Electronic structure and spectral properties of aurones as visible range fluorescent probes: a DFT/TDDFT study

Abstract

The absorption and emission spectra of aurone and its derivatives 1–4 have been investigated with density functional theory (DFT) and time-dependent density functional theory (TD-DFT). The performance of ten xc-functionals including BLYP, B3LYP, PBE0, BHHLYP, BMK, M06, M06-2X, M06-HF, LC-BLYP and CAM-B3LYP in combination with different basis sets has been analyzed. It turns out that within the selected TDDFT framework, B3LYP and PBE0 emerge as the most efficient functionals for the aurones studied. The experimentally determined spectral properties and substitution effects are well reproduced by calculations, which allowed a detailed assignment and interpretation of the spectra. The results reveal that the lowest energy transitions predominantly correspond to the π → π* transitions between the HOMO and LUMO with charge transfer (CT) character.

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1 Introduction

Aurones (2-benzylidenebenzofuran-3(2H)-ones) are a group of lesser known flavonoids that are structural isomers of flavones (Fig. 1). They are found in vegetables and especially in fruits and flowers where they contribute to their coloration.^1,2 Aurones are biosynthesized from chalcones by the key enzyme aureusidin synthase.³ In addition to their pigmentation role, aurones exhibit a wide variety of biological activities, including antifungal,⁴ antibacterial,⁵ insect antifeedant,⁶ antioxidant,⁷ and anticancer activities.^8,9 Moreover, they have also been described as inhibitors of tyrosinase,^10,11 acetylcholinesterase,¹² hepatitis C virus RNA-dependent RNA polymerase,¹³ histone deacetylase,¹⁴ monoamine oxidase,¹⁵ and ABCG2,¹⁶ and as inducers of NAD(P) H:quinone oxidoreductase 1.¹⁷ In particular, as an important class of organic heterocyclic dyes, aurones exhibit unique photochemical and photophysical properties, which render them useful in a variety of applications such as fluorescent labels and probes in biology and medicine.^18,19

Fig. 1 General structure of aurone, chalcone and flavone molecular scaffolds.

Shanker and coworkers²⁰ recently synthesized four amine-substituted aurone derivatives (Fig. 2) to discover fluorescent probes for biomolecules from new chromophores. The effect of substituents on the absorption and emission properties of the aurone chromophore has been explored and the results shown promising results in the potential application as fluorescent probes. In view of the considerable importance of these compounds and to further develop applications of these systems as fluorescent probes, it is essential to understand fundamentally about the structural and electronic basis of the optical properties of these chromophores.

Fig. 2 Structure and atom numbering of the four studied aurone derivatives.

Nowadays, quantum chemical calculations have been proven to be an important tool for investigation of the relationships between structures and spectral properties of the organic molecules and for the interpretation of experimental results arising from industrial interest and applications. In recent years, TD-DFT has been widely used in electronic transition energy predictions.^21–51 It appears as one of the most successful methods in terms of the balance between the accuracy and the computational cost. Indeed, recent benchmarks performed by several groups have concluded that TD-DFT's average accuracy for low-lying excited-states is in the 0.1–0.3 eV range.^52–55

Recently, Sigalas and coworkers have systematically studied the radical scavenging activity of a series of aurones with hydroxyl substitutions at DFT-B3LYP level.^56,57 The vibrational and electronic absorption spectra of 4′-nitro-aurone have been investigated theoretically (DFT/TD-DFT) and experimentally by Chaitanya et al.⁵⁸ Using the B3LYP/6-311++G (2d,2p) method, Chandraju and Fun have studied the FTIR and NMR spectra as well as some physical properties of 5,6-dimethyl-4′-nitro-aurone.⁵⁹ Despite this, to the best of our knowledge, there has been no report on the use of TD-DFT for the systematic investigation of spectral property of the aurones investigated.

In continuation of our theoretical research on spectral properties of molecules with unique optical properties,^60–63 we decided to study the electronic structure and absorption and emission spectra of aurone and its four aurone derivatives 1–4 (Fig. 2) by DFT and TD-DFT. The aim of the present study is to determine the structural and electronic properties of title compounds and to gain insights into the nature of spectra feature observed in the experiments. The relationship between structure and spectra as well as the effects of substitution on electronic spectra are discussed. From a theoretical point of view, it is valuable to use a computational design to predict the spectral properties before designing and synthesizing new chromophores as fluorescent probes.

2 Computational methods

All calculations have been performed with the Gaussian 09 suite of program.⁶⁴ The ground-state (S₀) geometry of each molecule has been fully optimized with default thresholds on residual forces and displacements. Subsequently, vibrational frequencies were calculated analytically at the same level of theory as in the previous step to verify the optimized structure. After the ground-state geometry optimization, the absorption spectrum of each molecule has been computed with TD-DFT formalism. The first excited-state (S₁) geometrical optimization was performed using the TD-DFT method. Fluorescence emission energies were computed from TD-DFT calculations based on the optimized geometry of the lowest excited state.

The performance of different DFT functionals in combination with different basis sets was explored. The vertical absorption energy have been computed employing a wide panel of exchange–correlation (xc) functionals, including pure GGA functional (BLYP),⁶⁵ global hybrid functionals (B3LYP,^65,66 PBE0,^67,68 BHHLYP⁶⁹), global hybrid meta GGA functionals (BMK,⁷⁰ M06, M06-2X and M06-HF),⁷¹ and recent long-range corrected and range-separated hybrids functionals (LC-BLYP^65,72 (ω = 0.47 bohr⁻¹) and CAM-B3LYP⁷³). To account for the solvation, the TD-DFT calculations have been combined with polarizable continuum model (PCM),^74,75 which has emerged as the effective tools to treat bulk solvent effects for both the ground- and excited-states.

3 Results and discussions

3.1 Ground and excited state geometries

The ground-state (S₀) geometry of the five aurones was optimized at the PBE0/6-311G(d,p) approach which has been applied successfully in the study of chalcones^60–63 and indigoids.⁵⁴ This computational model was further evaluated by comparing gas-phase optimized bond length and bond angle values with experimental ones (XRD) reported in the literature for Z-2-p-methoxyaurone.⁷⁶ Some selected parameters are listed in Table S1 in ESI.† It can be seen from Table S1† that the PBE0/6-311G(d,p) method is reasonably accurate in predicting geometrical parameters. The computed mean absolute error (MAE) for the bond lengths and angles is only 0.008 Å and 0.46°, respectively. As shown in Table S2 in ESI,† the differences between gas-phase and solvated (ethanol) geometries are very small. For instance, the MAE of bond lengths and bond angles for aurone are 0.001 Å and 0.1°, respectively. Therefore, we have selected the gas-phase PBE0/6-311G(d,p) for determining the ground-state structural parameters.

Both E- and Z-isomers of aurones can be found in nature, although the latter is much more abundant. According to our calculation, Z-isomers are more stable than E-isomers with energy differences of 3.07 kcal mol⁻¹ (aurone), 2.43 kcal mol⁻¹ (1), 2.55 kcal mol⁻¹ (2), 2.32 kcal mol⁻¹ (3) and 2.09 kcal mol⁻¹ (4). The thermodynamic stability of both isomers is similar, which can be one of the reasons for their simultaneous rise in nature. Our DFT calculations resulted in a planar geometry for Z- and E-isomers of all five aurones. Comparing the calculated bond lengths and angles of the two isomers for aurone (Table S3 in ESI†), we find that the corresponding values are not very much different, with the largest differences being less than 0.02 Å for bond lengths and 2.1° for bond angles. This indicates that isomerization has little effect on these geometrical parameters.

As observed in Table S4 in ESI,† the corresponding geometrical parameters of Z-aurones are very similar with each other. This indicates that the introduction of substituent has little effect on these geometric parameters. Moreover, the linkage between the benzofuranone system and phenyl ring with average bond lengths of C2–C3 (1.4846 Å), C2–C10 (1.3432 Å), C10–C1′ (1.4415 Å) and C2–O1 (1.3820 Å), suggests that these atoms are highly conjugated, leading to a π-bridge for the charge transfer (CT) between the benzofuranone system and phenyl ring B. According to the calculations, the key backbone of all aurones has a planar structure, while aurone 3 and 4 are not completely planar due to the deviation of amine substituents.

Similar to the ground state, the excited state geometry of the five aurones optimized using the TD-PBE0 method also adopt a planar structure, with the exception of some deviation from the plane in the amine substituents. It was noted that some notable difference exists in bond lengths and angles between the ground and excited state, especially for the bond angles. Comparison of the key structural parameters list in Table S5 in ESI and Table S4† shows that the bond lengths of excited state are prone to equalization, implying higher degree of conjugation than ground state geometry. The largest change of bond length presents in the central C2=C10 bond and the C3=O11 bond. For instance, upon excitation to the S1 state, the length of C2=C10 and C3=O11 bonds in aurone elongated by about 0.06 and 0.04 Å respectively, while that of the neighboring single bonds (C2–O1, C2–C3 and C10–C1′) shortened by average 0.03 Å. Compared to bond length, bond angles change more distinctly than that of the ground state. Moreover, the bond angles in coumaranone moiety changes more obviously than other parts with the largest deviation of about 2° compared to that of ground state. All of these changes in geometrical parameters serve to rationalize the observed large Stokes shifts.

3.2 Absorption spectra

On the basis of above geometrical study, a systemic evaluation of the performance of computation model on the TD-DFT step was performed based on the calculation of vertical absorption energy λ_max of Z-aurone. First, we evaluated the impact of the selected atomic basis set (BS) because excited-state properties are often significantly BS-dependent. Table 1 gives the λ_max,ab computed using different basis sets for a given geometry.

Table 1 The λ_max,ab (in nm) of Z-aurone obtained with PCM (ethanol)-TD-PBE0/X based on the geometries optimized at the PBE0/6-311G(d,p) level in gas phase^a

Basis sets (X)	λmax,ab
a The experimental value (in ethanol) is 377 nm.^20b Optimization using PCM model.
6-31G	356.35
6-31G(d)	359.08
6-311G(d,p)	365.57
6-311G(2d,2p)	366.54
6-31+G(d)	370.64(370.78)^b
6-311+G(d,p)	372.49
6-311++G(2d,2p)	373.43

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As shown in Table 1, the 6-311++G (2d,2p) basis set gives the best result relative to experimental value (377 nm). On the contrary, the 6-31G gives the poorest result. The extension of basis set from 6-31G to 6-311G (2d,2p) or from 6-31+G (d) to 6-311++G (2d,2p) leads to an increase in λ_max,ab. Adding extra polarization function to 6-311G (d,p), increases the λ_max,ab by only 1 nm, suggesting that the second set of polarization function is unnecessary. Adding diffuse function to 6-31G (d) or 6-311G (d,p) changes λ_max,ab by +11 nm or +7 nm, respectively, indicating diffuse function is necessary for TD-DFT calculation. From 6-31+G (d) to 6-311++G (2d,2p), the change of λ_max,ab is only 3 nm, while the computational time increases significantly. Therefore we have selected the 6-31+G (d) for TD-DFT calculation because it provides results close to 6-311++G (2d,2p) with much lower computational costs. When solvent effect was added in the geometrical optimization, almost no change of λ_max,ab was observed with respect to the data in gas phase (370.64 vs. 370.78 nm), indicating that the solvent effect has very small impact on the geometrical structure of the aurones.

Next, we investigated the impact of functional on the excitation energies. The results are collected in Table 2. Ten functionals were used for the TD-DFT calculations, including BLYP, B3LYP, PBE0, BMK, BHHLYP, M06, M06-2X, M06-HF, LC-BLYP and CAM-B3LYP. The accuracy of the calculated values was assessed against the experimental data.

Table 2 Comparison between computed and experimental λ_max,ab (in nm) for Z-aurone. The theoretical values are calculated at the PCM (ethanol)-X/6-31+G(d)//PBE0/6-311G(d,p) level

Functional	λmax,ab	f
a Ref. 20.
BLYP	433.42	0.3322
B3LYP	379.97	0.5058
PBE0	370.64	0.5396
M06	372.08	0.5650
BMK	345.53	0.6263
BHHLYP	329.78	0.7366
M06-2X	337.76	0.6404
M06-HF	308.08	0.7230
LC-BLYP	311.77	0.7175
CAM-B3LYP	341.06	0.6387
Exp.^a	377

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As shown in Table 2, B3LYP functional gives the most accurate λ_max,ab value, with discrepancy of only 3 nm relative to the experimental data. Hybrid functionals PBE0 and M06 also give a reasonable accurate result; the calculated λ_max are about 6 and 5 nm smaller than the experimental one, respectively. The pure functional BLYP presents too large λ_max,ab (+56 nm), while long-range corrected functionals (LC-BLYP and CAM-B3LYP) and other global hybrids seriously underestimate the λ_max,ab.

Beside aurone itself, we have also applied the same set of functionals for the four aurone derivatives 1–4 (Table 3) in order to provide complete information. For clarity, the calculated λ_max,ab are graphically displayed in Fig. 3. As can be seen from Table 3 and Fig. 3, the conventional global hybrid B3LYP gives the most accurate result compared to experimental values, with mean absolute error (MAE) of only 18.9 nm. The hybrids PBE0 and M06 functionals predict λ_max,ab with accuracy similar to that obtained at B3LYP level, with MAE of 25.4 and 27.7 nm, respectively. The similar accuracy between PBE0 and M06 can be rationalized by the comparable amount of HF-like exchange (25 versus 27%), which is the dominating factor for the performance of standard hybrid functional.⁷⁷ On the contrary, poor results were obtained using all other functionals, especially for LC-BLYP and M06-HF functionals. LC-BLYP and M06-HF dramatically underestimate the λ_max,ab with a MAE of up to 102 and 100 nm with respect to experimental values. In fact, it has been shown that M06-HF significantly overestimates the vertical transition energies for π → π* states.⁷⁸

Table 3 Comparison of calculated and experimental absorption maxima λ_max,ab (nm) in ethanol for aurone derivatives 1–4 at the PCM-X/6-31+G(d)//PBE0/6-311G(d,p) level^a

Functional	1		2		3		4		MAE^b
	λmax,ab	f	λmax,ab	f	λmax,ab	f	λmax,ab	f
a From ref. 20 in ethanol.b Mean absolute error of λmax,ab.
BLYP	459.97	0.7917	479.68	0.7126	548.20	0.7857	541.10	0.7929	46.7
B3LYP	404.08	0.9366	421.59	0.8667	478.63	0.9612	474.06	0.971	18.9
PBE0	393.84	0.9726	413.98	0.9191	463.63	1.0159	460.04	1.0256	25.4
M06	393.17	0.9629	408.92	0.8946	459.99	0.9921	456.02	1.0017	27.7
BMK	366.42	1.0442	382.06	0.9823	430.71	1.1106	429.22	1.1114	55.0
BHHLYP	348.63	1.1197	361.88	1.0442	402.22	1.1717	401.52	1.1640	76.9
M06-2X	357.51	1.0431	373.27	0.9829	417.17	1.1182	419.17	1.1075	64.8
M06-HF	324.51	1.1081	338.82	1.0456	376.36	1.2017	382.17	1.1697	99.8
LC-BLYP	326.07	1.1009	337.60	1.0671	369.26	1.2355	374.08	1.2032	102.0
CAM-B3LYP	358.49	1.0388	371.94	0.9962	412.53	1.1431	414.5	1.1265	66.1
Exp.	395		441		501		515

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Fig. 3 Comparison between the calculated and experimental λ_max,ab.

As can be seen from Fig. 3, the λ_max,ab decrease gradually with increasing HF exchange percentage from B3LYP (20%) to M06-HF (100%) method, although the trend between M06 and PBE0 are sometimes an exception. On the other hand, the oscillator strengths also increase gradually with increasing HF exchange percentage. These phenomena were also observed in previous studies, i.e., increasing the HF exchange ratio in the global hybrids yields smaller absorption maxima.^54,79–81

As shown in Tables 2 and 3 and Fig. 3, all functionals provide almost the same trend of the change of excitation energies for all compounds, which is in good agreement with experimental results. It was noted that the experimental observed weak red shift (only 14 nm) of λ_max,ab from 3 to 4 was not correctly reproduced by computation using pure GGA and conventional hybrid functionals. This can be attributed to the charge transfer character of the main electronic transitions in aurones 3 and 4. Indeed, the two hybrid meta-GGA functionals (M06-2X, M06-HF) and two long-range corrected functionals (LC-BLYP and CAM-B3LYP) reproduced this trend well. Despite the somewhat poor performance in description of the weak spectral shift, hybrid functionals PBE0 and B3LYP behave well in predicting the absorption maximum with MAE of only 25 nm (0.15 eV) and 19 nm (0.11 eV), respectively, in agreement with the level of accuracy expected at these levels of theory.²² Concerning the oscillator strengths (f), the highest oscillator strength is found for 4 and the lowest for aurone, which is consistent with the experimental results. As a whole, considering the accuracy and consistency, the following discussion are mainly based on the results obtained at the PCM-TD-PBE0/6-31+G(d) level.

Structurally, aurone and its derivatives 1–4 have the classic donor–acceptor π conjugate (D–π–A) characteristic with the electron deficient coumaranone moiety (A) linked to the electron donating ring B (D). As shown in Table 4, introduction of electron-donating amine substituents results in an obvious red-shift of λ_max,ab. The amine substituent (2) extends the λ_max,ab of the parent compound by about 43 nm into the visible region of the spectrum. The amide group (1) evokes the least red shift (only 23 nm) compared to parent aurone due to the fact that the nitrogen atom is bonded to the electron withdrawing carbonyl. Aurone 3 has considerably larger red shift relative to 2 (50 nm in ethanol). This might be due to the rigid ring structure in 3, which limits the free rotation of the N–C bond in amine, and then enhances the electron-donating ability of the amine.⁸²

Table 4 Calculated absorption wavelength λ_ab (eV, nm), main configuration and oscillator strength (f) for the studied aurones at the PCM-TD-PBE0/6-31+G(d) level

Molecule	Exp.^a	λab (eV/nm)	f	Configuration
a Ref. 20, in methanol.b Ref. 83, in ethanol.
Aurone	379 (4.06)^b	3.35/370.6 (S1)	0.5396	H → L (81%)
	316 (4.27)^b	3.92/316.3 (S3)	0.3463	H−1 → L (90%)
	279 (3.85)^b	4.56/272.1 (S5)	0.0965	H−4 → L (88%)
	251 (4.10)^b	5.01/247.6 (S6)	0.2325	H → L+1 (88%)
1	395 (4.09)	3.15/393.8 (S1)	0.9762	H → L (83%)
		3.75/330.8 (S3)	0.1433	H−1 → L (92%)
		4.55/272.4 (S5)	0.1462	H−4 → L (88%)
		4.71/263.3 (S7)	0.2854	H → L+1 (87%)
2	442 (4.33)	2.99/414.0 (S1)	0.9191	H → L (82%)
		3.77/328.5 (S3)	0.0391	H−1 → L (90%)
		4.58/270.9 (S5)	0.1443	H → L+1 (76%)
		4.65/266.6 (S6)	0.1733	H−4 → L (80%)
		4.75/261.1 (S7)	0.1595	H → L+2 (64%)
3	503 (4.15)	2.67/463.6 (S1)	1.0159	H → L (82%)
		3.73/332.6 (S3)	0.0228	H−1 → L (87%)
		4.20/295.1 (S5)	0.0772	H → L+1 (73%)
		4.36/284.5 (S6)	0.2126	H → L+2 (66%)
		4.56/272.1 (S7)	0.1740	H−4 → L (69%)
4	518 (4.34)	2.70/460.0 (S1)	1.0256	H → L (81%)
		3.49/354.9 (S2)	0.0062	H−1 → L (93%)
		4.20/295.2 (S5)	0.1225	H → L+1 (86%)
		4.54/273.4 (S6)	0.1475	H−4 → L (74%)
		4.55/272.7 (S7)	0.1423	H → L+3 (44%)
				H → L+2 (39%)

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It can be seen from Table 4 that there are four main absorption peaks for all studied aurones, being in line with the experimental results.^20,83 The first and the highest intensity absorption peak corresponds to the electronic transition from S₀ state to the higher energy S₁ state, in the range of 370–464 nm depending on the structures. The lowest lying singlet excited states for all title compounds comprise mainly an electronic transition from the highest occupied molecular orbital (HOMO, H in Table 4) to the lowest occupied molecular orbital (LUMO, L in Table 4), accounting for >80% of the total. The other two less intense peaks, in range of 316–355 nm and 248–295 nm, originate from H−1 → L and H → L+1 transitions, respectively. The fourth peak at about 270 nm is mainly due to H−4 → L transition, but H → L+2 and H → L+3 are also involved for aurones 2–4.

The electron density plots of these frontier molecular orbitals along with the HOMO and LUMO orbitals are depicted in Fig. 4 and S1 in ESI.† In general, the major frontier molecular orbitals demonstrate a typical π-type molecular orbital character. For parent molecule aurone, both the HOMO and LUMO are delocalized on the whole molecule, representing a typical π → π* transition. In the case of aurones 1 and 2, the HOMOs are mainly localized on benzene ring B, furanone moiety as well as the substituents, whereas the LUMOs are outspreaded on the whole molecule with a smaller contribution on substituents. Compared to aurone, the electron density in HOMOs of aurones 1 and 2 tend to accumulate on the donor portion (D) of the molecule, while those of LUMOs on the acceptor portion (A). Such trend is reflected more obviously in aurones 3 and 4. As shown in Fig. 4, the benzene ring A in coumaranone moiety almost give no contribution to HOMOs, whereas the benzene ring B present less contribution to LUMOs than that of 1 and 2. Clearly, the electron promotion from HOMO to LUMO in aurones 1–4 is accompanied by charge transfer from the donor moiety (D) to the acceptor group (A), so that the HOMO–LUMO transition has a mixed π → π* and CT character. This conclusion is confirmed by the natural transition orbital (NTO) analysis⁸⁴ (Fig. S2 in ESI†). As shown in Fig. S2,† the largest natural transition orbital eigenvalue for all compounds are larger than 0.99, indicating that the dominant excitation pair shown in Fig. S2† account for over 99% of the lowest energy transition. Clearly, the electron promotion is accompanied by charge transfer from the donor moiety (electron) to the acceptor (hole), especially for aurones 2–4.

Fig. 4 Electron density plots of the frontier molecular orbitals for S₀ state of the title compounds (isocontour value 0.02 au).

As far as the HOMO−1 is concerned, aurone and derivatives 1–2 present similar electron density distribution with each other, while different distribution was observed in the case of aurones 3–4. For aurone 3, the electron density is mainly localized on the benzene ring A and with little contribution from benzene ring B and amine N, while opposite distribution is presented in 4, in which the electron density is mainly centered on benzene ring B and amine N. As for LUMO+1, all the cases show similar electron density distribution with the corresponding LUMO. As shown in Fig. S1,† HOMO−4 in aurone and 2 are primarily localized on the benzene ring A and carbonyl group, whereas in aurones 3 and 4, the HOMO−4 mainly centered on the benzene ring A, central C=C bond, part of the benzene ring B and the amine N atom. Contrary to others, the HOMO−4 of aurone 1 presents unique character, which consist of the n-orbital of the amide group.

As stated above, E- and Z-isomers of aurones can coexist in solution at normal condition. Thus, the absorption maxima of E-isomers of aurones (Table S6 in ESI†) were also calculated for comparison. The results show that the two isomers present similar spectral properties. E-isomers present slightly longer wavelength absorption than Z-isomers, with the discrepancy of 8–13 nm depending on the structure. Moreover, the oscillator strengths of absorption maxima are significantly smaller for E-isomers than that of Z-isomers. These results are consistent with the experimental observation.

3.3 Emission spectra

The vertical emission energies of the five aurones have also been investigated using the TD-PBE0 method in their excited-state (S₁) optimized structure. The calculated emission energies, oscillator strength, transition character of the aurones using PBE0/6-31+G(d) are summarized in Table 5. As can be seen from Table 5, the computed emission maxima λ_max,em are in good agreement with experimental data for all compounds. The largest variation of vertical transition energy between calculation and experiment is less than 0.21 eV. Moving from parent aurone to aurone derivatives 1–4, there is an obvious red-shift for λ_max,em with introduction of amine substitutions, which are similar with that of absorption maxima. At the same time, the oscillator strength f increases from aurone to aurones 1–4. These trends are all consistent with the experimental results. The red-shift of λ_max,em can be explained by the fact that the lone electron pair of nitrogen in amine group join in molecular conjugation, which makes the conjugated-system of molecules become larger as shown in following FMOs.

Table 5 Calculated emission maxima λ_max,em, main configuration, oscillator strength (f) and stokes shift for the studied aurones at the PCM (ethanol)-TD-PBE0/6-31+G(d) level

Molecule	Exp.^a	λmax,em (eV/nm)	f	Assignment	Stokes shift (nm)
a Ref. 20.
Aurone	—	2.83/438.8	0.8748	L → H (99%)	68
1	482	2.62/473.0	1.2579	L → H (100%)	79
2	540	2.51/494.8	1.1514	L → H (100%)	81
3	580	2.29/541.2	1.2331	L → H (100%)	78
4	584	2.30/539.6	1.2316	L → H (100%)	80

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Stokes shift, the difference between the absorption and emission maxima, is a distinct characteristic of each fluorophore. Large Stokes shift is an important criterion for an ideal fluorescent probe. Commercially available fluorophores such as rhodamine, fluorescein, cyanines and boron dipyrromethenes usually have small Stokes shifts (typically less than 25 nm), which can lead to serious self-quenching and fluorescence detection errors because of excitation backscattering effects.⁸⁵ As shown in Table 5, all the five studied aurones have significantly larger Stokes shift (up to 81 nm), especially for the aurone derivatives 1–4. This means that these aurones compounds are potentially useful as fluorescent probe.

The computed electronic transitions in S₁ state reveal that the emission process is mainly due to a π* → π transition from LUMO to HOMO. By comparison, the shape of the HOMO and LUMO involved in S₁ state is similar with that of S₀ state (Fig. 4 and 5). The distribution of the FMOs suggests the CT nature of the emission process in aurones 1–4.

Fig. 5 Plots of HOMO (left) and LUMO (right) for the S₁ state of the studied aurones.

Compared to the Z-isomer, the E-isomer of aurones presents longer wavelength emission, with a shift of 10–30 nm depending on the structure. In addition, the oscillator strength of emission for E-isomers is significantly smaller than that of Z-isomers. Indeed, the emission intensity was decreased by irradiation at 400 nm in experiment. Our calculations are in good agreement with the experimental observations.

4 Conclusions

In this work, the structure as well as electronic and optical properties of aurone and its amine-substituted derivatives have been investigated with DFT and TDDFT method. The performance of different xc-funtionals and basis sets has been assessed. The nature of electronic transition has been analyzed and the effects of substitution on the optical properties have also been discussed. The computations are generally in good agreement with experimental observations, and allowed a detailed assignment and interpretation of the spectra.

All the five studied aurones have a planar structural backbone in both the S₀- and S₁-states due to π conjugation. However, the values of bond lengths and angles change significantly upon excitation, which is responsible for the large Stokes shift. The Z- and E-isomers of aurones can coexist due to their little difference of thermodynamic stability. The appearance of less stable E-isomer has slight effect on the geometrical and spectral position, but large influence on the intensity.

Among the tested functionals, hybrid functionals PBE0 and B3LYP behave well in predicting the absorption and emission maxima. The calculated transition energies using PCM-TD-PBE0/6-31+G(d) basis set have good agreement with the experimental findings in general. The calculated results show that introduction of amine substituent gives rise to red shift of λ_max. Acetylation of the amine shifts the absorption and emission maxima to shorter wavelength, while restricting the rotation of the amine nitrogen shifts the absorption and emission maxima to longer wavelength.

The calculations reveal that the lowest energy transitions in aurones 1–4 predominantly correspond to the π → π* transitions between HOMO and LUMO with intramolecular charge transfer (CT) nature. Our results provide a detailed characterization of the absorption and fluorescent properties of aurone and its derivatives.

To sum up, our calculations have provided reasonable results and a useful insight into the optical properties of the aurones. This theoretical information would be very useful in the design of aurone-based chromophores for fluorescent probes in biological applications.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (81202490, 81341084), Jiangsu Key Laboratory of New Drug Research and Clinical Pharmacy (ZR-XY201404), the Priority Academic Program Development of Jiangsu Higher Education Institutions and the Innovative Practice Training Program for Students of Jiangsu Higher Education Institutions (201410313052X). The authors are grateful to Prof. X. D. Gong (Department of Chemistry, Nanjing University of Science and Technology) for providing calculation facilities.

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Footnote

† Electronic supplementary information (ESI) available: The key geometric parameters of title compounds in ground and excited states, natural transition orbitals analysis as well as xyz file giving the Cartesian coordinates for all structures. See DOI: 10.1039/c5ra25733f

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