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MP2 static first hyperpolarizability of azo-enaminone isomers
Chemical Physics Letters 413 (2005) 356–361 www.elsevier.com/locate/cplett
MP2 static first hyperpolarizability of azo-enaminone isomers T.L. Fonseca a
a,*
, H.C.B. de Oliveira b, O.A.V. Amaral a, M.A. Castro
a
Instituto de Fı´sica, Universidade Federal de Goia´s, Campus II, Caixa Postal 131, 74001-970 Goiaˆnia, Goia´s, Brazil b Departamento de Cieˆncias Exatas, Universidade Estadual de Goia´s, 73807-250 Formosa, Goia´s, Brazil Received 6 July 2005; in final form 26 July 2005 Available online 22 August 2005
Abstract The dipole moment, static linear polarizability and first hyperpolarizability of donor–acceptor azo-enaminone isomers have been calculated with both Hartree–Fock (HF) method and second-order Møller–Plesset perturbation theory (MP2), using the 6-31G and 6-31G+p basis sets. Two structural isomers of substituted azo-enaminones have been studied to point out the first hyperpolarizability geometry-dependencies associated to the type of isomerization. Our results show that the relative orientation of donor groups in chromophores has an important impact on the magnitude of the first hyperpolarizability. 2005 Elsevier B.V. All rights reserved.
1. Introduction Due to potential applications in various photonic technologies, such as optical information processing and telecommunication, the non-linear optical (NLO) properties of organic molecular materials have been object of intense research [1–7]. An important class of NLO molecular materials is formed by donor–acceptor substituted p-conjugated organic molecules. In these molecular systems, the asymmetric polarization induced by incorporation of donor–acceptor groups can enhance the quadratic NLO properties. Previous studies have investigated structure–property relationships for donor–acceptor conjugated molecules [5–7], aiming at designing efficient organic second-order NLO materials. It has been shown, for example, that the combination of electron donor and acceptor strengths, connected to an organic p-delocalized framework, should be optimized in order to maximize the molecular hyperpolarizability of the NLO chromophores. Based on AM1 calculations, the first donor–acceptor azo-enaminones derivatives presented as potential can*
Corresponding author. Fax: +55 62 521 1014. E-mail address: [email protected] (T.L. Fonseca).
0009-2614/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.08.007
didates for application in second-order NLO processes were synthesized from the azo coupling between quinone diazides and acyclic enaminones [8,9]. Recently, new azo-enaminones have been synthesized by coupling of diazonium salts and enaminones and their experimental geometric parameters determined by X-ray diffraction [10–13]. It is also worthwhile stressing that these later azo-enaminone compounds are more flexible, as regards structural modifications, than those synthesized by quinone diazide route. Therefore, due to the delocalization of p-electrons these new compounds present an unusually low rotational barrier around the C@C double bond, giving rise to different geometrical isomers [10]. Structural studies, using multinuclear magnetic resonance revealed that azo-enaminone derivatives can exist in CDCl3 solution in the form of two geometrical isomers (Z and E). The different geometric forms affect the electronic structure of these compounds and, consequently, changes in their physical properties can be expected. In a recent work [14], we have investigated the nonlinear optical properties of these new azo-enaminones with appropriate substituents as well as some azoenaminones studied previously [9]. For the Z isomers of azo-enaminones, HF and MP2 calculations reported
T.L. Fonseca et al. / Chemical Physics Letters 413 (2005) 356–361
by us [14] have suggested that the incorporation of strong donor groups leads to a saturation of the first hyperpolarizability and that substitution effects of the nitro group at the ortho and meta positions gives rise to a marked diminution on the first hyperpolarizability. The purpose of this work is to investigate the impact of structural modifications associated to E isomerization on the NLO properties of p-nitro-azo-enaminones as function of the strength of the electron-donor groups. The model systems are isomers of azo-enaminones with –NO2 as the electron-acceptor group attached at para position of the phenyl ring and –NH2 as the electrondonor group. The strength donor character is varied by the replacement of an H atom of the aminic group by substituents such as –CH3 and –C(CH3)3. The influence of the replacement of –CH3 by –OCH2CH3 [8] on the electric properties of both Z and E isomers considering a representative group of azo-enaminones is also analyzed. The dipole moment, linear polarizability and first hyperpolarizability were calculated at HF and MP2 levels using the analytical (AN) and finite field (FF) approaches. Previous studies, based on MP2 calculations, have been reported showing the importance of the inclusion of electron correlation (EC) effects in order to obtain accurate estimates for the linear and nonlinear polarizabilities of different organic systems [14–22]. Other effects, such as frequency dispersion and nuclear motions, although not considered in this work are expected to play important roles on the calculations of the first hyperpolarizabilities [23,24]. However, previous calculations have shown that the vibrational contributions are usually negligible for second-harmonic generation processes [24].
357
Fig. 1. Molecular structures of the azo-enaminone isomers studied in this work (see also Table 1).
Table 1 Labels of the azo-enaminone isomers presented in Fig. 1 Compounds
Substituents D
X
Y
1A 1B 1C
H CH3 C(CH3)3
OH OH OH
CH3 CH3 CH3
2A 2B 2C
H CH3 C(CH3)3
H H H
CH3 CH3 CH3
3A 3B 3C
H CH3 C(CH3)3
OH OH OH
OCH2CH3 OCH2CH3 OCH2CH3
4A 4B 4C
H CH3 C(CH3)3
H H H
OCH2CH3 OCH2CH3 OCH2CH3
2. Computational details The NLO molecules studied in this work are displayed in Fig. 1 and specified in Table 1. We have used subscripts E or Z to represent the particular type of isomer. In such compounds, the benzene ring and a segment with NN, NC, and CC bonds provides the p-conjugated bridge. For all isomers, the geometries were fully optimized at HF and MP2 levels using the 6-31G basis set. In particular, for the compound ethyl 2-[(E)-5-chloro-2-hydroxy-4-nitro-phenylazo]-3-(E)-amino2-butenoate comparisons with the experimental values determined by X-ray diffraction [8] have shown that there is a good agreement between the HF/6-31G and MP2/6-31G results and the experimental data [14]. The indication that HF/6-31G calculations can provide good estimates of the molecular geometry of these compounds has also been drawn by Abe et al. [25] for heterocyclic pyridinium betaines. Here, the HF components of the permanent dipole moment (li), linear dipole polarizability (ai i) and of
the first dipole hyperpolarizability (bi j k) were calculated analytically using the coupled perturbed Hartree–Fock (CPHF) procedure. At the MP2 level, the calculation of these properties were performed numerically using the FF method. For all azo-enaminone compounds, the MP2 properties were obtained from FF calculations using positive and negative field strengths of the order of 0.001 a.u. At HF level, the numerical and analytical procedures give equivalent results for the dipole moment and polarizabilities, providing a strong indication that the FF numerical procedure is also appropriated to calculate the MP2 NLO properties of azo-enaminones. The values normally measured in experiments are the dipole moment magnitude, l, the average linear polarizability, Æaæ = (axx + ayy + azz)/3, and the the vector component of the first hyperpolarizability along the dipole P moment direction,P bvec ¼ i bi li =l ½i ¼ x; y; z, where bi is given by bi ¼ k bikk ½k ¼ x; y; z. Because of rotational invariance of these quantities, these values do
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not depend on the particular orientation of the coordinate system. The component bvec defined above is the quantity measured in electric field induced second harmonic generation (EFISH) experiments [26–28]. Using the 6-31G, 6-31G+p and 6-31G+d basis sets, the basis set effects on the dipole moment, linear polarizability and first hyperpolarizability of a representative set of azo-enaminones were analyzed in a previous work [14]. This study have shown that the 6-31G+p basis set gives results that are almost identical to those obtained using the 6-31G+d basis set, indicating that the addition of one p or one d diffuse function have an equivalent impact on the improvement of the calculated properties for these NLO molecules. The choice of the exponents of the p or d functions on each heavy atom was determined, at the HF level, by imposing the maximization of the bvec values [29]. This criterion is justifiable because the use of relatively small basis sets tends to underestimate the values of the calculated properties. In this Letter, the study of the basis set influence on the electrical properties is analyzed for both type of isomers by comparing the results obtained using the 6-31G basis set and the 6-31G+p augmented version of this set (extra p functions are added on the heavy atoms). The exponents used in calculations when p extra functions are added on heavy atoms are fp = 0.03 on carbon atoms, fp = 0.04 on nitrogen atoms and fp = 0.07 on the oxygen atom [14]. The electric properties and geometry optimization calculations, at HF and MP2 levels, were performed using the GAUSSIAN 03 [30] electronic structure package.
tence of different geometrical isomers in agreement with experimental observation for similar azo-enaminone compounds [10]. In order to estimate the changes on the bond distances of the p-conjugated segment between donor– acceptor groups with respect to the substituents as well as with the type of isomerization, a selected set of MP2 bond distances are listed in Table 2. The results show that the replacement of –CH3 by –OCH2CH3 practically does not affect the geometry of these compounds. It can be noted that the variations of bond lengths due to the incorporation of different donor groups at the aminic nitrogen (N1) (such as in compounds B and C) or the inclusion of the –OH group at the phenyl ring are, in general, very small, regardless the isomeric form of the azo-enaminones. For example, going from 2AE ! 2BE (2BE ! 2CE), the most significant variations are found for the C2–C4 bond distance with modifica˚ (+0.006 A ˚ ). Going from 2AE ! 1AE, tions of +0.012 A 2BE ! 1BE and 2CE ! 1CE variations of the order of ˚ are predicted for the N5–N6 and C7–C9 bond +0.015 A ˚ are distances, while changes of the order of 0.015 A observed for the N6–C7 bond length. Structural changes related to the type of isomerization have an impact more appreciable on C4–N5, N5–N6 and N6–C7. For these bond lengths, the MP2 results give variations of ˚ , 0.011 A ˚ , +0.007 A ˚ for 2AZ ! 2AE and +0.010 A ˚ , 0.014 A ˚ , +0.011 A ˚ for 2CZ ! 2CE. One +0.014 A can associate the modifications on these later parameters with changes on the degree of p-electron delocalization which in turn can have a beneficial effect on the first hyperpolarizability [5,7]. We can draw a close analogy between the basis set dependence and the electron correlation effects of dipole moment, linear polarizability and first hyperpolarizability of the E isomers with those obtained previously for the Z isomers [14] (included in the Tables for the sake of comparison), by analyzing the results quoted in Tables 3–5. The MP2 (HF) results for the E isomers show that the use of the 6-31G+p basis set leads to augmented values of l and Æaæ, as compared with those obtained with the 6-31G basis set, in the range between 3%
3. Results and discussion Table 2 lists the MP2 relative energies of the different isomers. The MP2/6-31G results predict that the 2-type Z isomers are more stable than the E counterparts by a small amount of energy which do not reach 3 kcal/mol. Even though the determination of the more stable molecular structure would require the use of a more sophisticated methodology [31], these results reveal a low Z–E isomerization energy, suggesting the coexis-
Table 2 ˚ ) and relative total energies (in kcal/mol) of E–Z azo-enaminone isomers MP2/6-31G results for optimized bond distances (in A
d(N1C2) d(C2C3) d(C2C4) d(C4N5) d(N5N6) d(N6C7) d(C7C8) d(C7C9) DE a
2AE
2BE
2CE
1AE
1BE
1CE
4AE
4BE
4CE
2AZa
2BZ
2CZ
1.357 1.517 1.417 1.411 1.315 1.449 1.413 1.417 0.023
1.355 1.516 1.429 1.407 1.317 1.448 1.414 1.417 2.33
1.355 1.516 1.435 1.406 1.318 1.448 1.414 1.417 2.81
1.355 1.517 1.419 1.409 1.330 1.434 1.419 1.432 –
1.354 1.516 1.432 1.406 1.332 1.434 1.419 1.432 –
1.354 1.516 1.439 1.405 1.333 1.434 1.419 1.432 –
1.361 1.518 1.411 1.410 1.314 1.451 1.412 1.417 –
1.360 1.517 1.422 1.405 1.315 1.451 1.412 1.417 –
1.360 1.516 1.428 1.404 1.316 1.451 1.412 1.417 –
1.353 1.519 1.422 1.401 1.326 1.442 1.414 1.417 0.00
1.351 1.518 1.431 1.393 1.331 1.439 1.414 1.418 0.00
1.352 1.519 1.438 1.392 1.332 1.437 1.415 1.418 0.00
Results were taken from [14].
T.L. Fonseca et al. / Chemical Physics Letters 413 (2005) 356–361 Table 3 HF and MP2 results for l (in D) of E-[Z] azo-enaminone isomers computed using different basis sets HF
MP2
6-31G
6-31+p
6-31G
6-31+p
1A 1B 1C
9.19 [8.62] 10.28 [9.46] 11.03 [10.04]
9.24 [8.70] 10.44 [9.63] 11.22 [10.25]
8.57 [7.87] 9.82 [8.87] 10.54 [9.40]
8.80 [8.17] 10.26 [9.35] 11.02 [9.91]
2A 2B 2C
7.84 [7.20] 8.94 [8.11] 9.71 [8.68]
7.88 [7.29] 9.09 [8.30] 9.89 [8.87]
6.61 [5.95] 7.82 [7.00] 8.48 [7.49]
6.80 [6.22] 8.22 [7.14] 8.94 [7.94]
3A 3B 3C
10.39 [9.36] 11.47 [10.36] 12.25 [10.83]
10.46 [9.76] 11.65 [10.55] 12.46 [11.05]
9.34 [8.32] 10.52 [9.18] 11.23 [9.59]
9.57 [8.67] 10.98 [9.67] 11.74 [10.14]
4A 4B 4C
8.91 [8.09] 10.00 [8.79] 10.76 [9.22]
8.98 [8.22] 10.18 [8.99] 10.98 [9.44]
7.38 [6.38] 8.55 [7.24] 9.21 [7.63]
7.63 [6.74] 9.03 [7.75] 9.74 [8.15]
1
HF and MP2 results for 1 and 2-type Z isomers taken from [14].
Table 4 HF and MP2 results for Æaæ (in 1024 esu) of E–[Z] azo-enaminone isomers computed using different basis sets HF
MP2
6-31G
6-31+p
6-31G
6-31+p
1A 1B 1C
24.28 [24.23] 26.59 [26.31] 31.64 [30.92]
26.49 [26.39] 28.75 [28.45] 34.04 [33.28]
28.12 [28.18] 31.14 [30.92] 36.80 [35.93]
31.64 [31.58] 34.63 [34.34] 40.71 [39.72]
2A 2B 2C
23.86 [23.85] 26.19 [25.86] 31.27 [30.48]
26.11 [26.04] 28.40 [28.05] 33.71 [32.89]
27.34 [27.61] 30.40 [30.27] 36.08 [35.29]
30.84 [31.01] 33.90 [33.71] 40.01 [39.13]
3A 3B 3C
25.96 [25.84] 28.24 [27.88] 33.29 [32.53]
28.24 [28.04] 30.47 [30.10] 35.75 [34.95]
29.93 [29.93] 32.94 [32.67] 38.62 [37.80]
33.54 [33.45] 36.51 [36.17] 42.61 [41.64]
4A 4B 4C
25.57 [25.43] 27.88 [27.50] 32.94 [32.26]
27.87 [27.69] 30.13 [29.73] 35.43 [34.59]
29.22 [29.32] 32.29 [32.12] 37.97 [37.21]
32.79 [32.79] 35.83 [35.60] 41.94 [41.07]
1
HF and MP2 results for 1 and 2-type Z isomers taken from [14].
Table 5 HF and MP2 results for bvec (in 1030 esu) of E–[Z] azo-enaminone isomers computed using different basis sets HF
MP2
6-31G
6-31+p
6-31G
6-31+p
1A 1B 1C
18.43 [14.29] 21.97 [15.07] 24.71 [14.97]
19.61 [15.49] 24.61 [17.15] 27.47 [16.89]
45.71 [33.21] 55.48 [34.31] 63.22 [33.10]
52.09 [38.65] 65.55 [41.69] 74.24 [40.28]
2A 2B 2C
22.13 [17.75] 26.01 [18.36] 29.09 [18.42]
24.13 [19.80] 29.58 [21.32] 32.88 [21.29]
58.12 [43.39] 70.29 [44.54] 79.82 [43.80]
66.32 [51.12] 82.38 [54.15] 93.11 [53.29]
3A 3B 3C
15.98 [12.00] 18.67 [12.60] 20.56 [12.57]
17.35 [13.27] 21.46 [14.74] 23.41 [14.47]
42.85 [33.59] 51.95 [35.37] 58.85 [34.65]
49.93 [39.63] 62.78 [43.41] 70.31 [42.23]
4A 4B 4C
20.49 [16.12] 23.84 [17.08] 26.25 [17.23]
22.60 [18.10] 27.43 [19.99] 30.00 [19.98]
57.45 [46.17] 68.70 [48.98] 77.09 [47.69]
66.44 [54.33] 81.44 [58.72] 90.63 [57.68]
1
HF and MP2 results for 1 and 2-type Z isomers taken from [14].
359
and 6% (0.5% and 2%) for l and between 10% and 13% (7% and 10%) for Æaæ. It can be observed that the first hyperpolarizability results are more sensitive to the basis set effects. The corresponding increase for the bvec values varies between 14% and 21% (6% and 15%), indicating that the determination of semiquantitative results for this property should require, at least, the inclusion of one p diffuse function on the 6-31G basis set. A similar conclusion with respect to basis set effects, for donor– acceptor nitrogen-containing molecules, was reported by Tsunekawa and Yamaguchi [29]. As regards the electron correlation effects our MP2 calculations of the electric properties were performed using MP2 equilibrium geometry. From now on, our discussions will be focused on the 6-31G+p results. Comparisons with the HF results displayed in Table 3 show that for all E isomers the EC effects diminishes the l values. In particular, for chromophores 2AE, 2BE and 2CE, the reduction factors, obtained by the MP2/ HF ratios, are, respectively, 14%, 10% and 10%. For Æaæ, the inclusion of EC increases the calculated values by an amount which varies between 18% and 20%. As observed previously, the MP2/HF ratios for the first hyperpolarizability reveal that the EC contribution leads to a substantial increase on the bvec values. For these compounds, the overall EC effect increases the bvec values by factors of, respectively, 175%, 178% and 183%. These results show the importance of EC effects in theoretical studies specially if they are to be used for a rational design of new molecules with quadratic NLO properties. One can observe from Table 4 that for 1 and 2-type E isomers the incorporation of strong donor groups enhances the linear polarizability values. For instance, MP2 (HF) results for 2B/2A and 2C/2B ratios show a systematic increase of Æaæ by 10% (9%) and 18% (19%) which is consistent with the incorporation of each one of the different substituents, indicating the additive nature of this property [32]. A similar trend have been reported for the Æaæ values of other substituted organic systems [33,34]. The introduction of these substituents has also an appreciable effect on the dipole moment and first hyperpolarizability. It can be obtained from Table 3 that the MP2 (HF) ratios for 2B/2A and 2C/2B show increases on the l values which are, respectively, of the order of 21% (15%) and 9% (9%). From Table 5, the corresponding factors for bvec are 24% (23%) and 13% (11%). In contrast with previous results reported for the Z isomers [14], the first hyperpolarizability of the E isomers is enhanced as the strength of the donor is increased. Since MP2 and HF results show a smaller increase when going from B to C than when going from A to B, it is expected that bvec would reach a saturation limit with the incorporation of groups with increasing donor strengths. In addition, the inclusion of the –OH group almost have no impact on the Æaæ values
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but leads to an increase of the dipole moment values. For instance, MP2 (HF) results for 1A/2A, 1B/2B and 1C/2C ratios show that the l values increase, respectively, by 29% (17%), 25% (15%) and 23% (13%). Differently, the –OH group bonded at the phenyl ring gives a decrease of the first hyperpolarizability values by factors of, respectively, 21% (19%), 20% (17%) and 21% (16%). The diminution of the bvec values of compounds 1 with the inclusion of the –OH group is a signature of the reduction of the push–pull intensity throughout the backbone of the molecules. The results presented in Tables 3 and 5 show that the effect of E–Z isomerization on the first hyperpolarizability is much more relevant than that observed for the dipole moment. In particular, MP2 (HF) ratios for 2AE/2AZ, 2BE/2BZ and 2CE/2CZ show that the different isomeric forms lead to increase on l values, respectively, of the order of 9% (8%), 15% (10%) and 13% (11%). For the first hyperpolarizability the corresponding ratios show substantial increments on bvec values of 30% (22%), 52% (39%) and 75% (54%), revealing that the E isomers possess much larger bvec values than those of the Z isomers. Knowing the bvec values of each isomer and the relative abundance of each specie in the sample it would be possible to obtain more appropriate estimates of the bvec value by means of an weighted average. Therefore, for organic systems with low isomerization energy this care is advisable in the interpretation of experimental results. With respect to the isomerization influence on the Æaæ values (Table 4), as expected, both MP2 and HF results show an almost negligible effect. Connections between structure and property can be preliminarily established from the results listed in Table 2. In order to assess the effect of the changes on bond distances of donor-conjugated bridge-acceptor related to type of isomerization on the first hyperpolarizability, test calculations were performed for 2-type E isomers considering the same geometric parameters of the corresponding Z isomers. The MP2/6-31G+p bvec values for the compounds 2AE, 2BE and 2CE are, respectively, 72.43 · 1030, 90.52 · 1030 and 102.88 · 1030 esu. Notice that these results are a little greater than those obtained with proper optimized geometry, indicating that the changes on the degree of the bond length alternation can affect the bvec values. This preliminary analyses shows that the bond distances have an important role in control the mobility of the p-electrons throughout the molecules. Nevertheless, these results clearly demonstrate that a more extensive conjugation path connecting the donor–acceptor groups provided by the relative orientation of the donor groups in the E isomers results in enhanced bvec values. Our HF and MP2 results show, in addition, that for molecules bearing the –OCH2CH3 group (compounds 3 and 4) the effects on these electrical properties due to the incorporation of electron-donor groups with different
strengths and the –OH group bonded to the phenyl ring lead to, in general, to conclusions which are similar to those reached regarding compounds 1 and 2. From Table 5, comparisons between results obtained for compounds 3 and 4 with those of 1 and 2 reveal that the inclusion of O-etil group has almost no impact on bvec. This result is expected since the replacement of of –CH3 by –OCH2CH3 has a minor impact on the geometric parameters.
4. Conclusion A systematic study of the dipole moment, linear polarizability and first hyperpolarizability of two structural isomers of azo-enaminones at HF and MP2 levels of calculations have been presented. The obtained results have shown similar trends for l, Æaæ and bvec with respect to the basis set dependence, electron correlation effects and the incorporation of the OH group for both isomers. In opposition, enhanced bvec values are obtained for the E isomers with the incorporation of donor groups with increasing strengths. The results also indicate that in order to reach the saturation regime of this property it would be required the incorporation of stronger donor groups. The impact of structural modifications related to the type of isomerization on the first hyperpolarizability is much more relevant than that observed for dipole moment. A more extensive conjugation throughout the molecule provided by the position of the aminic group in the E isomers leads to a substantial increase on the first hyperpolarizability. The possible coexistence of the E and Z isomers should be taken into account in the interpretation of experimental results.
Acknowledgements The authors gratefully acknowledge the financial support of the CNPq and FUNAPE/UFG Brazilian agencies.
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MP2 static first hyperpolarizability of azo-enaminone isomers T.L. Fonseca a
a,*
, H.C.B. de Oliveira b, O.A.V. Amaral a, M.A. Castro
a
Instituto de Fı´sica, Universidade Federal de Goia´s, Campus II, Caixa Postal 131, 74001-970 Goiaˆnia, Goia´s, Brazil b Departamento de Cieˆncias Exatas, Universidade Estadual de Goia´s, 73807-250 Formosa, Goia´s, Brazil Received 6 July 2005; in final form 26 July 2005 Available online 22 August 2005
Abstract The dipole moment, static linear polarizability and first hyperpolarizability of donor–acceptor azo-enaminone isomers have been calculated with both Hartree–Fock (HF) method and second-order Møller–Plesset perturbation theory (MP2), using the 6-31G and 6-31G+p basis sets. Two structural isomers of substituted azo-enaminones have been studied to point out the first hyperpolarizability geometry-dependencies associated to the type of isomerization. Our results show that the relative orientation of donor groups in chromophores has an important impact on the magnitude of the first hyperpolarizability. 2005 Elsevier B.V. All rights reserved.
1. Introduction Due to potential applications in various photonic technologies, such as optical information processing and telecommunication, the non-linear optical (NLO) properties of organic molecular materials have been object of intense research [1–7]. An important class of NLO molecular materials is formed by donor–acceptor substituted p-conjugated organic molecules. In these molecular systems, the asymmetric polarization induced by incorporation of donor–acceptor groups can enhance the quadratic NLO properties. Previous studies have investigated structure–property relationships for donor–acceptor conjugated molecules [5–7], aiming at designing efficient organic second-order NLO materials. It has been shown, for example, that the combination of electron donor and acceptor strengths, connected to an organic p-delocalized framework, should be optimized in order to maximize the molecular hyperpolarizability of the NLO chromophores. Based on AM1 calculations, the first donor–acceptor azo-enaminones derivatives presented as potential can*
Corresponding author. Fax: +55 62 521 1014. E-mail address: [email protected] (T.L. Fonseca).
0009-2614/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.08.007
didates for application in second-order NLO processes were synthesized from the azo coupling between quinone diazides and acyclic enaminones [8,9]. Recently, new azo-enaminones have been synthesized by coupling of diazonium salts and enaminones and their experimental geometric parameters determined by X-ray diffraction [10–13]. It is also worthwhile stressing that these later azo-enaminone compounds are more flexible, as regards structural modifications, than those synthesized by quinone diazide route. Therefore, due to the delocalization of p-electrons these new compounds present an unusually low rotational barrier around the C@C double bond, giving rise to different geometrical isomers [10]. Structural studies, using multinuclear magnetic resonance revealed that azo-enaminone derivatives can exist in CDCl3 solution in the form of two geometrical isomers (Z and E). The different geometric forms affect the electronic structure of these compounds and, consequently, changes in their physical properties can be expected. In a recent work [14], we have investigated the nonlinear optical properties of these new azo-enaminones with appropriate substituents as well as some azoenaminones studied previously [9]. For the Z isomers of azo-enaminones, HF and MP2 calculations reported
T.L. Fonseca et al. / Chemical Physics Letters 413 (2005) 356–361
by us [14] have suggested that the incorporation of strong donor groups leads to a saturation of the first hyperpolarizability and that substitution effects of the nitro group at the ortho and meta positions gives rise to a marked diminution on the first hyperpolarizability. The purpose of this work is to investigate the impact of structural modifications associated to E isomerization on the NLO properties of p-nitro-azo-enaminones as function of the strength of the electron-donor groups. The model systems are isomers of azo-enaminones with –NO2 as the electron-acceptor group attached at para position of the phenyl ring and –NH2 as the electrondonor group. The strength donor character is varied by the replacement of an H atom of the aminic group by substituents such as –CH3 and –C(CH3)3. The influence of the replacement of –CH3 by –OCH2CH3 [8] on the electric properties of both Z and E isomers considering a representative group of azo-enaminones is also analyzed. The dipole moment, linear polarizability and first hyperpolarizability were calculated at HF and MP2 levels using the analytical (AN) and finite field (FF) approaches. Previous studies, based on MP2 calculations, have been reported showing the importance of the inclusion of electron correlation (EC) effects in order to obtain accurate estimates for the linear and nonlinear polarizabilities of different organic systems [14–22]. Other effects, such as frequency dispersion and nuclear motions, although not considered in this work are expected to play important roles on the calculations of the first hyperpolarizabilities [23,24]. However, previous calculations have shown that the vibrational contributions are usually negligible for second-harmonic generation processes [24].
357
Fig. 1. Molecular structures of the azo-enaminone isomers studied in this work (see also Table 1).
Table 1 Labels of the azo-enaminone isomers presented in Fig. 1 Compounds
Substituents D
X
Y
1A 1B 1C
H CH3 C(CH3)3
OH OH OH
CH3 CH3 CH3
2A 2B 2C
H CH3 C(CH3)3
H H H
CH3 CH3 CH3
3A 3B 3C
H CH3 C(CH3)3
OH OH OH
OCH2CH3 OCH2CH3 OCH2CH3
4A 4B 4C
H CH3 C(CH3)3
H H H
OCH2CH3 OCH2CH3 OCH2CH3
2. Computational details The NLO molecules studied in this work are displayed in Fig. 1 and specified in Table 1. We have used subscripts E or Z to represent the particular type of isomer. In such compounds, the benzene ring and a segment with NN, NC, and CC bonds provides the p-conjugated bridge. For all isomers, the geometries were fully optimized at HF and MP2 levels using the 6-31G basis set. In particular, for the compound ethyl 2-[(E)-5-chloro-2-hydroxy-4-nitro-phenylazo]-3-(E)-amino2-butenoate comparisons with the experimental values determined by X-ray diffraction [8] have shown that there is a good agreement between the HF/6-31G and MP2/6-31G results and the experimental data [14]. The indication that HF/6-31G calculations can provide good estimates of the molecular geometry of these compounds has also been drawn by Abe et al. [25] for heterocyclic pyridinium betaines. Here, the HF components of the permanent dipole moment (li), linear dipole polarizability (ai i) and of
the first dipole hyperpolarizability (bi j k) were calculated analytically using the coupled perturbed Hartree–Fock (CPHF) procedure. At the MP2 level, the calculation of these properties were performed numerically using the FF method. For all azo-enaminone compounds, the MP2 properties were obtained from FF calculations using positive and negative field strengths of the order of 0.001 a.u. At HF level, the numerical and analytical procedures give equivalent results for the dipole moment and polarizabilities, providing a strong indication that the FF numerical procedure is also appropriated to calculate the MP2 NLO properties of azo-enaminones. The values normally measured in experiments are the dipole moment magnitude, l, the average linear polarizability, Æaæ = (axx + ayy + azz)/3, and the the vector component of the first hyperpolarizability along the dipole P moment direction,P bvec ¼ i bi li =l ½i ¼ x; y; z, where bi is given by bi ¼ k bikk ½k ¼ x; y; z. Because of rotational invariance of these quantities, these values do
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not depend on the particular orientation of the coordinate system. The component bvec defined above is the quantity measured in electric field induced second harmonic generation (EFISH) experiments [26–28]. Using the 6-31G, 6-31G+p and 6-31G+d basis sets, the basis set effects on the dipole moment, linear polarizability and first hyperpolarizability of a representative set of azo-enaminones were analyzed in a previous work [14]. This study have shown that the 6-31G+p basis set gives results that are almost identical to those obtained using the 6-31G+d basis set, indicating that the addition of one p or one d diffuse function have an equivalent impact on the improvement of the calculated properties for these NLO molecules. The choice of the exponents of the p or d functions on each heavy atom was determined, at the HF level, by imposing the maximization of the bvec values [29]. This criterion is justifiable because the use of relatively small basis sets tends to underestimate the values of the calculated properties. In this Letter, the study of the basis set influence on the electrical properties is analyzed for both type of isomers by comparing the results obtained using the 6-31G basis set and the 6-31G+p augmented version of this set (extra p functions are added on the heavy atoms). The exponents used in calculations when p extra functions are added on heavy atoms are fp = 0.03 on carbon atoms, fp = 0.04 on nitrogen atoms and fp = 0.07 on the oxygen atom [14]. The electric properties and geometry optimization calculations, at HF and MP2 levels, were performed using the GAUSSIAN 03 [30] electronic structure package.
tence of different geometrical isomers in agreement with experimental observation for similar azo-enaminone compounds [10]. In order to estimate the changes on the bond distances of the p-conjugated segment between donor– acceptor groups with respect to the substituents as well as with the type of isomerization, a selected set of MP2 bond distances are listed in Table 2. The results show that the replacement of –CH3 by –OCH2CH3 practically does not affect the geometry of these compounds. It can be noted that the variations of bond lengths due to the incorporation of different donor groups at the aminic nitrogen (N1) (such as in compounds B and C) or the inclusion of the –OH group at the phenyl ring are, in general, very small, regardless the isomeric form of the azo-enaminones. For example, going from 2AE ! 2BE (2BE ! 2CE), the most significant variations are found for the C2–C4 bond distance with modifica˚ (+0.006 A ˚ ). Going from 2AE ! 1AE, tions of +0.012 A 2BE ! 1BE and 2CE ! 1CE variations of the order of ˚ are predicted for the N5–N6 and C7–C9 bond +0.015 A ˚ are distances, while changes of the order of 0.015 A observed for the N6–C7 bond length. Structural changes related to the type of isomerization have an impact more appreciable on C4–N5, N5–N6 and N6–C7. For these bond lengths, the MP2 results give variations of ˚ , 0.011 A ˚ , +0.007 A ˚ for 2AZ ! 2AE and +0.010 A ˚ , 0.014 A ˚ , +0.011 A ˚ for 2CZ ! 2CE. One +0.014 A can associate the modifications on these later parameters with changes on the degree of p-electron delocalization which in turn can have a beneficial effect on the first hyperpolarizability [5,7]. We can draw a close analogy between the basis set dependence and the electron correlation effects of dipole moment, linear polarizability and first hyperpolarizability of the E isomers with those obtained previously for the Z isomers [14] (included in the Tables for the sake of comparison), by analyzing the results quoted in Tables 3–5. The MP2 (HF) results for the E isomers show that the use of the 6-31G+p basis set leads to augmented values of l and Æaæ, as compared with those obtained with the 6-31G basis set, in the range between 3%
3. Results and discussion Table 2 lists the MP2 relative energies of the different isomers. The MP2/6-31G results predict that the 2-type Z isomers are more stable than the E counterparts by a small amount of energy which do not reach 3 kcal/mol. Even though the determination of the more stable molecular structure would require the use of a more sophisticated methodology [31], these results reveal a low Z–E isomerization energy, suggesting the coexis-
Table 2 ˚ ) and relative total energies (in kcal/mol) of E–Z azo-enaminone isomers MP2/6-31G results for optimized bond distances (in A
d(N1C2) d(C2C3) d(C2C4) d(C4N5) d(N5N6) d(N6C7) d(C7C8) d(C7C9) DE a
2AE
2BE
2CE
1AE
1BE
1CE
4AE
4BE
4CE
2AZa
2BZ
2CZ
1.357 1.517 1.417 1.411 1.315 1.449 1.413 1.417 0.023
1.355 1.516 1.429 1.407 1.317 1.448 1.414 1.417 2.33
1.355 1.516 1.435 1.406 1.318 1.448 1.414 1.417 2.81
1.355 1.517 1.419 1.409 1.330 1.434 1.419 1.432 –
1.354 1.516 1.432 1.406 1.332 1.434 1.419 1.432 –
1.354 1.516 1.439 1.405 1.333 1.434 1.419 1.432 –
1.361 1.518 1.411 1.410 1.314 1.451 1.412 1.417 –
1.360 1.517 1.422 1.405 1.315 1.451 1.412 1.417 –
1.360 1.516 1.428 1.404 1.316 1.451 1.412 1.417 –
1.353 1.519 1.422 1.401 1.326 1.442 1.414 1.417 0.00
1.351 1.518 1.431 1.393 1.331 1.439 1.414 1.418 0.00
1.352 1.519 1.438 1.392 1.332 1.437 1.415 1.418 0.00
Results were taken from [14].
T.L. Fonseca et al. / Chemical Physics Letters 413 (2005) 356–361 Table 3 HF and MP2 results for l (in D) of E-[Z] azo-enaminone isomers computed using different basis sets HF
MP2
6-31G
6-31+p
6-31G
6-31+p
1A 1B 1C
9.19 [8.62] 10.28 [9.46] 11.03 [10.04]
9.24 [8.70] 10.44 [9.63] 11.22 [10.25]
8.57 [7.87] 9.82 [8.87] 10.54 [9.40]
8.80 [8.17] 10.26 [9.35] 11.02 [9.91]
2A 2B 2C
7.84 [7.20] 8.94 [8.11] 9.71 [8.68]
7.88 [7.29] 9.09 [8.30] 9.89 [8.87]
6.61 [5.95] 7.82 [7.00] 8.48 [7.49]
6.80 [6.22] 8.22 [7.14] 8.94 [7.94]
3A 3B 3C
10.39 [9.36] 11.47 [10.36] 12.25 [10.83]
10.46 [9.76] 11.65 [10.55] 12.46 [11.05]
9.34 [8.32] 10.52 [9.18] 11.23 [9.59]
9.57 [8.67] 10.98 [9.67] 11.74 [10.14]
4A 4B 4C
8.91 [8.09] 10.00 [8.79] 10.76 [9.22]
8.98 [8.22] 10.18 [8.99] 10.98 [9.44]
7.38 [6.38] 8.55 [7.24] 9.21 [7.63]
7.63 [6.74] 9.03 [7.75] 9.74 [8.15]
1
HF and MP2 results for 1 and 2-type Z isomers taken from [14].
Table 4 HF and MP2 results for Æaæ (in 1024 esu) of E–[Z] azo-enaminone isomers computed using different basis sets HF
MP2
6-31G
6-31+p
6-31G
6-31+p
1A 1B 1C
24.28 [24.23] 26.59 [26.31] 31.64 [30.92]
26.49 [26.39] 28.75 [28.45] 34.04 [33.28]
28.12 [28.18] 31.14 [30.92] 36.80 [35.93]
31.64 [31.58] 34.63 [34.34] 40.71 [39.72]
2A 2B 2C
23.86 [23.85] 26.19 [25.86] 31.27 [30.48]
26.11 [26.04] 28.40 [28.05] 33.71 [32.89]
27.34 [27.61] 30.40 [30.27] 36.08 [35.29]
30.84 [31.01] 33.90 [33.71] 40.01 [39.13]
3A 3B 3C
25.96 [25.84] 28.24 [27.88] 33.29 [32.53]
28.24 [28.04] 30.47 [30.10] 35.75 [34.95]
29.93 [29.93] 32.94 [32.67] 38.62 [37.80]
33.54 [33.45] 36.51 [36.17] 42.61 [41.64]
4A 4B 4C
25.57 [25.43] 27.88 [27.50] 32.94 [32.26]
27.87 [27.69] 30.13 [29.73] 35.43 [34.59]
29.22 [29.32] 32.29 [32.12] 37.97 [37.21]
32.79 [32.79] 35.83 [35.60] 41.94 [41.07]
1
HF and MP2 results for 1 and 2-type Z isomers taken from [14].
Table 5 HF and MP2 results for bvec (in 1030 esu) of E–[Z] azo-enaminone isomers computed using different basis sets HF
MP2
6-31G
6-31+p
6-31G
6-31+p
1A 1B 1C
18.43 [14.29] 21.97 [15.07] 24.71 [14.97]
19.61 [15.49] 24.61 [17.15] 27.47 [16.89]
45.71 [33.21] 55.48 [34.31] 63.22 [33.10]
52.09 [38.65] 65.55 [41.69] 74.24 [40.28]
2A 2B 2C
22.13 [17.75] 26.01 [18.36] 29.09 [18.42]
24.13 [19.80] 29.58 [21.32] 32.88 [21.29]
58.12 [43.39] 70.29 [44.54] 79.82 [43.80]
66.32 [51.12] 82.38 [54.15] 93.11 [53.29]
3A 3B 3C
15.98 [12.00] 18.67 [12.60] 20.56 [12.57]
17.35 [13.27] 21.46 [14.74] 23.41 [14.47]
42.85 [33.59] 51.95 [35.37] 58.85 [34.65]
49.93 [39.63] 62.78 [43.41] 70.31 [42.23]
4A 4B 4C
20.49 [16.12] 23.84 [17.08] 26.25 [17.23]
22.60 [18.10] 27.43 [19.99] 30.00 [19.98]
57.45 [46.17] 68.70 [48.98] 77.09 [47.69]
66.44 [54.33] 81.44 [58.72] 90.63 [57.68]
1
HF and MP2 results for 1 and 2-type Z isomers taken from [14].
359
and 6% (0.5% and 2%) for l and between 10% and 13% (7% and 10%) for Æaæ. It can be observed that the first hyperpolarizability results are more sensitive to the basis set effects. The corresponding increase for the bvec values varies between 14% and 21% (6% and 15%), indicating that the determination of semiquantitative results for this property should require, at least, the inclusion of one p diffuse function on the 6-31G basis set. A similar conclusion with respect to basis set effects, for donor– acceptor nitrogen-containing molecules, was reported by Tsunekawa and Yamaguchi [29]. As regards the electron correlation effects our MP2 calculations of the electric properties were performed using MP2 equilibrium geometry. From now on, our discussions will be focused on the 6-31G+p results. Comparisons with the HF results displayed in Table 3 show that for all E isomers the EC effects diminishes the l values. In particular, for chromophores 2AE, 2BE and 2CE, the reduction factors, obtained by the MP2/ HF ratios, are, respectively, 14%, 10% and 10%. For Æaæ, the inclusion of EC increases the calculated values by an amount which varies between 18% and 20%. As observed previously, the MP2/HF ratios for the first hyperpolarizability reveal that the EC contribution leads to a substantial increase on the bvec values. For these compounds, the overall EC effect increases the bvec values by factors of, respectively, 175%, 178% and 183%. These results show the importance of EC effects in theoretical studies specially if they are to be used for a rational design of new molecules with quadratic NLO properties. One can observe from Table 4 that for 1 and 2-type E isomers the incorporation of strong donor groups enhances the linear polarizability values. For instance, MP2 (HF) results for 2B/2A and 2C/2B ratios show a systematic increase of Æaæ by 10% (9%) and 18% (19%) which is consistent with the incorporation of each one of the different substituents, indicating the additive nature of this property [32]. A similar trend have been reported for the Æaæ values of other substituted organic systems [33,34]. The introduction of these substituents has also an appreciable effect on the dipole moment and first hyperpolarizability. It can be obtained from Table 3 that the MP2 (HF) ratios for 2B/2A and 2C/2B show increases on the l values which are, respectively, of the order of 21% (15%) and 9% (9%). From Table 5, the corresponding factors for bvec are 24% (23%) and 13% (11%). In contrast with previous results reported for the Z isomers [14], the first hyperpolarizability of the E isomers is enhanced as the strength of the donor is increased. Since MP2 and HF results show a smaller increase when going from B to C than when going from A to B, it is expected that bvec would reach a saturation limit with the incorporation of groups with increasing donor strengths. In addition, the inclusion of the –OH group almost have no impact on the Æaæ values
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but leads to an increase of the dipole moment values. For instance, MP2 (HF) results for 1A/2A, 1B/2B and 1C/2C ratios show that the l values increase, respectively, by 29% (17%), 25% (15%) and 23% (13%). Differently, the –OH group bonded at the phenyl ring gives a decrease of the first hyperpolarizability values by factors of, respectively, 21% (19%), 20% (17%) and 21% (16%). The diminution of the bvec values of compounds 1 with the inclusion of the –OH group is a signature of the reduction of the push–pull intensity throughout the backbone of the molecules. The results presented in Tables 3 and 5 show that the effect of E–Z isomerization on the first hyperpolarizability is much more relevant than that observed for the dipole moment. In particular, MP2 (HF) ratios for 2AE/2AZ, 2BE/2BZ and 2CE/2CZ show that the different isomeric forms lead to increase on l values, respectively, of the order of 9% (8%), 15% (10%) and 13% (11%). For the first hyperpolarizability the corresponding ratios show substantial increments on bvec values of 30% (22%), 52% (39%) and 75% (54%), revealing that the E isomers possess much larger bvec values than those of the Z isomers. Knowing the bvec values of each isomer and the relative abundance of each specie in the sample it would be possible to obtain more appropriate estimates of the bvec value by means of an weighted average. Therefore, for organic systems with low isomerization energy this care is advisable in the interpretation of experimental results. With respect to the isomerization influence on the Æaæ values (Table 4), as expected, both MP2 and HF results show an almost negligible effect. Connections between structure and property can be preliminarily established from the results listed in Table 2. In order to assess the effect of the changes on bond distances of donor-conjugated bridge-acceptor related to type of isomerization on the first hyperpolarizability, test calculations were performed for 2-type E isomers considering the same geometric parameters of the corresponding Z isomers. The MP2/6-31G+p bvec values for the compounds 2AE, 2BE and 2CE are, respectively, 72.43 · 1030, 90.52 · 1030 and 102.88 · 1030 esu. Notice that these results are a little greater than those obtained with proper optimized geometry, indicating that the changes on the degree of the bond length alternation can affect the bvec values. This preliminary analyses shows that the bond distances have an important role in control the mobility of the p-electrons throughout the molecules. Nevertheless, these results clearly demonstrate that a more extensive conjugation path connecting the donor–acceptor groups provided by the relative orientation of the donor groups in the E isomers results in enhanced bvec values. Our HF and MP2 results show, in addition, that for molecules bearing the –OCH2CH3 group (compounds 3 and 4) the effects on these electrical properties due to the incorporation of electron-donor groups with different
strengths and the –OH group bonded to the phenyl ring lead to, in general, to conclusions which are similar to those reached regarding compounds 1 and 2. From Table 5, comparisons between results obtained for compounds 3 and 4 with those of 1 and 2 reveal that the inclusion of O-etil group has almost no impact on bvec. This result is expected since the replacement of of –CH3 by –OCH2CH3 has a minor impact on the geometric parameters.
4. Conclusion A systematic study of the dipole moment, linear polarizability and first hyperpolarizability of two structural isomers of azo-enaminones at HF and MP2 levels of calculations have been presented. The obtained results have shown similar trends for l, Æaæ and bvec with respect to the basis set dependence, electron correlation effects and the incorporation of the OH group for both isomers. In opposition, enhanced bvec values are obtained for the E isomers with the incorporation of donor groups with increasing strengths. The results also indicate that in order to reach the saturation regime of this property it would be required the incorporation of stronger donor groups. The impact of structural modifications related to the type of isomerization on the first hyperpolarizability is much more relevant than that observed for dipole moment. A more extensive conjugation throughout the molecule provided by the position of the aminic group in the E isomers leads to a substantial increase on the first hyperpolarizability. The possible coexistence of the E and Z isomers should be taken into account in the interpretation of experimental results.
Acknowledgements The authors gratefully acknowledge the financial support of the CNPq and FUNAPE/UFG Brazilian agencies.
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