Abstract
The geometries of azobenzene compounds are optimized with B3LYP/6-311G* method, and analyzed with nature bond orbital, then their visible absorption maxima are calculated with TD-DFT method and ZINDO/S method respectively. The results agree well with the observed values. It was found that for the calculation of visible absorption using ZINDO/S method could rapidly yield better results by adjusting OWFπ-π (the relationship between π-π overlap weighting factor) value than by the TD-DFT method. The method of regression showing the linear relationship between OWFπ-π and BLN-N (nitrogen-nitrogen bond lengths) as OWF π-π=−8.1537+6.5638BL N-N, can be explained in terms of quantum theory, and also be used for prediction of visible absorption maxima of other azobenzne dyes in the same series. This study on molecules’ orbital geometry indicates that their visible absorption maxima correspond to the electron transition from HOMO (the highest occupied molecular orbital) to LUMO (the lowest unoccupied molecular orbital).
Keywords: Azobenzene compound, Nature bond orbital (NBO), Visible absorption maxima
INTRODUCTION
As one of the most important properties of dyes, the visible absorption maxima have been predicted by quantum theory (Kogo, 1985; Griffiths, 1982; Cheng et al., 1986; Türker, 2002; Machado et al., 2003). Time-dependent density functional theory is popularly used to deal with excited state and to calculate electron spectrum (Liao et al., 2003; Song et al., 2003; Carlo et al., 1999). Azobenzene compound is an important and valuable multi-functional dye with pure chromophoric properties, high molar extinction coefficient, and fine staining qualities. In this study, the visible absorption spectra of azobenzene compounds with the general structure shown in Fig.1 are discussed based on TD-DFT method and ZINDO/S method to obtain applicable results.
Fig. 1.
The general structure of azobenzene dyes
CALCULATION METHOD
All computation in this study was carried out with the Gaussian 98 package. The molecular geometries are optimized by B3LYP method with the 6-311G* basis, and then are analyzed by nature bond orbital (NBO) theory. Finally, the visible absorption maxima are calculated with TD-DFT/6-311G* method and ZINDO/S method respectively. In the process of computation based on ZINDO/S method, the relationship between π-π overlap weighting factor (OWFπ-π) and relevant geometry parameters reveal the change tendency of OWFπ-π.
RESULTS AND DISCUSSION
Geometry optimization
The optimized configurations with B3LYP/6-311G* are shown in Fig.2, and partial data on the optimized parameters are listed in Table 1. The initial geometries are obtained with PM3 method based on Hyperchem 7 package.
Fig. 2.
The optimized geometries based on B3LYP/6-311G* method
Table 1.
Partial data on optimized geometry parameters
| Compound | Substituent |
BLN-N (Å)a | CN15b | ||||
| R1 | R2 | R3 | R4 | R | |||
| 1 | H | H | H | H | CH2CH3 | 1.3092 | −0.7085 |
| 2 | CN | H | H | H | CH2CH3 | 1.3019 | −0.7076 |
| 3 | NO2 | H | H | H | CH2CH3 | 1.3036 | −0.7071 |
| 4 | SO2CH2COOH | H | H | H | CH2CH3 | 1.2971 | −0.6226 |
| 5 | CH=C(CN)2 | H | H | H | CH2CH3 | 1.3033 | −0.6662 |
| 6 | CHO | H | H | H | CH2CH3 | 1.3008 | −0.7078 |
| 7 | CN | CN | H | H | CH2CH3 | 1.2983 | −0.6727 |
| 8 | NO2 | H | CN | H | CH2CH3 | 1.3027 | −0.6817 |
The length of nitrogen-nitrogen bond
The net charge on N15
Table 1 shows that nitrogen-nitrogen bond lengths (BLN-N) are all shorter than those of common nitrogen-nitrogen single-bond (about 1.4 Å) but longer than those of double-bond (about 1.2 Å), which is attributed to the conjugation of the system. The average net charges on nitrogen of the diethylamine are negative.
Nature bond orbital analysis
Nature bond orbital analysis provides an efficient method for studying intermolecular bonding and interaction among bonds, and also provides a convenient basis for investigating charge-transfer or conjugative interaction in molecular systems (Alan et al., 1988; Carpenter and Weinhold, 1988; Yi, et al., 1994). Some electron donor orbitals, acceptor orbitals and the interacting stabilization energy resulted from the second-order micro-disturbance theory are listed in Table 2. The larger the E value, the more intensive is the interaction between electron donors and electron acceptors, i.e. the more donating tendency from electron donors to electron acceptors and the greater the extent of conjugation of the whole system. The analysis results of stronger electron donor diehylamine and its adjacent bonds whose E values are the largest among them are shown in Table 2. The serial number of atoms is the same as those shown in Fig.2.
Table 2.
Part of calculated results by NBO analysis
| Compound | Donor | Acceptor | E (kJ/mol) |
| 1 | LPa N15 | BD*b C6-C7 | 179.23 |
| 2 | LP N15 | BD* C5-C6 | 210.28 |
| 3 | LP N15 | BD* C6-C7 | 229.71 |
| 4 | LP N15 | BD* C6-C7 | 224.82 |
| 5 | LP N15 | BD* C6-C7 | 250.05 |
| 6 | LP N15 | BD* C5-C6 | 217.23 |
| 7 | LP N15 | BD* C6-C7 | 232.64 |
| 8 | LP N15 | BD* C6-C7 | 258.40 |
The lone pair electron
2-center antibond
As shown in Table 2, when there are electron accepting groups on the benzene ring (compounds 2–8), the stabilizing energy E between the lone pair electron N15 and carbon-carbon bond of the adjacent benzene ring is larger than those of without electron acceptors (compound 1). Furthermore, the greater electron accepting ability the acceptor has, the larger the E value is, i.e. the more intensive is the system delocalization, the greater is the extent of the system conjugation.
Visible absorption maxima
On the basis of the optimized geometries above, their visible absorptions are calculated by ZINDO/S method and B3LYP/6-311G* of TD-DFT method, respectively. Yuan et al.(2003) found that satisfactory results could not be obtained with fixed OWFπ-π value in the course of predicting visible absorption maxima of phthalocyanine compounds by ZINDO/S method. Whereas, the results agree well with experiment results if appropriate OWFπ-π value is selected. The observed and calculated visible absorption maxima of these compounds (Lü et al., 1993; Pan and Wang, 1994; Cheng et al., 1989) in this study are given in Table 3. Showing by comparison that although the obtained visible absorption maxima with TD-DFT method and ZINDO/S method are both consistent with observed values, the results with ZINDO/S method are closer to experimental data. Therefore, for computation of visible absorption maxima, the results by semi-empirical ZINDO/S method could be more precise in much shorter time by adjusting appropriate OWFπ-π value than those of TD-DFT method.
Table 3.
Observed visible absorption maxima and corresponding calculated results
| Compound | λobs (nm)a | λcal (nm)b | ZINDO/S |
|
| OWFπ-π | λcal (nm)c | |||
| 1 | 415 | 419.12 | 0.443 | 415.41 |
| 2 | 468 | 475.43 | 0.391 | 468.21 |
| 3 | 486 | 493.62 | 0.402 | 485.37 |
| 4 | 487 | 495.07 | 0.363 | 487.57 |
| 5 | 535 | 541.85 | 0.398 | 532.54 |
| 6 | 473 | 479.32 | 0.387 | 472.86 |
| 7 | 500 | 509.77 | 0.368 | 500.10 |
| 8 | 536 | 544.91 | 0.393 | 534.95 |
The observed visible absorption maxima
Calculated visible absorption maxima based on TD-DFT method
Calculated visible absorption maxima based on ZINDO/S method with adjusted OWF π-π value
The relationship between OWFπ-π and configuration parameters
To determine the relationship between OWFπ-π and configuration parameters, the method of stepwise regression was used for correlating OWFπ-π value with BLN-N, C N15 etc. showing that BLN-N has the best linear relationship with OWFπ-π just as in Eq.(1) and Fig.3 show, and that the coefficient R is 0.9939.
| OWFπ-π=−8.1537+6.5638BLN-N | (1) |
Fig. 3.
The relationship between OWF π-π and BL N-N
Fig.3 shows that the relationship between OWFπ-π and BLN-N is excellent. It is indicated in Eq.(1) and Fig.3 that the OWFπ-π value rises with the increase of BLN-N. In terms of quantum theory, the more single bond and less double bond properties the nitrogen-nitrogen bond has, i.e. the longer the BLN-N is, the greater is the conjugation of the molecular system, and the greater is the OWFπ-π value.
Electron transition
The absorption spectra of organic compounds stem from the ground-excited state vibrational transition of electrons. Calculations of molecular orbital geometry show that the visible absorption maxima of this kind of azobenzene dye correspond to the electron transition from HOMO to LUMO. The composition of HOMO and HUMO calculated by ZINDO/S method for the eight compounds mentioned above are listed in Table 4 on the percentage of the contribution of component atoms (values less than 1.5 have been excluded for the sake of simplicity). The serial numbers of atoms are consistent with those shown in Fig.2.
Table 4.
The %contribution of component atoms to HOMO and LUMO
| Compd. |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
||||||||
| Orbital | HOa | LUb | HO | LU | HO | LU | HO | LU | HO | LU | HO | LU | HO | LU | HO | LU |
| N1 | 18.1 | 16.1 | 10.4 | 15.7 | 6.1 | 15.8 | 13.2 | 13.6 | ||||||||
| N2 | 4.6 | 17.1 | 4.5 | 11.2 | 4.2 | 7.6 | 4.3 | 10.5 | 4.5 | 3.2 | 4.5 | 11.3 | 4.5 | 7.3 | 4.4 | 5.8 |
| C3 | 16.6 | 6.2 | 16.7 | 2.6 | 16.9 | 1.6 | 16.9 | 2.3 | 16.7 | 16.7 | 2.8 | 16.8 | 16.9 | |||
| C4 | 1.9 | 6.5 | 1.7 | 4.2 | 1.2 | 2.7 | 1.4 | 3.9 | 1.6 | 1.7 | 4.3 | 2.9 | 2.5 | |||
| C5 | 9.7 | 10.1 | 10.8 | 10.5 | 10.1 | 9.9 | 10.4 | 10.6 | ||||||||
| C6 | 8.4 | 10.4 | 7.9 | 5.7 | 7.2 | 3.6 | 7.6 | 5.2 | 7.7 | 8.1 | 5.8 | 7.4 | 3.5 | 7.0 | 2.8 | |
| C7 | 8.9 | 9.3 | 10.2 | 9.8 | 9.5 | 9.3 | 9.8 | 10.1 | ||||||||
| C8 | 2.1 | 6.1 | 1.7 | 3.9 | 2.5 | 1.5 | 3.8 | 1.7 | 3.9 | 1.5 | 2.8 | 2.5 | ||||
| C9 | 7.7 | 13.6 | 19.3 | 16.1 | 9.8 | 13.1 | 15.3 | 21.1 | ||||||||
| C10 | 5.9 | 5.87 | 3.9 | 5.5 | 2.1 | 5.0 | 2.1 | 3.8 | ||||||||
| C11 | 4.25 | 8.4 | 5.9 | 5.5 | 4.4 | 8.4 | 10.3 | |||||||||
| C12 | 1.6 | 9.9 | 14.85 | 15.8 | 14.9 | 7.9 | 12.9 | 19.6 | 15.8 | |||||||
| C13 | 3.85 | 8.4 | 5.6 | 5.3 | 3.9 | 3.9 | ||||||||||
| C14 | 6.4 | 6.34 | 3.9 | 5.3 | 2.6 | 6.3 | 10.3 | 7.3 | ||||||||
| N15 | 35.7 | 1.5 | 37.4 | 40.5 | 39.2 | 33.7 | 37.0 | 38.6 | 39.8 | |||||||
| C20/N20/S20 | 3.25 | 14.9 | 11.0 | 2.3 | 14.0 | 31.6 | ||||||||||
| C21/O21/N21 | 14.21 | 2.7 | 5.7 | 17.1 | 14.1 | 12.2 | 2.1 | |||||||||
| C22/O22 | 5.3 | 1.5 | 1.9 | |||||||||||||
| N23/C23 | 15.2 | |||||||||||||||
| C24/N24 | 11.6 | |||||||||||||||
| N25 | 4.8 | |||||||||||||||
HOMO, the highest occupied molecular orbital
LUMO, the lowest unoccupied orbital
Table 4 shows that the composition of HOMO and LUMO of compounds 1–8 is quite similar. HOMO is mainly composed of N15 and the atoms on the adjacent benzene ring, and LUMO generally consists of atoms on the other benzene ring and the electron accepting groups on it. From HOMO to LUMO, the contribution of atoms in the region around N15 and the adjacent benzene ring reduce obviously, while those around the other benzene ring and the substituent groups on it increase. Therefore, it can be concluded that visible absorption maxima of azobenzene dyes correspond to electron transition from regions around N15 and the adjacent benzene ring to those around another benzene ring and its substituent groups.
This kind of azobenzene dyes is a typical chromophoric system of electron donors and acceptors, with the main electron donor being, the N15 on the amine group and the main electron acceptor being comprised of the electron-accepting groups on another benzene ring. If there are electron-accepting groups on the azobenzene system with electron donors, the chain of system conjugation is extended, and the asymmetry of the whole dye molecular system is strengthened, so the excited energy is decreased, and the electron transition from HOMO to LUMO is facilitated and consequently leads to a bathochromic shift. This result is consistent with the results from NBO analysis. This is why the compounds without electron accepting groups on the benzene ring of the diazo group have shorter maximum absorption wavelength than others.
Prediction of visible absorption maxima
To illustrate the validity of the results obtained above, visible absorption maxima of some other azobenzene dyes in the same series are calculated. With B3LYP/6-311G* method, the geometries are optimized and the values of BLN-N are obtained. Then the values of OWFπ-π are obtained according to Eq.(1). Subsequently, the visible absorption maxima are calculated with ZINDO/S method. The results are shown in Table 5, together with directly calculated results by TD-DFT method and observed values (Lü et al., 1993; Pan and Wang, 1994; Cheng et al., 1989). Table 5 showing that the calculated results with ZINDO/S method is consistent with those observed, implies the good applicability of Eq.(1).
Table 5.
The observed visible absorption maxima and corresponding predicted results
| Substituent |
λobsa (nm) | λcalb (nm) | ZINDO/S method |
||||||
| R1 | R2 | R3 | R4 | R | BLN-N (Å)c | OWFπ-πd | λcal (nm) | ||
| CN | H | CN | H | CH2CH3 | 515 | 526.36 | 1.2981 | 0.367 | 512.07 |
| SO2CH2COOH | H | H | NHCOCH3 | CH2CH3 | 495 | 503.21 | 1.2982 | 0.368 | 502.10 |
| OCH3 | H | H | C3H6OCH3 | CH2CH2CN | 480 | 488.52 | 1.3044 | 0.408 | 487.76 |
The observed visible absorption maxima
Calculated visible absorption maxima based on TD-DFT method
The length of nitrogen-nitrogen bond
OWFπ-π value calculated by Eq.(1)
CONCLUSION
Gaussian 98 package was used to optimize the structures of some azobenzene compounds by B3LYP/6-311G* method. It was found that the stabilizing energy E is larger when there are electron donors on one benzene ring and electron acceptor on another ring, i.e. the extent of system conjugation is more intensive. The visible absorption maxima can be precisely calculated by both TD-DFT method and ZINDO/S method, but better results can be obtained by ZINDO/S method in much shorter time by selecting appropriate OWFπ-π value. The regression method revealed that there is excellent linear relationship between OWFπ-π and BLN-N. The prediction of the visible absorption spectra of some other compounds in the same series successfully proved the calculating method and the relationship obtained above. At the same time, the research on molecular orbital geometry shows that the visible absorption maxima of azobenzene compound correspond to the electron transition from HOMO to LUMO. These are helpful for improving the accuracy of predicting visible absorption maxima of dyes and for revealing the relationship between the visible absorption spectrum and molecular structure.
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