Article pubs.acs.org/JPCA
Why Bindschedler’s Green Is Redder Than Michler’s Hydrol Blue Seth Olsen* School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072 Australia S Supporting Information *
ABSTRACT: We offer a new physical interpretation of the color shift between diarylmethane dyes and their azomethine analogues. We use an isolobal analogy between state-averaged complete active space self-consistent field solutions for corresponding methines and azomethines to show that the shift contains a significant contribution from configuration interaction between a methine-like ππ* excitation and an nπ* excitation out of the azomethine lone pair. The latter does not exist in the corresponding methine systems. This picture is qualitatively inconsistent with traditional models of the shift based on molecular orbital perturbation theory of independent π-electron Hamiltonians. A key prediction is the existence of a dipole-allowed band in the blue/near-UV spectra of the azomethines, which has polarization parallel to the lowest energy band. This forces a revision of past assumptions about the nature of the low-energy spectra of the azomethines. A band at the predicted energies has been observed in solution-state spectra. absorption maximum of Bindschedler’s Green in methanol4 is 0.3 eV higher in energy than that of Michler’s Hydrol Blue in nitromethane, aqueous buffer or bound to amyloid fibrils.4−6 The retrodiction and interpretation of the “azomethine shift” between, e.g., Bindschedler’s Green vs Michler’s Hydrol Blue (cf. Scheme 1) was an early success of simple π-electron molecular orbital theory during the quantum chemical “πologic” era.7 A model of the shift advocated by Förster, Dewar, and Knott was based on perturbation theory relative to the Hückel Hamiltonian for the corresponding odd-alternant hydrocarbon frame (cf. Figure 1).8−10 In an alternant hydrocarbon, the pz orbital sites contributing to the π-electron system can be bipartitioned into “starred” and “unstarred” sets (cf. Figure 1) such that no site is in the same set as its neighbors. Cyanine-type chromogens usually correspond to odd-alternant hydrocarbons, wherein there is an excess starred site. The Hückel orbitals of odd-alternant hydrocarbons always include a nonbonding frontier π molecular orbital with amplitude only on the starred sites, located at the zero of energy (the ionization potential of carbon). All other π orbitals are split symmetrically in energy about this orbital. For the molecules in Scheme 1, all of which correspond to the oddalternant frame in Figure 1, the nonbonding orbital has a node on the bridge. Because the dyes in Scheme 1 are iso-πelectronic with the anion of the corresponding odd-alternant system, the nonbonding orbital is the highest-occupied π orbital. The lowest unoccupied orbital has some amplitude on the bridge. A local perturbation that lowers the energy of the bridge site will lower the energy of the lowest unoccupied
1. INTRODUCTION Azomethine dyes, like their methine analogues, are useful dyes because of a bright low-energy absorption associated with their charge-resonance electronic structure (cf. Scheme 1).1 For diarylmethanes (e.g., Michler’s Hydrol Blue and bisphenoxymethine cf. Scheme 1) and other N + 1 methine systems,2 substitution of the central carbon by an azomethine nitrogen shifts the first absorption band to the red. This is useful because it represents a strategy for the design of near-IR dyes.3 The first Scheme 1
Received: September 11, 2012 Revised: January 28, 2013 Published: February 8, 2013 © 2013 American Chemical Society
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perturbation theory can still be useful if the mixing between the π electron system and its environment are small. The author has recently shown that the low-energy electronic physics of diarylmethane dyes such as Michler’s Hydrol Blue and bisphenoxymethine (cf. Scheme 1) are describable using a family of analogous solutions to the same state-averaged complete active space self-consistent field (SA-CASSCF) problem.12,16,17 The active space has four electrons distributed in three orbitals (SA-CAS(4,3)), and the solutions map the frontier electronic structure of the dyes onto that of an allylic anion.18 Allyl is the simplest hydrocarbon frame for which the label “odd-alternant” is useful. In a localized orbital representation, the active space is spanned by orbitals localized on the terminal rings and bridge, analogous to the three pz orbitals contributing to an allylic π system. In delocalized (e.g., natural or pseudocanonical) representations, the orbitals are recognizably similar to the frontier orbitals predicted by the Hückel theory of an allylic anion. The SA-CASSCF model has a similar structure if it is averaged over two (SA2-CAS(4,3)) or three (SA3-CAS(4,3)) states, and most observables related to the lower two states are not sensitive to this choice. We have shown that this series of SA-CASSCF models gives good agreement with experimental transition dipole moments for all cases where data is available, and it correctly predicts the experimentally determined polarization directions of these transitions.16 It also provides good agreement with experimental electronic excitation energies, when used as a reference model for second-order multireference perturbation theory.12,16 The author has shown that the four-electron, three-orbital SA-CASSCF model describes the color changes predicted by the Förster−Dewar−Knott color rule when applied to a series of derivatives of Michler’s Hydrol Blue with substituents added to the methine bridge.12 The Förster−Dewar−Knott model describes the shift as a specific instance of this rule.9,10 The author has shown as well that the application of a SA2CAS(4,3) model to the corresponding methine/azomethine pairs in Scheme 1 captures the observed bathochromic shifts, but it was also noted that there is significant mixing between the π frontier orbitals and the lone pair nonbonding orbital of the azomethine.15 This mixing is a feature not treated in the original π-electron models. We thought to investigate further into the origins and consequences of this n-π mixing. This paper reports our findings. In this paper, we will offer a revised physical explanation of the azomethine shift between methines and azomethines in Scheme 1. A significant contribution to the color shift comes from a vibronically allowed configuration interaction between a diarylmethane-like ππ* excited state and a low-energy nπ* excited state associated with the azomethine lone pair. The latter state has no analog in the low-energy spectra of the corresponding methines.17,19−21 This mechanism is a qualitative revision of traditional models of the shift, which have been based on independent π-electron (Hückel) models.8−10 The coupling of the ππ* and nπ* excited states, is allowed because the ground-state minimum energy geometries of all dyes in Scheme 1 are noncoplanar (C2). There are experimental consequences that arise from the model, which can be used as a basis for testing. One of these is the prediction of a strongly allowed electronic absorption in the blue/near-UV for the azomethines, with polarization parallel to the lowest-lying band. This is qualitatively different than the behavior of diarylmethanes, for which the second electronic excitation is polarized orthogonal to the first.21−23 Spectra in the literature
Figure 1. Odd-alternant hydrocarbon reference system used for perturbational molecular orbital theory model of the azomethine shift for dyes in Scheme 1. Top: The p-electron systems of dyes in Scheme 1 are topologically equivalent to the odd-alternant hydrocarbon skeleton shown. It is is odd-alternant, so the sites can be bipartitioned into two disjoint sets (“starred” and “unstarred”) such that no two atoms from the same set are neighbors. In an odd-alternant system, the number of “starred” sites exceeds the number of “unstarred” by one. For the system shown, appropriate for all dyes in Scheme 1, the bridge is unstarred. The highest occupied π orbital is a nonbonding π orbital (NBO) with nodes on unstarred sites, including the bridge. Other orbitals are split symmetrically about this one. The lowest unoccupied orbital is antibonding with respect to the bridge (AO), and has amplitude on the bridge site. A perturbation that lowers the energy of the bridge site will lower the AO but will not affect the NBO. This is equivalent to a prediction of a red shift of the first excitation energy.
orbital at first order while leaving the highest occupied orbital energy invariant. Because Hückel theory is an independent particle theory, this corresponds to prediction of a red shift of the lowest excitation of the π-electron system. The Förster−Dewar−Knott model of the azomethine shift describes the shift as a consequence of a change in the singleparticle π-electron potential. Within this model, the azomethine shift is an example of a more general color-constitution relationship: “the Dewar−Knott color rule”. The same rule can be applied to predict color trends that occur upon addition at the methine site, in which case electron-withdrawing substituents are predicted to produce a red shift for the methines in Scheme 1.11,12 The Förster−Dewar−Knott model of the azomethine shift is based on a Hückel π-electron Hamiltonian; it does not explicitly treat interactions with electrons outside the π system. The assumption of π-separability for the dyes in Scheme 1 has traditionally been justified on the basis of the belief that they have a planar ground state, corresponding to C2v symmetry.13 This assumption is not supported by geometry optimization on the ground state of modern quantum chemical models.12,14−17 Still, even for nonplanar conjugated systems, low-order 2456
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theory, and also contracted multireference configuration interaction were not significantly different from those evaluated on the reference SA-CASSCF model. To characterize the vibronic couplings of the two lowestlying states of the azomethines, we reoptimized the geometries at the restricted Hartree−Fock level (RHF//cc-pvdz) and performed vibrational analyses at these points. Vibrational frequencies were scaled by 0.9, in accordance with usual practice.34 To simulate the resonance Raman spectra, we calculated the relative intensity according to a formula based on that of Heller, Sundberg and Tannor, which applies in the short-time limit.35 In this approximation, the relative intensity of the ground-state normal modes k and k′ is
suggest the predicted band was observed in as far back as 1938, but its significance was at the time unknown.24 The paper proceeds as follows. The next section describes the technical aspects of the computational quantum chemistry. Following this, we report key results. This includes geometries for ground-state minima and planar saddle point structures for dyes in Scheme 1, calculated excitation energies and transition dipole moments for the adiabatic states. We will establish an isolobal analogy25,26 between the SA-CASSCF solutions for the methines and azomethines in Scheme 1. We will use the isolobal analogy to perform a diabatic analysis of the low-energy spectrum of the azomethines. This analysis will show that there is significant configuration mixing between a methine-like ππ* state and the nπ* state associated with the lone pair orbital on the azomethine. This effect accounts for at least half of the azomethine shift for the dyes in Scheme 1. We will analyze the vibronic couplings associated with the electronic states of the methines and azomethines by simulation of the short-time resonance Raman spectra, and uncover signatures of diabatic state mixing in the vibronic couplings. We conclude the paper with a discussion of our results in the context of earlier theories, and propose strategies for experimental validation and/or refutation of our model. We cite evidence that a key prediction of the configuration interaction modelthat of a strongly allowed state in the blue/near UV regionis supported by spectra available in the literature.24
2 ω0k ′ ⎛ Vk ⎞ Ik = ⎜ ⎟ ω0k ⎝ Vk ′ ⎠ Ik ′
(1.1)
where ω0k is the frequency of the ground-state vibration associated with mode k and Vk is the gradient of the excitation energy along the mode (in mass-weighted coordinates). The gradients on the relevant states were calculated using the same SA-CASSCF solutions obtained at the RHF geometries. The only difference between (1.1) and the Heller−Sundberg− Tannor formula35 is that the gradient is taken on the excitation energy, not on the potential surface. This corrects for the fact that the excited-state gradients and ground-state minima are calculated with different electronic structure ansätze, so that the geometry is not at the ground-state minimum of the model used for the gradients. In the event that the calculation is done with the same ansatze for all states, so that the geometry is the ground-state minimum of the model used to calculate the gradients, (1.1) reduces to the Heller−Sundberg−Tannor formula. To analyze the electronic structure of the azomethines, we diabatize the electronic states against those obtained at a relaxed ground-state geometry with C2v symmetry. We did this at both MP2//cc-pvdz and RHF//cc-pvdz levels. To obtain this geometry, we first adjusted the ground-state geometry to have this symmetry, and reoptimized in the higher symmetry. The geometry was shown by vibrational analysis to be a firstorder saddle point on the RHF ground-state surface. The diabatization procedure used was as described by Simah et al. and implemented in MOLPRO as the DDR procedure.36 The procedure is implemented in two parts: first by performing a rotation of the active orbitals to achieve a least-squares fit against corresponding orbitals at a reference geometry, and then by performing a similar fit of the configuration interaction states against those at the reference geometry. The reference geometry used in each case was the optimized C2v structure. The diabatic transformation was calculated for the two excited states of B symmetry for the azomethines using the SA3CAS(6,4) reference model and was then applied to the SA3CAS(6,4)*PT2 state energies to generate an approximate SA3CAS(6,4)*PT2 diabatic Hamiltonian. The procedure is technically a quasi-diabatization, as strictly diabatic states cannot be obtained from transformations acting on a subspace of the electronic Hilbert space.37 In all cases the energies and structures of the SA-CASSCF states, and the ground state themselves, were the same regardless of whether or not symmetry was explicitly used in the calculation. Optimizations without explicit symmetry declaration converged to the C2 ground-state minima.
2. COMPUTATIONS All computational results were generated with the MOLPRO software.27 For each of the molecules in Scheme 1, a model geometry was generated by optimization on the ground-state surface of an MP2 electronic structure model28 using a cc-pvdz basis set29 (i.e., MP2//cc-pvdz; similar nomenclature is used below). For each of the diarylmethane (methine) dyes Michler’s Hydrol Blue and bisphenoxymethine, solutions to the twostate-averaged four-electron, three-orbital complete active space self-consistent field (SA2-CAS(4,3)) problem30 were obtained, again using a cc-pvdz basis set. These solutions have been described in previous work.15,31 For the azomethine dyes, solutions to the three-state sixelectron, four-orbital complete active space self-consistent field (SA3-CAS(6,4)) problem were obtained, again using a cc-pvdz basis set. The SA3-CAS(6,4) solutions were generated by starting with a previously described15 SA2-CAS(4,3) solution for these dyes, and expanding the active space to include the natural orbital with greatest character of the lone pair azomethine orbital, as judged by visual inspection. The SA2-CAS(4,3) and SA3-CAS(6,4) solutions were used as reference spaces for an internally contracted second-order multireference Rayleigh−Schrö dinger perturbation theory treatment (CASPT2) using the RS2C procedure in Molpro.32 All valence orbitals were correlated in the perturbation theory. A level shift33 of 0.1 au was applied. The zeroth-order Hamiltonian was constructed using the state-averaged pseudocanonical SA-CASSCF orbitals and was the same for all states. No explicit symmetry was invoked in the SA-CASPT2 calculations. Where excitation energies are reported, these refer to perturbation theory results unless otherwise indicated. Where dipole observables are reported, these were evaluated on the SA-CASSCF reference. The dipole observables extracted from first-order wave functions using different flavors of perturbation 2457
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Figure 2. Relevant geometries of azomethines Bindschedler’s Green (top left) and phenolindophenol (top right) and of analogous methines Michler’s Hydrol Blue (bottom left) and bisphenoxymethine (bottom right). Heavy atom bond lengths (Å) and internal bridge angles and bridge dihedrals (deg) are shown, as well as the difference between hydrogens in the 2,2′ positions. Parameters in bold refer to the ground-state minimum, which has C2 symmetry. Parameters in italics refer to a low energy saddle point with higher C2v symmetry. Geometries were obtained by optimization on the MP2//cc-pvdz ground-state potential surface. There are two possible C2 minima with opposing handedness for each dye, corresponding to distinct stereoisomers; only the right-handed stereoisomers are shown.
azomethines than in the methines; this indicates that the balance between conjugative stabilization and steric repulsion is a tighter trade-off in the methines. It is also reasonable to think that, because the nonbonding pair on the azomethine has a more compact spatial distribution than the C−H bonding pair in the methine, the repulsion of the lone pair with the azomethine bonding electrons would be stronger, favoring a more acute internal angle. The observation of a nonplanar ground-state geometry for Michler’s Hydrol Blue contradicts an early empirical suggestion belief that Michler’s Hydrol Blue is planar.13 This has been established by multiple independent modelling studies of the cationic diarylmethanes.14,15,17,38 Although the consequences of nonplanarity in Michler’s Hydrol Blue and bisphenoxymethine appear to be modest and quantitative, this paper will show that the consequences of nonplanarity (and the accompanying lowering of symmetry) are more profound for the azomethines. The ground-state minima of the dyes in Figure 2 occur in pairs with distinct handedness. We worked with the left-handed isomers. Ground-state-relaxed C2v geometries for the dyes are also shown in Figure 2. In both cases, the C2v structure was shown to be a first-order saddle point on the ground-state surface. It represents a transition-state geometry for the reaction that exchanges left- and right-handed stereoisomers. The energies of these structures, relative to the C2 ground-state minima, are listed in Table 1. The barrier height was significantly smaller on the RHF//cc-pvdz surface (
