- Email: [email protected]
Organic chromophores under tensile stress
Chemical Physics 289 (2003) 381–388 www.elsevier.com/locate/chemphys
Organic chromophores under tensile stress €hrig 1, Ulrike Troppmann 2, Irmgard Frank * Ute F. Ro Department Chemie, Ludwig-Maximilians-Universit€at M€unchen, Butenandtstr. 5-13 Haus E, D-81377 M€unchen, Germany Received 13 November 2002
Abstract The effect of tensile stress upon the optical properties of organic dye molecules has been investigated using semiempirical methods (AM1, INDO/S). It is found that some of the dyes exhibit significant changes of absorption wavelengths and/or oscillator strengths, which renders them suitable for mechanochromic single molecule experiments. The changes can be explained on the basis of the relevant frontier orbitals and the structural changes of the dyes upon exertion of tensile stress. 2003 Elsevier Science B.V. All rights reserved.
1. Introduction While theoretical chemists are very familiar with the idea of finding strong changes in optical properties when the structure of a molecule is distorted, color changes upon exertion of mechanical stress are relatively rarely observed in real samples. Obviously the electronic structure of most chromophores is not very much affected by moderate mechanical load, i.e., by mechanical load that does not yet induce decomposition of the system under experimental conditions. However, chromophores that sensitively change their optical
*
Corresponding author. E-mail address: [email protected] (I. Frank). 1 Present address: Laboratorium f€ ur Anorganische Chemie, Eidgen€ ossische Technische Hochschule Z€ urich, CH-8093 Z€ urich, Switzerland. 2 Present address: Max-Planck-Institut f€ ur Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany.
properties when being stretched would be of high interest as optical probes in nanodevices. Experimentally, the interplay between the optical properties of a molecule and its mechanics can be investigated by different approaches. On the one hand, there is the Ôphotomechanical effectÕ, the transformation of light into mechanical work [1], which has been described on a macroscopic scale already in the 1960s. It was observed that a nylon fiber which had been dyed with an azobenzene derivative shrunk by 0.1% in size upon irradiation. This effect was attributed to the photoinduced E–Z isomerization of the azochromophore [2,3]. Recently, the photomechanical effect in azobenzene has been used to build a light-driven motor on the basis of a single molecule [4]. On the other hand, mechanical stress may be used to influence the photophysics of a molecule. This Ômechanochromic approachÕ has been exploited mainly in two-dimensional or threedimensional crystals, in which the material
0301-0104/03/$ - see front matter 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0301-0104(03)00085-5
382
U.F. R€ohrig et al. / Chemical Physics 289 (2003) 381–388
changes color in response to a deformation (see e.g. [5]). In the case of crystalline colloidal arrays it has been demonstrated that compressive stress results in a reversible band shift of 55 nm [6,7]. This mechanochromic response has been attributed to the lattice deformation. A decrease in the interplanar spacing of the particles induces a decrease in the band gap. Recent advances in single molecule spectroscopy and in single molecule atomic force microscopy (AFM) provide the possibility to investigate the mechanochromic approach on a molecular scale, probing the photophysical behavior of a single chromophore subjected to controlled mechanical stress. In recent experiments, a polymer chain was covalently attached to both a surface and an AFM tip [8]. By controlled movement of the AFM tip, the polymer was stretched by a measurable force. In future experiments, a chromophore inserted in a polymer chain shall be expanded. The optical properties of the chromophore will be detected by single molecule optical spectroscopy. The choice of a suitable chromophore is of great importance for the success of the intended experiment. It has to meet certain spectroscopic and mechanical requirements, including: (1) an absorption wavelength well above 400 nm in order to minimize the background noise and the bleaching rate, (2) a high quantum yield and a sufficiently long lifetime to be observable in single molecule experiments, (3) synthetic availability and easy incorporation into a polymer chain, and (4) conformational flexibility. Hemicyanine dyes and Cy5 (Fig. 1(a)) seem to be the most promising chromophores with regard to these requirements. Prior to realizing the complex synthesis of a chromophore covalently bound to a single polymer attached to an AFM tip, quantum chemical calculations have been carried out in order to understand what kind of mechanochromic effects can be expected for the systems under investigation, and in order to give recommendations for the experiment. Exertion of mechanical stress will influence both the ground state and the excited state energy of the chromophore, and a change in the excitation energy can be expected. In addition to this observable, the oscillator strength of the
Fig. 1. (a) Chromophores under investigation. The carbon atoms where tensile stress is applied are marked with black circles. Hemicyanine dyes 1–9, Cy50 , and Cy5. (b) Model systems: ethylene, 1,3-butadiene, 1,3,5-hexatriene, and 1,3,5,7-octatetraene.
transition will be influenced as well as the fluorescence lifetime, due to the fact that some rotational and vibrational relaxation channels may become unavailable. Since at present no computationally efficient method is available to systematically calculate emission spectra for systems of that size, only excitation energies are investigated in this study. We assume that the effect of mechanical stress upon emission is comparable to the effect upon absorption in stiff molecules; in flexible molecules additional effects are to be expected due to geometrical relaxation. We find that there is no simple relation between mechanical load and change of optical properties that might be described by a simple model such as the particle in a box. However, predictions if a molecule changes its absorption wavelength or not when being stretched, are possible on the basis of the structure of the frontier orbitals.
2. Methods In order to gain insight into the effect of tensile stress upon conjugated carbon chains in general without the influence of a specific chromophore geometry, the polyenes ethylene, 1,3-butadiene, 1,3,5-hexatriene, and 1,3,5,7-octatetraene (Fig.
U.F. R€ohrig et al. / Chemical Physics 289 (2003) 381–388
1(b)) were investigated. Tensile stress was simulated by fixing the coordinates of the terminal carbon atoms to increasing values. At each point, the excitation energy was calculated in the optimized geometry. The same procedure was then applied to the 10 dyes (Fig. 1(a)). In this way, we calculated and analyzed the change in the: • heat of formation, • excitation energy, • orbitals involved in the transition, • energy of the frontier orbitals, • shape of the frontier orbitals, and • planarity of the p-system. In order to be able to compare the strain on systems of different size, the results are plotted with respect to the average length of the carbon–carbon double bonds within the polyene chain. All geometry optimizations were carried out in internal coordinates with the semiempirical method AM1 [9] as it is implemented in the program package MOPAC6.0 [10]. After a full optimization, the distance between two terminal methyl carbon atoms was stepwise increased by 0.1–0.2 A and held fixed during subsequent geometry optimizations, in order to simulate mechanical strain on the molecule. For Cy5, the molecule was slightly simplified by substituting four methyl groups by hydrogen atoms, and by replacing the substituents at the nitrogen atoms by two ethyl groups (Fig. 1(a), Cy50 ). These groups are not connected to the conjugated p-system and are not expected to significantly influence the optical and mechanical properties of the dye. In Cy50 , the distance between the terminal carbon atoms of the ethyl tails was successively increased. The excitation energy and the oscillator strength of the first singlet transition were calculated at each optimized geometry, using the INDO/S [11] method in the Gaussian 98 package [12]. The highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) were obtained by single point calculations, using AM1 as implemented in the Gaussian 98 program package. In order to test the accuracy of the semiempirical methods, the heats of formation, the orbital energies, and the orbital shapes were compared to the results of density functional theory (DFT) single point calculations.
383
For all DFT calculations, the BLYP functional [13,14] and the 6-31G basis set were used. AM1 yields good ground state geometries for the polyenes under consideration, although the geometries obtained with DFT calculations show slightly better agreement with experimental geometries (maximum deviation of bond lengths: , BLYP: 0.018 A ). In general, AM1 AM1: 0.024 A too short. For bonding distances are about 0.01 A the stretched molecules, the differences of the AM1 geometries as compared to the DFT geometries are larger, resulting in shorter bonding dis on average) and larger angles betances (0.017 A tween the carbon atoms. The shape of the frontier orbitals from AM1 and from DFT calculations is very similar. Our findings are in agreement with the notion that AM1, although parametrized for neutral molecules, yields generally reliable results for cations and anions [9,15]. In summary, the overall agreement between AM1 and DFT is sufficient to allow for the use of the computationally less demanding semiempirical method. Using the semiempirically optimized structures, INDO/S yields excitation energies in reasonable agreement with available experimental data, as it is shown in Tables 1 and 3. Restricted and unrestricted AM1 calculations for butadiene confirm that in the relevant region (carbon–carbon double bond distance smaller than ) no unpairing of spins has to be considered. 1.4 A In all molecules, the ground state energy increases approximately quadratically with the distance of the terminal carbon atoms within the experimentally relevant region. No significant anharmonicity is observed, because the average bond elongation along the chain is rather small, so that every bonded atom pair is still in the harmonic part of its potential when the whole chain contains enough energy to break one bond [16].
3. Results and discussion 3.1. Polyenes and theoretical considerations 3.1.1. Excitation energies The results of the INDO/S calculations for the first valence excitation of the polyenes stretched up
0 ); average expansion coefficient for the HOMO–LUMO transition (c); excitation energy under tensile stress (Eex ); Excitation energy in the optimized geometry (Eex oscillator strength (f ); energy of the HOMO (EHOMO ) and of the LUMO (ELUMO ). Experimental data [18–20] are given in brackets. All energies are given in eV.
D Max
1.44 0.45 )0.08 )0.41 1.15 0.21 )0.23 )0.50
Min D Max
)10.09 )9.16 )8.74 )8.42
Min
)10.55 )9.33 )8.76 )8.54
D
0.02 0.06 0.08 0.10 0.51 1.01 1.43 1.84
Max Min
0.49 0.95 1.35 1.74
D
0.83 0.31 0.09 0.04
Max
7.22 5.55 4.80 4.25
Min
6.59 5.24 4.71 4.21 Ethylene Butadiene Hexatriene Octatetraene
7.2 5.6 4.8 4.2
(7.66) (5.93) (4.93) (4.28)
0.68 0.69 0.70 0.70
ELUMO EHOMO f Eex c 0 Eex
Table 1 Effect of tensile stress upon the polyenes
0.29 0.24 0.15 0.09
U.F. R€ohrig et al. / Chemical Physics 289 (2003) 381–388
0.46 0.17 0.02 0.12
384
are shown in to a double bond length of 1.4 A Table 1. In all polyenes, the oscillator strength is almost unaffected by the strain. The expansion coefficient for the HOMO ! LUMO excitation (0.68–0.70) indicates that mainly the frontier orbitals are involved in the transition. The longer polyenes exhibit negative LUMO energies which is common for molecules with an extended conjugated p-system. The energetic change of the frontier orbitals upon stretching is shown in Fig. 2 (upper panel). Three effects can be observed: • the HOMO is destabilized, • the LUMO is stabilized, • the effects are strongest in ethylene and become less pronounced with increasing size of the psystem. These observations correlate with the decrease in the excitation energy with increasing strain (Fig. 2, lower panel). In accordance with the behavior of the frontier orbitals, the effect is strongest in ethylene and decreases with the size of the p-system. In butadiene, DEex amounts to 0.31 eV (corresponding to 13 nm) and is thus at the threshold of experimental traceability. Deviations from experiment of up to 0.5 eV for the excitation energies of ethylene and butadiene result from the fact that the INDO/S method was parametrized for excitation energies smaller than 5 eV. 3.1.2. Theoretical model Our observations can be explained within a model describing the effect of tensile stress upon organic conjugated p-systems. The frequently used model of the Ôparticle in a boxÕ does not hold for the description of tensile stress, because it only considers the change of the kinetic energy of the electrons with the size of the box and thus predicts a decrease in energy for all orbitals upon stretching. A look at the components of the Hartree–Fock energy at different bond elongation (Table 2) shows that small changes in the total energy EHF are produced by much bigger but opposite changes in single terms, which all decrease in absolute values. The destabilizing electron–electron and nucleus–nucleus interaction energies decrease due to the bond elongation, while the stabilizing one-electron terms Hii be-
U.F. R€ohrig et al. / Chemical Physics 289 (2003) 381–388
385
clei. This is the case for the bonding rg 1s orbital, but not for the anti-bonding ru 1s orbital, which has a nodal plane between the nuclei. These considerations explain the destabilization of the highest occupied molecular orbitals. The lowest unoccupied molecular orbitals, which possess more nodal planes, are less destabilized or even stabilized by tensile stress. In the following we will concentrate on the discussion of the effect of tensile stress on the frontier orbitals and correlate it to the change of optical properties. 3.2. Hemicyanine dyes 3.2.1. Chromophores with benzene ring substituted in para position Molecules 1, 2, 3, and 6 (Fig. 1(a)) share as a common structural feature the para-substituted benzene ring. 1, 2, and 3 differ only in the number of central double bonds, while 6 differs also in the ortho-substituted pyridine ring. Comparison of the calculated excitation energies in gas phase shows reasonable agreement with experimental data from solution (Table 3). The effect of tensile stress on the electronic transition is summarized in Table 3. We find no significant change in the optical properties, neither in the excitation energy nor in the oscillator strength. The structural changes due to the stress concern mainly bond distances and angles, and do not affect the planarity of the molecules. The frontier orbitals remain similar in shape in the relaxed and in the stretched geometries. The findings indicate that these chromophores are not well suited for experiment, since they do not display stress-dependent optical properties.
Fig. 2. Upper panel: energies of the frontier orbitals of ethylene (crosses), butadiene (diamonds), hexatriene (circles), and octatetraene (triangles) as a function of average double bond lengths. The HOMOs (dashed lines) are shifted up by 7.5 eV in order to facilitate comparison with the LUMOs (full lines). Lower panel: corresponding excitation energies.
come less negative due to the increased distance between electrons and nuclei. As outlined, e.g. in [17] for the case of a diatomic molecule, the virial theorem states that the average kinetic energy of the electron decreases with the nuclear distance around the equilibrium distance Re . The average potential energy between the nuclei increases with R. However, the change in potential energy only affects the electron if it has a high probability of being found between the nu-
Table 2 Energy differences (in eV) due to tensile stress in ethylene and hexatriene as calculated with AM1 ) Double bond lengths (A Ethylene Hexatriene
EHF Eel VKK P 2 ei PP ð2J KÞ P Hii
1.34
1.40
D
1.34
1.40
D
)310.35 )736.15 425.80 )215.06 521.10 )628.63
)310.17 )730.40 420.22 )212.36 518.04 )624.22
0.18 5.76 )5.58 2.70 )3.06 4.41
)876.74 )3298.06 2421.32 )590.86 2707.20 )3002.63
)874.86 )3178.82 2303.96 )578.90 2599.92 )2889.37
1.89 119.24 )117.36 11.96 )107.28 113.26
0 ); average expansion coefficient for the HOMO–LUMO transition (c); excitation energy under tensile stress (Eex ); Excitation energy in the optimized geometry (Eex oscillator strength (f ); energy of the HOMO (EHOMO ) and of the LUMO (ELUMO ). Experimental data for the excitation energies [21–23] are given in brackets. All energies are given in eV.
D Max
)4.87 )4.88 )4.90 )4.95 )5.00 )4.82 )4.90 )4.87 )4.95 )1.10 )4.90 )4.95 )4.98 )5.05 )5.11 )5.08 )5.14 )5.08 )5.09 )1.38
Min D Max
)10.34 )9.91 )9.59 )10.22 )10.55 )10.58 )10.47 )10.83 )10.10 )6.89
Min
)10.48 )10.04 )9.68 )10.26 )11.70 )10.63 )11.21 )11.40 )11.40 )6.93
D
0.08 0.16 0.19 0.57 0.63 0.15 0.15 0.33 0.23 0.63 1.46 1.78 2.04 0.72 0.63 1.19 0.89 1.05 1.37 1.24
Max Min
1.38 1.62 1.83 0.15 0.00 1.04 0.74 0.72 1.14 0.61 0.03 0.07 0.10 0.07 1.00 0.13 0.51 0.74 0.71 0.14
D Max
2.62 2.40 2.26 2.63 3.44 2.59 2.87 2.92 2.97 2.59
Min
0.67 0.64 0.62 0.65 0.52 0.65 0.66 0.66 0.52 ) 1 2 3 4 5 6 7 8 9 Cy50
2.59 (2.48–2.81) 2.33 (2.36–2.53) 2.16 2.63 3.44 2.59 (2.53–2.88) 2.87 2.92 2.94 2.57
2.59 2.33 2.16 2.56 2.44 2.46 2.36 2.18 2.26 2.45
ELUMO EHOMO f Eex c 0 Eex
Table 3 Effect of tensile stress on the dye molecules (numbering given in Fig. 1)
0.03 0.07 0.08 0.10 0.11 0.26 0.24 0.21 0.14 0.28
U.F. R€ohrig et al. / Chemical Physics 289 (2003) 381–388
0.14 0.13 0.09 0.04 1.15 0.05 0.74 0.57 1.30 0.04
386
3.2.2. Sterically hindered chromophore with benzene ring substituted in para position Chromophore 4 is similar to chromophore 1 in the substitution patterns of the aromatic rings, but some steric hindrance is induced by three additional methyl groups. In the relaxed molecule, the aromatic rings are nearly perpendicular to each other, so that the p-electrons cannot delocalize over the whole molecule. Due to the stretching, the steric hindrance becomes less pronounced and the rings become more co-planar, which allows for a higher p-electron delocalization and leads to a fivefold increase in the oscillator strength of the first singlet transition (Table 3). 3.2.3. Chromophores with benzene ring substituted in ortho position Molecules 7 and 8 are both substituted in ortho position at the benzene ring, but the substitution pattern at the pyridine ring differs. While in these two molecules the oscillator strength does not show a strong dependency on the elongation (Table 3), in both cases the excitation wavelength drops distinctly (0.5 resp. 0.7 eV) and is accompanied by a large destabilization of the HOMO (Fig. 3). This behavior can be rationalized by the shape of the frontier orbitals (shown in Fig. 4 for chromophore 7). The HOMO, which is localized on the largely deformed benzene ring, forms an additional nodal plane between the benzene ring and the amino substituent upon stretching. The changes in the LUMO are much smaller, since it is located mainly on the pyridine ring, that is less affected by structural changes. The alteration of the excitation energy of the chromophores 7 and 8 under tensile stress makes them promising candidates for experiments. 3.2.4. Sterically hindered chromophores with benzene ring substituted in ortho position Molecules 5 and 9 differ only in the number of central double bonds. Both contain a benzene ring substituted in ortho position, and both are nonplanar due to massive steric hindrance. Table 3 shows that these chromophores display a significant change in the excitation energy, and chro-
U.F. R€ohrig et al. / Chemical Physics 289 (2003) 381–388
387
transition, since the HOMO 1 ! LUMO transition plays an equally important role. All three orbitals are destabilized by strain, but the HOMO most drastically, so that the overall energy difference decreases in accordance with the excitation energy.
Fig. 3. Upper panel: energy of the frontier orbitals of chromophores 7 (circles) and 8 (crosses). The HOMOs (dashed lines) are shifted up by 7.5 eV in order to facilitate comparison with the LUMOs (full lines). Lower panel: corresponding excitation energies.
Fig. 4. Frontier orbitals of chromophore 7 in the relaxed and in an extended geometry.
mophore 5 additionally displays a prominent increase in the oscillator strength. The amplitude of the elongation correlates strongly with the value of the torsional angle. In contrast to molecule 4, the excitation energy decreases with increasing coplanarity of the rings and increasing delocalization of the p-electrons. In this case, the excitation cannot be approximated as a HOMO ! LUMO
3.2.5. Cy50 In contrast to the hemicyanine dyes, the two lowest lying excited singlet states of Cy50 are degenerate and display a negligible oscillator strength (f < 0:01). The lowest lying allowed transition involves HOMO-8 ! LUMO and HOMO-2 ! LUMO contributions. Since HOMO-8 and HOMO-2 are localized on the sulfate groups, tensile stress has no significant influence on their shape and energy, and the excitation energy is not dependent on tensile stress. However, the oscillator strength decreases by about 50%, which may be detectable in experiments.
4. Conclusions Our calculations on 10 dye molecules allow us to derive general rules about the influence of mechanical stress on dye molecules. Firstly, a significant influence on the absorption wavelength can be anticipated if binding interactions of the HOMO (or other occupied orbitals that are relevant for the specific transition) are clearly distorted by application of strain. Distortion of the LUMO causes much smaller changes (cf. dye 6). Secondly, a significant change of the oscillator strengths can be attained if sterical hindrance is lowered by stretching the molecule. Differentiation of the ground state energy with respect to the stretching coordinate yields an estimation of the force needed to stretch the molecules. In our static calculations we were able to expand the molecules up to a point that corresponds to a force of 6 nN. As we have shown previously with first-principles molecular dynamics simulations [16], the rupture force is influenced by the dynamics of the system which depends on the temperature, the pulling velocity, etc. Since our present calculations (at 0 K) do not take into account the destabilizing vibrational motion of the
388
U.F. R€ohrig et al. / Chemical Physics 289 (2003) 381–388
molecules, very high forces can be reached. The maximum forces attainable in the intended AFM experiment however amount to about 1 nN. Some of the systems under investigation exhibit significant changes of their optical properties already in this region. No detectable optical change can be expected for molecules 1, 2, 3, and 6. In contrast, the sterically hindered systems 4 and 5 show a sharp increase in oscillator strength below a force of 1 nN. Chromophores 5, 7, 8, and 9 show a large wavelength shift of 30–50 nm at low forces, rendering an experimental detection of the mechano-optical effect feasible. However, these chromophores absorb at relatively short wavelengths (in the range below 450 nm). Thus the background noise and high bleaching rates might cause problems in the experiment. For these reasons, chemical modifications of the dyes to achieve a bathochromic shift may be necessary. Finally, Cy5 may represent a good starting point for first tests, since it has been extensively used in single molecule spectroscopy; the calculated decrease in oscillator strength may be detectable experimentally. In conclusion, it is evident from our calculations that dye molecules may exhibit changes of their optical properties that are large enough to be determined in a single molecule experiment. However, the dyes have to be selected carefully. Furthermore, all attachments between surface, tip, polymer, and chromophore, will have to consist of strong covalent bonds to render forces in the order of 1 nN accessible.
Acknowledgements We thank Markus Seitz and Andreas Zumbusch for bringing the topic to our attention and for intensive discussions. We are grateful to the Volkswagen-Stiftung and the Bayerische Forschungsstiftung (FORMAT-Programm) for financial support. Computational resources provided by the Leibniz-Rechenzentrum are gratefully acknowledged.
References [1] O. Pieroni, A. Fissi, N. Angelini, F. Lenci, Acc. Chem. Res. 34 (2001) 9. [2] D.J.W. Bullock, C.W.N. Cumper, A.I. Vogel, J. Chem. Soc. (1965) 5316. [3] E. Merian, Textile Res. J. 36 (1966) 612. [4] T. Hugel, N.B. Holland, A. Cattani, L. Moroder, M. Seitz, H.E. Gaub, Science 296 (2002) 1103. [5] A.C. Edrington, A.M. Urbas, P. DeRege, C.X. Chen, T.M. Swager, N. Hadjichristidis, M. Xenidou, L.J. Fetters, J.D. Joannopoulos, Y. Fink, E.L. Thomas, Adv. Mater. 13 (2001) 421. [6] S.H. Foulger, P. Jiang, A.C. Lattam, D.W. Smith Jr., J. Ballato Jr., J. Langmuir 17 (2001) 6023–6026. [7] S.H. Foulger, P. Jiang, A.C. Lattam, D.W. Smith Jr., J. Ballato, Adv. Mater. 13 (2001) 1898–1901. [8] M. Grandbois, M. Beyer, M. Rief, H. Clausen-Schaumann, H.E. Gaub, Science 283 (1999) 1727. [9] M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. [10] J.J.P. Stewart, J. Comput. Aid. Mol. Des. 4 (1990) 1. [11] J. Ridley, M. Zerner, Theoret. Chim. Acta 32 (1973) 111. [12] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, Gaussian Inc., Pittsburgh, PA, 1998. [13] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [14] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [15] J.J.P. Stewart, in: Reviews in Computational Chemistry, VCH, New York, 1989, p. 45. [16] U.F. R€ ohrig, I. Frank, J. Chem. Phys. 115 (2001) 8670. [17] I.N. Levine, Quantum Chemistry, Prentice-Hall, Upper Saddle River, NJ, 2000. [18] G. Herzberg, Electronic Spectra and Electronic Structure of Polyatomic Molecules, Van Nostrand–Reinhold, New York, 1966. [19] M.B. Robin, Higher Excited States of Polyatomic Molecules, Academic Press, New York, 1985. [20] F. Sondheimer, D.A. Ben-Efraim, R. Wolevsky, J. Am. Chem. Soc. 83 (1961) 1675. [21] M. Matsui, S. Kawamura, K. Shibata, H. Muramatsu, Bull. Chem. Soc. Jpn. 65 (1992) 71. [22] I.A. Al-Ansari, Bull. Soc. Chim. Fr. 134 (1997) 593. [23] X. Cao, J.L. McHale, J. Chem. Phys. 109 (1998) 1901.
Organic chromophores under tensile stress €hrig 1, Ulrike Troppmann 2, Irmgard Frank * Ute F. Ro Department Chemie, Ludwig-Maximilians-Universit€at M€unchen, Butenandtstr. 5-13 Haus E, D-81377 M€unchen, Germany Received 13 November 2002
Abstract The effect of tensile stress upon the optical properties of organic dye molecules has been investigated using semiempirical methods (AM1, INDO/S). It is found that some of the dyes exhibit significant changes of absorption wavelengths and/or oscillator strengths, which renders them suitable for mechanochromic single molecule experiments. The changes can be explained on the basis of the relevant frontier orbitals and the structural changes of the dyes upon exertion of tensile stress. 2003 Elsevier Science B.V. All rights reserved.
1. Introduction While theoretical chemists are very familiar with the idea of finding strong changes in optical properties when the structure of a molecule is distorted, color changes upon exertion of mechanical stress are relatively rarely observed in real samples. Obviously the electronic structure of most chromophores is not very much affected by moderate mechanical load, i.e., by mechanical load that does not yet induce decomposition of the system under experimental conditions. However, chromophores that sensitively change their optical
*
Corresponding author. E-mail address: [email protected] (I. Frank). 1 Present address: Laboratorium f€ ur Anorganische Chemie, Eidgen€ ossische Technische Hochschule Z€ urich, CH-8093 Z€ urich, Switzerland. 2 Present address: Max-Planck-Institut f€ ur Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany.
properties when being stretched would be of high interest as optical probes in nanodevices. Experimentally, the interplay between the optical properties of a molecule and its mechanics can be investigated by different approaches. On the one hand, there is the Ôphotomechanical effectÕ, the transformation of light into mechanical work [1], which has been described on a macroscopic scale already in the 1960s. It was observed that a nylon fiber which had been dyed with an azobenzene derivative shrunk by 0.1% in size upon irradiation. This effect was attributed to the photoinduced E–Z isomerization of the azochromophore [2,3]. Recently, the photomechanical effect in azobenzene has been used to build a light-driven motor on the basis of a single molecule [4]. On the other hand, mechanical stress may be used to influence the photophysics of a molecule. This Ômechanochromic approachÕ has been exploited mainly in two-dimensional or threedimensional crystals, in which the material
0301-0104/03/$ - see front matter 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0301-0104(03)00085-5
382
U.F. R€ohrig et al. / Chemical Physics 289 (2003) 381–388
changes color in response to a deformation (see e.g. [5]). In the case of crystalline colloidal arrays it has been demonstrated that compressive stress results in a reversible band shift of 55 nm [6,7]. This mechanochromic response has been attributed to the lattice deformation. A decrease in the interplanar spacing of the particles induces a decrease in the band gap. Recent advances in single molecule spectroscopy and in single molecule atomic force microscopy (AFM) provide the possibility to investigate the mechanochromic approach on a molecular scale, probing the photophysical behavior of a single chromophore subjected to controlled mechanical stress. In recent experiments, a polymer chain was covalently attached to both a surface and an AFM tip [8]. By controlled movement of the AFM tip, the polymer was stretched by a measurable force. In future experiments, a chromophore inserted in a polymer chain shall be expanded. The optical properties of the chromophore will be detected by single molecule optical spectroscopy. The choice of a suitable chromophore is of great importance for the success of the intended experiment. It has to meet certain spectroscopic and mechanical requirements, including: (1) an absorption wavelength well above 400 nm in order to minimize the background noise and the bleaching rate, (2) a high quantum yield and a sufficiently long lifetime to be observable in single molecule experiments, (3) synthetic availability and easy incorporation into a polymer chain, and (4) conformational flexibility. Hemicyanine dyes and Cy5 (Fig. 1(a)) seem to be the most promising chromophores with regard to these requirements. Prior to realizing the complex synthesis of a chromophore covalently bound to a single polymer attached to an AFM tip, quantum chemical calculations have been carried out in order to understand what kind of mechanochromic effects can be expected for the systems under investigation, and in order to give recommendations for the experiment. Exertion of mechanical stress will influence both the ground state and the excited state energy of the chromophore, and a change in the excitation energy can be expected. In addition to this observable, the oscillator strength of the
Fig. 1. (a) Chromophores under investigation. The carbon atoms where tensile stress is applied are marked with black circles. Hemicyanine dyes 1–9, Cy50 , and Cy5. (b) Model systems: ethylene, 1,3-butadiene, 1,3,5-hexatriene, and 1,3,5,7-octatetraene.
transition will be influenced as well as the fluorescence lifetime, due to the fact that some rotational and vibrational relaxation channels may become unavailable. Since at present no computationally efficient method is available to systematically calculate emission spectra for systems of that size, only excitation energies are investigated in this study. We assume that the effect of mechanical stress upon emission is comparable to the effect upon absorption in stiff molecules; in flexible molecules additional effects are to be expected due to geometrical relaxation. We find that there is no simple relation between mechanical load and change of optical properties that might be described by a simple model such as the particle in a box. However, predictions if a molecule changes its absorption wavelength or not when being stretched, are possible on the basis of the structure of the frontier orbitals.
2. Methods In order to gain insight into the effect of tensile stress upon conjugated carbon chains in general without the influence of a specific chromophore geometry, the polyenes ethylene, 1,3-butadiene, 1,3,5-hexatriene, and 1,3,5,7-octatetraene (Fig.
U.F. R€ohrig et al. / Chemical Physics 289 (2003) 381–388
1(b)) were investigated. Tensile stress was simulated by fixing the coordinates of the terminal carbon atoms to increasing values. At each point, the excitation energy was calculated in the optimized geometry. The same procedure was then applied to the 10 dyes (Fig. 1(a)). In this way, we calculated and analyzed the change in the: • heat of formation, • excitation energy, • orbitals involved in the transition, • energy of the frontier orbitals, • shape of the frontier orbitals, and • planarity of the p-system. In order to be able to compare the strain on systems of different size, the results are plotted with respect to the average length of the carbon–carbon double bonds within the polyene chain. All geometry optimizations were carried out in internal coordinates with the semiempirical method AM1 [9] as it is implemented in the program package MOPAC6.0 [10]. After a full optimization, the distance between two terminal methyl carbon atoms was stepwise increased by 0.1–0.2 A and held fixed during subsequent geometry optimizations, in order to simulate mechanical strain on the molecule. For Cy5, the molecule was slightly simplified by substituting four methyl groups by hydrogen atoms, and by replacing the substituents at the nitrogen atoms by two ethyl groups (Fig. 1(a), Cy50 ). These groups are not connected to the conjugated p-system and are not expected to significantly influence the optical and mechanical properties of the dye. In Cy50 , the distance between the terminal carbon atoms of the ethyl tails was successively increased. The excitation energy and the oscillator strength of the first singlet transition were calculated at each optimized geometry, using the INDO/S [11] method in the Gaussian 98 package [12]. The highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) were obtained by single point calculations, using AM1 as implemented in the Gaussian 98 program package. In order to test the accuracy of the semiempirical methods, the heats of formation, the orbital energies, and the orbital shapes were compared to the results of density functional theory (DFT) single point calculations.
383
For all DFT calculations, the BLYP functional [13,14] and the 6-31G basis set were used. AM1 yields good ground state geometries for the polyenes under consideration, although the geometries obtained with DFT calculations show slightly better agreement with experimental geometries (maximum deviation of bond lengths: , BLYP: 0.018 A ). In general, AM1 AM1: 0.024 A too short. For bonding distances are about 0.01 A the stretched molecules, the differences of the AM1 geometries as compared to the DFT geometries are larger, resulting in shorter bonding dis on average) and larger angles betances (0.017 A tween the carbon atoms. The shape of the frontier orbitals from AM1 and from DFT calculations is very similar. Our findings are in agreement with the notion that AM1, although parametrized for neutral molecules, yields generally reliable results for cations and anions [9,15]. In summary, the overall agreement between AM1 and DFT is sufficient to allow for the use of the computationally less demanding semiempirical method. Using the semiempirically optimized structures, INDO/S yields excitation energies in reasonable agreement with available experimental data, as it is shown in Tables 1 and 3. Restricted and unrestricted AM1 calculations for butadiene confirm that in the relevant region (carbon–carbon double bond distance smaller than ) no unpairing of spins has to be considered. 1.4 A In all molecules, the ground state energy increases approximately quadratically with the distance of the terminal carbon atoms within the experimentally relevant region. No significant anharmonicity is observed, because the average bond elongation along the chain is rather small, so that every bonded atom pair is still in the harmonic part of its potential when the whole chain contains enough energy to break one bond [16].
3. Results and discussion 3.1. Polyenes and theoretical considerations 3.1.1. Excitation energies The results of the INDO/S calculations for the first valence excitation of the polyenes stretched up
0 ); average expansion coefficient for the HOMO–LUMO transition (c); excitation energy under tensile stress (Eex ); Excitation energy in the optimized geometry (Eex oscillator strength (f ); energy of the HOMO (EHOMO ) and of the LUMO (ELUMO ). Experimental data [18–20] are given in brackets. All energies are given in eV.
D Max
1.44 0.45 )0.08 )0.41 1.15 0.21 )0.23 )0.50
Min D Max
)10.09 )9.16 )8.74 )8.42
Min
)10.55 )9.33 )8.76 )8.54
D
0.02 0.06 0.08 0.10 0.51 1.01 1.43 1.84
Max Min
0.49 0.95 1.35 1.74
D
0.83 0.31 0.09 0.04
Max
7.22 5.55 4.80 4.25
Min
6.59 5.24 4.71 4.21 Ethylene Butadiene Hexatriene Octatetraene
7.2 5.6 4.8 4.2
(7.66) (5.93) (4.93) (4.28)
0.68 0.69 0.70 0.70
ELUMO EHOMO f Eex c 0 Eex
Table 1 Effect of tensile stress upon the polyenes
0.29 0.24 0.15 0.09
U.F. R€ohrig et al. / Chemical Physics 289 (2003) 381–388
0.46 0.17 0.02 0.12
384
are shown in to a double bond length of 1.4 A Table 1. In all polyenes, the oscillator strength is almost unaffected by the strain. The expansion coefficient for the HOMO ! LUMO excitation (0.68–0.70) indicates that mainly the frontier orbitals are involved in the transition. The longer polyenes exhibit negative LUMO energies which is common for molecules with an extended conjugated p-system. The energetic change of the frontier orbitals upon stretching is shown in Fig. 2 (upper panel). Three effects can be observed: • the HOMO is destabilized, • the LUMO is stabilized, • the effects are strongest in ethylene and become less pronounced with increasing size of the psystem. These observations correlate with the decrease in the excitation energy with increasing strain (Fig. 2, lower panel). In accordance with the behavior of the frontier orbitals, the effect is strongest in ethylene and decreases with the size of the p-system. In butadiene, DEex amounts to 0.31 eV (corresponding to 13 nm) and is thus at the threshold of experimental traceability. Deviations from experiment of up to 0.5 eV for the excitation energies of ethylene and butadiene result from the fact that the INDO/S method was parametrized for excitation energies smaller than 5 eV. 3.1.2. Theoretical model Our observations can be explained within a model describing the effect of tensile stress upon organic conjugated p-systems. The frequently used model of the Ôparticle in a boxÕ does not hold for the description of tensile stress, because it only considers the change of the kinetic energy of the electrons with the size of the box and thus predicts a decrease in energy for all orbitals upon stretching. A look at the components of the Hartree–Fock energy at different bond elongation (Table 2) shows that small changes in the total energy EHF are produced by much bigger but opposite changes in single terms, which all decrease in absolute values. The destabilizing electron–electron and nucleus–nucleus interaction energies decrease due to the bond elongation, while the stabilizing one-electron terms Hii be-
U.F. R€ohrig et al. / Chemical Physics 289 (2003) 381–388
385
clei. This is the case for the bonding rg 1s orbital, but not for the anti-bonding ru 1s orbital, which has a nodal plane between the nuclei. These considerations explain the destabilization of the highest occupied molecular orbitals. The lowest unoccupied molecular orbitals, which possess more nodal planes, are less destabilized or even stabilized by tensile stress. In the following we will concentrate on the discussion of the effect of tensile stress on the frontier orbitals and correlate it to the change of optical properties. 3.2. Hemicyanine dyes 3.2.1. Chromophores with benzene ring substituted in para position Molecules 1, 2, 3, and 6 (Fig. 1(a)) share as a common structural feature the para-substituted benzene ring. 1, 2, and 3 differ only in the number of central double bonds, while 6 differs also in the ortho-substituted pyridine ring. Comparison of the calculated excitation energies in gas phase shows reasonable agreement with experimental data from solution (Table 3). The effect of tensile stress on the electronic transition is summarized in Table 3. We find no significant change in the optical properties, neither in the excitation energy nor in the oscillator strength. The structural changes due to the stress concern mainly bond distances and angles, and do not affect the planarity of the molecules. The frontier orbitals remain similar in shape in the relaxed and in the stretched geometries. The findings indicate that these chromophores are not well suited for experiment, since they do not display stress-dependent optical properties.
Fig. 2. Upper panel: energies of the frontier orbitals of ethylene (crosses), butadiene (diamonds), hexatriene (circles), and octatetraene (triangles) as a function of average double bond lengths. The HOMOs (dashed lines) are shifted up by 7.5 eV in order to facilitate comparison with the LUMOs (full lines). Lower panel: corresponding excitation energies.
come less negative due to the increased distance between electrons and nuclei. As outlined, e.g. in [17] for the case of a diatomic molecule, the virial theorem states that the average kinetic energy of the electron decreases with the nuclear distance around the equilibrium distance Re . The average potential energy between the nuclei increases with R. However, the change in potential energy only affects the electron if it has a high probability of being found between the nu-
Table 2 Energy differences (in eV) due to tensile stress in ethylene and hexatriene as calculated with AM1 ) Double bond lengths (A Ethylene Hexatriene
EHF Eel VKK P 2 ei PP ð2J KÞ P Hii
1.34
1.40
D
1.34
1.40
D
)310.35 )736.15 425.80 )215.06 521.10 )628.63
)310.17 )730.40 420.22 )212.36 518.04 )624.22
0.18 5.76 )5.58 2.70 )3.06 4.41
)876.74 )3298.06 2421.32 )590.86 2707.20 )3002.63
)874.86 )3178.82 2303.96 )578.90 2599.92 )2889.37
1.89 119.24 )117.36 11.96 )107.28 113.26
0 ); average expansion coefficient for the HOMO–LUMO transition (c); excitation energy under tensile stress (Eex ); Excitation energy in the optimized geometry (Eex oscillator strength (f ); energy of the HOMO (EHOMO ) and of the LUMO (ELUMO ). Experimental data for the excitation energies [21–23] are given in brackets. All energies are given in eV.
D Max
)4.87 )4.88 )4.90 )4.95 )5.00 )4.82 )4.90 )4.87 )4.95 )1.10 )4.90 )4.95 )4.98 )5.05 )5.11 )5.08 )5.14 )5.08 )5.09 )1.38
Min D Max
)10.34 )9.91 )9.59 )10.22 )10.55 )10.58 )10.47 )10.83 )10.10 )6.89
Min
)10.48 )10.04 )9.68 )10.26 )11.70 )10.63 )11.21 )11.40 )11.40 )6.93
D
0.08 0.16 0.19 0.57 0.63 0.15 0.15 0.33 0.23 0.63 1.46 1.78 2.04 0.72 0.63 1.19 0.89 1.05 1.37 1.24
Max Min
1.38 1.62 1.83 0.15 0.00 1.04 0.74 0.72 1.14 0.61 0.03 0.07 0.10 0.07 1.00 0.13 0.51 0.74 0.71 0.14
D Max
2.62 2.40 2.26 2.63 3.44 2.59 2.87 2.92 2.97 2.59
Min
0.67 0.64 0.62 0.65 0.52 0.65 0.66 0.66 0.52 ) 1 2 3 4 5 6 7 8 9 Cy50
2.59 (2.48–2.81) 2.33 (2.36–2.53) 2.16 2.63 3.44 2.59 (2.53–2.88) 2.87 2.92 2.94 2.57
2.59 2.33 2.16 2.56 2.44 2.46 2.36 2.18 2.26 2.45
ELUMO EHOMO f Eex c 0 Eex
Table 3 Effect of tensile stress on the dye molecules (numbering given in Fig. 1)
0.03 0.07 0.08 0.10 0.11 0.26 0.24 0.21 0.14 0.28
U.F. R€ohrig et al. / Chemical Physics 289 (2003) 381–388
0.14 0.13 0.09 0.04 1.15 0.05 0.74 0.57 1.30 0.04
386
3.2.2. Sterically hindered chromophore with benzene ring substituted in para position Chromophore 4 is similar to chromophore 1 in the substitution patterns of the aromatic rings, but some steric hindrance is induced by three additional methyl groups. In the relaxed molecule, the aromatic rings are nearly perpendicular to each other, so that the p-electrons cannot delocalize over the whole molecule. Due to the stretching, the steric hindrance becomes less pronounced and the rings become more co-planar, which allows for a higher p-electron delocalization and leads to a fivefold increase in the oscillator strength of the first singlet transition (Table 3). 3.2.3. Chromophores with benzene ring substituted in ortho position Molecules 7 and 8 are both substituted in ortho position at the benzene ring, but the substitution pattern at the pyridine ring differs. While in these two molecules the oscillator strength does not show a strong dependency on the elongation (Table 3), in both cases the excitation wavelength drops distinctly (0.5 resp. 0.7 eV) and is accompanied by a large destabilization of the HOMO (Fig. 3). This behavior can be rationalized by the shape of the frontier orbitals (shown in Fig. 4 for chromophore 7). The HOMO, which is localized on the largely deformed benzene ring, forms an additional nodal plane between the benzene ring and the amino substituent upon stretching. The changes in the LUMO are much smaller, since it is located mainly on the pyridine ring, that is less affected by structural changes. The alteration of the excitation energy of the chromophores 7 and 8 under tensile stress makes them promising candidates for experiments. 3.2.4. Sterically hindered chromophores with benzene ring substituted in ortho position Molecules 5 and 9 differ only in the number of central double bonds. Both contain a benzene ring substituted in ortho position, and both are nonplanar due to massive steric hindrance. Table 3 shows that these chromophores display a significant change in the excitation energy, and chro-
U.F. R€ohrig et al. / Chemical Physics 289 (2003) 381–388
387
transition, since the HOMO 1 ! LUMO transition plays an equally important role. All three orbitals are destabilized by strain, but the HOMO most drastically, so that the overall energy difference decreases in accordance with the excitation energy.
Fig. 3. Upper panel: energy of the frontier orbitals of chromophores 7 (circles) and 8 (crosses). The HOMOs (dashed lines) are shifted up by 7.5 eV in order to facilitate comparison with the LUMOs (full lines). Lower panel: corresponding excitation energies.
Fig. 4. Frontier orbitals of chromophore 7 in the relaxed and in an extended geometry.
mophore 5 additionally displays a prominent increase in the oscillator strength. The amplitude of the elongation correlates strongly with the value of the torsional angle. In contrast to molecule 4, the excitation energy decreases with increasing coplanarity of the rings and increasing delocalization of the p-electrons. In this case, the excitation cannot be approximated as a HOMO ! LUMO
3.2.5. Cy50 In contrast to the hemicyanine dyes, the two lowest lying excited singlet states of Cy50 are degenerate and display a negligible oscillator strength (f < 0:01). The lowest lying allowed transition involves HOMO-8 ! LUMO and HOMO-2 ! LUMO contributions. Since HOMO-8 and HOMO-2 are localized on the sulfate groups, tensile stress has no significant influence on their shape and energy, and the excitation energy is not dependent on tensile stress. However, the oscillator strength decreases by about 50%, which may be detectable in experiments.
4. Conclusions Our calculations on 10 dye molecules allow us to derive general rules about the influence of mechanical stress on dye molecules. Firstly, a significant influence on the absorption wavelength can be anticipated if binding interactions of the HOMO (or other occupied orbitals that are relevant for the specific transition) are clearly distorted by application of strain. Distortion of the LUMO causes much smaller changes (cf. dye 6). Secondly, a significant change of the oscillator strengths can be attained if sterical hindrance is lowered by stretching the molecule. Differentiation of the ground state energy with respect to the stretching coordinate yields an estimation of the force needed to stretch the molecules. In our static calculations we were able to expand the molecules up to a point that corresponds to a force of 6 nN. As we have shown previously with first-principles molecular dynamics simulations [16], the rupture force is influenced by the dynamics of the system which depends on the temperature, the pulling velocity, etc. Since our present calculations (at 0 K) do not take into account the destabilizing vibrational motion of the
388
U.F. R€ohrig et al. / Chemical Physics 289 (2003) 381–388
molecules, very high forces can be reached. The maximum forces attainable in the intended AFM experiment however amount to about 1 nN. Some of the systems under investigation exhibit significant changes of their optical properties already in this region. No detectable optical change can be expected for molecules 1, 2, 3, and 6. In contrast, the sterically hindered systems 4 and 5 show a sharp increase in oscillator strength below a force of 1 nN. Chromophores 5, 7, 8, and 9 show a large wavelength shift of 30–50 nm at low forces, rendering an experimental detection of the mechano-optical effect feasible. However, these chromophores absorb at relatively short wavelengths (in the range below 450 nm). Thus the background noise and high bleaching rates might cause problems in the experiment. For these reasons, chemical modifications of the dyes to achieve a bathochromic shift may be necessary. Finally, Cy5 may represent a good starting point for first tests, since it has been extensively used in single molecule spectroscopy; the calculated decrease in oscillator strength may be detectable experimentally. In conclusion, it is evident from our calculations that dye molecules may exhibit changes of their optical properties that are large enough to be determined in a single molecule experiment. However, the dyes have to be selected carefully. Furthermore, all attachments between surface, tip, polymer, and chromophore, will have to consist of strong covalent bonds to render forces in the order of 1 nN accessible.
Acknowledgements We thank Markus Seitz and Andreas Zumbusch for bringing the topic to our attention and for intensive discussions. We are grateful to the Volkswagen-Stiftung and the Bayerische Forschungsstiftung (FORMAT-Programm) for financial support. Computational resources provided by the Leibniz-Rechenzentrum are gratefully acknowledged.
References [1] O. Pieroni, A. Fissi, N. Angelini, F. Lenci, Acc. Chem. Res. 34 (2001) 9. [2] D.J.W. Bullock, C.W.N. Cumper, A.I. Vogel, J. Chem. Soc. (1965) 5316. [3] E. Merian, Textile Res. J. 36 (1966) 612. [4] T. Hugel, N.B. Holland, A. Cattani, L. Moroder, M. Seitz, H.E. Gaub, Science 296 (2002) 1103. [5] A.C. Edrington, A.M. Urbas, P. DeRege, C.X. Chen, T.M. Swager, N. Hadjichristidis, M. Xenidou, L.J. Fetters, J.D. Joannopoulos, Y. Fink, E.L. Thomas, Adv. Mater. 13 (2001) 421. [6] S.H. Foulger, P. Jiang, A.C. Lattam, D.W. Smith Jr., J. Ballato Jr., J. Langmuir 17 (2001) 6023–6026. [7] S.H. Foulger, P. Jiang, A.C. Lattam, D.W. Smith Jr., J. Ballato, Adv. Mater. 13 (2001) 1898–1901. [8] M. Grandbois, M. Beyer, M. Rief, H. Clausen-Schaumann, H.E. Gaub, Science 283 (1999) 1727. [9] M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. [10] J.J.P. Stewart, J. Comput. Aid. Mol. Des. 4 (1990) 1. [11] J. Ridley, M. Zerner, Theoret. Chim. Acta 32 (1973) 111. [12] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, Gaussian Inc., Pittsburgh, PA, 1998. [13] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [14] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [15] J.J.P. Stewart, in: Reviews in Computational Chemistry, VCH, New York, 1989, p. 45. [16] U.F. R€ ohrig, I. Frank, J. Chem. Phys. 115 (2001) 8670. [17] I.N. Levine, Quantum Chemistry, Prentice-Hall, Upper Saddle River, NJ, 2000. [18] G. Herzberg, Electronic Spectra and Electronic Structure of Polyatomic Molecules, Van Nostrand–Reinhold, New York, 1966. [19] M.B. Robin, Higher Excited States of Polyatomic Molecules, Academic Press, New York, 1985. [20] F. Sondheimer, D.A. Ben-Efraim, R. Wolevsky, J. Am. Chem. Soc. 83 (1961) 1675. [21] M. Matsui, S. Kawamura, K. Shibata, H. Muramatsu, Bull. Chem. Soc. Jpn. 65 (1992) 71. [22] I.A. Al-Ansari, Bull. Soc. Chim. Fr. 134 (1997) 593. [23] X. Cao, J.L. McHale, J. Chem. Phys. 109 (1998) 1901.