrich, Alfa Aesar or Fisher Scientific and used as supplied.Tetrabutylammonium hexamolybdate 14 was synthesized according to previously published methods, as were the dipolar hexamolybdate derivatives 1 to 3. 9b,c Other organoimido hexamolybdate derivatives were synthesised using an adapted literature procedure, 15 under an atmosphere of dry nitrogen using standard Schlenk techniques, full details are given in the ESI.†

General physical measurements
FT-IR spectra were measured using PerkinElmer FT-IR spectrum BX and Bruker FT-IR XSA spectrometers.NMR spectra were acquired using a Bruker Ascend 500 (500 MHz) spectrometer and all shifts are quoted with respect to TMS using the solvent signals as a secondary standard (s = singlet, d = doublet, t = triplet, q = quartet, sex = sextet, dt = doublet of triplets, m = multiplet).Elemental analyses and accurate mass spectrometry were outsourced to London Metropolitan University, and the UK National Mass Spectrometry Service at Swansea University respectively.UV-Vis spectra were obtained by using an Agilent Cary 60 UV-Vis spectrophotometer.Cyclic voltammetric measurements were carried out using Autolab PGStat 30 potentiostat/ galvanostat.A single-compartment or a conventional threeelectrode cell was used with a silver/silver chloride reference electrode (3M NaCl, saturated AgCl), glassy carbon or platinum working electrode and Pt wire auxiliary electrode.Acetonitrile was freshly distilled (from CaH 2 ) and [N(C 4 H 9 -n) 4 ]BF 4 ,4 was used as the supporting electrolyte.Solutions containing ca. 10 À3 M analyte (0.1 M electrolyte) were degassed by purging with nitrogen.All E 1/2 values were calculated from (E pa + E pc )/2 at a scan rate of 100 mV s À1 and referenced to Fc/Fc + .

Z-Scan measurements
The two-photon absorption cross sections were measured at 806 nm by using open-aperture Z-scan method 16 with a femtosecond mode-locked Ti:sapphire laser (Coherent, Chameleon Ultra II: pulse duration: 140 fs; repetition rate: 80 MHz; wavelength range: 680-1080 nm).After passing through a beam expander (Â4), the laser beam was focused using an f = 15 cm lens and passed through a quartz cell (1 mm optical path length).The position of the sample cell was varied along the laser-beam direction (z-axis) using a Z-step motorized stage controlled by a computer.At constant incident excitation, the local power density within the sample is changed, and the corresponding transmitted laser beam, T(z), recorded with a silicon photodetector (Ophir PD300), is monitored in connection with the z-position of the cell.The on-axis peak intensity of the incident pulses at the focal point, I 0 , ranged from 2 to 5 GW cm À2 .If we assume that the linear absorption of the sample is negligible at the working wavelength and that the laser exhibits a Gaussian beam profile in space and time, the nonlinear absorption coefficient b can be calculated from the curve fitting to the experimental transmittance with the following equation: in which z 0 is the coordinate along the propagation direction of the focal point of the beam, l the optical path length.The 2PA crosssection, d, (in units of 1 GM: 10 À50 cm 4 s À1 photon À1 molecule À1 ) is then determined by using the relationship: in which h is the Planck constant, n the frequency of the incident laser beam, N A the Avogadro constant and c is the concentration of the chromophore (mol L À1 ).Rhodamine 6G in methanol (16.2 AE 2.4 GM at 806 nm) was used for the calibration of our measurement technique. 17The uncertainty in d is of the order of 20%.

X-ray crystallography
Crystals of 4Á2MeCN were obtained by room temperature vapour diffusion of diethyl ether into a solution of 4 in acetonitrile.
Structures of 1 to 3 have been previously published.9b,c Data were collected on an Oxford Diffraction XCalibur 3 diffractometer, data reduction, cell refinement and absorption correction were carried out using Agilent Technologies CrysAlisPro, 18 and the structure was solved using SHELXS-2014 19 via WinGX. 20efinement was achieved by full-matrix least-squares on all F 0 obtained, but twin data reduction and twin refinement were not successful, resulting in significant excess electron density on the Mo atoms in the final structure.Support provided by other data (mass spectra, elemental analysis) means that the identity of these atoms is not in question and the obtained structure provides a useful confirmation of connectivity.Restraints were applied to the thermal parameters of atoms in phenyl group, plus several positions on the {Mo 6 } units and tetrabutylammonium cations.Full crystallographic data and refinement details are presented in Table S1 (ESI †) and an ORTEP representation of the asymmetric unit is provided in Fig. S1 (ESI †).

Computational methods
DFT and TD-DFT calculations were carried out using the Gaussian16 suite 23 on the UEA high performance cluster for geometry optimisations and linear light absorption properties, and GAMESS 24 on a dedicated 8-core workstation for TPA cross sections.Geometry optimisations were performed using the range separated, Grimme D2 dispersion corrected hybrid functional oB97XD with the 6-311+G(d,p) basis set for C, H, N, O, and the LANL2DZ basis set for Mo atoms, as this approach was found to best reproduce experiment (Table S1, ESI †). 25 These were carried out first in the gas phase, and subsequently with acetonitrile solvent introduced using Truhlar and coworkers' SMD solvation model. 26TIGHT convergence thresholds on the residual forces on the atoms (1.5 Â 10 À5 Hartree/Bohr or Hartree/radian) were applied.For linear light absorption we used the same oB97XD/6-311+G(d,p)/LANL2DZ level of theory, with the SMD model for acetonitrile solvent.The 200 lowest energy transitions were calculated using a 50 : 50 mix of singlet and triplet transitions, but only the singlet absorptions proved significant.For calculations of two-photon absorption properties we used GAMESS with the range-separated CAM-B3LYP functional and Huzinaga's 3 Gaussian minimal basis set (MINI) with addition of one polarization function on heavy elements.Solvation (acetonitrile) was again applied using the SMD model.Assuming linearly polarized light, the rotationally averaged TPA probabilities in atomic units can be obtained from the TPA transition moment S: The macroscopic TPA cross section in cgs units can be obtained from the rotationally averaged TPA strength in atomic units and excitation energies (o 0 ) produced by GAMESS, using: where a is the fine structure constant (= 0.0072973525664) ; a 0 is the Bohr radius (= 5.3 Â 10 À9 cm); c is speed of light (= 2.99 Â 10 10 cm s À1 ); o is the photon energy (excitation energy, (o 0 )/2); N (= 16) and ffiffiffiffiffiffiffiffiffiffiffi p ln 2 p are both applied when compared to Z-scan single beam experiments 8,27 and G is the lifetime Gaussian broadening functions (= 0.1 eV), as previously employed 28 for comparison with experiment.The macroscopic TPA cross section in GM (Go ¨ppert-Mayer units) units were obtained from the calculated values in cgs units from eqn (2) multiplied by 10 5 as previously reported. 29

Molecular design, synthesis and structure
Our synthetic approach to hexamolybdate derivatives is based on the DCC-mediated coupling of anilines and other amines with (n-Bu 4 N) 2 [Mo 6 O 19 ], 30 although in our hands dimethylsulfoxide has proved a more reliable solvent for this chemistry than the commonly used acetonitrile. 9Of the compounds presented in Scheme 1, three are new (5 to 7).Of the others, 1 to 3 were previously published by us, and 4 by Wei and co-workers. 31The series is designed to test the effect of centrosymmetric, vs. C 2v geometry, and the influence of electron donors, on the linear and two-photon absorption properties of the compounds.Moreover, we wished to test steric demand (provided by the methyl groups of 5 and 7, compared to protons in equivalent positions in 4 and 6) as a means to protect against hydrolysis of the imido-bond -a problem for some hexamolybdate imido derivatives, notably 2.
Crystallisation of 4 to 7 proved much more challenging than for mono derivatives 1 to 3, 9 presumably because their higher charge leads to rapid precipitation from organic media.Nonetheless, crystals of 4 were obtained suitable for X-ray diffraction and the resulting structure is presented in Fig. 1 -notably, a Scheme 1 Hexamolybdate derivatives 1 to 7 included in this study.structure of this known material was not published before.It reveals the expected molecular ''dumbbell'' structure with two POMs bridged by the di-imido phenyl ligand.The Mo-N bond distance (1.71(1) Å) is within the range typically observed for imido-molybdate species, and although the C-N-Mo bond angle (161(1)1) is a little further from 1801 than we have typically observed in dipolar systems such as 1 to 3, 9 it is still linear enough to indicate significant Mo-N triple bond character.Consistent with the centrosymmetric structure, the phenyl group shows no sign of polarisation (such as the quinoidal structure evident in the phenyl groups of 1), however the {Mo 6 } units do show the typical imido-Lindqvist pattern of a shortened bond length from the imido-Mo to the central oxygen, lengthened equatorial bond lengths from the imido-Mo to the bridging oxygens, and a lengthened axial bond length from the Mo trans to the imido to the central oxygen. 32ectronic absorption spectra UV-vis spectra of the centrosymmetric and C 2v compounds 4 to 7 are shown in Fig. 2, while those of the dipolar compounds 1 to 3 are displayed in Fig. S2 (ESI †) and the data are summarised in Table 1.Two main types of band are observed -high energy bands between 200 and 300 nm associated with ligand pp* and O -Mo transitions, and a lower energy band (350 to 450 nm) we assign as an intra-hybrid charge transfer (IHCT) band.9b Depending on the nature of the organic group (e.g.presence of resonance donor or acceptor substituents) and geometry this band may have contributions from charge transfer both towards and away from the POM, and what are essentially pp* transitions perturbed and lowered in energy by participation of the POM orbitals.Introduction of a strong organic donor, such as the diphenylamino unit in 3, leads to dominant ligand-to-POM charge transfer (LPCT) and the pronounced red shift that is observed between phenylethynyl derivative 1, and 3. 9 TD-DFT calculations (vide infra) confirm that the lower energy bands of 4 to 7 all involve transitions from the imido-aryl groups, to orbitals that either have significant POM character or are entirely POM based, indicating that they are also LPCT in nature.
The spectra of the C 2v compounds 6 and 7 are essentially very similar to that of 1.This is because all three are based on small p systems with no strong electron donor, and no electron acceptor other than the POMs.The IHCT l max is found at 348 or 361 nm respectively, but is around twice as intense in the bis-POM systems 6 and 7 as in 1.This is consistent with involvement of the POM in the transition.The red shift observed on moving from 6, to the trimethylated analogue 7, is consistent with a HOMO level with strong participation from the phenyl group being raised in energy by the inductive electron donating methyls.Remarkably, the centrosymmetric ''dumbell'' derivatives 4 and 5 show by far the strongest, and longest wavelength absorption.The IHCT bands of these systems have l max values of 425 and 440 nm respectively, over 50 nm to the red of 1 and their C 2v analogues.In the absence of strong electron donors, this can be ascribed as consequence of better inter-acceptor (POM) communication in the 1,4-geometry, and their centrosymmetry, which leads to an intermediate 1B 1u state with an allowed transition from the 1A g ground state -of lower energy than the 1A -2A transition of comparable dipolar systems.8d UV-vis spectroscopy also enabled investigation of the effect of introducing steric bulk around the imido bond on its hydrolytic stability.The Mo-N bond can hydrolyse yielding the [Mo 6 O 19 ] 2À cluster and the parent amine, and many literature {Mo 6 } imido compounds feature methyl or isopropyl groups adjacent to the imido bond. 30,32Yet, neither quantitative nor qualitative information exists in the literature to indicate how such structural modifications can influence the vulnerability of  organoimido-polyoxometalates to hydrolysis.Thus, Fig. S3 (ESI †) shows the absorbance decline of ca. 10 À5 M solutions of compounds 4 (with protons in the ortho and meta positions) and 5 in kept in the dark in acetonitrile after deliberate addition of a large excess of water, monitored at the IHCT band l max .As neither [Mo 6 O 19 ] 2À nor the resulting anilines have any significant absorption at the IHCT l max , the absorbance loss at this wavelength is directly proportional to the extent of hydrolysis of the imido groups.For 4, around 25% of the absorbance is lost over the course of 10 hours, of which 10% is lost within the first hour.For 5, the loss is o3% over 10 hours, of which nearly all occurs in the first hour.This indicates a substantial stabilising influence, even for the relatively small methyl group, in return for only modest changes (red shift, decreased e) to the optical properties.

Electrochemistry
The hexamolybdate anion, [Mo 6 O 19 ] 2À has a reversible one electron reduction at À0.32 V vs. Ag/AgCl under the conditions used here.The mono-{Mo 6 } species 1 to 3 all show a similar reduction, 9 shifted negative by around 180 mV, as electron donation from the arylimido unit to the Mo d-orbitals makes the POM a weaker acceptor.The influence of arylacetylene donor ring systems connected to the 4-position of the imidophenyl group in these systems on the POM reductions is very weak, as 1 to 3 have reduction potentials within 5 mV of one another.At first glance, addition of a second, electron accepting imido-{Mo 6 } in the 3-or 4-position (i.e. in 4 to 7) also seems to have little effect on the reduction potential vs. 1 to 3 (Table 1).However, this is inconsistent with prior observations that p-donor or acceptor substituents (-NMe 2 , -NO 2 ) directly connected at the 4-position exert a large effect (AE70 mV) on the POM reduction potential, 9b and there is a noticeable shift to more negative potential in the 1,3-systems -particularly when comparing 5 vs. 7 (Fig. S4, ESI †).Close inspection reveals that all four bis-POM systems have a much larger DE p (4110 mV) than the near ideal one electron couples of 1 to 3 (DE p = 61-64 mV).Current responses with scan rate, and independence of the peak separation from scan rate, suggested that the observed waves consist of two overlapping, reversible one electron reductions at different potentials -that is reduction of one {Mo 6 } unit makes reduction of the second one more difficult.Differential pulsed voltammetry (DPV) indeed uncovers two processes for each of 4 to 7, separated by 73-82 mV from one another (Table 2 and Fig. S5-S8, ESI †).This shows that for 4 the first reduction (E 1 ) shifts around 90 mV more positive than those of 1 to 3, a similar effect to that previously observed for a para-nitro substituent (values in Table 2 are E p not E 1/2 ).Introducing methyl groups in 5 produces the expected, small negative shift in E 1 as the aryl group becomes more electron rich.The E 1 s of the 1,3 systems are less positively shifted vs. the mono-POM compounds, consistent with weaker through-bond communication in this geometry, but reveal a stronger effect for the methyl groups.This stronger effect of methylation in the 1,3 geometry may be explained through DFT-optimised geometries (vide infra) that suggest possible C-HÁ Á ÁO hydrogen bonding interactions between methyl groups and POMs.These lead to a shortening of POMÁ Á ÁPOM distances in both methylated structures (Table 4), with the effect being much more substantial in 6/7 (0.15 Å centre-to-centre, 0.621 Å closest OÁ Á ÁO) than in 4/5 (0.03 Å centre-to-centre, 0.03 Å closest OÁ Á ÁO).This would increase repulsion between the added electron and the negative charge on the second POM group.
As well as delineating trends in the first reduction potential, the DPV provides a direct means of assessing the level of communication between the POMs through the separation between the two reductive processes.This communication is quantified by comproportionation constant (K com ) derived from the difference in the redox potentials (DE), such that K com = e (D EÁF/RT) for one electron processes.33a,b K com allows assignment of the mixed-valence system according to the Robin-Day classification, where non-communicating redox centres are Class I (K com o 4), complete delocalisation is Class III (K com 4 10 6 ) and intermediate communication is Class II. 33While this classification is simple, it should be noted that other factors such as solvation, ion-pairing, and intra-molecular electrostatic effects can influence K com as well as through-bond communication.33c For 4 to 7, DE values fall into a narrow (o9 mV range), yielding K com values (17-25) consistent with weakly coupled Class II mixed valence behaviour, 33 and similar to values obtained for the 1,4-dicyanobenzene bridge in bisruthenium pentammine complexes. 34Comparing 1,4 and 1,3 geometries (4 vs. 6, 5 vs. 7) shows that communication is stronger for 1,4-consistent with expectations and the observation that the bridge participates in the LUMO for this geometry, but not for the 1,3 geometry.However, the difference is very small, particularly when the methyl groups are present, such that K com for 7 slightly exceeds that of 4. This may be explained by increased electron-electron repulsion when the two POM acceptors are closer in the 1,3-geometry, which increases with methylation as the POMs are forced closer together.Moreover, short C-HÁ Á ÁO contacts consistent with hydrogen bonding in the calculated structure of 7 may provide another means for charge on one POM to influence the bridge, and thus feed through to the second POM.

Two-photon absorption measurements
Measurement of third order NLO effects with nanosecond laser sources, for both electrostatic 35 and aliphatically bridged 12a POM hybrids have previously shown significant enhancements in non-linear absorption (1.1Â to 2.8Â) resulting from introduction of the POM.Due to a dependence on the LUMO level of the POM, these effects were ascribed to electron transfer to the POM -a longer time domain process consistent with nonsimultaneous absorption of the second photon as permitted by ns laser pulses.Ultrafast (ps) through-space electron transfer from excited dyes to POMs, and similarly rapid electron transfer from reduced POMs to excited or oxidised dyes has been previously documented. 36Thus, the non-linear absorption in these systems likely results from a combination of excited state absorption, absorption by the dye oxidised state and POM reduced states (which often have broad absorptions between 500 nm and the near-IR), and potentially even dye regenerated or reduced by electron transfer from the reduced POM, rather than enhancement of simultaneous TPA.However, a greater enhancement of non-linear absorption (4.5Â) measured by a ns source has been described for tetraphenylporphyrin derivatised with imido-Lindqvist units, 12b potentially indicating that the strong electronic coupling provided by the imido linkage also enhances simultaneous (intrinsic) TPA.Thus, to investigate intrinsic TPA in 1 to 7, we have obtained TPA cross sections by Z-scan measurements with a femtosecond 806 nm source (Table 3).Fig. S9-S10 (ESI †) display some typical z-scan traces of POM compounds, the linear correlation between the variation of transmission (DT) and the incident power confirms the two-photon absorption regime. 37The values of TPA cross sections are modest compared to very strong two-photon absorbers can exceed 10 4 GM), 8d but relatively small numbers of p-electrons are involved -and the cross sections normalized for the number of effective p-electrons 38 (d/N eff 2 ) are broadly comparable to efficient organic and metallo-organic two-photon absorbers. 39Notably, the highest normalized values are obtained for the centrosymmetric A-p-A, bis-POM derivatives 4 and 5 -whose d values approach those of dipolar 2 and 3 despite much smaller organic p-systems (lower N eff ), while mono-POM 1 with the same N eff produces no appreciable TPA cross section (likely due to the relative lack of CT character in mono-POM derivatives with no resonance electron donor 9b ).This clearly implies that the POMs play a role in the third order NLO properties of these compounds, as should be expected from the role TD-DFT (vide infra) shows that they play in the electronic transitions, and indicates that they are effective acceptors for use in TPA.But, unlike our observations for second order NLO, 9 it does not impute a general advantage to imido-POMs compared to efficient organic donor or acceptor moieties.This is because, based on known theory and structure/activity relationships for organic chromophores, the centrosymmetric geometry of 4 and 5 should be expected to yield more effective two photon absorbers than dipolar or C 2v systems.Indeed, similar or higher d/N eff 2 values than those of 4 and 5 can be obtained for stilbene bridged organic D-p-D structures, 38 and stilbene bridged dipolar organics have shown higher d/N eff 2 than 2 and 3. 39b Moreover, this comparison does not take account of the steric bulk and mass of the POM, which would be relevant considerations for the efficiency of any bulk TPA material.Within the bis-POM compounds, contrasting effects are seen for the methylated derivatives -a decrease in d upon methylation in the centrosymmetric 4 and 5 and an increase in C 2v 6 and 7.This is likely a result of the effect of shifts in the TPA allowed resonance wavelengths relative to the 403 nm second harmonic (SH) wavelength, induced by the more electron rich phenyl rings -it is notable that the change in d approximately tracks the change in the one photon extinction coefficient at 403 nm.The difference in TPA cross sections observed between C 2v and centrosymmetric systems is likely also related to the position of the TPA allowed resonance wavelengths, vs. the SH: for C 2v 6 and 7 the S 0 -S 1 transition is TPA allowed, and thus the TPA resonance wavelength should correspond to the linear absorption spectrum l max (ca.50 nm to the blue of the second harmonic), whereas for centrosymmetric 4 and 5 S 0 -S 1 is TPA forbidden and the TPA allowed S 0 -S 2 resonance will be accessible to the blue of the one-photon l max , and thus potentially quite close to the 403 nm SH wavelength.

Computational study
Accurate calculations of both linear light absorption, and nonlinear optical properties can be challenging for polyoxometalate derivatives, but recent work from Champagne and co-workers has shown that excellent results can be achieved for linear absorption and second-order non-linear optical properties (frequency doubling, b) using range-separated hybrid functionals. 25ccordingly, testing a number of functional/basis set combinations (Table S2, ESI †) on dumbbell compound 4 revealed that oB97XD/6-311+G(d,p)/LanL2DZ produced the best match to the crystallographically obtained bond lengths and angles.Replacing LanL2DZ with the larger LanL2TZ basis set was computationally expensive, and in fact slightly worsened the match on the MoRN-C angle.Extending the approach to 2, 3 and 5 to 7 also produced geometries consistent with known imido-species (Fig. 3 and Fig. S11, Table 4 and Table S3, ESI †) with Mo-N bond lengths of 1.73 to 1.79 Å and Mo-N-C angles of between 154 and 1771.The lower (more bent) end of this range is occupied by the dipolar and C 2v derivatives 2, 3, 6 and 7.
Calculation of UV-vis absorption properties (Gaussian, oB97X-D) produced a much better match to experimental spectra than prior calculations for dipolar 2 and 3 (Table S4, ESI †) using the SAOP model functional, 9c but show a very similar picture of the MO-to-MO transitions (Fig. S12 and S13, ESI †).For the centrosymmetric and C 2v systems, the match to experimental spectra is excellent (Table 5) -comparing the strongest calculated transition (based on oscillator strength) with the experimental l max indicates an overestimate of the  Effectively, this means that the amount of POM character increases in the transitions of 5 and there is a higher degree of charge separation for this compound.This may be a result of electron donation from the methyl groups, which raises the energy of bridge-based orbitals more than POM-based orbitals, and C-HÁ Á ÁO hydrogen bonds suggested by the short CÁ Á ÁO distances and near 1801 C-HÁ Á ÁO angles calculated for this compound.These may help enforce the observed more linear MoRN-C bond and shorter POM-POM distance, while also having a slight stabilising effect on POM based orbitalshelping favour transitions to the POM.
In the C 2v compounds the LUMO involves only POM orbitals, consistent with the more polar nature of these systems (Fig. 5, Fig. S15, ESI †).However, the HOMO -LUMO transition only makes a relatively small contribution to the light absorption properties which for both compounds are dominated by transitions from the HOMO and HOMO-1 to various LUMO+x.These all involve the aryl bridge but more strongly in the non-methylated     compound 6, consistent with the result for the linear systems.The underlying reasons are likely similar: although potential short C-HÁ Á ÁO interactions are present in both 6 and 7, 7 features more dramatic shortening of POMÁ Á ÁPOM distances than seen in the 4/5 pair, and methylation will have a similar effect on the energies of aryl orbitals as in the 1,4-systems.The reduced participation of the bridge in the acceptor orbitals of the transitions seen for the methylated systems is potentially significant for application of either geometry in charge separation, or of the C 2v compounds as a basis for 2nd order non-linear optical chromophores, but does not seem to influence the third order NLO properties -the pattern in both 4 vs. 5 and 6 vs. 7 is for the TPA cross section to simply track the corresponding one photon cross section, which the red shift from 4 to 5 decreases, but the red shift from 6 to 7 increases.Calculation of third order non-linear optical properties has previously only been carried out for a handful of polyoxometalate derivatives, using model potentials (LB94, SAOP, GRAC) 40 or the B3LYP hybrid 41 to obtain g by finite differentiation from the DFT energy calculation, and no experimental data has been presented for comparison.Here, we have tested TD-DFT as means to compute the TPA properties of 4 to 7. Obtaining accurate calculations of TPA can be a challenge by TD-DFT, 28,42 but reasonable success has been demonstrated for some organic chromophores 39c,43 and it is far less computationally expensive than higher accuracy CC methods. 42As oB97XD is not implemented for TD-DFT in GAMESS, we first calculated the linear absorption properties of compound 7 using CAM-B3LYP/6-311+G(d,p)/LanL2DZ, finding comparable results to those from Gaussian/oB97X-D (Table S5, ESI †).TPA tensor elements, energies, probabilities and cross sections were then calculated using CAM-B3LYP and the MINI basis set with one added polarization function (Table 6).This basis set represents a very strong approximation, but larger basis sets proved too computationally heavy to be practical.The computed s TPA values obtained for 4 and 7 are a reasonable match for experiment in terms of magnitude, but overall the computational results deviate widely from experimental trends.Notably, even for purely organic chromophores benchmarking studies of successful TD-DFT approaches have found substantial differences from experimental values as well as non-systematic deviations from experimental trends.43b In this study, the small basis set forced by the large systems, and comparison of cross-sections obtained from single-wavelength measurements with calculated values corresponding to TPA maxima can only increase the chance of such deviations.Moreover, geometry is a factor as DFT optimised geometries may not perfectly match solution averages, influencing the accessibility of the S 0 -S 1 and S 0 -S 2 transitions due to two photon selection rules (S 0 -S 2 is forbidden for centrosymmetric systems).Specifically, the methyl groups in 5 and 7 force much truer centrosymmetric and V-shaped geometries than seen for 4 and 5, and this is reflected in the computed S 0 -S 1 and S 0 -S 2 s TPA values.Thus, considering its accessibility, TD-DFT appears to be viable as a means of calculating 3 rd order NLO properties in POM derivatives.However, it is clear the approach needs refinement and optimisation, and a lot of computational power.

Conclusions
Three new, arylimido bridged bis-polyoxometalate species with centrosymmetric and C 2v geometries have been synthesised and their electrochemical, linear absorption and two-photon absorption properties studied by experiment and computation in the context of a larger family of dipolar and centrosymmetric arylimido POMs.The results show communication between the POM units in all bis-POM species, resulting in formation of class II mixed valence species upon reduction of one POM.The polyoxometalate acceptor groups are able to produce significant two-photon absorption cross sections from small p-systems, and structure-activity relationships in the POMderivatised materials are similar to those of purely organic TPA chromophores.Positioning methyl groups ortho-to the imido-linkages has a strong influence on POM-POM distances in the C 2v systems, resulting in increased electrochemically observed through-space communication while through-bond communication seems to decrease.Methylation also strongly stabilises the imido-linkages against hydrolysis.a Use of solvation and addition of the polarization function brought the calculated values significantly closer to experiment.b S 0 -S 3 was also calculated but cross sections were found to be vanishingly small.c Corresponds to 2o (i.e.2Â the energy of photons absorbed in the TPA transition).d Rotationally averaged TPA strength.

Fig. 1 X
Fig. 1 X-ray crystal structure of the molecular anion in 4Á2MeCN.Thermal ellipsoids are at the 30% probability level; C atoms are grey; N, purple; Mo, cyan; O, red; H atoms are white spheres of arbitrary radii.
transition energy of only around 0.2 eV for the centrosymmetric dumbbells 4 and 5, and a 0.05 eV overestimate to 0.1 eV underestimate for the C 2v systems 6 and 7.The overall pattern of the transition energies relative to one another is consistent with experiment, and expectations based on the geometries and the presence of the methyl groups in 5 and 7, which raise the level of the aryl-based LUMOs leading to a smaller HOMO-LUMO gap.For all four compounds, the HOMO/HOMO-1 involved in the transitions spreads across the entire arylimido unit, and also has some POM character (Fig.4, 5 and Fig.S14, S15, ESI †).The LUMO and LUMO+x acceptor orbitals are more POM-based in all cases, although a significant number also involve the p-bridge.This clear involvement of the POM as an acceptor in the electronic transitions, and presence of hybrid delocalized orbitals with participation from both POM and organic group, implies that the origin of TPA by the POM derivatives is the introduction of charge transfer character and the extension of the CT transitions onto the POM.The lack of TPA activity in 1 most likely results from the relative lack of CT character in its transitions, as shown previously by computation and electroabsorption spectroscopy.9bThere is very little change between the two centrosymmetric dumbbells 4 and 5 in the character of the HOMO and LUMO, and the various LUMO+x orbitals implicated in the transitions.In both cases the LUMO involves the p* orbitals of the bridge, the imido group and also d-orbitals in the equatorial plane as projected (Fig.4, Fig.S14, ESI †), and all of the LUMO+x orbitals are entirely POM based.However, there is a switch in the main contributor to the strongest transition (3.11 eV in 4, 3.03 eV in 5), which is HOMO -LUMO in 4 and HOMO -LUMO+2 in 5.

a
Central oxygen.b Distance between central oxygens of the two POMs.c Shortest OÁ Á ÁO distance between the two POMs.d Average of short (CÁ Á ÁO o3.6 Å) C-HÁ Á ÁO interactions in calculated structures.

Table 1
UV-visible absorption and electrochemical data for 1 to 7 in acetonitrile at 298 K l max /nm a (e, 10 3 M À1 cm À1 ) a Concentrations ca. 10 À5 M in MeCN.b Solutions ca. 10 À3 M in analyte and 0.1 M in [NBu 4 ][BF 4 ] at a glassy carbon working electrode with a scan rate of 100 mV s À1 .c Wave consists of two closely spaced oneelectron reductions, as shown by differential pulsed voltammetry.Ferrocene internal reference E 1/2 = 0.46 V, DE p = 80 mV.Data for 1 are from ref. 9b and for 2 and 3 from ref. 9c.This journal is © the Societies 2021 Phys.Chem.Chem.Phys., 2021, 23, 11807-11817 | 11811

Table 2
Deconvoluted electrochemical processes and K com of 4 to 7

Table 3
Two photon cross sections for 1 to 7 obtained by the Z-scan technique at 806 nm a Non-linear absorbance too weak for accurate measurement.journal is © the Owner 2021 Phys.Chem.Chem.Phys., 2021, 23, 11807-11817 | 11813

Table 6
Calculated two photon absorption properties of 4 to 7 using GAMESS at the CAM-B3LYP/MINI (+1 polarization function) level of theory, with SMD solvation (MeCN) a