Theoretical Studies of the Low-lying Excited Electronic States and Transition Energies of Naphthol Sulfonate Derivatives

Naphthols and their derivatives are photoacids whose acidity increases upon photoexcitation, thereby often undergoing the excited-state proton transfer (ESPT) in the gas-phase and aqueous solutions.^1-5 Although the ESPT of both 1-naphthol and 2-naphthol have been extensively studied, their sulfonate derivatives have also attracted attention in view of using them as fluorescence probes in a variety of aqueous media. Because the ESPT process is very sensitive to pH of medium, water structure, hydrogen bonding, etc., these photoacids have been frequently used to probe the microenvironment and to obtain structural and dynamical information in proteins and microheterogeneous media such as micelles and microemulsions.^6-8

Naphthols and their sulfonate derivatives show two absorption bands, usually one strong and the other weak, in the near UV region, and with excitation at ~330 nm, fluoresce at ~450 nm in aqueous solutions.^7b In order to better understand light absorption and the subsequent ESPT of these photoacids, detailed computational study on the electronic structure of these photoacids would be much desired. As a preliminary study on the electronic structure of naphthol sulfonate derivatives in aqueous solutions, we first attempted to investigate the excited states and their electronic properties of these photoacids in gas phase. Although OH substitution at the 1- or 2-position on the naphthalene ring of naphthol is expected to have different effects on the electronic structure, we focus on 2-naphthol and its sulfonate derivatives in the present study, because we are particularly interested in using 2-naphthol sulfonates as fluorescence probes in various media.^6-8

Of particular interest in the electronic structure of naphthol sulfonate derivatives are the two low-lying excited states. For extended polyacene molecules, there exist two low-lying singlet excited states, called ¹L_a and ¹L_b.⁹ The excitation to ¹L_a is optically allowed, but the excitation to ¹L_b optically forbidden. The ¹L_a state has significantly ionic, charge-separated character and a contribution from the HOMO → LUMO excitation is predominant, whereas the ¹L_b state is of more covalent in nature and has a contribution of both HOMO–1 → LUMO and HOMO → LUMO+1 excitations.^10,11 The relative order of these two states depends on the size of molecules. For naphthalene and related molecules, the ¹L_b state is lower in energy than the ¹L_a state.^11,12 However, the two low-lying excited states of substituted naphthalenes such as naphthols may not be purely ¹L_a and ¹L_b, but rather an admixture of the two states.

In the present study, the low-lying excited electronic states of 2-naphthol and a few selected sulfonate derivatives were investigated using high-level ab initio and DFT methods. The vertical transition energies and oscillator strengths to the singlet excited states were estimated at the EOM-CCSD and MCQDPT2 levels as well as at the TDDFT level using two different functionals. Among various sulfonated derivatives, 2-naphthol-6-sulfonate (2N6S), 2-naphthol-8-sulfonate (2N8S), and 2-naphthol-6,8-disulfonate (2N68S) were chosen for study. Depending on the orientation of OH moiety of these molecules, there exist cis and trans rotamers. The energy differences between the two rotamers are rather small, and we considered only cis rotamers in the present study. The structures of all molecules considered here are shown in Fig. 1. We are particularly interested in the nature of the two lowest excited ¹L_a and ¹L_b states, and how the sulfonate substitution affects the electronic structure of these states.

Figure1.

Molecular structures of (a) 2-naphthol, (b) 2-naphthol-6-sulfonate, (c) 2-naphthol-8-sulfonate, and (d) 2-naphthol-6,8-disulfonate. Also denoted is the numbering of carbon atoms.

Both ab initio and DFT methods were employed in the electronic structure calculations of 2-naphthol and its sulfonate derivatives, 2N6S, 2N8S, and 2N68S. For ab initio calculations, the equilibrium geometries of all molecules were optimized at the MP2/6-311++G(2d,2p) level. The 6-311++G(2d,2p) basis set was chosen because the geometries optimized using 6-311++G(d,p) were found to be slightly non-planar, suggesting that multiple polarization functions were needed for yielding correct planar geometries. Larger basis sets could not be used because the size of calculations became prohibitively large. Only for 2-naphthol, the 6-311++G(2df,2p) basis set was also employed to check the effect of larger basis set. For DFT calculations, two different functionals, B3LYP and ωB97X-D were utilized. B3LYP¹³ is the hybrid GGA functional and ωB97X-D¹⁴ the range-separated functional that includes long-range corrections as well as a built-in dispersion term. The equilibrium geometries of the molecules were optimized separately using each functional. The sufficiently large aug-ccpVTZ basis set was used to minimize the basis set effects in DFT calculations. The optimized equilibrium geometry for each molecule was confirmed to be of minimum structure by vibrational frequency calculations.

The vertical excitation energies were estimated using two different ab initio methods, equation-of-motion coupled cluster singles and doubles (EOM-CCSD)¹⁵ and multi-configuration quasi-degenerate second-order perturbation theory (MCQDPT2)^16,17 at the ground state geometries optimized at the MP2/6-311++G(2d,2p) level. For these excited-state calculations, the same 6-311++G(2d,2p) basis set was used. The EOM-CCSD calculations for 2-naphthol were also performed using 6-311++G(2df,2p). In the EOM-CCSD method, excited states are computed using the equation-of-motion scheme in conjunction with coupled cluster theory including single and double excitations.¹⁵ While EOM-CCSD requires very high computational cost because of its N⁶ scaling, it is one of the most accurate methods for excited state calculations, especially in describing the relative order and spacing of excited states.¹⁸ For a planar molecule of C_s symmetry, there are electronic states of A' and A″ symmetries. In the present EOM-CCSD excited-state calculations, the number of states to be solved for in the EOM was set to be large enough to include at least three different states for each symmetry.

The MCQDPT2 method is the multi-state formulation of multi-configurational reference perturbation theory (MRPT), developed by Nakano.¹⁶ The MRPT theory is the generalization of Møller–Plesset perturbation theory to the case of multi-configurational reference state.¹⁷ Instead of the singe-state approach to MRMP, the MCQDPT2 scheme allows the mixing of several reference states within the MRPT treatment. In the present MCQDPT2 calculations, two different active spaces were used: the small one, denoted as (4,5), has 5 active orbitals and 4 active electrons, and the large one denoted as (6,7) 7 active orbitals and 6 active electrons. For multi-state computations, five or six states of the same symmetry were averaged to yield the reference state.

We also performed the time-dependent DFT (TDDFT) calculations using the B3LYP and ωB97X-D functionals and the aug-cc-pVTZ basis set at the DFT optimized ground state geometries, and comparisons were made to the results of EOM-CCSD and MCQDPT2 calculations. All ab initio and DFT calculations except for MCQPDT2 were performed using the Gaussian 16 program package.¹⁹ The GAMESS program package was used for MCQDPT2 calculations.²⁰

The equilibrium structures of the ground states of 2-naphthol and sulfonate derivatives optimized at the MP2/6-311++G(2d,2p) level were all found to be planar with C_s symmetry, exhibiting the feature of typical aromatic ring systems. As mentioned earlier, there exist cis and trans rotamers for these molecules depending on the orientation of OH moiety. When the geometry optimization was conducted on the two rotamers of 2-naphthol, the cis rotamer was found to be more stable by 197 cm^–1 at the MP2/6-311++G(2d,2p) level, and we focused on cis rotamers for all molecules. The optimized geometrical parameters are given in Table 1. The changes in structural parameters of sulfonate derivatives relative to those of 2-naphthol were rather minimal. Although there is a very slight increase in C2–O bond length with the substitution of SO₃^– group, the naphthalene framework of sulfonate derivatives remains almost the same.

Table 2 shows the vertical transition energies and oscillator strengths to singlet excited states of 2-naphthol as well as leading orbital contributions to corresponding excitation calculated using various ab initio and TDDFT methods. For 2-naphthol and sulfonate derivatives considered here, the ground state is of A' symmetry, and the results for three different excited states for both A' and A'' symmetries are presented in Table 2 and subsequent tables. Fig. 2 presents the valence π molecular orbitals of 2-naphthol relevant in the present study. It is seen that the first four molecular orbitals are delocalized over the whole molecule, but the last one has a little Rydberg-type character.

Figure2.

Valence π molecular orbitals of 2-naphthol obtained at the HF/6-311++G(2d,2p) level (isovalue = 0.03). H and L denote HOMO and LUMO, respectively.

The EOM-CCSD calculations predict that the two lowest singlet A' excited states, 2 ¹A' and 3 ¹A' , are at the vertical transition energies of 4.30 and 5.03 eV, each of which corresponds to the ¹L_a or ¹L_b state. The EOM-CCSD results in Table 2 were obtained using 6-311++G(2df,2p) basis set, but the results calculated using smaller 6-311++G(2d,2p) basis set were also very similar. These transition energies are larger by ~0.5 eV, compared to the experimental absorption maxima of 2-naphthol observed in hexane,² but the energy spacing of 0.73 eV between the two states is in good agreement with the experimental value of 0.76 eV. Also, the oscillator strength of the 3 ¹A' state is found to be more than twice as large as that of the 2 ¹A' state. This result is also consistent with the experimental absorption spectrum where the second absorption band at the shorter wavelength is much stronger.^2,7b Therefore, it is assumed that the EOM-CCSD calculations provide quite accurate description of excited states, allowing for the errors in the absolute values of excitation energies.

Upon examination of the EOM amplitudes determined for the 2 ¹A′ and 3 ¹A′ states, these two states do not correspond exactly to pure ¹L_a or ¹L_b state. Rather, the 2 ¹A′ and 3 ¹A′ states appears to have mixed characters of both ¹L_a and ¹L_b. Based on much larger oscillator strength and slightly larger EOM amplitude of HOMO → LUMO excitation, it may be inferred that the 3 ¹A′ state possesses more character of ¹L_a state, and the 2 ¹A′ state more character of ¹L_b state. According to EOM-CCSD, the next two singlet excited states are of A'' symmetry and they are mostly due to the excitation to Rydberg-type σ* orbitals.

Also presented in Table 2 are the results of excited state calculations by MCQDPT2, which is based on the multi-configurational reference. We initially attempted MCQDPT2 calculations with the active space consisting of five active orbitals and four active electrons, denoted as MCQDPT2(4,5). The vertical transition energies obtained using this active space did not match the EOM-CCSD values: the vertical transition energy to the first excited state, 2 ¹A' was much larger, and the energy spacing between the 2 ¹A' and 3 ¹A' states was much smaller, compared to the EOM-CCSD values. MCQDPT2(4,5) calculations also suggest that the lowest 2 ¹A' state has more or less ¹L_a character, having larger contribution of HOMO → LUMO excitation, as opposed to the EOM-CCSD prediction.

In order to test whether this discrepancy is due to the small active space, we attempted another calculation using a larger active space. Here the active space consists of eight active orbitals and six active electrons, denoted as MCQDPT2(6,8). Using this active space, the vertical transition energy to the first excited state decreases considerably, but the transition energies estimated by MCQDPT2(6,8) are still too large by ~0.5 eV for the A' states and by ~0.3 eV for the A'' states, compared to the EOM-CCSD energies. Also, the nature of the two lowest ¹A' states are not changed by this large active space; the 2 ¹A' state has a larger contribution of HOMO → LUMO excitation, suggesting ¹L_a character. Although the reason for this deficiency is not clear, it is suspected that the state-averaged reference state in the MCQDPT2 calculations is not quite appropriate to treat equally all excited states of 2-naphthol.¹⁶

TDDFT calculations using two different functionals are also compared with the EOM-CCSD results. As shown in Table 2, the B3LYP functional generally predicts the vertical transition energies to be considerably smaller than the EOM-CCSD method. Also, the B3LYP functional predicts that the first excited state ¹A' is of ¹L_a character, resulting from HOMO → LUMO excitation with a larger oscillator strength, and the second excited ¹A' state is of ¹L_b character, contrary to EOM-CCSD prediction. It is well-known that the TDDFT method has limitations in describing ionic or charge-separated states, and these states is usually underestimated in energy.^21,22 In order to remedy these limitations, range-separated and/or long-range corrected functionals have often been suggested.^10b,23,24 Using the range-separated ωB97X-D functional with long-range corrections, the vertical transition energies are seen to increase considerably for all excited states. However, the ωB97X-D functional still predicts that the ¹L_a state with larger oscillator strength is lower in energy than the ¹L_b state, and the energy spacing between these two states is much smaller relative to experimental and EOM-CCSD values.

Table 3 presents the results of excited state calculations for 2N6S. The π molecular orbitals relevant to formation of low-lying excited states of 2N6S are shown in Fig. 3. In addition to π molecular orbitals similar to those of 2-naphthol, the orbital localized on the SO₃^– group, denoted as π_H-2, may also contribute to formation of excited states of sulfonate derivatives.

Figure3.

Valence π molecular orbitals of 2-naphthol-6-sulfonate obtained at the HF/6-311++G(2d,2p) level (isovalue of 0.03). H and L denote HOMO and LUMO, respectively.

The EOM-CCSD calculations show that the electronic structure of low-lying excited states of 2N6S are quite similar to that of 2-naphthol. While the vertical transition energies to the two lowest ¹A' states are larger by ~0.4–0.5 eV, compared to the experimental absorption maxima observed in water,⁸ the energy spacing between the two states is very close to experimental value with the discrepancy of 0.14 eV. The oscillator strength of the 3 ¹A' state decreases relative to that of 2-naphthol while it does not change for the 2 ¹A' state. It is also found that the two lowest ¹A' states have considerable mixing of ¹L_a and ¹L_b characters. Based on slightly larger oscillator strength, the 3 ¹A' state appears to have more ¹L_a character. Unlike the case of 2-naphthol, one excited state of A″ symmetry is positioned between the 2 ¹A' and 3 ¹A' states. The third ¹A' state originates mainly from the excitation of SO₃^– orbital to LUMO.

On the other hand, MCQDPT2(4,5) calculations using small active space suggest that the lowest excited 2 ¹A' state has more distinct character of ¹L_a state, having a significant contribution from HOMO → LUMO excitation, and the 3 ¹A' state has roughly ¹L_b character. Also, MCQDPT2(4,5) predicts the vertical transition energies to all ¹A' excited states to be much larger, compared to the corresponding EOM-CCSD values. Another calculation using larger active space (6,7), which consists of 7 active orbitals and 6 active electrons, were performed to see the effects of increasing the active space. This large active space results in the change in relative order of the two lowest excited states, unlike the case of 2-naphthol. It is difficult to discern the nature of the 2 ¹A' and 3 ¹A' states since these two states have mixed characters of ¹L_a and ¹L_b. Nevertheless, since the 3 ¹A' state has a distinct contribution of HOMO → LUMO transition, the 3 ¹A' state may be assumed to have more ¹L_a character and the 2 ¹A' state to have more ¹L_b character, in agreement with the assignment of EOM-CCSD. However, the spacing between these two states is determined to be too small with MCQDPT2(6,7), although the vertical transition energies to the 2 ¹A' and 3 ¹A' states decrease significantly with large active space. The reason for this discrepancy is not clear since the corresponding energy spacings predicted for 2N8S and 2N68S are quite reasonable.

TDDFT calculations using the B3LYP functional for 2N6S produced quite different electronic structure from those obtained by ab initio calculations. This is mainly due to the fact that DFT calculated molecular orbitals have different orders in energy than that of HF molecular orbitals: while the orbital localized on the SO₃^– group corresponds to HOMO–2 for HF molecular orbitals as shown in Fig. 3, this orbital, denoted as π'_H in Table 3, corresponds to HOMO for both functionals. Accordingly, the B3LYP functional predicts that the lowest excited 2 ¹A' state is attributed to excitation from this orbital and the next 3 ¹A' state is resulted from HOMO–1 → LUMO excitation of ¹L_a character. Also, the vertical transition energies of excited states of both A' and A'' symmetries are calculated to be notably smaller, compared to other methods.

On the other hand, the ωB97X-D functional results in much larger vertical transition energies and a different order in the excited states than B3LYP. The 2 ¹A' excited state resulted from HOMO–1 → LUMO excitation of ¹L_a character is predicted to be lower than the 3 ¹A' state of ¹L_b character. in contrast to the EOM-CCSD prediction. The spacing of ~0.45 eV between the two states is also seen to be too small, compared to experiment. The third 4 ¹A' state resulted from excitation of localized SO₃^– orbital, the same as the EOM-CCSD result. As in the case of 2-naphthol, the ωB97X-D functional is not quite successful in reproducing the excitation energies of the ¹L_a and ¹L_b states, and this suggests that the nature of these states may require a careful choice of DFT functional.

Table 4 presents the excited state calculations for 2N8S. The relevant π molecular orbitals of 2N8S are very similar to those of 2N6S (See Fig. S1). However, the π_H-2 orbital is slightly different from the corresponding orbital of 2N6S in that it is not quite localized on the SO₃^– group. The present calculations suggest that the electronic structure of 2N8S is not much different from that of 2N6S. The vertical transition energies, oscillator strengths, and MO contributions to excited states determined by each computational method are in line with the results obtained by the same method for 2N6S.

The vertical transition energy to the lowest excited state of 2N8S by EOM-CCSD is larger by ~0.4–0.5 eV than the experimental absorption maxima.^5c There is no information available on the second excited state of 2N8S. The energy spacing between the two lowest states by EOM-CCSD is seen to decrease slightly, compared to that of 2N6S. Upon examination of EOM amplitudes and oscillator strengths, the 2 ¹A' state appears to have ¹L_b character, while the 3 ¹A' state has a distinct ¹L_a character with a significantly large HOMO → LUMO contribution. Especially notable is that the oscillator strength of the 3 ¹A' state increases considerably, compared to the corresponding 3 ¹A' state of 2N6S.

MCQDPT2(6,7) calculations for 2N8S using large active space produce quite consistent results with the EOM-CCSD method. Although the vertical transition energies to the 2 ¹A' and 3 ¹A' states are determined to be much larger, the energy spacing between these two states is comparable to that of EOM-CCSD. The contribution of HOMO → LUMO transition to the 3 ¹A' state is significantly larger than to the 2 ¹A' state, in parallel with the EOM amplitudes. Therefore, it seems that the MCQDPT2 method using large active space performs much better for 2N8S, in contrast to the case of 2N6S.

As for TDDFT calculations, DFT calculated molecular orbitals have different orders in energy relative to HF molecular orbitals: the orbital localized on the SO₃^– group corresponds to HOMO for B3LYP and to HOMO–1 for ωB97X-D. Because of similar DFT orbital structure to that of 2N6S, TDDFT calculations yield very similar results to those of 2N6S. The B3LYP functional is not able to describe properly the electronic structure of 2N8S, along with very low vertical transition energies. The ωB97X-D functional predicts that the lowest excited state is of ¹L_a character, and the energy spacing between the two excited states is too small.

2N68S molecule has two SO₃^– groups, and the relevant π molecular orbitals are shown in Fig. S2. The basic features of these molecular orbitals are not much different from those of 2N6S or 2N8S. The results obtained for the excited states of 2N68S are presented in Table 5.

Overall, there is no significant changes in electronic structures of the ¹A' excited states of 2N68S, compared to mono-substituted naphthol sulfonates. The spacings between the two lowest ¹A' excited states estimated by both EOM-CCSD and MCQDPT2(6,7) match well the experimental data.^7b EOM-CCSD and MCQDPT2(6,7) calculations show that the first two ¹A' excited states have mixed character of ¹L_a and ¹L_b, but based on larger oscillator strength, the 3 ¹A' state appears to have more ¹L_a character. According to EOM-CCSD calculations, a number of excited states of A'' symmetry are considerably low in energy and thus they are positioned before the 4 ¹A' state.

The TDDFT calculations on the excited states of 2N68S also yield very similar results to those observed in the cases of 2N6S and 2N8S. The B3LYP functional predicts very different electronic structure mostly because of different molecular orbital structure obtained by B3LYP. The ωB97X-D functional predicts the lowest excited state to be of ¹L_a character, in contrast to ab initio methods.

In the present study, the low-lying excited electronic states of 2-naphthol and its sulfonate derivatives, 2N6S, 2N8S, and 2N68S, have been investigated by ab initio and DFT computational methods. The equilibrium structures of the ground states of 2-naphthol and all three sulfonate derivatives optimized at the MP2/6-311++G(2d,2p) level were found to be planar with C_s symmetry.

Although the vertical transition energies of the two lowest ¹A' excited states of 2-naphthol and its sulfonate derivatives predicted by EOM-CCSD are in general higher by ~0.5 eV, compared to experimental absorption maxima, the energy spacings between the two lowest states are in good agreement with experiment, suggesting that the EOM-CCSD method may provide good estimates for the relative order and energy spacings in the excited states. The EOM amplitudes indicate that the two lowest ¹A' excited states of these molecules have mixed characters of both ¹L_a and ¹L_b states. Interestingly, it is seen that the magnitude of oscillator strengths for the 3 ¹A' states of sulfonate derivatives increases or decreases relative that of 2-naphthol, while oscillator strengths of the 2 ¹A' states remain almost the same.

The MCQDPT2 calculations were performed using two different active spaces. The vertical transition energies obtained by MCQDPT2 are found to be considerably larger, compared to EOM-CCSD, but with the large active space (6,7), the transition energies become decreased and the spacings between the two lowest ¹A' excited states are in close agreement with the EOM-CCSD values, except for 2N6S. MCQDPT2 indicates that the two lowest ¹A' excited states of 2-naphthol and sulfonate derivatives have mixed character of ¹L_a and ¹L_b states. For sulfonate derivatives, the state with more ¹L_b character is predicted to be lower in energy than the state of ¹L_a character, consistent with the EOM-CCSD prediction. However, this order is reversed for 2-naphthol, and this deficiency of MCQDPT2 in characterizing the excited states of 2-naphthol should be further investigated.

The TDDFT method is found to have significant limitations in describing the excited states of 2-naphthol and sulfonate derivatives. Especially the B3LYP functional shows very poor performance due to different energy structure of molecular orbitals generated with B3LYP. Although the range-separated ωB97X-D functional improves the results on the excited states of these molecules, it is still predicted that the state of ¹L_a character is lower in energy than the state of ¹L_b character, in contrast to the EOM-CCSD prediction.