Design of Coupled Porphyrin Chromophores ... - ACS Publications

Article pubs.acs.org/JPCC

Design of Coupled Porphyrin Chromophores with Unusually Large Hyperpolarizabilities Nan Jiang,† Gérard Zuber,† Shahar Keinan,† Animesh Nayak,†,§ Weitao Yang,*,† Michael J. Therien,*,† and David N. Beratan*,†,‡,∥ †

Department of Chemistry, ‡Department of Biochemistry, and ∥Department of Physics, Duke University, Durham, North Carolina 27708, United States § Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States S Supporting Information *

ABSTRACT: A new series of push−pull porphyrin-based chromophores with unusually large static first hyperpolarizabilities are designed on the basis of coupled-perturbed Hartree−Fock and density functional calculations. The proper combination of critical building blocks, including a ruthenium(II) bisterpyridine complex, proquinoidal thiadiazoloquinoxaline, and (porphinato)zinc(II) units, gives rise to considerable predicted enhancements of the static nonlinear optical (NLO) response, computed to be as large as 11 300 × 10−30 esu, 2 orders of magnitude larger than the benchmark [5-((4′-(dimethylamino)phenyl)ethynyl)-15-((4″nitrophenyl)ethynyl)porphinato]zinc(II) chromophore. A two-state model was found to be useful for the qualitative description of the first hyperpolarizabilities in this class of NLO chromophores, which are predicted to have hyperpolarizabilities approaching the fundamental limit predicted to be attainable by empirical theoretical models.

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INTRODUCTION Nonlinear optical (NLO) materials have attracted considerable attention due to potential applications in optics and optoelectronics that include information storage, image processing, frequency conversion, optical signal processing, optical computing, and dynamic imaging.1−3 Inorganic crystals such as LiNbO3 and KTiOPO4 have been widely used in commercial NLO devices.2 Since the 1990s, however, a large number of organic compounds with extended conjugation have emerged as candidates for electrooptically functional elements in NLO materials.1,4−40 The advantages of organic materials over traditional inorganic crystals stem from their lower dielectric constants, potentially faster and larger NLO responses, and ease of processing; furthermore, the considerable topological and electronic structural diversity made available through chemical synthesis offers the opportunity for application-specific chromophore optimization. With respect to organic NLO materials, the donor-bridge (π-electron system)acceptor or push−pull structure, has served as a classic design motif.2,4−7,9−36,38−40 Although many theoretical41−52 and experimental groups have been working for decades on the design of new structures with large second order NLO properties, relatively few examples of chromophores have been delineated that possess βλ values (dynamic hyperpolarizabilities) that exceed 1000 × 10 − 3 0 esu at telecommunicatio ns-relevant wavelengths.9,13,14,17,24,25,28−30,33,37,53,54 Due in part to the fact that © 2012 American Chemical Society

a large fraction of these highly hyperpolarizable chromophores exploits a porphyrinic component, there has been increased interest in porphyrin-based NLO materials.12−14,17,18,25,26,29−36,55−62 Porphyrins and their corresponding ethynylated and ethyne-linked derivatives are attractive building blocks for such materials because of their extended electronic delocalization, large oscillator strengths, and substantial polarizabilities;12−14,38,61,63−76 in addition to providing for substantial βλ values, such porphyrin-based donorbridge-acceptor systems manifest excellent thermal stabilities.13,17,25,29,30,32,34,61 Benchmark examples of these robust structures that possess high βλ values include [5-((4′(dimethylamino)phenyl)ethynyl)-15-((4″-nitrophenyl)ethynyl)-10,20-diphenylporphinato]zinc(II) (D-PZn-A)13,14,17 and closely related structures,29,30,34 as well as chromophores where (porphinato)zinc(II) (PZn) and metal(II)polypyridyl (M) units are linked via an ethyne bridge (M-PZn species).25,26,29−33,36,57 The hyperpolarizabilities of these systems display complex irradiation wavelength dependences; measured values of βλ for these structures are as high as several thousand ×10−30 esu.13,14,17,25,29,30,32,33,36 In this paper, we examine theoretically porphyrin-based NLO chromophores based on established D-PZn-A and Ru-PZn Received: November 29, 2011 Revised: April 5, 2012 Published: April 9, 2012 9724

dx.doi.org/10.1021/jp2115065 | J. Phys. Chem. C 2012, 116, 9724−9733

The Journal of Physical Chemistry C

Article

Table 1. Computed Dipole Moment μ (Debye), First Hyperpolarizability βtotal (10−30 esu), Hyperpolarizability Density ρβ 0 a −30 1/4 3 3/2 7/2 int (10−30 esu), the Hyperpolarizability Limit βmax (10 esu, = 3 (eℏ/m) (N /E 0 10 )), the Intrinsic Hyperpolarizability β0 total max 2 2 2 2 (β0 /β0 ), the Transition Energy ΔEge (eV), the Transition Dipole Moment μge (Debye), and μge /ΔEge (Debye /eV ) of the Strongest Single Excitation within the Q- and B-Band Transition Manifoldsb B-band D-PZn-A D-PZn-E-PZn-A D-PZn-E-PZn-E-PZn-A D-PZn-E-E-PZn-A D-PZn-E-PC-E-PZn-A D-PZn-E-BTD-E-PZn-A D-PZn-E-TDQ-E-PZn-A Ru-PZn Ru-PZn-E-TDQ-E-PZn Ru-E-TDQ-E-PZn-E- TDQ-E-PZn Ru-PZn-E-TDQ-E-PZn-A Ru-E-TDQ-E-PZn-E- TDQ-E-PZn-A

μ

βtotal 0

ρβ

12.5 13.8 18.1 13.6 14.8 13.7 15.0 41.9 84 105 103 113

248 484 912 488 762 540 886 351 6427 14615 11813 26428

248 242 304 244 381 270 443 175 3214 7308 5907 13214

N

βmax 0

βint 0

ΔEge

μge /ΔEge

38 60 82 62 84 70 74 50 78 90 86 98

3817 9566 16894 10048 15504 7895 9663 7606 8849 12088 13547 16826

0.06 0.05 0.05 0.05 0.05 0.07 0.09 0.05 0.73 1.21 0.87 1.57

3.41 3.19 3.10 3.19 3.21 3.60 3.48 3.15 3.65 3.55 3.37 3.35

3.6 6.9 10.5 7.0 2.2 2.3 4.0 1.2 1.1 0.9 1.7 1.2

2

Q-band 2

ΔEge

μge2/ΔEge2

1.84 1.61 1.50 1.66 1.47 1.65 1.53 1.93 1.44 1.25 1.34 1.20

1.1 5.6 12.1 5.3 17.2 6.2 18.1 5.7 41.1 76.4 66.1 139.8

e is the electron charge, m is the electron mass, ℏ is Planck’s constant divided by 2π, N is the number of conjugated π electrons, and E10 is the energy of the B-band excitation. bAll calculations were performed in the gas phase using HF/6-31G(d). The hyperpolarizability was calculated using CPHF; the linear absorption spectrum was calculated using TDHF. Intrinsic hyperpolarizability computed by the approach of Kuzyk.14c a

Figure 1. Structures of D-PZn-A-based chromophores that feature multiple PZn units.

how proquinoidal linkage motifs influence the static hyperpolarizability. As such, we will not explore the hyperpolarizability frequency dispersion (see, e.g., recent ref 36 for related theoretical design considerations).

(ruthenium(II)[5-(4′-ethynyl-(2,2′;6′,2″-terpyridinyl))-10,20bis(2′,6′-bis(3,3-dimethyl-1-butyloxy)phenyl)porphinato]zinc(II)-(2,2′;6′,2″-terpyridine)2+) motifs incorporating bridges that introduce proquinoidal character into the D−A conjugation pathway.72,77−83 Our aim is to accomplish the meaningful theoretical design of NLO chromophores with enhanced hyperpolarizabilities, beyond those delineated thus far in benchmark D-PZn-A and Ru-PZn structures; we present a theoretical investigation of the electronic structure and NLO properties of proquinoidal variants of these chromophores in which 4,7-diethynylbenzo[c][1,2,5]thiadiazole (E-BTDE),84−87 6,13-diethynylpentacene (E-PC-E),88,89 and 9-diethynyl-6,7-dimethyl-[1,2,5]thiadiazolo[3,4-g]quinoxaline (ETDQ-E)72 units define a portion of the conjugated bridge connecting donor to acceptor. One such NLO chromophore examined in this study, Ru-E-TDQ-E-PZn-E-TDQ-E-PZn-A, is predicted to possess an extraordinarily large static first hyperpolarizability (β0) of 11 300 × 10−30 esu, approximately 2 orders of magnitude larger than that determined for the benchmark D-PZn-A (β0 ∼ 250 × 10−30 esu) and Ru-PZn (β0 ∼ 350 × 10−30 esu) structures.36 The present study focuses on

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COMPUTATIONAL DETAILS A microscopic polarization can be written μi (F ⃗) = μi0 +

∑ αijFj + j

+ ···

1 2!

∑ βijkFjFk + j,k

1 3!

∑ γijklFjFkFl i ,j,k

(1)

where Fi is the field in direction i, α is the polarizability tensor, β is the first hyperpolarizability tensor, and γ is the second hyperpolarizability tensor.1 The static first hyperpolarizability is β0total =

βx 2 + βy 2 + βz 2

(2)

where 9725



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Figure 2. Structures of D-PZn-A-based chromophores that feature augmented proquinoidal character along with that of the D-PZn-E-E-PZn-A benchmark.

βi =

1 3

∑ k=x ,y,z

Table 2. HOMO and LUMO Energies and HOMO−LUMO Energy Gaps for D-PZn-A-Based Chromophores That Feature Augmented Proquinoidal Character and Appropriate Reference Compoundsa

(βikk + βkik + βkki) (3)

The molecules reported here were geometry optimized using density functional theory with the hybrid B3LYP functional.90,91 The static hyperpolarizabilities were computed using coupled-perturbed Hartree−Fock (CPHF) theory.92,93 The linear-absorption spectra were computed using the timedependent Hartree−Fock (TDHF) method94 with 20 excited states. For the gas phase calculation, molecules containing ruthenium atoms were analyzed using the LAN2DZ basis set and a 6-31G(d) basis set was used otherwise. Acetonitrile solvation effects were included in the hyperpolarizability calculations using the polarizable continuum model (PCM) with UFF atomic radii for all atoms.95,96 With the PCM, the LANL2DZ basis set and the corresponding ECP were used97−99 for Ru, and the 6-31G(d) basis set was applied to all the other atoms. All of the calculations were carried out with the GAUSSIAN 09 package.100

a

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RESULTS AND DISCUSSION A. D-PZn-A-Based Chromophores That Feature Multiple PZn Units. To provide a point of comparison for the impact that augmented quinoidal character has upon the magnitude of the computed static first hyperpolarizability for these chromophores, we first examine the extent to which increasing numbers of PZn units in D-PZn-A-type structures influenced β0 values. It is well established that PZnn compounds featuring a meso-to-meso ethyne-bridged linkage topology display lowest energy transitions that gain in intensity and

chromophore

EHOMO/eV

ELUMO/eV

ΔE/eV

D-PZn-A D-PZn-E-PZn-A D-PZn-E-PZn-E-PZn-A D-PZn-E-E-PZn-A D-PZn-E-PC-E-PZn-A D-PZn-E-BTD-E-PZn-A D-PZn-E-TDQ-E-PZn-A

−6.174 −6.024 −5.809 −6.023 −5.485 −6.032 −5.892

−0.276 −0.560 −0.688 −0.560 −0.729 −0.594 −0.984

5.898 5.464 5.124 5.462 4.755 5.438 4.908

All calculations were performed using HF/6-31G(d).

Figure 3. Donor−(porphinato)zinc(II)−acceptor chromophores.

progressively red-shift with increasing numbers of PZn units.38,61,63−76 A comparison of the optical properties of DPZn-A, D-PZn-E-PZn-A, and D-PZn-E-PZn-E-PZn-A, optimized in C2v symmetry with identical (N,N-dimethylamino)phenyl donor and nitrophenyl acceptor groups, shows that extending the length of the conjugated network in these 9726



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ρβ = β /Np

Table 3. Computed Ground-State Dipole Moments (μ values) and Static First Hyperpolarizabilities (β0 values) for Various Donor−(Porphinato)zinc(II)−Acceptor Chromophoresa,b donor a

(CH3)2N-ϕH2N-ϕ-a ϕ-a HO-ϕ-a HS-ϕ-a Cl-ϕ-a (CH3)2N-ϕ-a (CH3)2N-ϕ-a (CH3)2N-ϕ-a H-b (CH3)2N-ϕ-b

acceptor

μ/Debye

β0/10−30 esu

-ϕ-NO2 -ϕ-NO2 -ϕ-NO2 -ϕ-NO2 -ϕ-NO2 -ϕ-NO2 -ϕ-CHO -ϕ-CF3 -ϕ-COOH -[Ru(tpy)2]2+ -[Ru(tpy)2]2+

12.48 12.55 8.87 9.26 8.28 5.45 9.34 8.64 7.61 32.69 43.47

233 193 101 132 137 102 181 151 182 547 1,918

a Calculations utilized HF/6-31G(d). LAN2DZ.

b

(4)

where β is the first hyperpolarizability and Np is the number of porphyrin units in the molecule. As shown in Table 1, ρβ values of 248, 242, and 304 × 10−30 esu are computed for D-PZn-A, D-PZn-E-PZn-A, and D-PZn-E-PZn-E-PZn-A respectively; note that these values vary by only a small amount. As such, NLO properties of bulk materials will not likely benefit from simply extending the conjugation length of the hyperpolarizable molecular unit, as expected from previous analysis.8 Other strategies that enhance electronic coupling among the porphyrin-based building blocks may give rise, however, to chromophoric ρβ values that increase nonlinearly with increasing conjugation length. The data in Table 1 arise from quantum chemical calculations (coupled perturbed Hartree−Fock analysis) that do not rely on a few-state approximation in computing β. Nonetheless, the two-state model39,101though of limited value for quantitative prediction of β values or for predictions of their frequency dispersionis useful to describe the evolution of the properties of the structures in Figure 1 as a function of chain length. In this model:

Calculations utilized HF/

structures has only a modest impact upon the ground-state dipole moment; relative to D-PZn-A, μ increased only by 9.7% for D-PZn-E-PZn-A and 44% for D-PZn-E-PZn-E-PZn-A. The first hyperpolarizability increased linearly with the number of porphyrins, consistent with previous theoretical results.13,14 Note that related Zn−Au-based donor−acceptor porphyrin dyads were found recently to display large hyperpolarizabilities at λinc = 1064 nm relative to their corresponding (porphinato) metal chromophoric building blocks.14b It is important to underscore that if the nonlinear response grows only linearly with molecular dimensions, larger molecules present little differential advantage in a bulk material. The hyperpolarizability per unit length (ρβ, the hyperpolarizability density) in these linear molecules is given by

β=

3μge 2 Δμge ΔEge 2

(5)

where μge is the transition dipole moment between the ground state |g⟩ and the charge-transfer excited state |e⟩, Δμge is the difference between the dipole moments of ground and excited states, and ΔEge is the transition energy between the ground and excited states. Δμge is nearly constant in this family of charge-transfer systems, so the quadratic terms ΔEge2 and μge2 dominate β. Although this treatment neglects explicit multistate contributions and the intrinsic frequency dispersion of β, it is a

Figure 4. Structures of Ru-PZn-based chromophores that feature augmented proquinoidal character. 9727



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species.72 Enhancement of excited-state π-conjugation, reduction of the lowest electronic transition energy, and amplification of the oscillator strength of this absorption, all serve to increase the magnitude of first hyperpolarizability, as expected from eq 5. Our computations examine the influence that diethynyl (EE), E-PC-E, E-BTD-E, and E-TDQ-E units have upon the nature of bridge conjugation and the magnitude of the first hyperpolarizability in D-PZn-A-based chromophores. Taking D-PZn-E-PZn-A and the analogous chromophore that utilizes an E-E bridge [15-((4′-(dimethylamino)phenyl)ethynyl)-15′((4″-nitrophenyl)ethynyl)-bis[(5,5′-10,20-diarylporphinato)zinc(II)]butadiyne, D-PZn-E-E-PZn-A] as benchmarks, we interrogated the extent to which proquinoidal E-PC-E, EBTD-E, and E-TDQ-E π-conjugative components increase the cumulenic resonance contribution to the ground and electronically excited singlet states, augment the electronic communication among the component PZnE units, and enhance the computed first hyperpolarizability in these structures (Figure 2). The calculated HOMO and LUMO energies and HOMO− LUMO energy gaps of these D-PZn-Sp-PZn-A complexes appear in Table 2. In these structures, the computed HOMO energy levels increase in the order D-PZn-E-BTD-E-PZn-A < D-PZn-E-E-PZn-A < D-PZn-E-TDQ-E-PZn-A < D-PZn-E-PCE-PZn-A. In contrast, the calculated LUMO energy levels decrease with increasing bridge proquinoidal character: D-PZnE-E-PZn-A > D-PZn-E-BTD-E-PZn-A > D-PZn-E-PC-E-PZnA > D-PZn-E-TDQ-E-PZn-A. These trends of HOMO and LOMO energies are the same as those found in experimental investigations of PZn-Sp-PZn compounds.72 Indeed, the proquinoidal spacer moiety decreases the HOMO−LUMO gaps compared to D-PZn-E-PZn-A. The computed HOMO− LUMO gaps for these D-PZn-Sp-PZn-A chromophores relative to the D-PZn-E-PZn-A benchmark (5.464 eV) are highlighted in Table 2. Compared with those of D-PZn-E-PZn-E-PZn-A, in which the central E-PZn-E can be considered as a spacer, the HOMO−LUMO gaps for D-PZn-E-TDQ-E-PZn-A and DPZn-E-PC-E-PZn-A are much lower; this result is congruent with earlier experiments72 that show that proquinoidal Sp electronic structure, in contrast to Sp π-aromatic size, can be the more important determinant of the extent of π-conjugation. The transition dipole moments and the hyperpolarizability densities of these D-PZn-Sp-PZn-A complexes are listed in Table 1; the magnitudes of these values correlate with the established trends in the extent of the proquinoidal resonance contribution observed in experimental linear absorption spectra for PZn-Sp-PZn compounds72 (D-PZn-E-TDQ-E-PZn-A > DPZn-E-PC-E-PZn-A > D-PZn-E-BTD-E-PZn-A > D-PZn-E-EPZn-A). Note, as well, that the reported first excitation energies72 of the corresponding PZn-Sp-PZn species have the same ordering as the HOMO−LUMO gaps computed for these D-PZn-Sp-PZn-A species: D-PZn-E-E-PZn-A > D-PZn-EBTD-E-PZn-A > D-PZn-E-TDQ-E-PZn-A > D-PZn-E-PC-EPZn-A. The trends in μge2/ΔEge2 calculated within the context of the two-state model track as expected with the magnitudes of the computed hyperpolarizabilities. Although two-state descriptions of the first hyerpolarizability are of limited value for making quantitative predictions (and also fail to describe the frequency dispersion of β),36 the model captured general electronic structural trends (vide supra) and has also proven useful to define approximate “fundamental limits” on the magnitude of β.14c Table 1 shows these

Figure 5. (a) Experimental Ru-PZn-E-TDQ-E-PZn linear absorption spectrum. (b) Calculated Ru-PZn-E-TDQ-E-PZn linear absorption spectrum with the PCM in acetonitrile, the LANL2DZ basis set, and the corresponding ECP for Ru and the 6-31G(d) basis set for all the other atoms.

useful touchstone for the interpretation of the computational data. It has been reported that both the B- and Q-band transitions contribute to the β0 values in the M-PZN compounds.36 The transition energies computed for both the B- and the Q-band decrease slightly with increasing conjugation length as expected [D-PZn-A: B-band (3.413 eV), Q-band (1.84 eV); D-PZn-EPZn-A: B-band (3.192 eV), Q-band (1.61 eV); D-PZn-E-PZnE-PZn-A: B-band (3.104 eV), Q-band (1.50 eV)]. The μge2/ ΔEge2 values of both the B- and the Q-band for D-PZn-E-PZnA and D-PZn-E-PZn-E-PZn-A increase relative to D-PZn-A. Indeed, the two-state model is valuable for interpreting the computed first-hyperpolarizability trends. B. D-PZn-A-Based Chromophores That Feature Augmented Proquinoidal Character. Introducing quinoidal character into highly conjugated multi(porphyrin) compounds is an established strategy for reducing ΔEge2.13,38,68,72,102 A series of bis[(porphinato)zinc(II)] compounds (PZn-Sp-PZn structures) featuring proquinoidal spacers was recently reported, and their electrooptical properties described.72 Steady-state optical, potentiometric, transient pump−probe spectroscopic, and computational data point to the existence of electronically excited singlet states that display augmented quinoidal character relative to the S0 state in these PZn-Sp-PZn 9728



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Figure 6. Orbitals associated with the optical transitions for (a) D-PZn-A, (b) D-PZn-E-TDQ-E-PZn-A, (c) Ru-PZn-A, (d) Ru-PZn-E-TDQ-E-PZnA, and (e) Ru-E-TDQ-E-PZn-E-TDQ-E-PZn-A.

phenyl−OH, phenyl−SH > phenyl−Cl, phenyl−H. Similarly, when (dimethylamino)phenyl is chosen as the donor, nitrophenyl is the strongest acceptor among the four phenyl-based acceptors: phenyl−NO2 > phenyl−COH, phenyl−COOH > phenyl−CF3. D. Ru-PZn-Based Chromophores That Feature Augmented Proquinoidal Character. The experimental β1300 value for Ru-PZn determined by hyper-Rayleigh light scattering (HRS) measurements is 5100 × 10−30 esu.25 The β0 value for Ru-PZn is calculated as 547 × 10−30 esu on the basis of coupled-perturbed Hartree−Fock methods in the gas phase, twice the computed value of D-PZn-A (233 × 10−30 esu); these values compare favorably with those derived from a more sophisticated computational approach that relies on Thomas− Kuhn sum rules, chromophore electronic absorption properties,

computed intrinsic maximum values. Many of the proquinoidal species have computed β values near the fundamental limit. C. Alternative Donors and Acceptors. The first hyperpolarizability βtotal generally increases with the donor and 0 acceptor strengths until an optimal asymmetry is achieved.8 On the basis of the structure of the donor-(porphinato)zinc(II)acceptor motif shown in Figure 3, four additional acceptors and five additional donors were selected for further analysis. The computed dipole moments and static first hyperpolarizabilities of these compounds are shown in Table 3. The nitrophenyl acceptor was retained in the compounds, and the hyperpolarizabilities of six species with different donors were analyzed. The (dimethylamino)phenyl group is the strongest donor that generates the largest hyperpolarizability among the compounds: phenyl−N(CH3)2 > phenyl−NH2 > 9729



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PZn-A, and Ru-E-TDQ-E-PZn-E-TDQ-E-PZn-A, respectively. RuE-TDQ-EPZnE-TDQ-EPZn-A has the largest predicted hyperpolarizability among them: 40 times larger than the RuPZn benchmark and 2 orders of magnitude greater than that computed for D-PZn-A. These Ru-PZn-based chromophores having proquinoidal conjugation motifs possess stronger transition-dipole moments and slightly lower transition energies relative to D-PZn-A and D-PZn-E-TDQ-E-PZn-A (Table 1). The μge2/ΔEge2 values predict key hyperpolarizability trends: taking the B-band transition of Ru-E-TDQ-E-PZn-E-TDQ-EPZn-A as an example, the transition dipole moment is a factor of 5 larger than that of D-PZn-A, and the transition energy is 0.7 times smaller than computed for D-PZn-A. These spectroscopic differences result in a 40-fold difference in μge2/ ΔEge2 for the two compounds, which is almost identical to the computed Ru-E-TDQ-E-PZn-E-TDQ-E-PZn-A-to-Ru-PZn hyperpolarizability ratio. The frontier orbitals for D-PZn-A, D-PZn-E-TDQ-E-PZn-A, Ru-PZn-A, Ru-PZn-E-TDQ-E-PZn-A, and Ru-E-TDQ-E-PZnE-TDQ-E-PZn-A were studied on the basis of gas phase calculations. For D-PZn-A and D-PZn-E-TDQ-E-PZn-A, the electron density is located mainly on the electron donor ((dimethylamino)phenyl group) in the HOMO and nearby occupied molecular orbitals, whereas the electron density on the LUMO and nearby unoccupied molecular orbitals is mainly localized on the electron acceptor (nitrophenyl group). However, it turns out that the gas phase calculations do not provide the expected orbital localization descriptions for the [Ru(tpy)2]2+ containing compounds: the electron density of the LUMO computed in the gas phase without counterions is mainly localized on the donor ((polypyridyl)ruthenium(II) group) in Ru-PZn-A, Ru-PZn-E-TDQ-E-PZn-A, and Ru-ETDQ-E-PZn-E-TDQ-E-PZn-A). To provide a more realistic description, further calculations were necessitated; these are described in detail in the following section. E. Effects of Basis Set and and Solvent. The counterintuitive localization characteristics described above for the RuPZn-based chromophores may result from the absence of solvent and counterions in the calculations, as well as from an insufficient basis set. The influence of solvent and basis set chosen for Ru-PZn-E-TDQ-E-PZn on the frontier orbitals and computed linear absorption spectrum was examined. In summary, with a PCM for acetonitrile, the LANL2DZ basis set and the corresponding ECP for Ru, and a 6-31G(d) basis set for all of the other atoms in the molecule, we find a linear absorption spectrum (Figure 5) in reasonable agreement with experiment and with the expected frontier orbital descriptions (Figure 6). The hyperpolarizabilities for all of the structures listed in Table 1 are calculated with this approach (Table 4), and the relevant occupied and unoccupied molecule orbitals for representative compounds are shown in Figure 6. The hyperpolarizability of Ru-E-TDQ-E-PZn-E-TDQ-E-PZn-A is 11 272 × 10−30 esu, which is 20-fold larger than that of D-PZnA and 30-fold larger than that of Ru-PZn based on the PCM acetonitrile analysis. The gas phase calculations predict that the hyperpolarizability of Ru-E-TDQ-E-PZn-E-TDQ-E-PZn-A is 2 orders of magnitude larger than that of D-PZn-A and about 40 times larger than that of Ru-PZn. These gas phase calculations indicate electron density in the HOMO and nearby occupied orbitals is localized mainly on the electron donating (dimethylamino)phenyl group in D-PZn-A and D-PZn-ETDQ-E-PZn-A, and on the (polypyridyl)ruthenium(II) group in Ru-PZn-A, Ru-PZn-E-TDQ-E-PZn-A, and Ru-E-TDQ-E-

Table 4. Computed Dipole Moments (μ values, Debye), First Hyperpolarizabilities (β values, in 10−30 esu), and the Hyperpolarizability Densities (ρβ values, 10−30 esu) for RuPZn-Based Chromophores That Feature Augmented Proquinoidal Charactera D-PZn-A D-PZn-E-PZn-A D-PZn-E-PZn-E-PZn-A D-PZn-E-E-PZn-A D-PZn-E-PC-E-PZn-A D-PZn-E-BTD-E-PZn-A D-PZn-E-TDQ-E-PZn-A Ru-PZn Ru-PZn-A Ru-PZn-E-TDQ-E-PZn Ru-E-TDQ-E-PZn-E-TDQ-E-PZn Ru-PZn-E-TDQ-E-PZn-A Ru-E-TDQ-E-PZn-E-TDQ-E-PZn-A

μ

β0

ρβ

13.7 14.5 14.8 14.2 15.3 14.4 15.6 41.9 57.9 115.6 137.4 131.9 152.5

513 715 714 692 849 694 1268 351 920 1774 8044 3394 11272

513 357 238 346 425 347 634 175 460 887 4022 1697 6607

a

The hyperpolarizabilities were calculated using CPHF. For compounds that do not contain a Ru(tpy)2 donor, the calculations were performed using the 6-31G(d) basis set. For systems that featured the Ru(tpy)2 donor, the calculations were performed using the Lanl2dz basis set and the corresponding ECP for Ru and the 631G(d) basis set for all the other atoms with PCM in acetonitrile.

Figure 7. Molecular orbital energy diagram summarizing frontier orbital energies computed using HF/6-31G* for D-PZn-A and D-PZnE-TDQ-E-PZn-A, the Lanl2dz basis set and the corresponding ECP for Ru, and the 6-31G(d) basis set for all the other atoms for Ru-PZnA, Ru-PZn-E-TDQ-E-PZn-A, and Ru-E-TDQ-E-PZn-E-TDQ-E-PZnA. All calculations were performed using the PCM of acetonitrile.

and experimental hyperpolarizabilities to compute the frequency-dependent hyperpolarizability spectrum.36 Figure 4 considers Ru-PZn-based chromophoric structures that feature TDQ spacer components and 4-nitrophenyl electron acceptors. The computed dipole moments (Table 1) of these Ru-PZnE-TDQ-E-PZn, Ru-E-TDQ-E-PZn-E-TDQ-E-PZn, Ru-PZn-ETDQ-E-PZn-A, and Ru-E-TDQ-E-PZn-E-TDQ-E-PZn-A chromophores are large, almost 1 order of magnitude larger than the value determined for D-PZn-A (12.5 Debye). The calculated static first hyperpolarizability densities are 3.2 × 10−27, 7.3 × 10−27, and 13.2 × 10−27 esu for Ru-PZn-E-TDQ-EPZn, Ru-E-TDQ-E-PZn-E-TDQ-E-PZn, Ru-PZn-E-TDQ-E9730



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for the benchmark D-PZn-A (512 × 10−30 esu) benchmark. For the species computed to possess enhanced hyperpolarizabilities, these studies underscore that augmented transition dipole moments and lower transition energies relative to key benchmark chromophores play prominent roles in performance enhancement. Importantly, these studies suggest that the combination of the TDQ spacer and [Ru(tpy)2]2+-based donor moieties constitute particularly effective building blocks for the elaboration of high performance NLO materials that exploit (porphinato)metal chromophores. It will be particularly intriguing to see whether or not these chromophores, when synthesized and probed experimentally, will surpass the predicted intrinsic limit14c predicted for β.

PZn-E-TDQ-E-PZn-A), whereas the electron density on the LUMO and nearby unoccupied molecular orbitals is localized mainly on the electron accepting nitrophenyl and proquinoidal spacer TDQ groups. Electron flow from the donor to the acceptor generates a dipole moment difference Δμge, that enhances the hyperpolarizability in the two-state model. To better understand the NLO enhancements in these push−pull chromophores, we examined the frontier orbitals and key electronic transitions for D-PZn-A, D-PZn-E-TDQ-EPZn-A, Ru-PZn-A, Ru-PZn-E-TDQ-E-PZn-A, and Ru-E-TDQE-PZn-E-TDQ-E-PZn-A. The energies of the ten highest occupied orbitals and ten lowest unoccupied orbitals of the five compounds are shown in Figure 7. For D-PZn-A, the HOMO and LUMO energies and the HOMO−LUMO gap are −6.27, −0.38, and 5.9 eV, respectively. The D-PZn-E-TDQ-EPZn-A HOMO (−6.03 eV) is destabilized by 0.24 eV, whereas its LUMO (−1.07 eV) is stabilized by 0.69 eV relative to the analogous D-PZn-A orbitals, producing a lower HOMO− LUMO gap (4.96 eV). The calculated HOMO−LUMO energy gaps of Ru-PZn-A, Ru-PZn-E-TDQ-E-PZn-A, and Ru-E-TDQE-PZn-E-TDQ-E-PZn-A are 5.76 eV, 4.59 and 4.32 eV, respectively, further underscoring the impact of augmented proquinoidal character upon the frontier orbital (FO) energy levels of these PZn-based chromophores. Comparing the data displayed in Figure 7 for Ru-E-TDQ-E-PZn-E-TDQ-E-PZn-A with that for Ru-PZn-E-TDQ-E-PZn-A highlights that extensive LUMO stabilization is the dominant factor that modulates the HOMO−LUMO gap. The energy gap ordering is D-PZn-A > D-PZn-E-TDQ-E-PZn-A; Ru-PZn-A > Ru-PZn-E-TDQ-EPZn-A > Ru-E-TDQ-E-PZn-E-TDQ-E-PZn-A, which is opposite the order of transition dipole moments and hyperpolarizabilities, consistent with the two-state model.

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ASSOCIATED CONTENT

S Supporting Information *

Full author list for refs 21, 62, and 100. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support from the DARPA Predicting Real Optimized Materials project through ARO is gratefully acknowledged (W911NF-041-0243) for the studies of nonlinear optical materials design (to N.J). S.K. acknowledges support from the UNC EFRC: Center for Solar Fuels, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001011 and DOE ASCR under SciDAC-e award DE-FC02-06ER25764. D.N.B. thanks NSF (CHE-1012357) and DOE ASCR under SciDAC-e award DE-FC02-06ER25764 for support. M.J.T. thanks NSEC (DMR-0425780) for support. W.Y. thanks NSF (CHE-09-11119) for support.

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CONCLUSIONS A new series of (polypyridyl)ruthenium(II)−proquinoidal spacer−(porphinato)zinc(II) chromophores was designed. The molecular geometries were optimized using density functional theory, and the static first hyperpolarizabilities were calculated using coupled-perturbed Hartree−Fock methods. The gas phase and PCM (acetonitrile) model hyperpolarizabilities were calculated using the LANL2DZ basis set and the corresponding ECP for Ru with a 6-31G(d) basis set for all of the other atoms. The hyperpolarizability density is not predicted to increase through conjugation length expansion achieved by simply increasing the number of intervening porphyrin units between donor and acceptor. Proquinoidal spacers, in contrast, decrease both the HOMO−LUMO energy gaps and the first excitation energy relative to values computed for benchmark D-PZn-A and RuPZn structures. As such, the proquinoidal units are predicted to increase the first hyperpolarizability density, with D-PZn-E-TDQ-E-PZn-A having the largest computed hyperpolarizability of proquinoidal chromophores based on the DPZn-A motif considered in this study. The acceptor and donor units that produce the largest hyperpolarizability densities are the nitrophenyl and bis(terpyridyl)ruthenium(II) groups, respectively. The supermolecular chromophore Ru-E-TDQ-E-PZn-ETDQ-E-PZn-A, which exploits the proquinoidal diethynylthiadiazoloquinoxaline moiety, a bis(terpyridyl)ruthenium(II) donor, and a nitorphenyl acceptor, is computed to possess an extraordinarily large predicated static first hyperpolarizability (β0) of 11 272 × 10−30 esu, 20 times larger than that calculated

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REFERENCES

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