Large Hyperpolarizabilities at Telecommunication-Relevant Wavelengths in Donor–Acceptor–Donor Nonlinear Optical Chromophores

Abstract

Octopolar D₂-symmetric chromophores, based on the MPZnM supermolecular motif in which (porphinato)zinc(II) (PZn) and ruthenium(II) polypyridyl (M) structural units are connected via ethyne linkages, were synthesized. These structures take advantage of electron-rich meso-arylporphyrin or electron-poor meso-(perfluoroalkyl)porphyrin macrocycles, unsubstituted terpyridyl and 4′-pyrrolidinyl-2,2′;6′,2″-terpyridyl ligands, and modulation of metal(II) polypyridyl-to-(porphinato)zinc connectivity, to probe how electronic and geometric factors impact the measured hyperpolarizability. Transient absorption spectra obtained at early time delays (t_delay < 400 fs) demonstrate fast excited-state relaxation, and formation of a highly polarized T₁ excited state; the T₁ states of these chromophores display expansive, intense T₁ → T_n absorption manifolds that dominate the 800–1200 nm region of the NIR, long (μs) triplet-state lifetimes, and unusually large NIR excited absorptive extinction coefficients [ε(T₁ → T_n) ∼ 10⁵ M^–1 cm^–1]. Dynamic hyperpolarizability (β_λ) values were determined from hyper-Rayleigh light scattering (HRS) measurements, carried out at multiple incident irradiation wavelengths spanning the 800–1500 nm spectral domain. The measured β_HRS value (4600 ± 1200 × 10^–30 esu) for one of these complexes, RuPZnRu, is the largest yet reported for any chromophore at a 1500 nm irradiation wavelength, highlighting that appropriate engineering of strong electronic coupling between multiple charge-transfer oscillators provides a critical design strategy to realize octopolar NLO chromophores exhibiting large β_HRS values at telecom-relevant wavelengths. Generalized Thomas–Kuhn sum (TKS) rules were utilized to compute the effective excited-state-to-excited-state transition dipole moments from experimental linear-absorption spectra; these data were then utilized to compute hyperpolarizabilities as a function of frequency, that include two- and three-state contributions for both β_zzz and β_xzx tensor components to the RuPZnRu hyperpolarizability spectrum. This analysis predicts that the β_zzz and β_xzx tensor contributions to the RuPZnRu hyperpolarizability spectrum maximize near 1550 nm, in agreement with experimental data. The TKS analysis suggests that relative to analogous dipolar chromophores, octopolar supermolecules will be likely characterized by more intricate dependences of the measured hyperpolarizability upon irradiation wavelength due to the interactions among multiple different β tensor components.

Short abstract

Coupling of multiple charge-transfer oscillators generates D₂-symmetric octopolar NLO chromophores that exhibit large β_HRS values at telecom-relevant wavelengths.

Introduction

Applications in telecommunications, data storage, sensor protection, and imaging drive interest in nonlinear optical (NLO) materials.¹⁻⁴ Organic NLO materials have been the focus of much attention due to their ease of processing, and the fact that molecular design can tailor the NLO responses for targeted applications.²

Dipolar chromophores based on a donor–bridge–acceptor (D-Br-A) framework define the most widely studied NLO motif.⁵⁻²⁰ The highly polarizable porphyrin unit figures prominently in many D-Br-A chromophores that exhibit large dynamic hyperpolarizabilities.^{9,10,15,16,18−30} Earlier studies demonstrate that ethynyl linkages between multiple porphyrinic components, or between porphyrin moieties and other strong oscillators, give rise to unusually polarizable and hyperpolarizable chromophores³¹⁻⁴⁰ that manifest exciting NLO properties.⁴¹⁻⁵⁰

An interesting class of porphyrin-based chromophores are those in which (porphinato)zinc(II) (PZn) and metal(II) polypyridyl (M) units are linked via an ethyne bridge; many of these compositions feature extraordinarily large frequency-dependent first hyperpolarizabilities (i.e., high β_λ values). In these MPZn supermolecules, PZn π–π* and (polypyridyl)-metal based charge-resonance absorption oscillator strength are extensively mixed, and the respective charge transfer (CT) transition dipoles of these chromophoric units are aligned along the highly conjugated molecular axis. These chromophores evince significant PZn–(polypyridyl)metal electronic interactions, display unusual dependences of the sign and magnitude of the hyperpolarizability upon the incident irradiation frequency, and exhibit substantial β_λ values at telecommunications-relevant wavelengths.^{16,21−23,26,41,42,47}

Extensive research over the last several decades has led to the development of dipolar, D-Br-A chromophores having large hyperpolarizabilities across the 1300–1500 nm spectral domain.^{6,12,16,51,52} Translation of large dipolar molecular hyperpolarizabilities into corresponding bulk-phase macroscopic NLO materials requires ordering of the hyperpolarizable chromophores in a noncentrosymmetric fashion. Dipolar molecules tend to organize in centrosymmetric, antiparallel orientations as their respective ground states possess nonzero dipole moments; such ordering drastically diminishes bulk NLO properties relative to that which could be realized through uniform noncentrosymmetric chromophoric organization. Experimental strategies, such as dispersion of dipolar chromophores in a polymeric host material followed by electric field poling, are known to increase the degree of noncentrosymmetric chromophore orientation in bulk phase materials; the net dipolar order achieved within such macroscopic materials using such approaches rarely exceeds that of a few percent of the total weight fraction of the chromophore present.⁵³⁻⁵⁹

Octopolar molecules, which have no permanent dipole moments and are noncentrosymmetric, may provide an approach to achieving macroscopic NLO active assemblies.⁶⁰⁻⁷² Most examples of octopolar NLO chromophores have either D_3h or T_d symmetry. While D₂ and D_2d symmetries are also appropriate for octopolar NLO chromophore designs, D₂- and D_2d-symmetric NLO octopoles that manifest exceptional hyperpolarizabilities are unusual.^73,74 It was shown recently that strongly coupled, D₂-symmetric oscillators designed from (porphinato)zinc(II) (PZn) and metal(II) polypyridyl (M) structural units connected via ethyne bridges define an exceptional class of octopolar NLO chromophores.²¹ HRS depolarization experiments demonstrated that the measured hyperpolarizabilities (β_HRS values, where β_HRS² = [⟨β_zzz²⟩ + ⟨β_xzz²⟩] = 120/35 β_xyz² for octopolar (T_d, D₂, or D_2d) compounds) of these MPZnM structures arise predominantly from conformers in which torsional angles between the terpyridyl units and the PZn plane are approximately equal in magnitude and opposite in sign,²¹ suggesting that modest solution-phase structural subpopulations of these MPZnM chromophores possess exceptional hyperpolarizabilities.

Here, we report a series of octopolar D₂-symmetric chromophores, based on the MPZnM motif, that demonstrate that strong electronic coupling between multiple charge-transfer oscillators can provide octopolar NLO chromophores that exhibit impressive β values at 1500 nm. While wavelengths near 1500 nm define a critically important telecommunications spectral region, no molecular chromophore has thus far been delineated that exhibits a dynamic hyperpolarizability measured at a 1.5 μm incident irradiation wavelength that exceeds 700 × 10^–30 esu;^{27,61,65,74−81} this work provides new insights into the design of octopolar NLO chromophores, and demonstrates the utility of MPZnM compositions for realizing substantial β_HRS values at long wavelengths.

Results and Discussion

Design and Synthesis

RuPZnRu (1), P₁RuPZnP₁Ru (2), P₁RuR_fPZnP₁Ru (3), and 5,10-P₁RuR_fPZnP₁Ru (4) (Scheme 1) were synthesized by metal-catalyzed cross-coupling^{16,32,82−89} of an appropriate 4′-brominated ruthenium bis(2,2′;6′,2″-terpyridine) synthon (RuBr or P₁RuBr) and a (di-meso-ethynylporphinato)zinc(II) (EPZnE) complex (Scheme 1). These chromophores are based on the MPZnM motif,^21,89 in which two bis(terpyridyl)metal(II) units are connected to a PZn meso carbon position via ethynyl connectivity. RuPZnRu, P₁RuPZnP₁Ru, P₁RuR_fPZnP₁Ru, and 5,10-P₁RuR_fPZnP₁Ru were isolated as described in the Supporting Information; tetrakis(hexafluorophosphate) salts of these chromophores were used in all the spectroscopic experiments described below.

Scheme 1. General Synthetic Scheme for Compounds 1–4,

(A) Synthetic route to compounds 1–4. (B) Molecular structure of RuPZn.

(a) Pd₂(dba)₃, AsPh₃, THF, CH₃CN, Et₃N, 60 °C.

Previous work establishes that (i) strongly coupled D₂ symmetric oscillators can provide impressive octopolar NLO chromophores, (ii) MPZnM measured hyperpolarizabilities derive largely from conformers in which the torsional angles between the terpyridyl and porphyryl units are approximately equivalent in magnitude and opposite in sign, and (iii) the observed octopolar NLO response derives from the collective response of the component dipolar RuPZn supermolecular units.²¹ Compounds 1–4 provide a compact set of chromophores that probe how electronic and geometric factors impact the measured hyperpolarizability at long irradiation wavelengths. These structures take advantage of electron-rich 10,20-diarylporphyrin (1, 2) or electron-deficient 10,20-bis(perfluoroalkyl)porphyrin frameworks (3, 4), unsubstituted terpyridyl (1) and 4′-pyrrolidinyl-2,2′;6′,2″-terpyridyl ligands (2, 3, 4), and modulation of metal(II) polypyridyl-to-(porphinato)zinc connectivity (3, 4). The bis[meso-(perfluoroalkyl)porphinato]zinc(II) unit provides a PZn chromophoric building block that features HOMO and LUMO levels stabilized by ∼0.3 eV relative to the corresponding orbitals of [5,15-diarylporphinato]zinc(II);^40,90−92 this electronic structural modification of the PZn chromophore provides a convenient means to modulate the supermolecular charge resonance character that originates from M and PZn electronic and excitonic interactions that derive from the porphyrin meso-carbon-to-terpyridyl-carbon ethynyl linkage.^16,42 Likewise, relative to an unsubstituted terpyridyl ligand, the 4′-pyrrolidinyl substituent modulates terpyridyl ligand π*energy levels and diminishes the E_1/2(M^3+/2+) value of the bis(terpyridyl)ruthenium(II) structure by 0.3 eV, regulating the respective energies of the PZn_n-derived π → π* and bis(terpyridyl)metal(II) charge-transfer states.⁴¹ Further, as both the effective chromophore optical symmetry and the nature of the dipolar coupling between independent RuPZn units in larger MPZn-based supermolecules dramatically modulate NLO response,⁸⁹ chromophores 3 and 4 provide insight on how transition dipole moment orientation influences electronic structure and the measured hyperpolarizability.⁹⁴

Electronic Absorption and Potentiometric Data

The electronic absorption spectra (EAS) of these species (Figure 1, Table 1) indicate strong mixing of the PZn-based oscillator strength with ruthenium terpyridyl charge resonance bands. Note that EAS of 1–4 differ markedly from the EAS acquired for their respective ethynyl-PZn and (terpyridyl)ruthenium building blocks (see Figure S1). It is important to note in this regard that supermolecular chromophores 1–4 retain spectroscopic qualities that trace their origin to those of well-studied PZn and [Ru(tpy)₂]²⁺ oscillators. For instance, 1–4 show (i) strong, porphyrin B-state derived (ε > 100,000 M^–1 cm^–1) absorptions near 460 nm; (ii) visible bands centered at ∼525 nm that feature (terpyridyl)metal-to-ligand singlet charge transfer (¹MLCT) character and porphyrin ligand oscillator strength contributions; and (iii) bands localized between 600 and 700 nm that exhibit both porphyrinic ¹π–π* Q-state and charge resonance character that derive from conjugation expansion^10,15,95 and the strong electronic coupling between the (porphinato)metal and (terpyridyl)metal units.^16,42 In order to simplify comparison of the spectral properties of these conjugated supermolecules with those of common porphyrin and (terpyridyl)metal(II) benchmarks, we preserve MLCT (d−π*), Soret (B)-band, and Q-band (π–π*) transition labels. When these terms are used in reference to the absorptions of MPZnM chromophores, they denote only the dominant contributor to the oscillator strength of the specific transition, as MLCT, ligand, Soret, and Q electronic states are extensively mixed in these supermolecules.

Figure 1.

Electronic absorption spectra of (A) RuPZnRu, (B) P₁RuPZnP₁Ru, (C) P₁RuR_fPZnP₁Ru, and (D) 5,10-P₁RuR_fPZnP₁Ru recorded in CH₃CN solvent at 20 °C.

Table 1. Electronic Absorption^a and Potentiometric Data^b for Compounds 1–4.

	abs band maxima [nm] (ε/105 [M–1 cm–1])			potentiometric data (mV)
	B band	1MLCT	Q bands	ZnP0/+	ZnP+/2+	M2+/3+	tpy–/0	ZnP–/0
RuPZnRu (1)c,d	467 (1.31)	510 (1.29)	697 (1.33)	920	1155	1450	–895	–1330
P1RuPZnP1Ru (2)e	466 (1.33)	525 (1.18)	706 (1.22)	855	1195	980	–925	–1410
P1RuRfPZnP1Ru (3)e	463 (1.42)	533 (1.80)	612 (0.28)	1380		975	–755	–965
			663 (1.06)
5,10-P1RuRfPZnP1Ru (4)e	462 (1.42)	532 (1.70)	612 (0.26)	1405		970	–690	–1030
			664 (0.99)

^aAll absorption spectra were recorded in CH₃CN; [chromophore] = 1 μM.

^bExperimental conditions: [chromophore] = 1–4 mM; scan rate = 0.5 V/s; reference electrode = Ag/AgCl; working electrode = Pt disk. E_1/2 values are reported relative to SCE; the ferrocene/ferrocenium couple (0.43 V vs SCE) was used as an internal standard.

^cPotentiometric data recorded in 0.1 M TBAPF₆/DMF electrolyte/solvent system.

^dTaken from refs (42) and (96).

^ePotentiometric data recorded in 0.1 M TBAPF₆/CH₃CN electrolyte/solvent system.

Figure 1 shows that, for all of these compounds, dramatic oscillator strength transfer from the B band to the Q band arises from the coupling between two chromophoric units. Despite significant modulation of the ruthenium oxidation potential (Table 1), incorporation of a pyrrolidine donor on the metal complex has little effect on the ground-state electronic absorption spectrum, because the moderate intensity ¹MLCT transition is buried underneath the strong porphyrin-derived S₀ → S₂ absorption manifold, as is evident from spectra recorded for compounds 1 and 2. Changing PZn ancillary 10,20-meso substitution from an electron rich 3,5-bis(3,3-dimethyl-1-butyloxy)phenyl to an electron deficient heptafluoropropyl group (compare structures of compounds 2 and 3; Figure 1B,C) substantially blue shifts (∼850 cm^–1) the low energy Q-state-derived absorption band maximum. Note also that substitution of the PZn ancillary meso aryl moiety with a perfluoroalkyl substituent (Figure 1C,D) drives increased porphyrin ligand oscillator strength contributions to the transition manifold centered near 525 nm, which features augmented metal-to-ligand charge transfer character relative to that observed for compounds 1 and 2 (Figure 1A,B). Potentiometric data for supermolecular chromophores 1–4 are compiled in Table 1.

Excited-State Dynamics

Pump–probe transient absorption spectroscopic studies of 1–4 demonstrate excited-state dynamical characteristics and transient spectral features closely related to those reported for the archetypal dipolar supermolecular donor–acceptor ruthenium(II) [5-(4′-ethynyl-(2,2′;6′2″-terpyridinyl))-10,20-bis(2′,6′-bis(3,3-dimethyl-1-butyloxy)phenyl)porphinato]zinc(II)-(2,2′;6′,2″-terpyridine)²⁺ bis(hexafluorophosphate) chromophore, RuPZn (Scheme 1).^41,42,89 In this respect, it is important to appreciate that the excited-state relaxation dynamics of RuPZn and related chromophores^41,42 exhibit significant departures from those characteristic of simple (porphinato)metal and (terpyridyl)metal species. Monomeric (porphinato)zinc(II) species relax typically through both the singlet and triplet manifolds, leading to nanosecond (singlet) and millisecond (triplet) deactivation time scales;³¹ at room temperature, the initially prepared [Ru(tpy)]²⁺ electronically excited state relaxes rapidly to the low-lying metal-to-ligand charge transfer (triplet) surface,⁹⁷⁻⁹⁹ where fast intersystem crossing dynamics are driven by thermal population of a low-lying ³MC state, resulting in a ³MLCT lifetime of only a few hundred picoseconds at 298 K.¹⁰⁰ In RuPZn,^41,42 transient absorption spectra obtained at early time delays (t_delay < 400 fs) demonstrate fast excited-state relaxation and formation of a highly polarized T₁ excited state; the combined effects of rapid intersystem crossing and strong coupling to low-lying MLCT states gives rise to excited-state lifetimes >10 μs, and a negligible excite-state population loss to ground-state on the intersystem crossing time scale (τ_isc ∼ 4 ps) following S₀ → S₁ excitation. Pump–probe transient optical spectroscopic and dynamical investigations of RuPZn electronically excited states reveal prominent spectral characteristics that include (i) visible spectral domain bleaching due to ground-state depletion, (ii) a broad, weak transient absorption in the spectral region between the B- and Q-state ground-state bleaches, and (iii) an unusually broad, intense T₁ → T_n absorption manifold that spans the 800–1200 nm spectral range.^41,42

Figure 2 highlights transient absorption spectral data for chromophores 1–4 obtained over a 200 fs-to-1 ns time domain. The transient absorption signals observed at the earliest time delays over the 700–900 nm spectral region suggest that initially prepared excited states for compounds 1–4 are less conjugated than their respective corresponding relaxed excited states. Supermolecules 1 and 2 manifest an ∼15 ps time constant component that leads to an increase in the intensity of the T₁ → T_n NIR transient absorption manifold; these dynamics are associated with torsional motion about the ethynyl bridge.^33,41,42,101 Global analysis of the excited-state transient dynamical data acquired for 3 and 4 indicates an ultrafast relaxation process (τ_relaxation < 1 ps) that leads to an increase in the intensity of the T₁ → T_n NIR transient absorption band. This effect likely derives from the electronic structure of the bis[meso-(perfluoroalkyl)porphinato]zinc(II) units of 3 and 4: as the potentiometrically determined HOMO levels of these electron deficient PZn chromophoric building blocks are stabilized by ∼0.3 eV relative to the corresponding orbitals of [meso-arylporphinato]zinc(II),^40,90−92 enhanced ground-state charge-resonance interactions between the metal terpyridyl and PZn units drive reduced torsional angle conformational heterogeneity between the porphyryl and terpyridyl least-squares planes relative to that exhibited by 1 and 2. The more planar, conformationally uniform nature of the chromophore 3 and 4 ground states relative to those of 1 and 2 is thus reflected in their order-of-magnitude diminished τ_relaxation values, as their mean terpyridyl-(porphinato)metal torsional angles more closely resemble those of their respective relaxed electronically excited states.^41,42

Figure 2.

Representative magic angle femtosecond transient absorption spectra recorded for (A) RuPZnRu, (B) P₁RuPZnP₁Ru, (C) P₁RuR_fPZnP₁Ru, and (D) 5,10-P₁RuR_fPZnP₁Ru at time delays noted. Experimental conditions: λ_ex = (A) 695 nm, (B–D) 672 nm; pump energy = ∼0.5 μJ/pulse; solvent = acetonitrile; T = 20 °C.

Figures 3 and S2 highlight transient absorption spectral data acquired for chromophores 1–4 over ns-to-μs time domains; Table 2 tabulates excited-state lifetimes, T₁ → T_n absorption maxima, and T₁ → T_n absorption extinction coefficients for these compounds. Note that these estimated T₁ → T_n extinction coefficients (ε∼ 10⁵ M^–1 cm^–1) are calculated from fs transient absorption spectra acquired at 1 ns following excitation, and were estimated by comparing the excited-state absorption to the Q_x-band derived ground-state bleach (having a known extinction coefficient), following a method detailed previously.⁴² Note that λ_max(T₁ → T_n) increases modestly with incorporation of the pyrrolidine group on the terpyridyl ligand (1, λ_max(T₁ → T_n) = 980 nm; 2, λ_max(T₁ → T_n) = 1006 nm), congruent with enhanced electronic delocalization within the compound 2 T₁ state. Note also that relative to 1, the enhanced ground-state charge-resonance interactions between the metal terpyridyl and PZn units of chromophores 3 and 4 that derive from the electron-deficient perfluoroalkyl-substituted porphyrin macrocycle result also in red-shifted λ_max(T₁ → T_n) values (3, λ_max(T₁ → T_n) = 996 nm; 4, λ_max(T₁ → T_n) = 988 nm). In sum, Figures 2 and 3 and Table 2 data underscore that the combination of fast intersystem crossing, long triplet-state lifetimes, and unusually large ε(T₁ → T_n) values make chromophores 1–4 exceptional excited-state absorbers for this region of the NIR.

Figure 3.

Nanosecond pump–probe transient absorption spectra of (A) P₁RuPZnP₁Ru (2), (B) P₁RuR_fPZnP₁Ru (3), and (C) 5,10-P₁RuR_fPZnP₁Ru (4) recorded at time delays noted. Experimental conditions: solvent = deaerated acetonitrile; λ_ex = 532 nm; pump energy =1–3 mJ/pulse; ambient temperature.

Table 2. Electronically Excited Triplet State Spectral Data^a for Compounds 1–4.

chromophore	λmax (T1 → Tn)b (nm)	ε/105 M–1 cm–1 (T1 → Tn)c	τT (μs)d
RuPZnRu (1)	980e	1.48	10.4e
P1RuPZnP1Ru (2)	1006	1.32	9.0
P1RuRfPZnP1Ru (3)	996	1.22	3.3
5,10-P1RuRfPZnP1Ru (4)	988	1.14	3.3

^aAll spectral data were acquired in acetonitrile solvent.

^bλ_max (T₁ → T_n) values were determined from transient absorption spectra recorded at a 1 ns time delay.

^cThe excited-state extinction coefficients were estimated using a method described previously;⁴² reported values were determined at the T₁ → T_n λ_max.

^dThe triplet-state lifetimes were determined using μs time domain transient absorption measurements carried out in dry dearated acetonitrile solvent.

^eλ_max (T₁ → T_n) and triplet lifetime were reported previously.⁴²

Nonlinear Optical Properties

For chromophores with charge transfer (CT) transitions that dominate the NLO response, the dynamic hyperpolarizability can be approximated using a two-state description of β (eq 1).

1

Here, P_ge is the oscillator strength for the CT transition, Δμ_ge the dipole moment difference between ground and CT excited states, E_op the energy gap between the two states, and E_inc the incident irradiation energy.^102,103 Within the limited context of a single two-level model for charge transfer (along the molecular z-axis) dominated dipolar molecules, β_n′ is an excellent approximation for β_zzz. Dipolar RuPZn-based chromophores are characterized by large CT transition oscillator strengths (P_ges), and significant dipole-moment differences between the ground and excited electronic states (Δμ_ges). These species exhibit complicated nonlinear responses because of two- and three-level contributions arising from mixing of transitions that possess (porphinato)zinc B-, (porphinato)zinc Q-, and ruthenium-to-ligand (MLCT)-state character, and the fact that these transitions have Δμ_ges with both positive and negative sign.^16,22,41

A two-state model to describe the electronic hyperpolarizability is appealing for its simplicity and qualitative description of the underlying physical principles. The direct linkage to experimental data, namely, transition dipole moments, optical transition energies, and energy detunings from resonance, is particularly appealing. While of qualitative use for exploring structure–hyperpolarizability relationships, the two-level model does not describe the frequency dispersion of the hyperpolarizability with quantitative accuracy. We recently developed and used generalized Thomas–Kuhn sum (TKS) rules to describe the frequency-dependent hypolarizabilities in a manner that retains the appealing simplicity and direct linkage to linear absorption spectra, while incorporating the influence of multiple excited states that contribute to the hyperpolarizability. Within this framework, a satisfactory description was found for the frequency dispersion of the hyperpolarizabilities for dipolar chromophores.²² Here, we use this approach to describe qualitatively octopolar chromophores with more than two excited states that contribute to the irradiation-wavelength dependent hyperpolarizability. Since multiple absorption manifolds contribute to the nonlinear response in RuPZn-based chromophores, and the transitions that dominate these manifolds possess distinct transition dipole directions, octopolar chromophores 1–4 are anticipated to exhibit complex hyperpolarizability spectra.

Table 3 lists dynamic hyperpolarizability (β_λ) values for compounds 1–3, determined from hyper-Rayleigh light scattering (HRS) measurements carried out at different incident irradiation wavelengths (λ_incs) in CH₃CN solvent. The total HRS intensities listed in Table 3 (i.e., the total magnitude of the HRS signal with polarization parallel and perpendicular to the Z-polarized fundamental laser beam, β_HRS² = [⟨β_zzz²⟩ + ⟨β_xzz²⟩]) provide an average hyperpolarizability value that has not been separated into specific hyperpolarizability tensor components for a specific molecular symmetry.^104,105 For chromophores 1–3, hyperpolarizabilities were measured at multiple incident wavelengths, producing a “hyperpolarizability spectrum”; such data are important, as these may be used in combination with appropriate theoretical frameworks to identify electronic states that contribute to the NLO response at a specific λ_inc, and thereby provide chromophore design insights necessary to optimize the hyperpolarizability at the frequency of interest. Table 3 reports irradiation wavelength-dependent measured hyperpolarizabilities for RuPZnRu (1), P₁RuPZnP₁Ru (2), P₁RuR_fPZnP₁Ru (3), and the dipolar RuPZn benchmark.

Table 3. Dynamic Hyperpolarizabilities [β_HRS, (× 10^–30 esu)]^a and Depolarization Ratios (ρ) Determined from Hyper-Rayleigh Experiments.

	800 nm	840 nm	1064 nm	1300 nm	1320 nm	1340 nm	1500 nm	ρb
RuPZnc	200 ± 30	700 ± 100		1300 ± 100	1320 ± 70	90 ± 40	110 ± 4	3.8
RuPZnRu (1)	190 ± 30	450 ± 70	1000 ± 100	260 ± 80	660 ± 40	710 ± 40	4600 ± 1200	1.7
P1RuPZnP1Ru (2)	220 ± 10	510 ± 80	300 ± 40		180 ± 70		600 ± 100	1.9
P1RuRfPZnP1Ru (3)	180 ± 10	390 ± 60					30 ± 4	1.8

^aTotal HRS intensity as noted in the text at the indicated wavelength.

^bMeasured at λ_inc = 800 nm.

^cHyperpolarizability values for RuPZn have been reported previously.^16,22 A blank entry indicates a β_HRS value <30 × 10^–30 esu.

As a case in point, note that RuPZnRu (Table 3) displays a complex hyperpolarizabilty dispersion: at λ_inc = 800 nm, the measured hyperpolarizability (β₈₀₀ = 190 ± 30 × 10^–30 esu) is modest. The magnitude of β_λ increases as the irradiation wavelength is tuned to 840 and 1064 nm (β₈₄₀ = 450 ± 70 × 10^–30 esu; β₁₀₆₄ = 1000 ± 100 × 10^–30 esu), decreases as λ_inc moves further to the red (β₁₃₀₀ = 260 ± 80 × 10^–30 esu), increases steadily at slightly longer irradiation wavelengths (β₁₃₂₀ = 660 ± 40 × 10^–30 esu; β₁₃₄₀ = 710 ± 40 × 10^–30 esu), but increases dramatically at λ_inc = 1500 nm (β₁₅₀₀ = 4600 ± 1200 × 10^–30 esu). This β_HRS value is the largest yet reported for any chromophore at λ_inc = 1500 nm.

Table 3 further tabulates depolarization ratio measurements determined at λ_inc = 800 nm. The depolarization ratio, ρ, is the ratio of the HRS signal intensity (I) parallel to (I_∥) and perpendicular to (I_⊥) the incident polarization (ρ = I_∥/I_⊥ = ⟨β_zzz²⟩/⟨β_xzz²⟩). HRS depolarization ratio measurements provide information regarding the optical symmetry of states that give rise to the NLO response. For a classic dipolar NLO chromophore such as disperse red 1, ρ = 3.4; for an octopolar NLO chromophores such as 1,3,5-trihydroxy-2,4,6-trinitrobenzene and crystal violet, ρ = 1.5. Measured depolarization ratios for chromophores 1–3 are ∼1.8; these data, in combination with the chemical topology of the structures, are congruent with the D₂ octopolar nature of these structures.

Thomas–Kuhn Sum-over-States (TKS) Analysis

A central goal in nonlinear optics is to establish conceptual frameworks to understand and to tune the hyperpolarizability and frequency dependant nonlinear response. Addressing these design challenges in the frequency domain is especially significant since NLO devices function at finite wavelengths, making it difficult to generalize design-response principles that may be established at either shorter or longer wavelengths. Nonetheless, quantum chemical analysis^15,106−114 can be of great value in the regime of nonzero frequency. Developing predictive methods to describe β_λ remains an open challenge.¹¹⁵ One bottleneck to predicting β_λ is the inclusion of multiple excited states that impact the electronic hyperpolarizability. Excitation energies, the transition moments, basis set, treatment of solvation, and level of electronic structure theory are all well-known to influence the computed nonlinear electronic response. Prior studies^9,16,116 have interpreted β_λ qualitatively in the context of the two electronic state model (eq 1). This model includes resonant enhancement from one and two photon resonant terms. The excitation energies and the oscillator strengths are provided by the linear absorption spectra. However, the data derived from linear spectra are not adequate to make predictions of hyperpolarizabilities. The reason is that the linear absorption spectra lack transition dipole moment information linking multiple excited states, and this information is needed for three-state (or higher) β_λ computation.

We recently showed that the generalized Thomas–Kuhn sum (TKS) rules may be used to compute the effective excited-state-to-excited-state transition dipole moments (within a few-state model) using the experimental linear-absorption spectra. These data can then be used to estimate the hyperpolarizabilities as a function of frequency, including two- and three-state contributions for RuPZn and related dipolar chromophores.²² TKS analysis uses linear-absorption data to extract the transition dipoles and energies of a small number of “effective” excited electronic states, thus providing key input data required to compute β_λ (Supporting Information). Our earlier studies found that while structures may possess similar absorption spectra, the frequency-dependent hyperpolarizabilities may be very different because of differences in the influence of excited-state-to-excited-state transition moments.

The TKS analysis enables the use of linear optical absorption spectra and a few hyperpolarizability measurements to estimate the full frequency-dependent NLO response for RuPZn and related dipolar chromophores. Nonetheless, it is critical to recognize that the octopolar D₂ symmetric structure for chromophores 1–3 requires that both β_zzz and β_xzx tensors be computed, making a corresponding TKS analysis of the NLO octopole structures of current interest more complex than those modeled earlier. The fact that the present analysis includes only a limited number of effective excited states makes the octopolar NLO analysis described here more qualitative than that of our earlier studies.

With these caveats in mind, we performed a basic TKS analysis for the RuPZnRu chromophore using its linear-absorption spectrum and the frequency-dependent hyperpolarizability data compiled in Table 3. As β_zzz and β_xzx tensor components play key roles in determining the hyperpolarizability spectrum for RuPZnRu, Figure 4 compares the computed wavelength-dependent contributions of these tensor components relative to the computed β_zzz tensor contribution for RuPZn (Figure 4A),²² which largely determines the β_λ spectrum for the dipolar benchmark RuPZn. Figure 4B,C shows the frequency-dependent two- and three-state computed contributions to β_zzz and β_xzx values for RuPZnRu. These data indicate that, for RuPZnRu, the two- and three-state contributions to β_zzz are of smaller magnitude over the entire hyperpolarizability spectrum compared to that computed for RuPZn. This finding underscores the fact that off-diagonal beta tensor components are of critical importance in determining the hyperpolarizability spectrum of octopolar molecules. Congruent with experiment, the TKS computed β_zzz value for RuPZn is large at ∼1300 nm. Similarly, the corresponding calculated β_zzz and β_xzx contributions for RuPZnRu at λ_inc = 1300 nm are modest, in line with experimental data (Table 3). Note, however, that both the β_zzz and β_xzx frequency dependent tensor elements for RuPZnRu reach maxima near 1550 nm, in agreement with the observed large β_HRS value (4600 ± 1200 × 10^–30 esu; Table 3) measured for this chromophore at 1500 nm. At this level of analysis, the TKS rules indicate that relative to analogous dipolar chromophores, octopolar supermolecules will be likely characterized by more intricate dependences of the measured hyperpolarizability upon irradiation wavelength due to the interactions among multiple different β tensor components.

Figure 4.

Comparison of the computed hyperpolarizability tensors β_zzz for (A) RuPZn and (B) RuPZnRu, and (C) β_xzx for RuPZnRu. The two-level contribution from the Q_x-derived transition is β₁₁; the two-level contribution from the ¹MLCT-derived transition is β₂₂; the two-level contribution from the B-derived transition is β₃₃; β₁₂, β₂₁, β₁₃, β₃₁, β₂₃, and β₃₂ are the three-level contributions from the coupling of ¹Q_x-, ¹MLCT-, and B-derived excited states. See the Supporting Information for further details.

Experimental Section

Materials and Instrumentation

Inert atmosphere manipulations were carried out under argon prepurified by passage through an O₂ scrubbing tower (Schweizerhall R3-11 catalyst) and a drying tower (Linde 3 Å molecular sieves). Air-sensitive solids were handled in a Braun 150-M glovebox. Standard Schlenk techniques were employed to manipulate oxygen and moisture sensitive chemicals. ACS grade CHCl₃, CH₂Cl₂, CH₃CN, and hexanes solvents were purchased from Fisher Scientific. Tetrahydrofuran (Fisher Scientific, HPLC grade) was either distilled from potassium/benzophenone or purified using an Innovative Technology Puresolv solvent purification system. Triethylamine was distilled from CaH₂; acetonitrile was purified by distillation from CaH₂. Pd(PPh₃)₄, PdCl₂(PPh₃)₂, Pd₂(dba)₃, and CuI were obtained from either Aldrich or Strem Chemicals. All other commercially available reagents were used as received. An inert atmosphere was maintained in all reactions unless otherwise stated. Chromatographic purification (silica gel, 60 Å pore size, 230–400 mesh, EM Scientific or Silicycle) of all newly synthesized compounds was accomplished on the benchtop. All NMR solvents were used as received. Chemical shifts for ¹H NMR spectra are relative to the internal reference (tetramethylsilane) in CDCl₃, or solvent residual protium (acetonitrile-d₃, δ = 1.93 ppm, THF-d₈, δ = 1.85, 3.76 ppm). The number of attached protons and coupling constants are found in parentheses following the chemical shift values. Laboratory instrumentation has been described previously.⁸⁹

Ultrafast Transient Absorption Experiments

Instrumentation used to acquire ultrafast transient absorption spectra has been described previously.^41,89,117 Samples for these studies were prepared, manipulated, and handled as described earlier.^41,89 Following acquisition of pump–probe spectroscopic data, linear absorption spectroscopy confirmed that all samples investigated were robust.

Nanosecond Transient Absorption Experiments

Nanosecond transient absorption spectra were acquired utilizing an Edinburgh Instruments LP920 laser flash photolysis spectrometer and Edinburgh L900 Software. Pump pulses were generated from a Q-switched Nd:YAG laser (Quantel, Brillant) and a dual-crystal OPO (OPOTEK, Vibrant LDII). The temporal width of the pump pulses was ∼5 ns; the energy of the pulses exiting the OPO was controlled using neutral density filters. A Xe flash lamp was used as a white light probe source, and a CCD array detector enabled acquisition of transient data over the 185–875 nm wavelength domain. Both the LP920 and Opotek OPO are computer interfaced and controlled by the L900 software. Transient spectra reported derive from data acquired over ∼20–50 scans. Samples were prepared in 1 cm quartz cells and deaerated by 3 freeze–pump–thaw cycles prior to excitation. Excited-state lifetimes were calculated via monoexponential fitting using Origin 9.1 software.

Hyper-Rayleigh Light Scattering (HRS) Measurements

Femtosecond HRS experiments were performed according the method published earlier.^27,118,119 The main difference with respect to previous studies involves the spectral domain of these measurements, which included a large number of measurement wavelengths extending to 1500 nm.^16,21,89 For this extended set of wavelengths, a variety of reference compounds [crystal violet (CV; β₈₀₀ (methanol) = 208.6 × 10^–30 esu),¹²⁰p-nitroaniline (pNA; β₁₀₆₄ (acetonitrile) = 8.7 × 10^–30 esu),¹²¹ and disperse red 1 (DR1; β₁₃₀₀ (chloroform) = 22.4 × 10^–30 esu)]¹¹⁹ were used. Reference values at nearby wavelengths were derived from the two-level model. These values have been shown to provide an excellent set of self-consistent points of reference to quantitatively study the frequency dispersion of the hyperpolarizability for porphyrin-derived chromophores.^{16,21,27,89,122}

The chromophores were dissolved in acetonitrile, and passed through 0.2 μm filters. For the external references in different solvents, standard local field correction factors were applied , where n is the refractive index of the solvent at the sodium D line (1.330 for methanol; 1.344 for acetonitrile; and 1.446 for chloroform). HRS data were acquired using procedures described previously to ensure linearity of the HRS signal and that self-absorption of the second harmonic signal was insignificant;⁸⁹ depolarization ratios were likewise determined using approaches detailed in earlier work.⁸⁹

Chromophore Synthesis

An exemplary synthesis of bisruthenium(II) 5,15-bis[4′-ethynyl-(2,2′;6′,2″-terpyridinyl)]bis[10,20-bis(2′,6′-bis(3,3-dimethyl-1-butyloxy)phenyl)porphinato]zinc(II)-bis(4′-pyrrolidin-1-yl-2,2′;6′2″-terpyridine) tetrakis(hexafluorophosphate) (P₁RuPZnP₁Ru, 2) follows below. Synthetic procedures and characterization data for all other compounds may be found in the Supporting Information.

Bisruthenium(II) 5,15-Bis[4′-ethynyl-(2,2′;6′,2″-terpyridinyl)]bis[10,20-bis(2′,6′-bis(3,3-dimethyl-1-butyloxy)phenyl)porphinato]zinc(II)-bis(4′-pyrrolidin-1-yl-2,2′;6′2″-terpyridine) Tetrakis(hexafluorophosphate) (P₁RuPZnP₁Ru, 2)

[5,15-Diethynyl-10,20-bis[2′,6′-bis(3,3-dimethyl-1-butyloxy)phenyl]porphinato]zinc (50 mg, 0.0513 mmol) and ruthenium(II) (4′-bromo-2,2′;6′,2″-terpyridine)(4′-pyrrolidin-1-yl-2,2′;6′,2″-terpyridine)bis(hexafluorophosphate) (P₁RuBr) (Scheme 1, 115 mg, 0.1143 mmol) were placed into a 100 mL Schlenk tube with a stir bar. Trisdibenzylideneacetone dipalladium(0) (7 mg, 7.7 μmol) and triphenylarsine (31 mg, 0.1013 mmol) were added. A solvent mixture of dry THF (12 mL), CH₃CN (24 mL), and Et₃N (4 mL) was completely degassed via three freeze–pump–thaw cycles and added to the Schlenk tube. The reaction mixture was then stirred under argon atmosphere at 55 °C for 16 h, following which it was cooled to room temperature and the solvent evaporated. The residue was purified by column chromatography on silica gel, eluted with a mixed solvent of CH₃CN:H₂O:saturated aqueous KNO₃ = 90:9:1. The major red-brown band was collected and the solvent evaporated. The residual dark brown solid was dissolved in a minimum volume of CH₃CN, and excess ammonium hexafluorophosphate and H₂O were added. A dark brown precipitate (2, 110 mg, 0.0389 mmol, 76% yield based on initial bis-ethynyl porphyrin) was collected by filtration. ¹H NMR (CD₃CN): δ 9.77 (d, J = 4.5 Hz, 4H), 9.14 (s, 4H), 8.75 (d, J = 4.5 Hz, 4H), 8.58 (d, J = 8.0 Hz, 4H), 8.30 (d, J = 8.0 Hz, 4H), 7.84 (t, J = 7.0 Hz, 4H), 7.70–7.63 (m, 10H), 7.39 (d, J = 5 Hz, 4H), 7.21 (d, J = 5 Hz, 4H), 7.12 (t, J = 6 Hz, 4H), 6.99 (d, J = 8.5 Hz, 4H), 6.92 (t, J = 6 Hz, 4H), 3.83 (t, J = 7 Hz, 8H), 3.63 (s, 8H), 2.07 (s, 8H), 0.66 (t, J = 7 Hz, 8H), 0.03 (s, 36 H). Vis (CH₃CN): λ_max [nm] (ε [× 10^–5 M^–1 cm^–1]) 465 (1.33), 525 (1.18), 705 (1.22). MS (MALDI-TOF) m/z: 2385 (calcd for C₁₂₈H₁₂₂F₆N₁₈O₄PRu₂Zn (M – 3PF₆)⁺ 2387), 2528 (calcd for C₁₂₈H₁₂₂F₁₂N₁₈O₄P₂Ru₂Zn (M – 2PF₆)⁺ 2532), and 2674 (calcd for C₁₂₈H₁₂₂F₁₈N₁₈O₄P₃Ru₂Zn (M – PF₆)⁺ 2678).

Conclusion

Octopolar D₂-symmetric chromophores, based on the MPZnM motif in which (porphinato)zinc(II) (PZn) and ruthenium(II) polypyridyl (M) structural units are connected via ethyne linkages, were probed using linear and nonlinear optical spectroscopic methods to determine how electronic and geometric factors impact measured hyperpolarizabilities. Linear electronic spectra of these RuPZnRu, P₁RuPZnP₁Ru, P₁RuR_fPZnP₁Ru, and 5,10-P₁RuR_fPZnP₁Ru chromophores (Figure 1) display (i) strong, porphyrin B-state derived (ε > 100,000 M^–1 cm^–1) absorptions near 460 nm; (ii) visible bands centered at ∼525 nm, that feature (terpyridyl)metal-to-ligand singlet charge transfer (¹MLCT) and porphyrin ligand oscillator strength contributions; and (iii) high oscillator strength absorption manifolds in the 600–700 nm range that exhibit both porphyrinic ¹π–π* Q-state and charge resonance character that derive from conjugation expansion^10,15,95 and the strong electronic coupling between the (porphinato)metal and (terpyridyl)metal units. Transient absorption spectra obtained at early time delays (t_delay < 400 fs) demonstrate fast excited-state relaxation, and formation of a highly polarized T₁ excited state; the T₁ states of these chromophores exhibit a broad, intense T₁ → T_n absorption manifold over the 800–1200 nm spectral domain, long (μs) triplet-state lifetimes, and unusually large NIR absorptive extinction coefficients [ε(T₁ → T_n) ∼ 10⁵ M^–1 cm^–1].

Dynamic hyperpolarizability (β_λ) values were determined from hyper-Rayleigh light scattering (HRS) measurements carried out at multiple incident irradiation wavelengths spanning the 800–1500 nm spectral domain. These RuPZn-based octopolar chromophores feature complex hyperpolarizability spectra, as (i) multiple transitions contribute to the nonlinear response and (ii) the dipole directions of these directions may be of identical or opposite sign. The measured β_HRS value for one of these complexes, RuPZnRu, is the largest yet reported for any chromophore at λ_inc = 1500 nm (4600 ± 1200 × 10^–30 esu), highlighting that engineering of strong electronic coupling between multiple charge-transfer oscillators provides a critical design strategy to realize octopolar NLO chromophores that exhibit impressive β_HRS values at long, telecom-relevant wavelengths.

Generalized Thomas–Kuhn sum (TKS) rules were used to compute the effective excited-state-to-excited-state transition dipole moments from experimental linear-absorption spectra; these data were then utilized to compute hyperpolarizabilities as a function of frequency, that include two- and three-state contributions for both the β_zzz and β_xzx tensor components to the RuPZnRu hyperpolarizability spectrum. This qualitative analysis shows that the β_zzz and β_xzx tensor contributions to the RuPZnRu hyperpolarizability spectrum reach maxima near 1550 nm, in agreement with experimental data. This qualitative TKS analysis finds that octopolar molecules will be likely characterized by more intricate dependences of the measured hyperpolarizability upon irradiation wavelength due to the interactions among multiple different β tensor components.

Supporting Information Available

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acscentsci.6b00291.

• Characterization, electrochemical, and computational data, experimental details, and electronic absorption spectra (PDF)

Author Contributions

All authors contributed to writing this manuscript and have given their approval to the final version.

The authors declare no competing financial interest.