Theoretical Study on the Electronic Structures and Spectral Properties of 1,8-Naphthalimide Derivatives①

WANG Yn GAO Hui YANG Ping

NIE Guang-Huaa SONG Xin-Jiana, b②

a (Key Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Hubei Minzu University, Enshi 445000, China)

b (College of Forestry and Horticultrue, Hubei Minzu University, Enshi 445000, China)

1 INTRODUCTION

1,8-Naphthalimide derivatives have attracted immense interest owing to their good optical, thermal and chemical stabilities, and the diversity of structure modification[1]. They comprise a special class of fl uorophores and luminophores and are widely used in a number of areas including the coloration of polymers[2], chemosensor[3], biosensor[4], organic light emitting diodes (OLEDs)[5],fl uorescence switchers[6], liquid crystal displays[7],and ion probes[8].

It is reported that 1,8-naphthalimide derivatives substituted at the 4-position with electron-donating groups can increase fl uorescent quantum yields and tune easily the emission wavelengths to longer ranges[5]. A series of 1,8-naphthalimide derivatives were synthesized with substituents in the 4 posi-tion such as N-substituted groups[9,10], C-substituted groups[11,12]and O-substituted groups[13,14].However, there are few studies on the aryloxy substitution at the 4-position of 1,8-naphthalimide.In order to exploit blue emitters with reduced propensity of concentration quenching, rigid phenoxy substituents were introduced into the 4-position of 1,8-naphthalimides, and tert-butyl substituents were introduced at different positions of the phenoxy groups[15].

To the best of our knowledge, theoretical calculation on the absorption and emission spectra is a useful tool to further understand the relationship between structure and property, and it plays an important role in understanding and predicting luminescent properties of organic materials[16-19].Some semi-empirical and DFT calculations have also participated in exploring naphthalimides[20-23]and uncover their electronic properties. In this work, we present a detailed theoretical analysis of the ground state (S0)and the lowest excited state(S1)characters of three 4-phenoxy-1,8-naphthalimide derivatives. Our aim is to investigate the vertical excitation energies for 4-phenoxy-1,8-naphthalimide derivatives in the presence of tertbutyl substituents at different positions of the phenoxy groups and to gain insights on the nature of the spectra feature observed in the experiments.The effects of various basis sets and different functionals on the absorption and emission spectra of 1 have also been studied. We expect that some significant information can be obtained for synthetic design of new functional molecules for applications in OLEDs.

2 COMPUTATIONAL MODEL AND METHODS

Three 1,8-naphthalimide molecules investigated differ mainly in the substituents of C(1)and C(5)(Fig. 1). In order to examine the effects of the basis sets on the absorption and emission spectra,geometry optimizations of the ground (S0)and first excited (S1)states for compound 1 are performed by means of the density functional theory (DFT)with hybrid functional B3LYP[24,25]and configuration interaction singles (CIS)method with ten basis sets, i.e., 6-31G, 6-31G(d), 6-31+G, 6-31+G(d), 6-31+G(d,p), 6-311G, 6-311G(d), 6-311+G, 6-311+G(d), and 6-311+G(d,p). The vertical transition energies are calculated by the TD-DFT methodology using the same basis sets based on the optimized geometries. In view of the excitation energy, calculated results are affected by the choice of functional. Based on the 6-311+G(d,p)basis set, other than B3LYP, three different functionals, PBE0[26], CAM-B3LYP[27], and wB97-XD[28], have also been employed in DFT and TD-DFT calculations for compound 1. The hybrid functional B3LYP, containing 20% Hartree Fock(HF)exchange, the PBE0 functional, whose HF exchange increases to 25%, the CAM-B3LYP and wB97XD functionals are long-range-corrected hybrids functionals. The geometrical and electronic structures of S0and S1for compounds 2 and 3 are optimized by using DFT//B3LYP/6-311+G(d,p)and CIS/6-311+G(d,p)methods, respecttively. For all the optimized geometries, vibrational frequencies are calculated using the same method as the optimization and the absence of imaginary frequencies confirm the stability of the ground state and excited state geometries. Following the optimized S0and S1geometries, the absorption and emission wavelengths are calculated at the TD-DFT//B3LYP/6-311+G(d,p)level.In order to compare our results with those obtained in experiments, we add the solvent effects using self-consistency reaction field (SCRF)theory of model polarizable continuum models (PCMs)[29]in all calculations incorporating chloroform as the solvent. All of our calculations are performed with the Gaussian 09W program[30].

3 RESULTS AND DISCUSSION

3. 1 Computational method investigation:basis set and functional

The fi rst area of research we considered was a comparison of the total energy together with the absorption and emission wavelength of compound 1 obtained using ten basis sets and four functionals.The purpose was to determine the effect of basis sets and functionals on the vertical absorption and emission properties. As expected, the total energy decreases considerably with the increase of the basis set size. The ten basis sets reproduce the experimental absorption wavelengths well, with the largest deviation (±7 nm)calculated by 6-31+G and 6-31G(d)basis sets and the smallest (3 nm)by 6-311+G(d)and 6-311+G(d,p)basis sets. For the emission spectra, the basis sets were observed to affect the wavelengths to a larger extent than the absorption spectra. The largest difference between the calculated and experimental values is 27 nm for 6-31G basis set and the smallest is 10 nm for the 6-311+G(d,p)basis set. It is well known that basis sets have an important effect on the accuracy of calculated results[31]. Usually, diffusion and polarization functions could improve the calculated accuracy. The above results illustrated that 6-311+G(d,p)is more suitable in modeling such systems. Therefore, the calculations for the rest of the systems were carried out using the 6-311+G(d,p)basis set.

The absorption and emission wavelength(λabs/λem), oscillator strength (f), and excitation energy (ΔE)calculated by different functionals are listed in Table 1. From Table 1, it can be seen that the calculated total energy varies as different functionals, whose value is the highest calculated by PBE0 and the lowest by B3LYP. Data in Table 2 also show that increasing the HF exchange ratio in the global hybrids yields lager absorption and emission transition energies, which range from 3.36 eV (B3LYP)to 3.47 eV (PBE0)for absorption and from 2.96 eV (B3LYP)to 3.04 eV (PBE)for emission. Even higher transition energy is found with the wB97XD hybrids (3.79 eV for absorption and 3.21 eV for emission), while the CAM-B3LYP (3.77 eV for absorption and 3.19 eV for emission)shows an intermediate behavior between wB97XD and PBE0. In fact, B3LYP provides transition energies smaller than the experimental observation for absorption, while CAMB3LYP, wB97XD, and PBE0 overestimate the experimental transition energy in the range of 0.08～0.40 eV. But for emission, all the four functionals overestimate the experimental transition energy in the range of 0.06～0.32 eV. The minimal deviation between experimental[15]and calculated values of transition energies, obtained by B3LYP,is –0.03 eV for absorption and 0.06 eV for emission, maintaining the best one and within the typical error bar. Such small discrepancies indicate that the geometry optimization of the S0and S1states in the presence of a solvent is successful,and that the B3LYP functional within the TDDFT method in cooperation with PCM is the best method to reproduce the experimental spectra of these molecules. Therefore, in the rest of the paper,we will discuss the calculations done with the B3LYP functional and 6-311+G(d,p)basis set only.The B3LYP functional, a widely used hybrid functional, has become a standard for DFT calculations on organic molecules in the literature.

Table 1. Absorption and Emission Wavelength (λabs/λem), Oscillator Strength (f)and Excitation Energy (ΔE)of Compound 1 Calculated by Different Functionals

3. 2 Ground state geometries

The bond lengths, bond angles and dihedral angles of compounds 1, 2 and 3 calculated at the B3LYP/6-311+G(d,p)levels listed in Table 2 are consistent with the atom numbering scheme given in Fig. 1. So far, the experimental data of X-ray diffraction for the title compounds are not available in the literature. It is seen from the molecular structure that the molecule consists of two parts, the naphthalimide moiety and the substituted benzene group linked by one O atom. As shown in Table 2, with increasing the tert-buty number at C(1)and C(5)in the phenoxy group, the naphthalimide moieties have almost the same geometric characters including similar bond lengths, bond angles, and dihedral angles. All C–C bond lengths(about 1.40 ?)in the naphthalene ring are between the distance of the normal C–C single bond (1.54 ?)and C=C double bond (1.34 ?). The distances between C(13)and C(14)(1.4807 ? in 1, 1.4808 ? in 2, and 1.4807 ? in 3)and between C(17)and C(19)(1.4725 ? in 1, 1.4727 ? in 2, and 1.4723 ? in 3)are shorter than a normal C–C single bond.The C(14)–N(16)bond distance (1.4023 ? in 1,1.4024 ? in 2, and 1.4023 ? in 3)and C(17)–N(16)bond distance (1.4080 ? in 1, 1.4077 ? in 2, and 1.4079 ? in 3)fall between the normal C=N double bond (1.27 ?)and C–N single bond (1.47 ?). Besides, the dihedral angles between the two phenyl rings (C(9), C(10), C(11), C(12), C(13),C(22); C(8), C(9), C(22), C(19), C(20), C(21))are all close to 180o and the pyridine ring forms dihedral angels close to zero to the former two phenyl rings, indicating the coplanarity of the three rings (naphthalimide moiety)is wonderful[32].

Table 2. Optimized Geometrical Parameters Calculated by the PCM-B3LYP/6-311+G(d,p)Method

Fig. 1. Chemical structures of the investigated 1,8-naphthalimide derivatives

However, with increasing the tert-buty number at C(1)and C(5)in phenoxy, the geometric structure of the phenyl undergoes some changes from each other. For example, the calculated C(2)–C(3)bond length for 2 and 3 is shorter than that in 1,while the C(4)–C(5)and C(5)–C(6)are lengthened.But all the C–C bond distances in the benzene ring(about 1.40 ?)take the typical value of aromatic benzene. It is notable that the dihedral angles between the phenyl and naphthalimide moiety are comparable to those in 2 and 3, and they are different from those in 1. The optimized dihedral angles (C(3)–C(4)–O(7)–C(8)= 93.88° and C(4)–O(7)–C(8)–C(21)= –0.53°)in 1 show the p orbital of the oxygen atom is conjugated with the naphthalimide group but the naphthalimide moiety and the benzene ring are orthogonal with almost no electronic conjugation. However, owing to the introduction of one tert-buty group onto the C(5)atom and two tert-buty groups onto the C(1)and C(5)atoms in the phenoxy moiety, the dihedral angle C(3)–C(4)–O(7)–C(8)decreases to 61.41° in 2 and 67.67° in 3 while C(4)–O(7)–C(8)–C(21)increases to 21.01° in 2 and 19.85° in 3. These simultaneous increase and decrease in dihedral angles predict the conjugation for the p orbital of oxygen atom to the naphthalimide group is decreased and it is partly conjugated with the benzene ring,which results in prolonged conjugation length.

3. 3 Electronic structures

It is useful to examine the HOMO and LUMO of molecules to provide the framework for the excited state. In addition, the relative ordering of the occupied and virtual orbitals provides a reasonable qualitative indication of the excitation properties. To gain insight into the influence of different substitutions, molecular orbital plots(HOMO and LUMO)and HOMO/LUMO energy gaps in S0and S1of these compounds are plotted in Fig. 2. Fig. 2 clearly indicates that, both in S0and S1states, as the substituent number on the phenyl is changed from none (1), one (2), to two (3), the energy levels of LUMO decrease slightly, while the energy levels of HOMO increase significantly.Thus, the HOMO-LUMO energy gaps of 2 and 3 are smaller than 1. The HOMO-LUMO energy gaps of these new dyes obey the following order: 1＞ 2 ＞ 3, which is in good agreement with the measured absorption and emission wavelengths in experiment, in the order of 1 ＜ 2 ＜ 3.

Fig. 2. Molecular orbital plots (LUMO and HOMO)and HOMO/LUMO energy gaps of the S0 and S1 states for compounds 1, 2 and 3

In the S0states of 1, the LUMO and HOMO are located on the naphthalimide group and oxygen atom, and the benzene unit has essentially no contribution to the HOMO/LUMO, which is in good agreement with the structure that the naphthalimide group and the benzene unit are orthogonal with almost no electronic conjugation. The LUMOs are also centralized on the naphthalimide group and oxygen atom as that of 1 for 2 and 3. A remarkable difference, however, is observed in HOMO. Due to the enhanced conjugation between the electrons in the naphthalimide group, oxygen atom and the benzene unit, the HOMOs are delocalized over the naphthalimide group, oxygen atom and the benzene unit in 2 and 3, giving an extended molecular orbital which boosts the stability of the system[33]. The S1orbitals are almost the same as those of S0for all compounds and the overlap between HOMO and LUMO is large.

3. 4 Optical properties

It is well-known that the PCM evaluating solvent effect is a powerful tool to treat the vertical absorption and emission spectra in solvents. At the TD-B3LYP/6-311+G(d,p)level, the absorption and emission spectra of the 1,8-naphthalimide derivatives under chloroform solvent were calculated respectively with SCRF theory of the PCM model.The calculated vertical excitation energies as well as the absorption and emission wavelength associated with their oscillator strengths and configurations are listed in Table 3. Based on this optimized geometry, three lower excited states were calculated and only the S1state mainly corresponding to the HOMO → LUMO transition has high intensity,which is suggested by their large oscillator strength(f)values. The transition energies to these states are found to be 3.36 eV (369 nm), 3.24 eV (383 nm), and 3.17 eV (391 nm)for 1, 2, and 3, respectively, which are in good agreement with the experimental absorption wavelengths, 366 nm for 1, 369 nm for 2, and 374 nm for 3. The wavelengths have a red-shift with the tert-butyl number increasing in the phenoxy group, giving evidence that they have longer conjugation systems, which is in accordance with the optimized geometries and electronic structures.

Table 3. Absorption and Emission Wavelength (λ), Oscillator Strength (f)and Excitation Energy (ΔE)of Compounds 1, 2 and 3 Calculated by PCM-TD-B3LYP/6-311+G(d,p)Relative to the Experimental Data

Our calculations indicate that the maximum emission observed at 429～444 nm in the experiment[15]corresponding to the S1states is mainly related to an electron transition from LUMO to HOMO. The results of TD-DFT calculations are in good agreement with the emission spectra observed experimentally with discrepancies of 10 nm for 1, 6 nm for 2, and 12 nm for 3. The emission wavelengths of 2 and 3 are red-shifted compared with that of 1, conf i rming the enhanced conjugation in the molecules induced by increasing the tert-buty moiety, which is in accordance with the absorption characteristics.

4 CONCLUSION

Four functionals and ten basis sets, in the frame of DFT and TDDFT, were used to study the absorption and emission properties of the 4-phenoxy-N-(2-hydroxyethyl)-1,8-naphthalimide, 1. It was found that the choice of functional has a greater effect than the basis sets on the absorption and emission spectra. In our study, B3LYP functional and 6-311+G(d,p)basis set in combination with the PCM method were a suitable method for the calculation of absorption and emission spectra.The electronic structures together with the absorption and emission spectra of compounds 1, 2 and 3 containing different number of tert-buty groups were investigated by TD-DFT calculation at the B3LYP/6-311+G(d,p)level. The calculated geometric characters indicate that a prolonged conjugation length is formed with the tert-buty number increasing. We also found that the maximum wavelengths of the absorption and emission spectra undergo red-shift from 1 to 2 and 3, which is consistent with the experimental results. Hopefully, this theoretical investigation on the electronic and optical properties of 1,8-naphthalimide-based derivatives could give some hints for the design of more efficient functional materials in OLEDs.

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