- Email: [email protected]
Structural and vibrational analysis of azodendrimers by molecular orbital methods
23 June 2000
Chemical Physics Letters 323 Ž2000. 407–415 www.elsevier.nlrlocatercplett
Structural and vibrational analysis of azodendrimers by molecular orbital methods Shigenori Tanaka a
a,)
, Satoshi Itoh a , Noriyuki Kurita
b
AdÕanced Materials and DeÕices Laboratory, Toshiba Research and DeÕelopment Center, 1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, Japan b Department of Knowledge-Based Information Engineering, Toyohashi UniÕersity of Technology, Tempaku-cho, Toyohashi 441-8580, Japan Received 14 February 2000; in final form 3 May 2000
Abstract The structural optimization and normal-mode analysis are performed for the aryl ether azodendrimers on the basis of the semi-empirical molecular orbital methods. Through the geometrical characterization for the stable structures, the fractal dimension and the degree of azo core wrapping are found to provide key parameters related to the unique photoinduced isomerization. We also find that the normal-mode frequency distribution is virtually invariable irrespective of the molecular structure and generation of azodendrimers. The importance of normal-mode distribution gap in the range of 700–900 cmy1 is suggested regarding the efficient vibrational energy transfer to the azo core region. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Dendrimers are nano-sized hyperbranched macromolecules with a regular tree-like structure made up of repeating units arranged in a hierarchical and self-similar fashion w1x. They have recently attracted increasing attention w2–4x as artificial light-harvesting antennae for photon energy transduction similar to biological photosynthetic systems. In a recent, remarkable experiment, Jiang and Aida w5x have found that a large aryl ether azodendrimer undergoes cis-to-trans isomerization at the interior azo unit upon exposure to weak infrared ŽIR. light with the frequency of about 1600 cmy1 . Because the activa-
) Corresponding author. Fax: q81-44-520-1801; e-mail: [email protected]
tion energy for the isomerization is 0.84 eV, this experimental result suggests that ‘multiphotonic’ or ‘up-conversion’ processes involving at least five quanta are induced by weak IR irradiation. The photon energies converted to molecular vibrations migrate in the interior of molecule and are transferred to the azo core with little dissipation into irrelevant modes. These salient features are supposed to be intimately related to the unique dendritic structure and a number of potential applications of dendrimers to novel photofunctional materials have been suggested. However, the microscopic mechanism of the photoinduced isomerization remains to be elucidated. In order to provide a theoretical basis for investigating the mechanism of the photon energy transduction and the subsequent cis-to-trans isomerization, in this Letter we report on the structural and vibrational
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 5 5 2 - 2
408
S. Tanaka et al.r Chemical Physics Letters 323 (2000) 407–415
analyses of aryl ether azodendrimers performed on the basis of molecular orbital ŽMO. methods. Since the number of atoms involved in the large azodendrimers showing the IR-induced isomerization exceeds 500, we employ the semi-empirical MO method such as MNDO, AM1, and PM3 schemes as a best compromise between accuracy and computational demand. We first optimize the molecular structures of trans- and cis-azodendrimers and characterize them to study the relationship between the dendritic structure and the efficient light-harvesting function. The calculations of the vibrational normal modes are then carried out for the optimized structures and their implications concerning the intramolecular vibrational energy transfer are discussed.
2. Methods We have carried out the electronic structure calculations for the azodendrimers on the basis of quantum-chemical MO methods. Although the molecular simulations regarding the structural and vibrational properties of macromolecules involving more than hundreds of atoms are usually performed by the classical molecular mechanics andror dynamics calculations, the inaccuracies of the interatomic force field assumed in the model often cause erroneous results, and this is especially so in the case of novel materials. The simulations taking into account the degree of freedom for the electronic states are thus desirable, if the computational demand is allowable. The molecular formula and weight for the aryl ether azodendrimers used by Jiang and Aida w5x is unambiguously assigned in terms of the ‘generation’, n, that is the number of the aromatic layers, and the total number of atoms, N, involved in the azodendrimer molecule is 9 = 2 nq 2 y 32. The number of atoms for the aryl ether azodendrimers with n s 4 and 5, which show the IR-induced cis-to-trans isomerization, is then N s 544 and 1120, respectively. The computational cost for performing the ab initio MO calculations is thus formidable, and we have relied on the use of the MOPAC programs w6,7x with the semi-empirical MNDO, AM1, and PM3 Hamiltonians. All the calculations have been performed for an isolated molecule in a vacuum. In order to tentatively
assess the accuracy of the semi-empirical methods concerning the structural and vibrational properties of the azodendrimers, we have carried out the structural optimization and the normal-mode analysis for the trans- and cis-azobenzenes, and have compared the results with those obtained by the ab initio ŽHartree–Fock, Møller–Plesset, and density functional. calculations w8x and also by experiments. The semi-empirical methods have reproduced the experimental molecular structures of the azobenzenes with accuracy comparable to Žor slightly inferior to. the ab initio methods. Regarding the vibrational normal modes, the semi-empirical calculations have been found to give poorer agreement with experiments, especially in the frequency range of 1500–2000 cmy1 , than the ab initio calculations do, whereas the overall reproduction of the experimental results Že.g., concerning the distribution of the normal-mode frequencies. by the semi-empirical methods is rather satisfactory. 3. Molecular structure The molecular structures were optimized for the trans and cis aryl ether azodendrimers with the 1–4 generations. ŽThe nth generation azodendrimer is hereafter referred to as L nAZO.. The criterion for the convergence of structural optimization was taken as the energy gradient norm being less than 0.1 ˚ The initial structures for the optimizakcalrmolrA. tion were prepared by combining various dendritic fragments, each of which had been optimized in advance, so that the overlap of the atoms was carefully avoided. The azodendrimer molecule is composed of two dendron parts deriving from both the ends of the central azo group w5x. In the case of the azodendrimers whose generation is equal to or less than three, the two dendron subunits have been found to be nearly planar with the use of the MNDO approximation. The two dendron planes are then nearly perpendicular for the trans-azodendrimers and form a stepladder-like structure for the cis-azodendrimers. When using the AM1 and PM3 approximations instead, we observe that the optimized dendron structures are somewhat rounded. In the case of the fourth-generation azodendrimers ŽL4AZO., it becomes rather difficult for the dendron
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subunits to maintain the planar structure since the atoms pertaining to the exterior end groups begin to be overlapped. In addition, we have found a number of stable conformations with the local-minimum energy for both the trans- and cis-isomers, depending on the initial structures for the optimization, probably because of the structural frustration due to the overlapping of atoms. For the trans-structures, we have obtained six locally stable conformations whose heat of formation, H, falls in the range of y1465.4 to y1461.4 kcalrmol using the MNDO Hamiltonian. The features regarding the dendron structures are then characterized as perpendicular, coplanar, spherical, dumb-bell type, and so on. Among them, the perpendicular structure was the lowest in H Žthe most stable. in the MNDO approximation. We illustrate in Fig. 1a–c the perpendicular, coplanar, and dumb-bell type structures optimized in the MNDO scheme. In the case of the PM3 calculations, on the other hand, we have found that the optimized structures become more rounded than those for the MNDO case, which is analogous to the cases for the lower generations. The heat of formation was much more dispersed Ž; 37 kcalrmol. among the six metastable trans structures in comparison to the MNDO case, and the spherical structure, shown in Fig. 1d, was found to be energetically the most stable. As for the cis-L4AZO, we have found three locally stable conformations in the MNDO and PM3 calculations. The most stable structures obtained in the MNDO and PM3 schemes are depicted in Fig. 2, showing a fairly rounded, stepladder-like structure. Dendrimers show a variety of salient photonic functions. For instance, when they are photoexcited, it seems that the excitation energy is efficiently funnelled toward the ‘reaction center’ along the branching pathways w2–4x and its leaking into the irrelevant channels such as the solvent modes is prevented by the close-packed, rigid outer shell. These functions are often referred to as the ‘antenna’ and ‘shell’ effects w9x, and are supposed to be intimately related to the unique dendritic architecture. To study the relationship between the molecular structure and the photofunctionality of the aryl ether azodendrimers, we have calculated the radial distribution of atoms around the central azo group using the optimized structures obtained above. Fig. 3 illustrates the radial distribution function r Ž r . of atoms
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except the nitrogen atoms as a function of the distance r from the middle point of the central N-N bond in the cases of the most stable, fourth- and third-generation trans- and cis-azodendrimers optimized by the MNDO method. We observe in this figure that the radial distribution for these highergeneration dendrimer atoms shows an oscillatory, shell-like structure, whereas this feature virtually disappears for the cis-L3AZO. These characteristic features of r Ž r . are common to all the conformations obtained by the MNDO and PM3 calculations. Experimentally w5x, the aryl ether azodendrimers show the IR-induced cis-to-trans isomerization for the generation n 0 4. To quantitatively study the difference in the molecular structure between the L3AZO and L4AZO, we have estimated the fractal dimension w10,11x by analyzing the number of atoms involved within a sphere of radius r around the central azo group, M Ž r ., which is obtained by radially integrating r Ž r . calculated for all the conformations. The fractal dimension d is then evaluated in terms of the r dependence of M Ž r ., that is M Ž r . A r d. In the case of the cis structure, the fractal dimension for the L3AZO is 1.9 and 2.0 in the MNDO and PM3 calculations, respectively, reflecting the planarity Žtwo-dimensionality. of the dendron subunits. For the L4AZO, on the other hand, the Žaveraged. fractal dimension is found to be 2.2 and 2.3 in the MNDO and PM3 calculations, respectively, suggesting the improved capability of the dendrons to collect the photons from wider directions. This quantitative difference may be related to the enhancement of the antenna effect in the L4AZO. We observe in Fig. 2 that the azo group ‘core’ in the cis-dendrimers is located at the position somewhat deviating from the molecular center, and thus the azo group is not completely wrapped by the surrounding dendrons. Such insufficient protection of the azo core may cause the loss of the shell effect. This degree of the core wrapping can be quantitatively measured by the deviation of the middle point of the central N-N bond, r 0 , from the center of N mass, rc s Ý is1 r irN, where r i is the position of the ith atom. Normalizing < r 0 y rc < by the root-meansquare deviation of all the atomic positions from r 0 , we have defined a parameter D, which is generally smaller when the degree of core wrapping is higher. In the case of trans structure, D does not exceed
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Fig. 1. Stable structures for the trans-L4AZO optimized by the MNDO Ža. – Žc. and PM3 Žd. calculations: Ža. perpendicular type Žthe heat of formation H s y1465.4 kcalrmol., Žb. coplanar type Ž H s y1465.0 kcalrmol., Žc. dumb-bell type Ž H s y1461.4 kcalrmol., and Žd. spherical type Ž H s y1429.4 kcalrmol.. The purple, green, blue, and red balls represent the nitrogen, carbon, hydrogen, and oxygen atoms, respectively.
0.10 for n ( 4. In the case of cis structure, on the other hand, D takes a value of 0.54, 0.48, 0.47, and
0.40 for n s 1, 2, 3, and 4, respectively, averaged over all the conformations obtained in the MNDO
Fig. 2. Most stable structures for the cis-L4AZO optimized by the MNDO Ža. Ž H s y1461.7 kcalrmol. and PM3 Žb. Ž H s y1425.7 kcalrmol. calculations. The assignment of colors for the atoms is the same as in Fig. 1.
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Fig. 3. Radial distribution function r Ž r . of all the atoms but the nitrogen atoms as a function of the distance r from the middle point of the central N-N bond calculated in the MNDO scheme for Ža. the trans-L3AZO Žtriangles and dashed line. and transL4AZO Žcircles and solid line for the most stable structure; see Fig. 1a., and Žb. the cis-L3AZO Žtriangles and dashed line. and cis-L4AZO Žcircles and solid line for the most stable structure; see Fig. 2a..
approximation. In the PM3 approximation, it takes a value of 0.59, 0.49, and 0.39 for n s 1, 3, and 4, respectively. A critical value of D s 0.40 thus appears to distinguish between the cis-L3AZO and cis-L4AZO with respect to the degree of core wrapping, and possibly to the shell effect. 4. Normal-mode analysis The information on the vibrational normal modes is essential for the study of the cis-to-trans isomer-
ization in the aryl ether azodendrimers since the reaction takes place via the intramolecular vibrational energy excitation and transfer triggered by IR irradiation w5x. We have carried out the calculations of the vibrational normal modes on the basis of the optimized structures for azodendrimers and, for comparison, azobenzenes w8x. We show in Fig. 4a a comparison of the normalmode frequency distribution calculated in the MNDO approximation for the L4AZO, in which the phonon Žvibrational mode. density of states ŽDOS. is illustrated for the perpendicular and coplanar trans structures and the most stable cis structure. It is remarkable that the calculated phonon DOSs are nearly identical over the whole frequency range in spite of the significant difference in the molecular structures observed in Figs. 1 and 2. The similarity of the phonon DOS for the aryl ether azodendrimers is also observed among the different generations. For example, we show in Fig. 4b a comparison of the normalized phonon DOS between the cis-L4AZO and L3AZO calculated in the MNDO approximation. These two DOS curves are almost completely overlapped over the whole frequency range and markedly different from the DOS curve for the cis-azobenzene shown for the sake of comparison. The analogous identity regarding the normalized phonon DOS is also observed in the comparison between the L3AZO and L1AZO Žnot shown., and is independent of the approximation employed, as seen in Fig. 4c illustrating the DOS curves calculated in the PM3 approximation. Thus, we have found, through realistic quantumchemical calculations, a kind of scaling property or invariance with regard to the distribution of the vibrational normal-mode frequencies for the aryl ether azodendrimers with the generation n s 1–4. Such an identity of the normalized phonon DOS irrespective of the generation and the molecular structure seems to suggest that, in addition to the self-similar architecture of dendrons, the normalmode frequencies are essentially determined by the local modes pertaining to the small constituent units or fragments of the whole dendrimer molecule. In fact, we have observed that the vibrational normal modes are relatively localized spatially in the higher-generation dendrimers when their eigenvectors and associated harmonic oscillations are de-
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picted by means of the computer graphics ŽSpaceFinder, DAIKIN-COMTEC..
5. Discussion In this section we discuss the implications of our calculated results in relation to the IR-induced cis-
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to-trans isomerization of the aryl ether azodendrimers. It is observed in Fig. 4 that the phonon DOS for the azodendrimers has a characteristic gap structure in the range of about 700–900 cmy1 , which is in marked contrast with the case of azobenzene. This DOS gap is common to all the generations and to all the approximation methods such as MNDO, AM1, and PM3 employed in the calculations. In order to investigate the implication of this gap, we have counted the number of normal modes belonging to the frequency regions of 500–600 cmy1 , 700–900 cmy1 and Žfor the sake of emphasis. 750–900 cmy1 , and also the number of normal modes associated with the motion of the central azo group in the same frequency regions. The results calculated in the PM3 approximation for the third- and Žmost stable. fourth-generation cis-azodendrimers and the cisazobenzene are shown in Table 1, where the ratio of the number of normal modes for a frequency region to their total number for the whole frequency region Ž27 = 2 nq 2 y 102 for the nth generation azodendrimers and 66 for the azobenzene. and the ratio of the number of normal modes associated with the nitrogen motion to that for all the modes in the same frequency region are also shown in the parentheses. Here, the criterion for judging whether or not a normal mode is associated with the motion of the azo group has been chosen so that at least one component of the normal-mode displacement eigenvectors pertaining to the central nitrogen atoms exceeds 0.01 for the L3AZO and 0.2 for the azobenzene. It is noted that an analogous criterion regarding the motion of carbon atoms next to the nitrogen
Fig. 4. Distribution of the normal-mode frequencies for the aryl ether azodendrimers Žand the azobenzene, for comparison.. The phonon density of states ŽDOS. is normalized so that the sum of the contributions from all the normal modes is set equal to unity, where the Gaussian distribution with the dispersion of 15 cmy1 Ž20 cmy1 in the case of azobenzene. is assigned to each normal mode. Ža. Phonon DOS for the L4AZO: solid, dashed, and dotted lines Žall of which are nearly identical. denote the results for the most stable cis structure, the perpendicular trans structure, and the coplanar trans structure, respectively, calculated in the MNDO scheme. Žb. Phonon DOS for the Žmost stable. cis-L4AZO Žsolid line., the cis-L3AZO Ždotted line., and the cis-azobenzene Ždashed line. calculated in the MNDO scheme. Žc. Phonon DOS calculated in the PM3 scheme. Otherwise the same as in Žb..
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Table 1 Number of vibrational normal modes belonging to the specific frequency range and its ratio Žshown in parenthesis. to the total number of normal modes for the cis-azodendrimers and cisazobenzene calculated in the PM3 scheme Župper row.. Shown in the lower row are the number of the normal modes associated with the motion of the central azo group and its ratio Žshown in parenthesis. to the number of all the modes in the same frequency range Molecule
Mode
Azobenzene
All N-N All N-N All
L3AZO L4AZO
Frequency range Žcmy1 . 500–600
700–900
750–900
2 Ž3.0%. 2 Ž100%. 45 Ž5.9%. 42 Ž93%. 97 Ž6.0%.
7 Ž10.6%. 4 Ž57%. 15 Ž2.0%. 8 Ž53%. 31 Ž1.9%.
6 Ž9.1%. 3 Ž50%. 8 Ž1.0%. 3 Ž38%. 9 Ž0.6%.
atoms has led to an analogous result. We also note that the results for the L4AZO are virtually the same as those for the L3AZO due to the similarity of the vibrational characteristics, as mentioned above. In the light of the theories respecting the intramolecular vibrational energy redistribution w12,13x, the vibrational energy excited in a molecule tends to be preferably transferred to the modes whose frequency forms a simple integral ratio to the excitedmode frequency through the nonlinear Fermi resonance. Therefore, the excitation energy of the 1600 cmy1 stretching mode for aromatic rings in the azodendrimers w5x would be favorably transferred to the modes existing in about 700–900 cmy1 and 500–600 cmy1 regions through the 2:1 and 3:1 resonances, respectively. It is noted here that the aromatic stretching modes with the frequencies of about 1600 cmy1 are expected to be excited not only in the peripheral region of the dendrimer but also near the azo core region because of the spread of IR irradiation andror the subsequent resonant energy transfer between the aromatic rings. For the modes in the 700–900 cmy1 region, as seen in Table 1, the ratio of modes associated with the motion of the azo group is about a half in both the cases of azobenzene and azodendrimers. Although this ratio is not so low in comparison to that in other frequency regions generally, it is fairly lower than that in the 500–600 cmy1 region. In the case of azobenzene, the excitation energy transferred to the 700–900 cmy1 region would thus dissipate into a number of channels which are irrelevant to the cis-to-trans isomeriza-
tion. In the case of azodendrimers, on the other hand, such an energy dissipation is effectively avoided due to the phonon DOS gap. The excitation energy favorably transferred to the 500–600 cmy1 region would then be efficiently utilized for the isomerization, because a large part of the modes in this region are associated with the motion of the azo group, as seen in Table 1. Regarding the vibrational patterns of the normal modes, we have observed through the computer graphics that a number of modes in the 500–600 cmy1 and 700–900 cmy1 regions actually show bending motions of C–N-N–C associated with the cis-to-trans isomerization. The vibrational properties of the aryl ether azodendrimers have thus been found to favor an efficient utilization of the IR-excited vibrational energy for the cis-to-trans isomerization. It is remarked, however, that this advantage is common to all the generations and therefore does not distinguish between the third- and fourth-generations with respect to the occurrence of the isomerization. The quantitative differences regarding the fractal dimension and the degree of core wrapping, as discussed in Section 3, may then provide key factors governing the IR-induced isomerization of the azodendrimers. In addition, the effects of geometric bias and energy gradient w2–4x associated with the hierarchical and self-similar dendritic architectures, and the effects of ‘spherical’ morphology w5,14x may play important roles. Finally, the present calculations have been carried out for isolated dendrimer molecules in a vacuum. The effects of surrounding solvent and intermolecular interactions remain to be investigated. 6. Conclusions We have performed the structural optimization and the normal-mode analysis for the trans and cis aryl ether azodendrimers with the generation n ( 4 on the basis of the semi-empirical MO methods such as MNDO, AM1, and PM3 schemes. We have calculated the stable molecular structure, the intramolecular atomic distribution, the fractal dimension, the degree of core wrapping, and the normal-mode frequency distribution, and have discussed their implications in relation to the anomalous IR-induced cisto-trans isomerization observed experimentally. The
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fractal dimension and the degree of core wrapping are markedly different between the third- and fourth-generation azodendrimers, and may be related with the antenna and shell effects which are essential for the occurrence of the isomerization. We have also found that the normalized phonon DOS for the aryl ether azodendrimers is virtually invariable irrespective of the molecular structure and the generation, and that it has a characteristic gap structure in the frequency range of about 700–900 cmy1 , which seems to be associated with the efficient transfer of the vibrational energy excited with 1600 cmy1 to the azo core region.
Acknowledgements We would like to thank Prof. T. Aida and Prof. O. Kitao for useful discussions and comments.
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References w1x D.A. Tomalia, A.M. Naylor, W.A. Goddard III, Angew. Chem. Int. Ed. Engl. 29 Ž1990. 138. w2x C. Devadoss, P. Bharathi, J.S. Moore, J. Am. Chem. Soc. 118 Ž1996. 9635. w3x R. Kopelman, M. Shortreed, Z.-Y. Shi, W. Tan, Z. Xu, J.S. Moore, A. Bar-Haim, J. Klafter, Phys. Rev. Lett. 78 Ž1997. 1239. w4x A. Bar-Haim, J. Klafter, R. Kopelman, J. Am. Chem. Soc. 119 Ž1997. 6197. w5x D.-L. Jiang, T. Aida, Nature 388 Ž1997. 454. w6x J.J.P. Stewart, MOPAC 93, Fujitsu, Tokyo, 1993. w7x J.J.P. Stewart, MOPAC 2000, Fujitsu, Tokyo, 1999. w8x N. Kurita, S. Tanaka, S. Itoh, in preparation. w9x M. Kawa, J.M.J. Frechet, Chem. Mater. 10 Ž1998. 286. ´ w10x M.L. Mansfield, Polymer 35 Ž1994. 1827. w11x M. Murat, G.S. Grest, Macromolecules 29 Ž1996. 1278. w12x T. Uzer, W.H. Miller, Phys. Rep. 199 Ž1991. 73. w13x T.J. Minehardt, J.D. Adcock, R.E. Wyatt, Chem. Phys. Lett. 303 Ž1999. 537. w14x D.-L. Jiang, T. Aida, J. Am. Chem. Soc. 120 Ž1998. 10895.
Chemical Physics Letters 323 Ž2000. 407–415 www.elsevier.nlrlocatercplett
Structural and vibrational analysis of azodendrimers by molecular orbital methods Shigenori Tanaka a
a,)
, Satoshi Itoh a , Noriyuki Kurita
b
AdÕanced Materials and DeÕices Laboratory, Toshiba Research and DeÕelopment Center, 1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, Japan b Department of Knowledge-Based Information Engineering, Toyohashi UniÕersity of Technology, Tempaku-cho, Toyohashi 441-8580, Japan Received 14 February 2000; in final form 3 May 2000
Abstract The structural optimization and normal-mode analysis are performed for the aryl ether azodendrimers on the basis of the semi-empirical molecular orbital methods. Through the geometrical characterization for the stable structures, the fractal dimension and the degree of azo core wrapping are found to provide key parameters related to the unique photoinduced isomerization. We also find that the normal-mode frequency distribution is virtually invariable irrespective of the molecular structure and generation of azodendrimers. The importance of normal-mode distribution gap in the range of 700–900 cmy1 is suggested regarding the efficient vibrational energy transfer to the azo core region. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Dendrimers are nano-sized hyperbranched macromolecules with a regular tree-like structure made up of repeating units arranged in a hierarchical and self-similar fashion w1x. They have recently attracted increasing attention w2–4x as artificial light-harvesting antennae for photon energy transduction similar to biological photosynthetic systems. In a recent, remarkable experiment, Jiang and Aida w5x have found that a large aryl ether azodendrimer undergoes cis-to-trans isomerization at the interior azo unit upon exposure to weak infrared ŽIR. light with the frequency of about 1600 cmy1 . Because the activa-
) Corresponding author. Fax: q81-44-520-1801; e-mail: [email protected]
tion energy for the isomerization is 0.84 eV, this experimental result suggests that ‘multiphotonic’ or ‘up-conversion’ processes involving at least five quanta are induced by weak IR irradiation. The photon energies converted to molecular vibrations migrate in the interior of molecule and are transferred to the azo core with little dissipation into irrelevant modes. These salient features are supposed to be intimately related to the unique dendritic structure and a number of potential applications of dendrimers to novel photofunctional materials have been suggested. However, the microscopic mechanism of the photoinduced isomerization remains to be elucidated. In order to provide a theoretical basis for investigating the mechanism of the photon energy transduction and the subsequent cis-to-trans isomerization, in this Letter we report on the structural and vibrational
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 5 5 2 - 2
408
S. Tanaka et al.r Chemical Physics Letters 323 (2000) 407–415
analyses of aryl ether azodendrimers performed on the basis of molecular orbital ŽMO. methods. Since the number of atoms involved in the large azodendrimers showing the IR-induced isomerization exceeds 500, we employ the semi-empirical MO method such as MNDO, AM1, and PM3 schemes as a best compromise between accuracy and computational demand. We first optimize the molecular structures of trans- and cis-azodendrimers and characterize them to study the relationship between the dendritic structure and the efficient light-harvesting function. The calculations of the vibrational normal modes are then carried out for the optimized structures and their implications concerning the intramolecular vibrational energy transfer are discussed.
2. Methods We have carried out the electronic structure calculations for the azodendrimers on the basis of quantum-chemical MO methods. Although the molecular simulations regarding the structural and vibrational properties of macromolecules involving more than hundreds of atoms are usually performed by the classical molecular mechanics andror dynamics calculations, the inaccuracies of the interatomic force field assumed in the model often cause erroneous results, and this is especially so in the case of novel materials. The simulations taking into account the degree of freedom for the electronic states are thus desirable, if the computational demand is allowable. The molecular formula and weight for the aryl ether azodendrimers used by Jiang and Aida w5x is unambiguously assigned in terms of the ‘generation’, n, that is the number of the aromatic layers, and the total number of atoms, N, involved in the azodendrimer molecule is 9 = 2 nq 2 y 32. The number of atoms for the aryl ether azodendrimers with n s 4 and 5, which show the IR-induced cis-to-trans isomerization, is then N s 544 and 1120, respectively. The computational cost for performing the ab initio MO calculations is thus formidable, and we have relied on the use of the MOPAC programs w6,7x with the semi-empirical MNDO, AM1, and PM3 Hamiltonians. All the calculations have been performed for an isolated molecule in a vacuum. In order to tentatively
assess the accuracy of the semi-empirical methods concerning the structural and vibrational properties of the azodendrimers, we have carried out the structural optimization and the normal-mode analysis for the trans- and cis-azobenzenes, and have compared the results with those obtained by the ab initio ŽHartree–Fock, Møller–Plesset, and density functional. calculations w8x and also by experiments. The semi-empirical methods have reproduced the experimental molecular structures of the azobenzenes with accuracy comparable to Žor slightly inferior to. the ab initio methods. Regarding the vibrational normal modes, the semi-empirical calculations have been found to give poorer agreement with experiments, especially in the frequency range of 1500–2000 cmy1 , than the ab initio calculations do, whereas the overall reproduction of the experimental results Že.g., concerning the distribution of the normal-mode frequencies. by the semi-empirical methods is rather satisfactory. 3. Molecular structure The molecular structures were optimized for the trans and cis aryl ether azodendrimers with the 1–4 generations. ŽThe nth generation azodendrimer is hereafter referred to as L nAZO.. The criterion for the convergence of structural optimization was taken as the energy gradient norm being less than 0.1 ˚ The initial structures for the optimizakcalrmolrA. tion were prepared by combining various dendritic fragments, each of which had been optimized in advance, so that the overlap of the atoms was carefully avoided. The azodendrimer molecule is composed of two dendron parts deriving from both the ends of the central azo group w5x. In the case of the azodendrimers whose generation is equal to or less than three, the two dendron subunits have been found to be nearly planar with the use of the MNDO approximation. The two dendron planes are then nearly perpendicular for the trans-azodendrimers and form a stepladder-like structure for the cis-azodendrimers. When using the AM1 and PM3 approximations instead, we observe that the optimized dendron structures are somewhat rounded. In the case of the fourth-generation azodendrimers ŽL4AZO., it becomes rather difficult for the dendron
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subunits to maintain the planar structure since the atoms pertaining to the exterior end groups begin to be overlapped. In addition, we have found a number of stable conformations with the local-minimum energy for both the trans- and cis-isomers, depending on the initial structures for the optimization, probably because of the structural frustration due to the overlapping of atoms. For the trans-structures, we have obtained six locally stable conformations whose heat of formation, H, falls in the range of y1465.4 to y1461.4 kcalrmol using the MNDO Hamiltonian. The features regarding the dendron structures are then characterized as perpendicular, coplanar, spherical, dumb-bell type, and so on. Among them, the perpendicular structure was the lowest in H Žthe most stable. in the MNDO approximation. We illustrate in Fig. 1a–c the perpendicular, coplanar, and dumb-bell type structures optimized in the MNDO scheme. In the case of the PM3 calculations, on the other hand, we have found that the optimized structures become more rounded than those for the MNDO case, which is analogous to the cases for the lower generations. The heat of formation was much more dispersed Ž; 37 kcalrmol. among the six metastable trans structures in comparison to the MNDO case, and the spherical structure, shown in Fig. 1d, was found to be energetically the most stable. As for the cis-L4AZO, we have found three locally stable conformations in the MNDO and PM3 calculations. The most stable structures obtained in the MNDO and PM3 schemes are depicted in Fig. 2, showing a fairly rounded, stepladder-like structure. Dendrimers show a variety of salient photonic functions. For instance, when they are photoexcited, it seems that the excitation energy is efficiently funnelled toward the ‘reaction center’ along the branching pathways w2–4x and its leaking into the irrelevant channels such as the solvent modes is prevented by the close-packed, rigid outer shell. These functions are often referred to as the ‘antenna’ and ‘shell’ effects w9x, and are supposed to be intimately related to the unique dendritic architecture. To study the relationship between the molecular structure and the photofunctionality of the aryl ether azodendrimers, we have calculated the radial distribution of atoms around the central azo group using the optimized structures obtained above. Fig. 3 illustrates the radial distribution function r Ž r . of atoms
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except the nitrogen atoms as a function of the distance r from the middle point of the central N-N bond in the cases of the most stable, fourth- and third-generation trans- and cis-azodendrimers optimized by the MNDO method. We observe in this figure that the radial distribution for these highergeneration dendrimer atoms shows an oscillatory, shell-like structure, whereas this feature virtually disappears for the cis-L3AZO. These characteristic features of r Ž r . are common to all the conformations obtained by the MNDO and PM3 calculations. Experimentally w5x, the aryl ether azodendrimers show the IR-induced cis-to-trans isomerization for the generation n 0 4. To quantitatively study the difference in the molecular structure between the L3AZO and L4AZO, we have estimated the fractal dimension w10,11x by analyzing the number of atoms involved within a sphere of radius r around the central azo group, M Ž r ., which is obtained by radially integrating r Ž r . calculated for all the conformations. The fractal dimension d is then evaluated in terms of the r dependence of M Ž r ., that is M Ž r . A r d. In the case of the cis structure, the fractal dimension for the L3AZO is 1.9 and 2.0 in the MNDO and PM3 calculations, respectively, reflecting the planarity Žtwo-dimensionality. of the dendron subunits. For the L4AZO, on the other hand, the Žaveraged. fractal dimension is found to be 2.2 and 2.3 in the MNDO and PM3 calculations, respectively, suggesting the improved capability of the dendrons to collect the photons from wider directions. This quantitative difference may be related to the enhancement of the antenna effect in the L4AZO. We observe in Fig. 2 that the azo group ‘core’ in the cis-dendrimers is located at the position somewhat deviating from the molecular center, and thus the azo group is not completely wrapped by the surrounding dendrons. Such insufficient protection of the azo core may cause the loss of the shell effect. This degree of the core wrapping can be quantitatively measured by the deviation of the middle point of the central N-N bond, r 0 , from the center of N mass, rc s Ý is1 r irN, where r i is the position of the ith atom. Normalizing < r 0 y rc < by the root-meansquare deviation of all the atomic positions from r 0 , we have defined a parameter D, which is generally smaller when the degree of core wrapping is higher. In the case of trans structure, D does not exceed
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Fig. 1. Stable structures for the trans-L4AZO optimized by the MNDO Ža. – Žc. and PM3 Žd. calculations: Ža. perpendicular type Žthe heat of formation H s y1465.4 kcalrmol., Žb. coplanar type Ž H s y1465.0 kcalrmol., Žc. dumb-bell type Ž H s y1461.4 kcalrmol., and Žd. spherical type Ž H s y1429.4 kcalrmol.. The purple, green, blue, and red balls represent the nitrogen, carbon, hydrogen, and oxygen atoms, respectively.
0.10 for n ( 4. In the case of cis structure, on the other hand, D takes a value of 0.54, 0.48, 0.47, and
0.40 for n s 1, 2, 3, and 4, respectively, averaged over all the conformations obtained in the MNDO
Fig. 2. Most stable structures for the cis-L4AZO optimized by the MNDO Ža. Ž H s y1461.7 kcalrmol. and PM3 Žb. Ž H s y1425.7 kcalrmol. calculations. The assignment of colors for the atoms is the same as in Fig. 1.
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Fig. 3. Radial distribution function r Ž r . of all the atoms but the nitrogen atoms as a function of the distance r from the middle point of the central N-N bond calculated in the MNDO scheme for Ža. the trans-L3AZO Žtriangles and dashed line. and transL4AZO Žcircles and solid line for the most stable structure; see Fig. 1a., and Žb. the cis-L3AZO Žtriangles and dashed line. and cis-L4AZO Žcircles and solid line for the most stable structure; see Fig. 2a..
approximation. In the PM3 approximation, it takes a value of 0.59, 0.49, and 0.39 for n s 1, 3, and 4, respectively. A critical value of D s 0.40 thus appears to distinguish between the cis-L3AZO and cis-L4AZO with respect to the degree of core wrapping, and possibly to the shell effect. 4. Normal-mode analysis The information on the vibrational normal modes is essential for the study of the cis-to-trans isomer-
ization in the aryl ether azodendrimers since the reaction takes place via the intramolecular vibrational energy excitation and transfer triggered by IR irradiation w5x. We have carried out the calculations of the vibrational normal modes on the basis of the optimized structures for azodendrimers and, for comparison, azobenzenes w8x. We show in Fig. 4a a comparison of the normalmode frequency distribution calculated in the MNDO approximation for the L4AZO, in which the phonon Žvibrational mode. density of states ŽDOS. is illustrated for the perpendicular and coplanar trans structures and the most stable cis structure. It is remarkable that the calculated phonon DOSs are nearly identical over the whole frequency range in spite of the significant difference in the molecular structures observed in Figs. 1 and 2. The similarity of the phonon DOS for the aryl ether azodendrimers is also observed among the different generations. For example, we show in Fig. 4b a comparison of the normalized phonon DOS between the cis-L4AZO and L3AZO calculated in the MNDO approximation. These two DOS curves are almost completely overlapped over the whole frequency range and markedly different from the DOS curve for the cis-azobenzene shown for the sake of comparison. The analogous identity regarding the normalized phonon DOS is also observed in the comparison between the L3AZO and L1AZO Žnot shown., and is independent of the approximation employed, as seen in Fig. 4c illustrating the DOS curves calculated in the PM3 approximation. Thus, we have found, through realistic quantumchemical calculations, a kind of scaling property or invariance with regard to the distribution of the vibrational normal-mode frequencies for the aryl ether azodendrimers with the generation n s 1–4. Such an identity of the normalized phonon DOS irrespective of the generation and the molecular structure seems to suggest that, in addition to the self-similar architecture of dendrons, the normalmode frequencies are essentially determined by the local modes pertaining to the small constituent units or fragments of the whole dendrimer molecule. In fact, we have observed that the vibrational normal modes are relatively localized spatially in the higher-generation dendrimers when their eigenvectors and associated harmonic oscillations are de-
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picted by means of the computer graphics ŽSpaceFinder, DAIKIN-COMTEC..
5. Discussion In this section we discuss the implications of our calculated results in relation to the IR-induced cis-
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to-trans isomerization of the aryl ether azodendrimers. It is observed in Fig. 4 that the phonon DOS for the azodendrimers has a characteristic gap structure in the range of about 700–900 cmy1 , which is in marked contrast with the case of azobenzene. This DOS gap is common to all the generations and to all the approximation methods such as MNDO, AM1, and PM3 employed in the calculations. In order to investigate the implication of this gap, we have counted the number of normal modes belonging to the frequency regions of 500–600 cmy1 , 700–900 cmy1 and Žfor the sake of emphasis. 750–900 cmy1 , and also the number of normal modes associated with the motion of the central azo group in the same frequency regions. The results calculated in the PM3 approximation for the third- and Žmost stable. fourth-generation cis-azodendrimers and the cisazobenzene are shown in Table 1, where the ratio of the number of normal modes for a frequency region to their total number for the whole frequency region Ž27 = 2 nq 2 y 102 for the nth generation azodendrimers and 66 for the azobenzene. and the ratio of the number of normal modes associated with the nitrogen motion to that for all the modes in the same frequency region are also shown in the parentheses. Here, the criterion for judging whether or not a normal mode is associated with the motion of the azo group has been chosen so that at least one component of the normal-mode displacement eigenvectors pertaining to the central nitrogen atoms exceeds 0.01 for the L3AZO and 0.2 for the azobenzene. It is noted that an analogous criterion regarding the motion of carbon atoms next to the nitrogen
Fig. 4. Distribution of the normal-mode frequencies for the aryl ether azodendrimers Žand the azobenzene, for comparison.. The phonon density of states ŽDOS. is normalized so that the sum of the contributions from all the normal modes is set equal to unity, where the Gaussian distribution with the dispersion of 15 cmy1 Ž20 cmy1 in the case of azobenzene. is assigned to each normal mode. Ža. Phonon DOS for the L4AZO: solid, dashed, and dotted lines Žall of which are nearly identical. denote the results for the most stable cis structure, the perpendicular trans structure, and the coplanar trans structure, respectively, calculated in the MNDO scheme. Žb. Phonon DOS for the Žmost stable. cis-L4AZO Žsolid line., the cis-L3AZO Ždotted line., and the cis-azobenzene Ždashed line. calculated in the MNDO scheme. Žc. Phonon DOS calculated in the PM3 scheme. Otherwise the same as in Žb..
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Table 1 Number of vibrational normal modes belonging to the specific frequency range and its ratio Žshown in parenthesis. to the total number of normal modes for the cis-azodendrimers and cisazobenzene calculated in the PM3 scheme Župper row.. Shown in the lower row are the number of the normal modes associated with the motion of the central azo group and its ratio Žshown in parenthesis. to the number of all the modes in the same frequency range Molecule
Mode
Azobenzene
All N-N All N-N All
L3AZO L4AZO
Frequency range Žcmy1 . 500–600
700–900
750–900
2 Ž3.0%. 2 Ž100%. 45 Ž5.9%. 42 Ž93%. 97 Ž6.0%.
7 Ž10.6%. 4 Ž57%. 15 Ž2.0%. 8 Ž53%. 31 Ž1.9%.
6 Ž9.1%. 3 Ž50%. 8 Ž1.0%. 3 Ž38%. 9 Ž0.6%.
atoms has led to an analogous result. We also note that the results for the L4AZO are virtually the same as those for the L3AZO due to the similarity of the vibrational characteristics, as mentioned above. In the light of the theories respecting the intramolecular vibrational energy redistribution w12,13x, the vibrational energy excited in a molecule tends to be preferably transferred to the modes whose frequency forms a simple integral ratio to the excitedmode frequency through the nonlinear Fermi resonance. Therefore, the excitation energy of the 1600 cmy1 stretching mode for aromatic rings in the azodendrimers w5x would be favorably transferred to the modes existing in about 700–900 cmy1 and 500–600 cmy1 regions through the 2:1 and 3:1 resonances, respectively. It is noted here that the aromatic stretching modes with the frequencies of about 1600 cmy1 are expected to be excited not only in the peripheral region of the dendrimer but also near the azo core region because of the spread of IR irradiation andror the subsequent resonant energy transfer between the aromatic rings. For the modes in the 700–900 cmy1 region, as seen in Table 1, the ratio of modes associated with the motion of the azo group is about a half in both the cases of azobenzene and azodendrimers. Although this ratio is not so low in comparison to that in other frequency regions generally, it is fairly lower than that in the 500–600 cmy1 region. In the case of azobenzene, the excitation energy transferred to the 700–900 cmy1 region would thus dissipate into a number of channels which are irrelevant to the cis-to-trans isomeriza-
tion. In the case of azodendrimers, on the other hand, such an energy dissipation is effectively avoided due to the phonon DOS gap. The excitation energy favorably transferred to the 500–600 cmy1 region would then be efficiently utilized for the isomerization, because a large part of the modes in this region are associated with the motion of the azo group, as seen in Table 1. Regarding the vibrational patterns of the normal modes, we have observed through the computer graphics that a number of modes in the 500–600 cmy1 and 700–900 cmy1 regions actually show bending motions of C–N-N–C associated with the cis-to-trans isomerization. The vibrational properties of the aryl ether azodendrimers have thus been found to favor an efficient utilization of the IR-excited vibrational energy for the cis-to-trans isomerization. It is remarked, however, that this advantage is common to all the generations and therefore does not distinguish between the third- and fourth-generations with respect to the occurrence of the isomerization. The quantitative differences regarding the fractal dimension and the degree of core wrapping, as discussed in Section 3, may then provide key factors governing the IR-induced isomerization of the azodendrimers. In addition, the effects of geometric bias and energy gradient w2–4x associated with the hierarchical and self-similar dendritic architectures, and the effects of ‘spherical’ morphology w5,14x may play important roles. Finally, the present calculations have been carried out for isolated dendrimer molecules in a vacuum. The effects of surrounding solvent and intermolecular interactions remain to be investigated. 6. Conclusions We have performed the structural optimization and the normal-mode analysis for the trans and cis aryl ether azodendrimers with the generation n ( 4 on the basis of the semi-empirical MO methods such as MNDO, AM1, and PM3 schemes. We have calculated the stable molecular structure, the intramolecular atomic distribution, the fractal dimension, the degree of core wrapping, and the normal-mode frequency distribution, and have discussed their implications in relation to the anomalous IR-induced cisto-trans isomerization observed experimentally. The
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fractal dimension and the degree of core wrapping are markedly different between the third- and fourth-generation azodendrimers, and may be related with the antenna and shell effects which are essential for the occurrence of the isomerization. We have also found that the normalized phonon DOS for the aryl ether azodendrimers is virtually invariable irrespective of the molecular structure and the generation, and that it has a characteristic gap structure in the frequency range of about 700–900 cmy1 , which seems to be associated with the efficient transfer of the vibrational energy excited with 1600 cmy1 to the azo core region.
Acknowledgements We would like to thank Prof. T. Aida and Prof. O. Kitao for useful discussions and comments.
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