Dipolar Ferrocene and Ruthenocene Second-Order Nonlinear Optical

Article pubs.acs.org/Organometallics

Dipolar Ferrocene and Ruthenocene Second-Order Nonlinear Optical Chromophores: A Time-Dependent Density Functional Theory Investigation of Their Absorption Spectra Seyhan Salman,†,‡ Jean-Luc Brédas,† Seth R. Marder,† Veaceslav Coropceanu,*,† and Stephen Barlow*,† †

School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States ‡ Genetics and Bioengineering, Istanbul Bilgi University, Eyup 34060, Istanbul, Turkey S Supporting Information *

ABSTRACT: The origin of the two prominent solvatochromic near-UV/visible/near-IR absorptions observed for donor− (π-bridge)−acceptor chromophores with ferrocene donors has been investigated using TD-DFT methods. Both chromophores with relatively weak (4-nitrophenyl) and strong acceptors (1,3-diethyl-2-thiobarbituric acid and 3-dicyanomethylidene-2,3-dihydrobenzothiophene-1,1-dioxide) were considered, as were ferrocene and octamethylferrocene donors. Computational predictions of optical properties made using the B3PW91 functional were found to be in good agreement with experimental data. The calculations reveal a complex orbital picture that varies from compound to compound, contribution of multiple configurations to some of the important states, and significant contributions from more than one transition to the experimentally observed bands. Natural transition orbitals have been used to gain an understanding of the charge redistribution associated with the transitions. The relatively weak lowenergy bands of the ferrocene derivatives were generally found to have both d−d and metal-to-π-bridge/acceptor charge-transfer character. The stronger higher energy bands were found to be associated with charge transfer from cyclopentadienyl rings and the π bridge toward the acceptor group. The experimental spectra of ruthenocene chromophores differ significantly from those of the analogous ferrocene chromophores; however, the calculations reproduce the key differences and indicate a similar origin for the contributing transitions.

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acidic than benzoic acid.22,23 The stability of both the neutral FeII and cationic FeIII species, the possibility of convenient interconversion between the two oxidation states using mild redox reagents, and the ease of chemical functionalization have led to the use of ferrocenes as prototypical donor building blocks in, for example, mixed-valence species,24 magnetic charge-transfer salts,25 dyads and triads for studying photoinduced charge transfer,26,27 and redox-active sensors for ions.28 Not surprisingly, therefore, ferrocene was among the first organometallic moieties to be investigated as a donor in second-order nonlinear optical (NLO) chromophores29 and remains one of the most widely examined species.14,18,19,30−32 The polarization of a system by an electrical or optical field and, therefore, the linear and nonlinear polarizabilities can be expressed, through perturbation theory, as a summation of terms describing the coupling of ground and electronic excited states over all the excited states of the system (i.e., as a sum over states, SOS).33 Both two- and three-level terms contribute

INTRODUCTION Applications such frequency doubling, electrooptic modulation, and, more recently, terahertz generation and detection require materials with large second-order optical susceptibilities, χ(2); one approach to such materials is to use molecular organic or organometallic chromophores with large second-order polarizabilities, β, arranged in noncentrosymmetric arrays obtained through crystallization,1−3 electric-field poling,4−6 or selfassembly approaches.7−9 Suitable chromophores typically employ a π donor linked through a conjugated bridge to a π acceptor.10−13 In addition to all-organic donors and acceptors, organometallic and metal−organic donors and, to a lesser extent, acceptors, have been studied.14−19 The donor properties of ferrocenein an electron transfer sensewere recognized soon after its discovery,20 when it was found to form the ferrocenium ion when treated with relatively mild oxidants.21 Furthermore, data reported in several early papers were consistent with ferrocene acting as a relatively electron rich π system toward substituents: for example, CO stretches of carbonyl derivatives were observed at lower frequencies than those of analogous derivatives of benzene,22 while both ferrocene mono- and dicarboxylic acids are less © 2013 American Chemical Society

Special Issue: Ferrocene - Beauty and Function Received: June 26, 2013 Published: September 11, 2013 6061

dx.doi.org/10.1021/om400617d | Organometallics 2013, 32, 6061−6068

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to the SOS expression for β, but in the case of pseudolinear dipolar molecules in which transitions from the ground state, g, to an excited state, e, have significant charge-transfer (CT) character, the two-level terms typically dominate.10,34 Two-level contributions to the zero-frequency (static) value of β take the form β0(2‐level) ∝ μge 2 Δμge /Ege 2 ∝ fge Δμge /Ege 3

dependent density functional theory (TD-DFT). Although TDDFT calculations42 have been increasingly applied to organometallic systems, including various classes of acceptor-functionalized ferrocenes,43−51 the origin of the two bands in ferrocenyl−polyene−acceptor NLO dyes has not been addressed in detail with TD-DFT methods. The range of chromophores chosen for the present study includes “firstgeneration” examples with relatively weak nitrophenyl acceptors (such as the prototypical Fc[1]NB, Chart 1)38 and examples with much stronger nonaromatic hetrocyclic acceptors,52,53 where crystallographic data indicate considerably more important contributions to the electronic structure from charge-separated resonance structures.54 As a further test of the reliability of the TD-DFT methods used, we have also included octamethylferrocene (Fc″) 39 and ruthenocene (Rc)38,53 analogues of the ferrocene (Fc) chromophores in our study. An example incorporating the hypothetical octamethylruthenocenyl donor Rc″[1]NB is also included. The compounds under consideration are shown in Chart 1.

(1)

where Ege is the energy of the excited state, μge and f are the transition dipole moment and oscillator strength, respectively, linking it to the ground state, and Δμge is the change in dipole moment between ground and excited states.35,36 Moreover, in many simple organic donor−bridge−acceptor chromophores, such as (E)-4-dimethylamino-4′-nitrostilbene, the lowest lying transition is a strong π−π* transition with significant CT character, well-separated in energy from higher lying states. In cases such as this, β can be well approximated by a single twolevel term of the type given in eq 1. Ferrocene chromophores, however, show spectra somewhat more complicated than those for simple organic chromophores and for many other examples of organometallic chromophores. Thus, whereas (E)-4-dimethylamino-4′-nitrostilbene shows a single strong near-UV/visible absorption at at 424 nm,37 (E)-4nitrostyrylferrocene, Fc[1]NB (Chart 1), shows a relatively

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COMPUTATIONAL METHODOLOGY

Geometry optimizations of the metallocene compounds were carried out at the DFT level with different exchange-correlation functionals, including B3LYP, M06, and B3PW91. The Los Alamos National Laboratory double-ζ (LANL2DZ)55 basis set was used for Fe and Ru and the 6-31G** basis set for the remaining atoms. All three functionals give geometries in good agreement with crystallographic data. In particular, the bond length alternation (BLA)the average difference between the lengths of formally single and double bonds in the π bridgeis well reproduced, being considerably smaller for the Mc[3]TB and Mc[3]SDS chromophores (BLAexptl = 0.054−0.073 Å;54 BLAcalcd = 0.052−0.066 Å) than for the Mc[n]NB species (BLAexptl = 0.10−0.13 Å;56,57 BLAcalcd = 0.09−0.11 Å), consistent with the stronger π-acceptor character of the TB and SDS acceptors. A more detailed comparison of geometries is provided in the Supporting Information (Tables S1 and S2). The ground-state geometries of selected compounds (Fc[1]NB, Fc[2]NB, Fc[3]TB, Fc[3]SDS) were also optimized in a dielectric medium (to model the effects of 1,4-dioxane as a solvent) at the DFT/ M06 level, in combination with the polarized continuum model (PCM), to monitor the effect of solvent on their main geometrical features. On the basis of M06-optimized ground-state geometries, excited-state vertical transition energies of metallocene-based donor− acceptor compounds were calculated with TD-DFT42 employing several density functionals: M06, M06-2X, ωB97 (with default and tuned ω values), ωB97X, CAM-B3LYP, and B3PW91 (in vacuum and solvent) using 6-31G** and 6-311G* basis sets. The excited-state dipole moments were computed for selected states with TD-DFT (B3PW91/LANL2DZ/6-311G*) from the population analysis using the CI density;58 Δμge values were calculated as the differences with respect to the ground-state values. To obtain a better insight into the nature of the excited states, natural transition orbital (NTO) analyses were performed following TD-DFT calculations.59 All calculations were performed using the Gaussian 09 program.60 Experimental spectra were reused from previous work39 or acquired using compounds synthesized as previously reported.39,52,53

Chart 1

strong higher energy (HE) transition (356 nm in 1,4-dioxane) and a weaker lower energy (LE) transition (496 nm).38 This presence of a weaker LE and stronger HE band is quite general; moreover, both of these transitions are typically strongly solvatochromic, suggesting that both have the CT character necessary for contributing to β through terms of the type shown in eq 1. This is further supported by values of Δμge obtained by Stark spectroscopy for several examples, including Fc[2]NB and Fc″[3]SDS (Chart 1)39 and a variety of derivatives with pyridinium-based acceptors,40 which, combined with experimental values of Ege and μge, indicate that the states associated with both bands make important two-level contributions to β. Several efforts have been made to understand the origin of these transitions on the basis of (1) Hückel and DFT orbital calculations and the relationship between experimental transition energies and donor, bridge, and acceptor strength38,39 and (2) ZINDO calculations of transition energies.41 Here we investigate the spectroscopy of these chromophores using time-

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RESULTS AND DISCUSSION Comparison of Functionals. The electronic transitions of the chromophores shown in Chart 1 were calculated using TDDFT employing several density functionals (see Tables S3−S14 in the Supporting Information for all data). Use of the M06 and M06-2X functionals led to significantly underestimated values of f for the weak LE bands. The ωB97 functional strongly overestimates the transition energies and yields oscillator strengths in rather poor agreement with experiment. When 6062


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used with a tuned ω value,61,62 the ωB97 functional gives oscillator strengths for the LE band in better agreement with experiment, but the transition energies for the LE bands are still overestimated vs experiment (ca. 0.3 eV for Mc[n]NB species and 0.6−0.9 eV for Mc[3]TB and Mc[3]SDS compounds). The transition energies of the stronger HE bands are also overestimated when either M06 or ωB97 is employed. The CAM-B3LYP functional reproduces the spectra of the Mc[3]SDS chromophores reasonably well, albeit with significantly overestimated transition energies, but is much less successful at reproducing the LE characteristics of the Mc[n]NB and Mc[3]TB compounds. The B3PW91 functional appears to give the best overall description of the spectral properties, reproducing both energies and oscillator strengths of the experimental HE and LE bands well. It is worth noting that this functional has previously been used to successfully model the spectra of other acceptor-substituted ferrocene derivatives.43,44 Therefore, the following discussion is based on the TD-DFT estimates of S0 → Sn vertical transition energies, oscillator strengths (f), and excited-state dipole moments (μe) derived using the B3PW91 functional. Frontier Orbitals. Some of the frontier orbitals of representative compoundsFc[1]NB and Fc[3]TBobtained at the B3PW91/LANL2DZ/6-31G** level are shown in Figure 1, while those for the other compounds are shown in the Supporting Information (Figures S2−S5). The HOMO of Fc[1]NB has a dominant iron d orbital contribution (dx2−y2 if the z axis is defined as the pseudo-5-fold axis of the metallocene and the x axis is parallel to the Mc−vinyl bond vector), along with significant coefficients on the π bridge. The HOMO-1 and HOMO-3 are essentially d orbitals (dxy and dz2, respectively). The HOMO-2 has large coefficients on the ethylene portion of the bridge and can be described as an out-of-phase combination of the local HOMO of 4-nitrostyrene and the highest cyclopentadienyl-based orbital of ferrocene, with some additional Fe contributions. The LUMO and LUMO+1 are both primarily located on the nitrostyrene portion of the molecule. The picture is very similar to that derived from extended Hückel calculations,38 DFT calculations using the BP86 functional,39 and UV photoelectron spectroscopy,39 the main difference being that in the picture suggested by those studies the HOMO through HOMO-2 were largely composed of iron d orbitals and the HOMO-3 was similar to the HOMO-2 obtained in the present study. The LUMO and LUMO+1 wave functions for the other Mc[n]NB compounds are similar to those found for Fc[1]NB, but the filled orbitals show some differences (see Figures S2− S5 in the Supporting Information). For Fc[2]NB the π-bridge contributions to the HOMO and HOMO-2 are more and less significant, respectively. The HOMO of Fc″[1]NB shows less π-bridge character than that of Fc[1]NB, and the HOMO-3 has considerable cyclopentadienyl character, instead of being an Fe d orbital. The HOMO-3 of Rc[1]NB is similar to the HOMO2 of Fc[1]NB, while its HOMO-2 is metal-based. For Rc[2]NB and Rc[1]NB, HOMO-1 through HOMO-3 are all metallocene-based, with only the HOMO having significant π-bridge character. The LUMO and LUMO+1 wave functions for all the Mc[3]TB and Mc[3]SDS dyes are located on the π bridge and the acceptor groups, and the HOMO in each case has both metal and π-bridge character. A peculiarity of the Mc[3]TB series is the presence of high-lying sulfur p orbitals: the HOMO-1 wave functions of Fc[3]TB (Figure 1) and Rc[3]TB

Figure 1. Selected molecular orbitals of Fc[1]NB (left) and Fc[3]TB (right) calculated at the B3PW91/LANL2DZ/6-31G**DFT level.

and the HOMO-2 wave function of Fc″[3]TB are essentially pure sulfur “lone pairs”, while there are also significant sulfur contibutions to other orbitals, notably the HOMO of Fc[3]TB (Figure 1). The HOMO-3 wave functions of Fc[3]TB and Fc″[3]TB and the HOMO-2 wave functions of Fc[3]SDS and Fc″[3]SDS are similar to the HOMO-2 of Fc[1]NB in having significant cyclopentadienyl and π-bridge contributions, while the metal contributions to these orbitals vary. Overall, the calculations show that there is considerable variation in the ordering and composition of the filled frontier orbitals with variations in metal, metallocene methylation, πbridge length, and acceptor. Therefore, models for the spectra of these compounds that assume all dyes have an orbital structure analogous to that of Fc[1]NB, such as those described in refs 38 and 39, are clearly somewhat simplistic. Spectra of Nitrobenzene Derivatives. We first consider the spectra of chromophores incorporating the 4-nitrophenyl group in detail since, although ferrocene second-order NLO chromophores with much greater molecular nonlinearities have subsequently been developed, the earliest29 and many subsequent examples32,38,56,63−66 have employed this group or related aromatic acceptors. Moreover, Fc[1]NB has served as a prototypical example in the discussion of the assignment of the 6063


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two transitions mentioned above.38,39,41 On the basis of orbital energies and the effect of structural variation on spectra, the HE band has been assigned to a CT transition from the π-bridge/ cyclopentadienyl-based HOMO-3 (similar to the HOMO-2 of the present study, Figure 1) to the acceptor/π-bridge LUMO (similar to the LUMO shown in Figure 1).38,39 The same studies assign the LE band to a CT transition from an Fe d orbital to either the bridge-based LUMO+1 (the LUMO having little spatial overlap with the iron d orbitals)38 or the LUMO.39 A ZINDO study suggested, on the other hand, that the HE band is essentially an iron-to-nitrobenzene transition, while the LE band is a ligand-field transition, the discrepancy between calculated and experimental transition energies and oscillator strengths for this transition being attributed to neglect of Herzberg−Teller coupling.41 Figure 2 compares the B3PW91/LANL2DZ/6-311G*calculated transitions for Fc[1]NB with the experimental Figure 3. Dominant hole (left) and particle (right) NTOs for selected transitions of Fc[1]NB in vacuum obtained from TD-DFT calculations (with eigenvalues, λ, indicating the contribution of the NTOs shown).

at a similar energy (2.43 and 2.39 eV in vacuum and in dioxane, respectively) and is considerably stronger ( f = 0.041 in vacuum, 0.075 in dioxane), suggesting that it is this transition that is largely responsible for the observed LE band. The NTOs shown in Figure 3 indicate that this transition is very similar to the S0 → S1 transition, the primary difference being the nature of the metal d orbital (dx2−y2) contributing to the hole NTO. This description is rather similar to that suggested in ref 38, differing from that suggested in ref 39 in that the particle NTO more closely resembles the molecular LUMO+1 than the LUMO. Although the particle NTO has some metal d character, the S0 → S2 transition is calculated to have considerable CT character, as indicated by the calculated molecular dipole moment increase, Δμge (ca. 4.2 D in vacuum, 7.3 D in dioxane), inconsistent with the ZINDO study.41 The calculations suggest that the observed HE band (experimentally seen at Ege = 3.46 eV, f = ca. 0.57 in 1,4dioxane) is due to several overlapping transitions, the strongest of which is S0 → S7 (Ege = 3.40 eV, f = 0.44 in vacuum; Ege = 3.24 eV, f = 0.50 in dioxane). The hole NTO (Figure 3) is closely related to the HOMO-2 shown in Figure 1 (i.e., more or less equivalent to the HOMO-3 of refs 38 and 39), which has its highest density on the ethylene bridge and the substituted cyclopentadienyl ring. The particle NTO closely resembles the LUMO of Fc[1]NB: there are significant contributions from the nitro acceptor and also from the π bridge (including the benzene ring), along with a small metal contribution. This description of the HE band is, therefore, rather similar to that proposed in refs 38 and 39 and differs markedly from that of ref 41. The CT character of the S0 → S7 transition is also reflected in the calculated Δμge values of 10.7 and 14.3 D for vacuum and dioxane, respectively. Using eq 1 and the TD-DFT values of f, Δμge, and Ege the two-level contribution to the static second-order polarizability, β0, from the HE band can be estimated to be approximately 10× that of the LE band in vacuum and ca. 5× larger in dioxane.67 It is worth remembering, however, that β and each two-level contribution to β are frequency-dependent quantities, their values depending on the detuning energy between the transition energy and the energies of photons involved in the

Figure 2. Experimental absorption spectrum of Fc[1]NB in 1,4dioxane (black line) with transitions energies and oscillator strengths for the seven lowest-lying states obtained from calculations shown as vertical bars for vacuum (red) and 1,4-dioxane (blue).

spectrum; experimental and calculated values of Ege and f are given in the Supporting Information (Tables S3 and S12). Together, the data indicate that, as discussed above, the present method reproduces the energies and oscillator strengths, f, well in the region of both HE and LE bands. Inclusion of solvent in the calculations leads to somewhat underestimated transition energies but gives values of f in better agreement with experiment. The calculations indicate that each transition, especially those at energy similar to the experimental LE band, is the result of extensive configuration interaction. Accordingly, the transitions cannot be readily represented in terms of single pairs of molecular orbitals; we use natural transition orbitals (NTOs)59 to provide a clearer picture of the charge restribution associated with each transition. The dominant NTOs (Figure 3) suggest that the S0 → S1 transition can be well-described as having both d−d and CT character, the CT occurring from one of the iron d orbitals (dxy using the convention used in the discussion of molecular orbitals) to the π bridge and nitrobenzene acceptor. While the calculated transition energies (2.41 and 2.39 eV in vacuum and in dioxane, respectively) are close to the experimentally observed LE maximum (2.49 eV), the oscillator strength (f = 0.0015 in vacuum, 0.0057 in dioxane) is calculated to be much smaller than the experimental value (ca. 0.07). However, the calculations also predict that the S0 → S2 transition is located 6064


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similar description to the S0 → S7 transitions of their iron analogues. Spectra of Derivatives with Strong Heterocyclic Acceptors. The B3PW91 calculations reproduce experimental trends in the spectra of not only chromophores with relatively weak nitrobenzene acceptors but also the Mc[n]TB and Mc[n]SDS series. It should be noted, however, that the transition energies tend to be somewhat overestimated in this class of compounds, both with and without inclusion of solvent. As in the case of the Mc[n]NB chromophores, however, inclusion of solvent leads to values of f for the LE band in better agreement with experiment. The interpretation of the spectra of Fc[3]SDS (Figure 4) and Fc″[3]SDS (Figure S7 in the Supporting Information)

NLO phenomena in question. Accordingly, the relative importance of the contribution of the two bands to values of β determined by frequency doubling or electrooptic measurements may well differ from those to β0.35 Calculations reproduce the key differences between the experimental spectra of Fc[1]NB and Fc[2]NB (see Figure S6 in the Supporting Information) and reveal some differences in the origin of the transitions. The calculations for Fc[2]NB suggest that S0 → S5 and S0 → S7 have comparable oscillator strengths in vacuum and so both contribute significantly to the HE band: while the NTOs for the latter (Figure S10 in the Supporting Information) are similar to those for the S0 → S7 transition of Fc[1]NB, the former is a mixture of a CT transition from a d orbital and the π bridge to a LUMO-like orbital and a d−d transition. The calculations in vacuum afford a larger value of Δμge for both S0 → S5 and S0 → S7 than for S0 → S2. Inclusion of solvent in the calculation leads to a change in the energetic ordering of the first two transitions and also increases the oscillator strength of S0 → S3 (mixed d−d and bridge/d orbital to LUMO CT) to a value comparable to that for both S0 → S5 and S0 → S7 transitions. Moreover, the value of Δμge calculated for S0 → S1 (10.0 D) is larger than those for S0 → S3 (7.4 D) and S0 → S5 (8.1 D), although still smaller than that for S0 → S7 (20.0 D). This may be compared to the results of Stark spectroscopy in frozen 2-methyltetrahydrofuran (MeTHF), which suggest that Δμge for the LE band is ca. 1.4× that of the HE band,39 although the experiment does not enable us to distinguish the individual contributions of different transitions to each band. Use of eq 1, taking into account the contibutions of multiple transitions to the bands, again suggests that the major two-level contributor to β0 is the HE band (ca. 15× and 3× that of the LE in vacuum and in dioxane, respectively). The ratio of two-level contributions calculated for dioxane approaches the ratio of ca. 1.7 estimated from experimental values of f and Ege in dioxane and Δμge in frozen MeTHF.39 For Fc″[1]NB the main contributors to LE and HE bands are still S0 → S2 and S0 → S7, respectively. The dominant NTOs (Figure S12 in the Supporting Information) are similar to those seen for Fc[1]NB except that the particle NTOs for the S0 → S1 and S0 → S2 transitions of Fc″[1]NB resemble the LUMO, rather than the LUMO+1; accordingly, the calculated value of Δμge for S0 → S2 (9.3 D in vacuum) is markedly larger than for its Fc analogue. Thus, the B3PW91 calculations suggest an assignment of the spectrum of Fc″[1]NB more in accord with that of ref 39 than that of ref 38, but the opposite for Fc[n]NB (n = 1, 2). In other words, a single assignment is apparently not applicable to all chromophores of this type. Experimentally, the spectrum of Rc[1]NB shows two overlapping bands with comparable oscillator strengths; this feature is well reproduced by the calculations (especially when solvent is included; Figure S6 (Supporting Information)). The particle NTO for the main contributor to the LE band of the ruthenocenyl compounds Rc[1]NB, Rc[2]NB, and Rc″[1]NB (S0 → S1 or S0 → S2, depending on the compound in question and whether or not solvent is included) also closely resemble the appropriate LUMOs, with the hole NTOs being essentially d orbitals (with some π bridge contribution evident in Rc[2]NB). In contrast to those of Fc[n]NB and Fc″[1]NB, the main contributors to the HE bands of the ruthenium species are the S0 → S4 transitions; however, the NTOs (Figures S13−S16 in the Supporting Information) indicate a

Figure 4. Experimental absorption spectrum of Fc[3]SDS in 1,4dioxane (black line) with transitions energies and oscillator strengths for the seven lowest-lying states obtained from TD-DFT calculations shown as vertical bars for vacuum (red) and 1,4-dioxane (blue).

suggested by the calculations is reasonably straightforward: in each case the main contributors to the relatively weak LE and stronger HE bands are S0 → S2 and S0 → S3 transitions, respectively. The particle NTOs for both transitions closely resemble the LUMOs of the molecules; the hole NTOs for the S0 → S2 transitions are essentially the iron dx2−y2 orbital, while those for S0 → S3 have significant iron, cyclopentadienyl, and πbridge contributions (Figure 5 and Figures S22 and S23 (Supporting Information)). A similar picture is suggested for Rc[3]SDS (Figures 6 and 7), although here the main contributor to the HE transition is S0 → S4, and there is more π-bridge contribution to the hole NTO of the LE

Figure 5. Dominant hole (left) and particle (right) NTOs for selected transitions of Fc[3]SDS in vacuum obtained from TD-DFT calculations (with eigenvalues, λ, indicating the contribution of the NTOs shown). 6065


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S17, S19, and S20 in the Supporting Information) is more complicated, due in part to the role played by sulfur nonbonding orbitals. Calculations under in suggest the main contributor to the LE band of Fc[3]TB (S0 → S2) involves CT from both iron and sulfur to the π-bridge/acceptor; in contrast to the low-lying transitions of other chromophores, a small decrease in state dipole moment is calculated to be associated with this transition (and, therefore, a contribution to β0 opposing that from the HE band). Both S0 → S6 (CT from iron and, to a lesser extent, π-bridge to π-bridge/acceptor, mixed with d−d character) and S0 → S7 (sulfur, iron, and πbridge to π-bridge/acceptor) contribute to the HE band. In dioxane, the situation is even more complicated: three transitions with more or less comparable values of f contribute to the HE band. For Rc[3]TB in vacuum, the LE band is essentially a ruthenium d orbital to π bridge/acceptor CT transition, while the HE absorption involves charge redistribution from ruthenium, cyclopentadienyl, and sulfur to the π bridge. A somewhat different picture is obtained in dioxane, in which there are two low-lying transitions similar in energy to one another (S0 → S1 and S0 → S3, both essentially d to LUMO CT), the combined oscillator strength of which (f = 0.98) exceeds that of the higher energy transition (S0 → S5, f = 0.77, ruthenium/cyclopentadienyl/π bridge to LUMO CT with considerably reduced sulfur-based contributions), consistent with experimental observation of a strong single maximum with a shoulder on its high-energy side (see Figure S7 in the Supporting Information).

Figure 6. Experimental absorption spectrum of Rc[3]SDS in 1,4dioxane (black line) with transitions energies and oscillator strengths for the seven lowest-lying states obtained from TD-DFT calculations shown as vertical bars for vacuum (red) and 1,4-dioxane (blue).

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CONCLUSION TD-DFT calculations based on the B3PW91 functional reproduce the key features of the experimental near-UV/ visible/near-IR absorption spectra of dipolar second-order NLO dyes based on both ferrocene (two bands, the lower energy band being weaker) and ruthenocene (two overlapping bands of comparable strength or a low-energy maximum with a weaker high-energy shoulder) donors. The calculations suggest a description of the origin of the absorptions observed in compounds of this type more complex than that given in previous studies.38,39,41 The molecular orbital picture is more complex than that suggested in refs 38 and 39, with considerable variation in the ordering and composition of the frontier orbitals, even within the Mc[n]NB series. The TDDFT calculations suggest that the transitions are the result of significant configuration interaction, further limiting the general applicability of the molecular orbital picture. Moreover, although for some compounds, such as Fc[1]NB, the calculations suggest one transition accounts for most of the observed oscillator strength for each observed band, in others, two (or even more) transitions contribute significantly to one of the observed bands. The inclusion of solvent in the calculations makes a significant difference to the calculated oscillator strengths and, in some cases, the ordering and NTO description of the excited states. Nevertheless, surveying all the compounds examined, the LE absorptions can generally be characterized as having both d−d (consistent with ref 41) and d to π bridge/acceptor CT (consistent with refs 38 and 39) character, with the hole NTO also having some π bridge character in some cases. The HE band is generally due to a CT transition from the metal, the cyclopentadienyl rings, and the π bridge to an NTO resembling the molecular LUMO. Thus, although the calculations suggest a much more complicated relationship between chemical structure, orbital structure, and

Figure 7. Dominant hole (left) and particle (right) NTOs for selected transitions of Rc[3]SDS in vacuum obtained from TD-DFT calculations (with eigenvalues, λ, indicating the contribution of the NTOs shown).

transition (S0 → S2 in vacuum, S0 → S1 in dioxane). Moreover, the calculations, especially in dioxane, indicate that the lower energy transition has the larger oscillator strength, consistent with the experimental observation of a single maximum with a weak shoulder on its high-energy side (Figure 6). Values of Δμge for LE and HE bands of Fc″[3]SDS are calculated to be ca. 14.2 and 10.6 D, respectively, in vacuum and ca. 16.7 and 12.0 D in dioxane; these can be compared to values from Stark spectroscopy in frozen MeTHF of ca. 18 and 9 D.39 Using eq 1 and these values, along with the corresponding calculated transition energies and oscillator strengths, indicates that the 2-level contribution of the LE band to β0 is ca. 1.2× (vacuum) or 0.9× (dioxane) that of the HE band. Thus, although, in comparison to experimental estimates (using Stark values of Δμge) that the LE band contribution is ca. 3× that of the HE band, the calculations suggest a reduced importance for the LE band’s contribution to β0, they do agree with the experimentally based suggestion that the relative importance of the LE band increases from Fc[2]NB to Fc″[3]SDS.39 Fc″[3]TB (Figures S7 and S18 in the Supporting Information) is also relatively simple: S0 → S2 and S0 → S7 (vacuum) or S0 → S5 (dioxane) are the main contributors to the LE and HE bands, respectively, and can be wellapproximated as CT transitions from an iron d orbital to a LUMO-like orbital (albeit with relatively more π-bridge character and less acceptor character) and HOMO-3 (largely cyclopentadienyl and bridge) to LUMO transitions, respectively. The situation with Fc[3]TB and Rc[3]TB (Figures S7, 6066


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(17) Coe, B. J. In Comprehensive Coordination Chemistry II; Ward, M. D., Ed.; Elsevier: Oxford, U.K., 2004; Vol. 9. (18) Thompson, M. E.; Djurovich, P. E.; Barlow, S.; Marder, S. R. In Comprehensive Organometallic Chemistry III; O’Hare, D., Ed.; Elsevier: Oxford, U.K., 2006; Vol. 12. (19) Coe, B. J. Coord. Chem. Rev. 2013, 257, 1438. (20) Kealy, T. J.; Pauson, P. L. Nature 1951, 168, 1040. (21) Wilkinson, G.; Rosenblum, M.; Whiting, M. C.; Woodward, R. B. J. Am. Chem. Soc. 1952, 74, 2125. (22) Woodward, R. B.; Rosenblum, M.; Whiting, M. C. J. Am. Chem. Soc. 1952, 74, 3458. (23) Benkeser, R. A.; Goggin, D.; Schroll, G. J. Am. Chem. Soc. 1954, 76, 4025. (24) Barlow, S.; O’Hare, D. Chem. Rev. 1997, 97, 637. (25) Miller, J. S.; Epstein, A. J. Angew. Chem., Int. Ed. Engl. 1994, 33, 385. (26) Imahori, H.; Tamaki, K.; Guldi, D. M.; Luo, C.; Fujitsuka, M.; Ito, O.; Sakata, Y.; Fukuzumi, S. J. Am. Chem. Soc. 2001, 123, 2607. (27) Ratera, I.; Sporer, C.; Ruiz-Molina, D.; Ventosa, N.; Baggerman, J.; Brouwer, A. M.; Rovira, C.; Veciana, J. J. Am. Chem. Soc. 2007, 129, 6117. (28) Beer, P. D. Acc. Chem. Res. 1998, 31, 71. (29) Green, M. L. H.; Marder, S. R.; Thompson, M. E.; Bandy, J. A.; Bloor, D.; Kolinsky, P. V.; Jones, R. J. Nature 1987, 330, 360. (30) Barlow, S.; Marder, S. R. Chem. Commun. 2000, 1555. (31) Heck, J.; Dabek, S.; Meyer-Friedrichsen, T.; Wong, H. Coord. Chem. Rev. 1999, 190−192, 1217. (32) Peris, E. Coord. Chem. Rev. 2004, 248, 279. (33) Orr, B. J.; Ward, J. F. Mol. Phys. 1971, 20, 513. (34) Oudar, J. L.; Chemla, D. S. J. Chem. Phys. 1977, 66, 2664. (35) Linear and nonlinear polarizabilities are frequency-dependent quantities, and this dispersion is often significant when considering values related to specific applications or measurements. In the case of second-harmonic generation measurements, such as EFISH and HRS, the undamped expression for the frequency dependence of a two-level contribution to β is

transition characteristics than assumed in refs 38 and 39, the overall picture of charge redistribution deduced from the NTOs is in fact quite similar. The charge redistributions associated with the two bands is also similar to that suggested by TD-DFT studies of the two bands of various cyanovinylferrocenes43 and of 2,3-diferrocenylmaleimide.47 Consistent with the CT character suggested by the NTOs, significant dipole-moment changes are generally calculated for the transitions corresponding to the LE bands and to the HE bands, indicating significant two-level contributions to β are to be expected from both bands.

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ASSOCIATED CONTENT

S Supporting Information *

Tables of geometric details, transition energies, and oscillator strengths obtained using different functionals and through experiment, figures comparing experimental spectra and calculated transition energies and oscillator strengths for all experimentally examined chromophores, figures showing frontier orbitals and NTOs for all chromophores, tables of calculated ground- and excited-state dipole moments, and a table of coordinates for optimized structures. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail for V.C.: [email protected]. *E-mail for S.B.: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Science and Technology Program of the National Science Foundation for support (DMR-0120967).

β(− 2ω ; ω , ω) = β0(Ege 4)/[(Ege 2 − (2ℏω)2 )(Ege 2 − (ℏω)2 )] where ℏω is the energy of the incident photons. In the case of the electrooptic effect:

REFERENCES

β(− ω ; ω , 0) = β0(Ege 2 − (ℏω)2 /3)Ege 2 /(Ege 2 − (ℏω)2 )2

(1) Marder, S. R.; Perry, J. W.; Schaefer, W. P. Science 1989, 245, 626. (2) Radhakrishnan, T. P. Acc. Chem. Res. 2008, 41, 367. (3) Jazbinsek, M.; Mutter, L.; Günter, P. IEEE J. Select. Top. Quantum Electron. 2008, 14, 1298. (4) Burland, D. M.; Miller, R. D.; Walsh, C. A. Chem. Rev. 1994, 94, 31. (5) Ahlheim, M.; Barzoukas, M.; Bedworth, P. V.; Blanchard-Desce, M.; Fort, A.; Hu, Z.-Y.; Marder, S. R.; Perry, J. W.; Runser, C.; Staehelin, M.; Zysset, B. Science 1996, 271, 335. (6) Dalton, L. R.; Benight, S. J.; Johnson, L. E.; Knorr, D. B.; Kosilkin, I.; Eichinger, B. E.; Robinson, B. H.; Jen, A. K.-Y.; Overney, R. M. Chem. Mater. 2011, 23, 430. (7) Li, D.; Ratner, M. A.; Marks, T. J.; Zhang, C.; Yang, J.; Wong, G. K. J. Am. Chem. Soc. 1990, 112, 7389. (8) Ashwell, G. J.; Hargreaves, R. C.; Baldwin, C. E.; Bahra, G. S.; Brown, C. R. Nature 1992, 357, 393. (9) Wang, C.; Zhang, T.; Lin, W. Chem. Rev. 2012, 112, 1084. (10) Kanis, D. R.; Ratner, M. A.; Marks, T. J. Chem. Rev. 1994, 94, 195. (11) Zyss, J.; Nicoud, J.-F. Curr. Opinion Solid State Mater. Sci. 1996, 1, 533. (12) Denning, R. G. J. Mater. Chem. 1995, 5, 365. (13) Dalton, L. R.; Sullivan, P. A.; Bale, D. H. Chem. Rev. 2010, 110, 25. (14) Long, N. J. Angew. Chem., Int. Ed. Engl. 1995, 34, 21. (15) Whittall, I. R.; McDonagh, A. M.; Humphrey, M. G.; Samoc, M. Adv. Organomet. Chem. 1998, 42, 291. (16) Di Bella, S. Chem. Soc. Rev. 2001, 30, 355.

For example, see: Singer, K. D.; Kuzyk, M. G.; Sohn, J. E. J. Opt. Soc. Am. B 1987, 4, 968. (36) It should be noted that the second hyperpolarizbility is a thirdrank tensor, while the transition dipole moments and change in state dipole moment are vectors. However, in a pseudolinear system these vectors will both be very well approximated by their projection onto the long molecular axis (here defined as x), and the two-level β contribution will be dominated by the βxxx tensorial component. (37) Liu, Z.-q.; Fang, Q.; Wang, D.; Cao, D.-x.; Xue, G.; Yu, W.-t.; Lei, H. Chem. Eur. J. 2003, 9, 5074. (38) Calabrese, J. C.; Cheng, L.-T.; Green, J. C.; Marder, S. R.; Tam, W. J. Am. Chem. Soc. 1991, 113, 7227. (39) Barlow, S.; Bunting, H. E.; Ringham, C.; Green, J. C.; Bublitz, G. U.; Boxer, S. G.; Perry, J. W.; Marder, S. R. J. Am. Chem. Soc. 1999, 121, 3715. (40) Coe, B. J.; Docherty, R. J.; Foxon, S. P.; Harper, E. C.; Helliwell, M.; Raftery, J.; Clays, K.; Franz, E.; Brunschwig, B. S. Organometallics 2009, 28, 6880. (41) Kanis, D. R.; Ratner, M. A.; Marks, T. J. J. Am. Chem. Soc. 1992, 114, 10338. (42) Runge, E.; Gross, E. K. U. Phys. Rev. Lett. 1984, 52, 997. (43) Nemykin, V. N.; Makarova, E. A.; Grosland, J. O.; Hadt, R. G.; Koposov, A. Y. Inorg. Chem. 2007, 46, 9591. (44) Nemykin, V. N.; Hadt, R. G. J. Phys. Chem. A 2010, 114, 12062. (45) Trujillo, A.; Fuentealba, M.; Carrillo, D.; Manzu, C.; LedouxRak, I.; Hamon, J.-R.; Saillard, J.-Y. Inorg. Chem. 2010, 49, 2750. 6067


Organometallics

Article

(46) Kato, S.-i.; Roberts Beels, M. T.; La Porta, P.; Schweizer, W. B.; Boudon, C.; Gisselbrecht, J.-P.; Biaggio, I.; Diederich, F. o. Angew. Chem., Int. Ed. Engl. 2010, 49, 6207. (47) Solntsev, P. V.; Dudkin, S. V.; Sabin, J. R.; Nemykin, V. N. Organometallics 2011, 30, 3037. (48) Plażuk, D.; Zakrzewski, J.; Nakatani, K.; Makal, A.; Woźniak, K.; Domagała, S. RSC Adv. 2012, 2, 3512. (49) Schäfer, J.; Scheurer, M.; Speiser, B.; Kuźnika, W.; Kityk, I. V. Spectrochim. Acta, Part A 2012, 95, 193. (50) Huesmann, H.; Förster, C.; Siebler, D.; Gasi, T.; Heinze, K. Organometallics 2012, 31, 413. (51) Kulhánek, J.; Bureš, F.; Kuznik, W.; Kityk, I. V.; Mikysek, T.; Růzǐ čka, A. Chem. Asian J. 2013, 8, 465. (52) Alain, V.; Fort, A.; Barzoukas, M.; Chen, C. T.; BlanchardDesce, M.; Marder, S. R.; Perry, J. W. Inorg. Chim. Acta 1996, 242, 43. (53) Alain, V.; Blanchard-Desce, M.; Chen, C. T.; Marder, S. R.; Fort, A.; Barzoukas, M. Synth. Met. 1996, 81, 133. (54) Kinnibrugh, T. L.; Salman, S.; Getmanenko, Y. A.; Coropceanu, V.; Porter, W. W.; Timofeeva, T. V.; Matzger, A. J.; Brédas, J.-L.; Marder, S. R.; Barlow, S. Organometallics 2009, 28, 1350. (55) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 299. (56) Togni, A.; Rihs, G. Organometallics 1993, 12, 3368. (57) The structures in ref 56 are of analogues of Fc[1]NB and Fc[2] NB (and of Fc[3]NB) in which the Fc donor is replaced by enantomerically pure 2-vinylferrocen-1-yl. (58) Zhang, Y.; Champagne, B. J. Phys. Chem. 2013, 117, 1833. (59) Martin, R. L. J. Chem. Phys. 2003, 118, 4775. (60) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; ; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; ; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Keith, T.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J., Gaussian 09, Revision B.01; Gaussian Inc., Wallingford, CT, 2010. (61) Baer, R.; Neuhauser, D. Phys. Rev. Lett. 2005, 94, 043002. (62) Baer, R.; Livshits, E. Annu. Rev. Phys. Chem. 2010, 61, 85. (63) Cheng, L.-T.; Tam, W.; Meredith, G. R.; Marder, S. R. Mol. Cryst. Liq. Cryst. 1990, 189, 137. (64) Coe, B. J.; Jones, C. J.; McCleverty, J. A.; Bloor, D.; Cross, G. J. Organomet. Chem. 1994, 464, 225. (65) Malaun, M.; Reeves, Z. R.; Paul, R. L.; Jeffrey, J. C.; McCleverty, J. A.; Ward, M. D.; Asselberghs, I.; Clays, K.; Persoons, A. Chem. Commun. 2001, 49. (66) Chiffre, J.; Averseng, F.; Balavoine, G. G. A.; Daran, J.-C.; Iftime, G.; Lacroix, P. G.; Manoury, E.; Nakatani, K. Eur. J. Inorg. Chem. 2001, 2221. (67) Two-level terms associated with higher lying states will also contribute to β, although the energy denominator (eq 1) means that, in general, these will be less important than those from the HE and LE bands unless very large values of both μge and Δμge are associated with the relevant transitions. A detailed study to assess the importance of the two-level terms associated with these states, or of three-level terms, is beyond the scope of the present work.

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Dipolar Ferrocene and Ruthenocene Second-Order Nonlinear Optical

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