Exceptional three- to six-photon absorption at organometallic dendrimers

The light-intensity dependence of multi-photon absorption (MPA) affords outstanding spatial control. Furthermore, compared to the higher-energy photons needed for analogous linear absorption, the lower-energy photons involved in MPA often correspond to important wavelengths, such as those of the biological and telecommunications “windows”. It is therefore of crucial importance to develop molecules that exhibit outstanding MPA cross-sections. However, although progress has been made with two-photon absorption, there is currently a dearth of efficient instantaneous n-photon absorbers (n > 2), a key reason being the scarcity of structure–property studies required to understand higher-order MPA. We herein report systematically-varied metallodendrimers up to third-generation in size, together with their nonlinear absorptive responses over the spectral range 600–2520 nm. We show that the dendrimers exhibit exceptional instantaneous three- to six-photon absorption cross-sections, with maximal values increasing with dendrimer generation and installation of solubilizing group, and we report that changing the groups at the dendrimer periphery can shift the wavelengths of the nPA maxima. We also describe time-dependent DFT studies that have facilitated assignment of the key linear and nonlinear transitions and disclosed the crucial role of the metal in the outstanding MPA performance.


Introduction
Instantaneous multi-photon absorption (MPA) is a nonlinear optical (NLO) process involving the near simultaneous absorption of two or more photons.MPA has attracted ever-increasing interest from both the applied and fundamental perspectives. 1he light intensity dependence of MPA can afford exquisite three-dimensional control of interaction volume, because any subsequent "action" can be localized to the focal point of a laser, at which the light is sufficiently intense so as to manifest MPA effects.This 3D control has demonstrated or proposed uses in micromachining, data storage, photodynamic therapy, biological imaging, theranostics, and many other applications.Another practical advantage stems from the fact that the MPA excitation process involves n-photons of frequency (n/n) for an overall transition energy hn.The use of such longer wavelength photons can result in decreased photo-damage, while simultaneously opening up technologically important spectroscopic regions (e.g. the windows where tissue and other biological material transparency are maximized: near-infrared I (NIR-I), 650-950 nm; NIR-II, 1000-1350 nm; NIR-III, 1550-1870 nm; and a newly proposed window, 2080-2340 nm). 2,3Essential to the development of MPA materials are wavelength-tunable laser systems to interrogate these spectral regions, with a particular need for ultra-short (femtosecond) low-repetition rate pulses to ensure instantaneous rather than stepwise effects are assayed.
The key to exploiting MPA is the development of materials with exceptional MPA merit.At the molecular level, MPA efficiency is usually quantied in terms of the n-photon absorption cross-sections s n .][6][7][8][9][10] Less is known of higher-order effects, although crucial advances have been made, largely with 3PA/s 3 ; 11,12 reports of 4PA/s 4 have been much less frequent, 13,14 while descriptions of 5PA/s 5 and even higher-order MPA are sparse (Table S1 †). 15,16To some extent, this deciency reects the lack of routine access to the aforementioned low repetition rate, ultra-short pulse length long-wavelength-tunable lasers that are needed to drive the development of structure-activity relationships.
8][19] Their monodisperse nature permits control of optical properties, and their hyperbranched structures facilitate maximization of both effective-chromophore density and molecular solubility.Organic dendrimers have commanded most attention, but organometallic dendrimers that exploit the exibility in metal valence electron count and coordination geometry are also of interest.Square-planar platinumcontaining dendrimers, for example, have been explored as optical limiters. 20Progression from 16 valence electron (VE) platinum to 18 VE metal centers is a logical approach to improve NLO responses because these properties are dependent on electron-richness as well as ease of polarization.With this in mind, we have previously carried out wavelength-dependence NLO studies of zero-and rst-generation ruthenium alkynyl dendrimers, [21][22][23][24][25][26] and reported their 2PA, 3PA and, in one case, 26 4PA activity.These interesting results have prompted us to examine the effect of varying dendrimer content in a more rigorous fashion, to assess the impact of dendrimer generation and composition on MPA.We herein report the syntheses and characterization of systematically-varied zeroth-to thirdgeneration ruthenium alkynyl dendrimers with varying dendrimer framework linker length, peripheral functionalization, and solubilizing group incorporation, together with widewavelength femtosecond Z-scan studies that have disclosed their exceptional instantaneous 2PA-6PA performance, identi-ed record MPA coefficients, and aided in the development of structure-MPA property relationships (the MPA studies of a few of the dendrimers that lack peripheral substituents have been reported in a preliminary fashion). 27We also report computational studies of linear optical properties and 2PA that permit assignment of the major linear and nonlinear optical transitions, and thereby help to rationalize the experimental observations.

Synthesis and characterization of ruthenium alkynyl dendrimers
The systematically varied dendrimers in Fig. 1 permit assessment of the inuence of dendrimer generation and composition on MPA.These ruthenium alkynyl dendrimers are large pelectron-delocalized macromolecules for which the constituent wedges and dendrons have rigid conjugated sub-units, and for which certain design considerations needed to be taken into account prior to synthesis.The 1,4-phenyleneethynylene (PE)based linkages must be a minimum length to avoid insuperable steric congestion at the periphery of the second-and thirdgeneration dendrimers.The design of these PE linkages also needs to consider the "effective conjugation length", 28 which is likely to be a key factor in maximizing NLO response scaled by molecular size.While the branching inherent in the dendritic construction aids solubility in comparison to that of similarsize linear analogues, 26 it may still be insufficient to ensure the solubility of higher-generation dendrimers, so linear alkyl substituents were incorporated in the larger examples of the present study to enhance solubility (linear alkyl groups were chosen in preference to alternatives such as alkoxy groups, to avoid perturbing the OPE p-systems that contribute to the NLO effects).With these considerations in mind, the resultant suite of dendrimers depicted in Fig. 1 permits assessment of the impact on MPA merit of varying generation (zeroth-to thirdgeneration), peripheral substituent (chlorido, phenylethynyl, 4-nitrophenylethynyl), core linker (1PE or 2PE to ruthenium), and OPE linker (0PE to 3PE between ruthenium centers and dendrimer branching points), as well as the effect of introducing solubilizing substituents (ethyl groups).
The synthetic procedures are described in the ESI † and are depicted in Schemes S1-S7.† The dendrimers were constructed by sequences of well-established procedures: vinylidene for chlorido ligand substitution, deprotonation of vinylidene ligands to form alkynyl ligands, protodesilylation of trialkylsilylprotected alkynes to afford terminal alkynes, and Sonogashira palladium-catalyzed C-C coupling.Overall, the chloridoterminated dendrimers were synthesized by divergent routes, while the 4-nitrophenyl-/phenyl-alkynyl-terminated dendrimers were accessed by a combination of divergent and convergent means.In all cases, the dendrimer syntheses exploited the steric control of the extent of metalation of a 1,3,5-trisubstituted arene that is possible with the sterically demanding ligated metal center trans-[Ru(k 2 -dppe) 2 ]. 29 This di-rather than trisubstitution, even in the presence of an excess of ruthenium reagent, affords rapid access to the dendrimer generation-dening 1,3,5-C 6 H 3 X 2 Y branching points, and thereby the key dendritic "wedge" intermediates, without the need for the protection/deprotection protocols required in analogous purely organic dendrimer synthesis.
The new complexes were initially characterized by a combination of 1 H, 13 C, and 31 P NMR and IR spectroscopies, and satisfactory elemental analyses (Fig. S1-S45 †).The 31 P NMR spectra, in particular, proved useful in conrming reaction completion and product composition because resonances arising from the trans-[Ru(C^CR)Cl(k 2 -dppe) 2 ] (49-50 ppm) and trans-[Ru(C^CR)(C^CR 0 )(k 2 -dppe) 2 ] (53-55 ppm) environments are well-separated.The dendrimers were further characterized by diffusion-ordered spectroscopy (DOSY: Fig. S46-S48 †), size-exclusion chromatography (SEC), transmission electron microscopy (TEM), and MS.DOSY conrmed the product purity; the Stejskal-Tanner plot-derived diffusion coefficients revealed that the high-generation dendrimers, as expected, diffuse more slowly than the low-generation dendrimers (Fig. S49 †) and, more importantly, that dendrimer diffusion is clearly distinguishable from that of possible impurities/by-products (such as branches, dendrons, wedges and other fragments).The Stokes-Einstein equation-derived hydrodynamic radii increase with increasing generation and installation of solubilizing ethyl groups, and upon proceeding from chlorido to phenylethynyl and then 4-nitrophenylethynyl peripheral ligands (Fig. S50 †).The hydrodynamic radii of the dendrimers are smaller than the corresponding radii of gyration calculated from molecular mechanics-optimized geometries (Fig. S51 †), with the disparity increasing with increasing generation, presumably due to the increasing proclivity of the dendrimer to rotate out of planarity.The SEC traces for all dendrimers exhibited a single peak, a narrow distribution for the number-averaged molecular weights (M n ), and dispersity values consistent with the presence of uniform ruthenium dendrimers for which M n values coincide with their formula weights (Fig. S52 †).TEM micrographs of a representative example (2G 22,03,01 ) revealed individual molecules with diameters of ca.7.5 nm, 27 consistent with that calculated by molecular modelling (Fig. S53 †).MS proved to be of limited utility due to the low ionization efficiency of the dendrimers, the highest molecular weight example for which it proved useful being the chlorido-functionalized 1G 22,00 -Cl.This complex afforded MS signals that were simulated as corresponding to [M − 6Cl + nMeCN] 6+ (n = 4-6), 27 behavior that is consistent with the experimentally-observed facile ligand substitution at trans-

Experimental and computational studies of linear optical properties
The UV-vis-NIR spectra of the dendrimers are shown in Fig. S54 and S55, † with important data for the dendrimers and their precursors being listed in Tables 1 and S2, † respectively.Proceeding from chlorido-to phenylethynyl-terminated dendrimer results in little change in the lowest-energy bands, but an increase in absorptivity at wavelengths corresponding to higher-energy absorptions, while installation of nitro acceptor groups at the peripheral phenylethynyl ligands results in the appearance of a lower-energy band.Calculations on related monometallic model complexes suggest that the lowest energy band in the spectra of the chlorido-and phenylalkynylcontaining dendrimers corresponds to charge transfer from Ru to the OPE-containing ligand, 32 while that in the spectra of the nitro-containing examples corresponds to ligated ruthenium to nitrophenyl charge transfer. 28,33Dendrimer generation increase while otherwise maintaining dendrimer composition Fig. 1 Organoruthenium dendrimers in this study.[Ru]: trans-[Ru(k 2 -dppe) 2 ] (dppe = 1,2-bis(diphenylphosphino)ethane).Wavy lines: equivalent dendrons at dendrimer cores.Names follow the format: (i) nG (n-th generation dendrimer), (ii) xy (x and y phenyleneethynylene units between the branching points and the ligated Ru at each generation level, commencing at the core), (iii) a comma "," separating the "xy" numbers of OPE units at each generation level, and in some cases (iv) -s (installation of solubilizing Et groups at the central phenylene of the OPE unit between the firstand second-generation branching points).
results in a general increase in absorptivity scaling roughly with molecular size, but no change in prole.
To shed more light on the UV-vis-NIR spectra, and in particular understand charge transfer within the dendritic interior, further computational studies were undertaken in the present work.Once again, due to the size of the dendrimers, it was necessary to approach assignment of the underlying transitions responsible for the linear absorption bands by undertaking on monometallic models of the key components of the dendrimers, specically, the trans- approximation that previous studies on monometallic complexes had conrmed was an acceptable compromise to mitigate computational expense. 34The geometry-optimized coordinates are given in Tables S3-S9 † (PBE0 (ref.35)/6-31G(d), 36 no symmetry constraints, D3BJ dispersion correction, 37 PCM CH 2 Cl 2 (ref.38 and 39)).The low-energy absorption bands were calculated using both the hybrid functional PBE0 and the long-range corrected functional CAM-B3LYP (6G(d,p)/ SDD non-metal/Ru basis sets) [40][41][42][43] (Table S10 †).The latter was found to signicantly overestimate the transition energies and, as the former was found to better approximate the experimental data, PBE0 was employed for the subsequent linear absorption computations.

Experimental studies of nonlinear optical properties
The complexes in the present study are insufficiently emissive to employ multiphoton-excited uorescence to measure their nonlinear absorption, so nonlinear absorptive and nonlinear refractive data for the dendrimers and their key precursors were obtained   The nonlinear absorption maximal values of the dendrimers are collected in Table 1, organized by core OPE linker (G x , x = 1, 2), dendrimer generation (nG, n = 0-3), and peripheral substituent (-NO 2 = 4-nitrophenylethynyl, "blank" = phenylethynyl, -Cl = chlorido).The phenylethynyl-terminated dendrimers exhibit nonlinear absorption maxima at 700-750 nm, 875-900 nm, 1200-1250 nm, and 1650 nm, conrmed to be 2PA, 2PA, 3PA, and 4PA in nature, respectively, from the intensity dependencies of the corresponding open-aperture fs Z-scan traces (3G 22,03,02,01 -s: Fig. S85-S89 †), and supported by the location of the nPA maxima at wavelengths close to the corresponding multiples of that of the linear absorption maxima.The chlorido-terminated dendrimers exhibit nonlinear absorption maxima at similar wavelength ranges of ca.650-750 nm (2PA), 1200-1300 nm (3PA), and 1600-1850 nm (4PA), while the 4-nitrophenyl-terminated dendrimers show nonlinear absorption maxima at the red-shied wavelengths of ca.650-875 nm (2PA), 1200-1450 nm (3PA), and 1600-2000 nm (4PA); the red-shi following installation of peripheral nitro substituent mimics the corresponding multiple of the 1PA prole with its longer wavelength MLCT to the nitro group, and is of a sufficient extent that 3G 22,03,02,01 -NO 2 exhibits appreciable 4PA at wavelengths beyond 2000 nm (Fig. 3).In general, the s n maximal values increase with generation increase and installation of nitro group; the increased activity accompanying generation increase results in measurable 4PA being observed for all nG (n > 0) examples.Focusing on the s 4 data, for which few precedent structure-activity guidelines exist, the 4PA crosssections increase with dendrimer generation, installation of alkyl solubilizing groups, and progression from peripheral chlorido and nitrophenylalkynyl to phenylalkynyl ligand.
The maximal nonlinear absorption values of the precursors 16-18, 20, 24, and 35 were also determined and are collected in Table S2, † together with those of the key intermediates 22, 26, and 36.The data reveal signicant 2PA and 3PA activity for all precursors and intermediates, and with the largest examples 35 and 36 also displaying measurable 4PA, outcomes consistent with the behavior of the dendrimers.
The molecular weight-scaled performances of certain dendrimer synthesis intermediates also deserve comment (Table S2 †).The hexaruthenium wedge precursor 26, with a strongly dipolar composition, exhibits the largest s 2 /M value (4.44 GM mol −1 g −1 at 900 nm).The Sonogashira coupling precursors 35 and 36 are, effectively, organometallic dendrimers that are peripherally hexaiodo-and dodecaiodo-functionalized, respectively, and thereby benet from a strong heavy-atom effect, with striking s 2 /M parameters, the largest s 3 /M parameter from the present study (36), signicant s 4 activity, and the second largest s 4 /M parameter (35).
As mentioned above, the maximal values increase with dendrimer generation and, indeed, the third-generation dendrimers and some of the second-generation examples are sufficiently active as to also show measurable higher-order MPA at longer wavelengths, the maximal data being collected in Table 2 and the wavelength dependencies being shown in Fig. 4, S65, S67 and S69, † with the assignments again being supported by intensity dependencies of the corresponding open-aperture fs Z-scan traces (3G 22,03,02,01 -s: Fig. S85-S89 †).Note that the small red-shi in s n maxima seen on replacing phenylalkynyl by chlorido peripheral   (0.00192 × 10 −140 cm 10 s −4 photon −4 at 2100 nm, fs nonlinear transmission) 16 and a spiro-fused ladder-type oligo(p-phenylene) (9320 × 10 −140 cm 10 s −4 photon −4 at 1540 nm, 120 fs Z-scan and ve-photon excited uorescence). 15The present data reveal an increase in s 5 with generation increase, replacement of phenylalkynyl by chlorido ligand, and installation of solubilizing alkyl groups, and with the s 5 /M data revealing that the dendrimer generation increases are super-linear in nature.Dendrimers 3G 22,03,02,01 -s and 3G 22,03,02,01 display the rst quantiable molecular 6PA data for organometallics and only the second and third overall, the precedent being the aforementioned spiro-fused ladder-type oligo(p-phenylene) which is active at a much shorter incident wavelength (86.7 × 10 −170 cm 12 s −5 photon −5 at 1820 nm, 120 fs Z-scan and six-photon excited uorescence). 15As with s 4 and s 5 , the s 6 and s 6 /M data increase with introduction of the ethyl solubilizing groups.

Computational studies of two-photon absorption
(non-metal atoms) basis sets; further details are given in the ESI †).Calculation of 2PA spectra is computationally demanding, so the two-photon transition strengths were computed using the ten lowest excited states only.Despite this necessary simplication, the calculations are generally in good agreement with the experimental results; the 2PA proles are similar, with one (1-M-1/1-M-1(dppe)), two (1-M-2/1-M-2(dppe)), and three (1-M-3/1-M-3(dppe)) maxima in the 450 nm range, and the signicant red shi in the lowest-energy 2PA maximum that is seen experimentally upon lengthening the OPE alkynyl ligand being reproduced computationally (Table 3 and Fig. 5).We note that the shortest wavelength 2PA maxima coincide with the onset of one-photon absorption and deconvoluting experimental data in this wavelength range is known to be difficult, 56 so comments are necessarily cautious.The 2PA peak of 1-M-1 at 574 nm is attributed to the largest transition moment (4.32 eV (287 nm): Table S12 †), corresponding to the linear MLCT transition at 285 nm (1-M-1 calc.) and 328 nm (1-M-1(dppe) exp.).Similarly, the lower-lying 2PA maximum of 1-M-2 and the lowest-lying 2PA maximum of 1-M-3 correspond to metal-to-alkynyl-ligand charge transfer, con-rming the key role the metal plays in the MPA merit of these complexes.
The calculated 2PA cross-sections for 1-M-n (n = 1-3) are collected in Table 3, together with those of the experimental complexes 1-M-n(dppe) (n = 1-3).The increase in maximal values seen on proceeding from 1-M-1 to 1-M-3 reproduces the experimental trend seen with 1-M-n(dppe) (n = 1-3).The clear increase in s 2 (both maximal value and integrated intensity) upon OPE alkynyl ligand lengthening highlights the desirability of incorporating the longer OPE units in MPA materials, and conrms that the OPE-rich dendrimer composition in the present study is ideal for MPA efficiency.

Conclusions
The present study has identied optimal compositions for MPAefficient molecules.The trans-[Ru(k 2 -dppe) 2 ] modules incorporate polarizable low oxidation state pseudo-octahedral electronrich metal centers, for which stepwise chemistry at the two axial sites permits the designed construction of p-electrondelocalizable architectures in which the metal engages in strong low-energy MLCT interactions.The trans-[Ru(k 2 -dppe) 2 ] units impart greatly superior solubility and optical nonlinearity to those of analogous purely organic aryleneethynylene-based structures.The resultant metallodendrimers have been denitively identied by a combination of small molecule and macromolecule characterization techniques.
Multi-photon absorption studies have identied exceptional performance across a spectral range extending deep into the NIR region.The dendrimers exhibit outstanding 2PA, 3PA, and 4PA cross-sections.Installation of peripheral nitro substituents red-shis the MPA maxima, such that exceptional 4PA is seen at wavelengths beyond 2000 nm.Structural modications that enhance MPA merit have been identied: increasing the length of the OPE linkage to the core, installation of alkyl solubilizing groups, and peripheral phenylalkynyl ligand incorporation are all benecial compositional changes.Examination of the synthesis intermediates has identied peripheral iodination as a further benecial compositional change.Computational studies of linear and two-photon absorption suggest the use of the 3PE linker as optimum for pdelocalization and maximizing MPA merit.
In addition to record values of (2-4)PA, the present study has also afforded molecules exhibiting higher-order MPA.Rare examples of molecular 5PA have been found with the secondand third-generation metallodendrimers.Generation increase, installation of peripheral chlorido ligands, and incorporation of alkyl solubilizing groups have been identied as molecular modications that improve 5PA.The second and third examples of molecular 6PA have been found with the thirdgeneration metallodendrimers; these exhibit activity at much longer wavelengths than the only extant literature example.The s 6 and s 6 /M parameters of the dendrimers increase on incorporation of alkyl substituents at the OPE group between the rstand second-generation branching points.

Fig. S56 -
Fig. S56-S62, † and natural transition orbitals for the low-energy transitions are shown in Fig. S63.† A number of observations can be made.Contributions to these frontier orbitals are dominated by the OPE ligands and the metal, the exceptions being the smallest complexes for which there is charge-transfer involving the Ru(k 2 -dHpe) 2 moiety (1-M-2: LUMO+1; 1-M-3: LUMO+2).Increasing the number of phenylethynyl units in unsymmetrical complexes while otherwise maintaining complex composition (proceeding from 1-M-2 to 1-M-3 and nally 1-M-4) results in a diminishing LUMO ) HOMO contribution to, and a diminishing red-shi in, the lowestenergy band, which is predominantly C 2 RuC 2 Ph to OPE charge-transfer in character; a similar trend is seen proceeding from 1-M-2 to 2-M-3.Increasing the number of phenylethynyl units in symmetrical complexes (proceeding from 1-M-1 to 2-M-2 and then 3-M-3) results in diminishing LUMO ) HOMO contributions to, and diminishing red-shis for, the lowestenergy bands, which correspond to symmetric charge transfer from the core C 2 RuC 2 unit to the OPE ligands.Comparison of the positional isomers 1-M-3 and 2-M-2, and 1-M-4 and 2-M-3, reveals that the isomers with the phenylethynyl ligand (1-M-n (n = 3, 4)) exhibit the lower energy bands.The LUMOs of the 1-M-n using a combination of open-aperture and closedaperture Z-scan experiments over the spectral range 600-2520 nm, and employing low-repetition rate ca.130 femtosecond light pulses.The open-aperture experiments revealed very large absorptive nonlinearities that have been replotted as the corresponding multi-photon absorption cross-sections in Fig. 3, 4 and S64-S84.† The multi-photon absorption plots also contain the linear optical absorption spectra plotted at twice to six-times the wavelength, to highlight the coincidence or nearcoincidence of multiples of certain bands to MPA bands.In particular, the wavelengths of the maximal values of the intensity dependence-assigned MPA correspond closely to the appropriate multiples of the wavelengths of the low-energy MLCT bands (assigned by analogy with the low-energy bands of the model complexes which are predominantly LUMO )HOMO and MLCT in nature), rather than multiples of the higher-energy, more intense, MLCT/ILCT/LLCT admixtures.This correlation with the low-energy MLCT bands emphasizes the importance of ligated metal modules and of certain types of charge transfer in the MPA performance.The closed-aperture experiments show negative or zero g real values for all compounds, with the negative maximal values occurring in regions of signicant MPA; this is consistent with the anticipated dependence of g real on all nonlinear absorption processes through a nonlinear Kramers-Krönig relationship.44

Fig. 4
Fig. 4 Wavelength dependence of the nonlinear absorption of 3G 22,03,02,01 .Plots of s 2 (blue scatter), s 3 (red scatter), s 4 (green scatter), s 5 (purple scatter), and s 6 (orange scatter) overlaid on the UV/ Vis spectrum (black line), and including plots of the UV/Vis spectrum as a function of twice (blue line), three times (red line), four times (green line), five times (purple line), and six times (orange line) the wavelength.

Table 1
Linear optical absorption and two-to four-photon absorption cross-section maxima a

Table 2
Linear optical absorption and fiveand six-photon absorption cross-section maxima a Solvent CH 2 Cl 2 .b nm.c a