The experimental studies on the determination of the ground and excited state dipole moments of some hemicyanine dyes

Transcription

1 Spectrochimica Acta Part A 63 (2006) The experimental studies on the determination of the ground and excited state dipole moments of some hemicyanine dyes Janina Kabatc, Borys Ośmiałowski, Jerzy Pączkowski University of Technology and Agriculture, Faculty of Chemical Technology and Engineering, Seminaryjna 3, Bydgoszcz, Poland Received 14 March 2005; received in revised form 25 May 2005; accepted 25 May 2005 Abstract The ground state (µ g ) and excited state (µ e ) dipole moments of 15 hemicyanine dyes were studied at room temperature. They were estimated from solvatochromic shifts of the absorption and the fluorescence spectra as function of the solvent dielectric constant (ε) and refractive index (n). In this paper we applied the Stokes shift phenomena not only for the determination of the difference in the dipole moment of excited state and ground state, but to determine the value of polarizability α as well. The obtained results show that excited state dipole moments of hemicyanine dyes are in the range from 5 to 15 Debye, and the difference between the excited and ground state dipole moments vary from 1 to 7 Debye. The excited and ground state dipole moments difference (µ e µ g ) obtained for selected dyes are positive. It means that the excited states of the dyes under the study are more polar than the ground state ones. Additionally, the value of both polarizability (α) and the Onsager radius (a) of each investigated hemicyanine dye molecule are determined, and the ratio of α/a 3 for each dye were calculated, which oscillate from 0.29 to The increase in dipole moment has been explained in terms of the nature of excited state and its resonance structure Elsevier B.V. All rights reserved. Keywords: Hemicyanine dyes; Ground state; Excited state; Dipole moment; Stokes shift 1. Introduction The nature and the energy of electronically excited states of dye molecule determine its photophysical properties. Generally, dealing with chromophore molecules, one concerns their behavior in condensed phases, liquids, viscous liquids and solids. The effect of the media on the absolute and relative energies of the electronic states of solute molecules is, therefore, of considerable importance in photophysics and photochemistry [1,2]. The effect a of solvent on UV vis absorption spectra can be used to determine the magnitude as well as direction of electric dipole moment of solute molecule in its first electronically excited state. The dipole moment of an electronically excited state is an important property that provides information about the electronic and geometrical structure of the molecule in its short-lived excited state. The excited state Corresponding author. Tel.: ; fax: address: nina@atr.bydgoszcz.pl (J. Kabatc). dipole moments of fluorescent dye molecules such as those studied here determine the tunability range of the emission energy as a function of the medium polarity. Whereas the ground state dipole moment of a chemical system can be measured, not many reliable techniques are available for the estimation of the dipole moment of short-lived species such as electronically excited states of a molecule or the photochemical transient such as, for example, radical. Among the existing methods for the determination of the change in the dipole moments associated with electronic excitation of a molecule, the most popular ones are based on a linear correlation between the wavenumbers of the absorption and fluorescence maxima ( ν ab, ν fl ) and a solvent polarity functions which usually involves both the dielectric constant (ε) and the refractive index (n) of the medium [3 6]. A radiative transition (absorption or emission) connects a relaxed initial state to a Franck Condon (FC) final state. When, the molecule is surrounded by a liquid solvent or solid matrix each state is stabilized (or destabilized, as the case maybe) by an energy E s, which is the solvation energy. The /$ see front matter 2005 Elsevier B.V. All rights reserved. doi: /j.saa

2 J. Kabatc et al. / Spectrochimica Acta Part A 63 (2006) difference in the solvation energy of the final and initial states in various solvents is observed in solvatochromic shift. The solvatochromic shifts are the experimental evidence about this energy change. The various theories of solvatochromic shifts are interesting because they try to relate the solvatochromic shifts to the electron distribution of the molecule in its excited states, specially, to the total dipole moment µ and/or to the average polarizability α. These quantities are important for description of the intramolecular charge transfer in molecular excited states, and of intermolecular charge transfer in exciplexs [2,7,8]. The dipole moments in the ground and excited states have been determined using different techniques for many substituted organic molecules [9 12]. Dyes based on the hemicyanine (aminostyryl pyridinium) chromophore have been thoroughly investigated in the past to establish the relation between molecular structure and color and for their solvatochromism. However, there are no reports available in literature on the determination of µ g and µ e values of hemicyanine dyes possessing the benzothiazole moiety. The zwitterionic hemicyanine dyes consist of a positively charged chromophore and a negative counter ion as shown in Chart 1. Their solvatochromism exhibits a striking symmetry: an increasing polarity of the solvents gives rise to blue shift of the absorption spectrum and a red shift of the emission spectrum. Hemicyanine dyes exhibit a significant charge displacement when the molecules are excited from the ground state to an excited state. This large charge displacement is an indication for a large polarizability [13]. A prior knowledge of dipole moments of electronically excited species is often useful in design of non-linear optical materials. As part of our research program on nonsymmetrical series of cyanine dyes, we report the determination of ground and excited state dipole moments of 3-ethyl-2-(p-substituted styryl)benzothiazolium salts, by solvent perturbation method [3,14] based on absorption and fluorescence shifts in various solvents Theory It has been observed that many laser dyes exhibit shifts in their absorption and emission spectra when the solvent is varied. The variation in the solvent may be Chart 1.

3 526 J. Kabatc et al. / Spectrochimica Acta Part A 63 (2006) change from polar to non-polar or the reverse, change in the dielectric constant of the solvent, and change in the polarizability of the solvent. In many cases not only a shift in the fluorescence spectrum is observed but often the emission is accompanied by a shift in the absorption spectrum of the compound. The effect of solvent on the absorption and emission spectra may give useful information regarding physical properties of solute such as dipole moment and polarizability changes of the molecule in the ground and excited state [2]. Since the excited state of the molecule is different from the ground state, for example it may have a greater dipole moment, than the ground state of a particular molecule may change very little from solvent to solvent, but the excited state may be quite different because of its dipole moment. Thus, there may be little spectral change in the ground state of molecule but a large one in emission spectrum as the solvent is changed [2]. Upon the excitation of a molecule the electron, which is raised to a new electronic level, is excited in much less time than it takes the whole molecule to rearrange itself with the solvent environment. Scheme 1 shows the energy level diagram for a molecule which has a dipole moment in ground state different in magnitude and direction from that of the solvent (in this case the solvent is polar). Upon excitation the dipole moment of the molecule is changed and the solvent molecules had no enough time to reorient to the lowest energy orientation with respect to the excited state dipole. After about s the solvent molecules have had the chance to rearrange themselves into the most favorable alignment with the excited state dipole. These results in lowering the energy of a initial FC excited Scheme 1. Franck Condon effect demonstrated for dipole-dipole interaction between solvent and solute. S 0, ground state, S 1, Franck Condon excited state, S 1E equilibrium excited state. state S 1 to energy of an equilibrium excited state S 1E.Ifthe difference between Franck Condon (FC) excited state and the equilibrium excited state for polar solvent is greater than the difference between the FC excited state in the non-polar solvent, the fluorescence, as one goes from polar to non-polar solvent, will undergo a blue shift [2]. The change in dipole moment of a molecule in excited state with respect to ground state is determined by using two methods based on internal electric field effect (Solvatochromism) Method 1 The universal interaction between solute and solvent molecules is due to solvent acting as a dielectric medium. Therefore, according to Bakshiev [15], Chamma and Viallet [16] the shift between the absorption and emission spectra is related to the dielectric constant and the refractive index of solvent [2,17]. Based on quantum mechanical perturbation theory [3,14] of absorption (ν ab ) and fluorescence (ν fl ) band shift of a spherical solute in different solvents of varying permittivity (ε) and refractive index (n) and Inamdar s studies [3], the difference in the dipole moment between the ground and the first excited singlet state describes following equations [18]: ν ab ν fl = m 1 f (ε, n) + constant (1) The model of dipole in a dielectric medium [19] that is used to derive Eq. (1) also gives Eq. (2) for the sum of ν ab + ν fl : ν ab + ν fl = m 2 [f (ε, n) + 2g(n)] + constant (2) ν ab and ν fl are the peak absorption and emission (steady-state fluorescence) frequencies, where [ ] f (ε, n) = 2n2 + 1 ε 1 n ε + 2 n2 1 n 2 (3) + 2 is solvent polarity parameter [11] and g(n) = 3 2 with [ n 4 1 (n 2 + 2) 2 ] m 1 = 2(µ e µ g ) 2 hca 3 (5) and m 2 = 2(µ2 e µ2 g ) hca 3 (6) where h is the Planck s constant, c the velocity of light in vacuum, whereas µ g and µ e are the dipole moments in the ground and excited states, respectively. The parameters m 1 and m 2 can be obtained from the absorption and fluorescence band shifts (Eqs. (1) and (2)). If the ground and excited states are parallel, the following expressions are obtained on the (4)

4 J. Kabatc et al. / Spectrochimica Acta Part A 63 (2006) basis of Eqs. (5) and (6) [3,18]: ( )[ m2 m 1 hca 3 ] 1/2 µ g = (7) 2 2m 1 ( )[ m1 + m 2 hca 3 ] 1/2 µ e = (8) 2 2m 1 The Onsager radius an of the solute molecule can be determined by ab initio calculations. It should be noted that the solvent polarity function f(ε, n) in this method is different from Lippert Mataga function [6] Method 2 Based on the Lippert Mataga relationship [20] and taking into consideration the polarizability of the molecule in the solvent (Ghazy [2]), the parameter f in Eq. (1) is expressed by following equation: f (ε, n) = ( 1 2α a 3 ε 1 2ε+1 n2 1 2n 2 +1 )( n 2 1 2n α a 3 ε 1 2ε+1 ) (9) where α is the real part of the complex polarizability of the molecule under investigation. The relation between µ and f(ε, n) yields also straight line of slope m 1 given by Eq. (5). To determine the variable f(ε, n) the value of α/a 3 must be known. The value α/a 3 of dissolved molecules can be determined if the oscillator strength f is treated as an invariant quantity in transition from vapor to solution where only dielectric effect appears. The oscillator strength f is given by [2,20]: φ(n) 3mc πe 2 ε ν dν = f B (10) where ε ν dν is the experimental value of the absorption integral of solution; m and e are the mass and the charge of the electron, respectively. The correction function φ(n) depends on the effective internal electric field acting on the molecule in the solution. Taking into account the individual properties of the dissolved molecules and the polarization resulting from dipole induced in the molecule under the effect of light wave the correction function φ(n) can be expressed by Eq. (11) [2,20]: φ(n) = (2n2 + 1) 2 ( 9n 3 1 α 2n 2 ) 2 a 3 2n 2 (11) + 1 Substituting the above expression for φ(n) into Eq. (10) one gets: 1 (g ε ν dν) 1/2 = 1 B 1/2 α 1 2n 2 2 a 3 B 1/2 2n 2 (12) + 1 where g = 3mc (2n 2 + 1) 2 πe 2 9n 3 (13) Eq. (12) is a straight line intersecting the axis of ordinates in the point B 1/2 and with a slope equal (α/a 3 )(1/B 1/2 ) and this, in turn, allows to obtain the value of α/a 3. From Eq. (1) the difference between the dipole moments of the excited and ground states (µ e µ g ) can be calculated [2]. 2. Experimental The investigated 3-ethyl-2-(p-substituted styryl)benzothiazolium iodides were synthesized in our laboratory. The synthesis, purification and characterization of hemicyanine dyes have been described elsewhere [21]. The molecular structure and abbreviation of these dyes are given in Chart 1. The solvents used in the present studies were: 1,4- dioxane, benzene, chloroform, ethyl acetate, tetrahydrofuran (THF), 1,2-dichloromethane, 1,2-dichloroethane, acetone, acetonitrile, N,N-dimethylformamide (DMF), dimethylsulfoxide (DMSO). All solvents were the spectroscopic grade and were used without any additional purification. The solvents were characterized by their static dielectric constant (ε) and refractive index (n) at20 C. A concentrated (ca. 1 mm) stock solution was prepared separately for each dye by dissolving required amount of the dye in ethanol. The solution for spectral measurement was prepared by adding 1 ml of above solution to a 100 ml volumetric flask containing spectroscopic grade solvent. The absorption spectra were recorded with a Varian Cary 3E spectrophotometer, and fluorescence spectra were obtained with a Hitachi F-4500 spectrofluorimeter. The fluorescence measurements were performed at an ambient temperature. Onsager cavity radii (a) of all molecules tested were determined theoretically using the molecules optimized geometry. To estimate the ground state dipole moments of the dye molecules under investigation ab initio calculations were carried out using B3 LYP/6-31 G (2df, 2p) method. All calculations were carried out with Gaussian 03 program [22]. 3. Results and discussion The polarity of a molecule depends on its electron distribution. The absorption of an additional energy will cause the transition of an electron from HOMO to the LUMO orbital. The movement of electron from the ground state orbital to the higher energy orbital will cause a change of dipole moment with respect to the ground state dipole moment. For the estimation of the excited state dipole moments the absorption and emission spectra of dye molecules in different polarity solvents were recorded. In the present work we used 11 solvents with dielectric constant (ε) varying from 2.2 to 48. Fig. 1 shows, for the illustration, the absorption and fluorescence spectra of HC 1 obtained in 1,4-dioxane, ethyl acetate, THF, acetone, acetonitrile and DMF.

5 528 J. Kabatc et al. / Spectrochimica Acta Part A 63 (2006) Fig. 1. Electronic absorption and fluorescence emission spectra of the dye HC 1 in different solvents at 293 K. The spectrum as it is presented in Fig. 1 shows considerable spectral shifts as the dielectric constant is increasing. The partial loss of mirror symmetry between the emission and absorption spectra and the large Stokes shift suggest that the molecular geometry of the dye in the ground state and first excited state is different [2]. The observed spectral shift is correlated with the polarity parameters (dielectric constant and refractive index) of solvents. Figs. 2 5 present the spectral shifts (in cm 1 ) ν ab ν fl and ν ab + ν fl for HC 2 and HC 12 versus the solvent polarity function f(ε, n) and f(ε, n)+2g(n). As can be seen from figures the data fit to the straight lines. The dipole moments estimated from the obtained linear relationships for all dyes tested are summarized in Table 1. The slopes of, respectively, paired plots (for example Figs. 2 and 4) were used also to estimate the dipole moments (µ e /µ g ) ratio. Fig. 3. Plot of ν ab + ν fl (cm 1 ) vs. f(ε, n)+2g(n) for HC 2 in various solvents. The error bar is equal ±2%. Fig. 4. Plot ν ab ν fl (cm 1 ) vs. f(ε, n) for HC 12 in different solvents. The error bar is equal ±5%. Fig. 2. Plot ν ab ν fl (cm 1 ) vs. f(ε, n) for HC 2 in different solvents. The error bar is equal ±5%. Fig. 5. Plot of ν ab + ν fl (cm 1 ) vs. f(ε, n)+2g(n) for HC 12 in various solvents. The error bar is equal ±2%.

6 J. Kabatc et al. / Spectrochimica Acta Part A 63 (2006) Table 1 Dipole moments of the ground and excited state estimated for all dyes tested Molecule Radius a (Å) µ g (D) µ e (D) µ (D) µ e /µ g HC HC HC HC HC HC HC HC HC HC HC HC HC HC As it was mentioned earlier, the values of µ e and µ g were determined using spectral shift in absorption and emission spectra and µ g determined basing on Eqs. (7) and (8). The estimated dipole moments of the excited state of hemicyanine dyes range from 5 to 14 Debye. The difference in the excited and ground state dipole moments µ = µ e µ g oscillate in the range of 1 6 D. The calculated change in dipole moment upon excitation corresponds to an intermolecular displacement of a charge upon excitation in the range from to 1.25 Å. Basing on the quantum chemical parametrization AM1 of MOPAC program package [23] Fromherz calculated the intramolecular displacement of charge upon excitation for a molecule similar to HC 1 (see Chart 1). According to Fromherz, the charge displacement is equal 2.17 Å for the molecule represented by structure C (see Chart 2) and is greater in comparison to the values obtained for the dyes under the study. Basing on our and Fromhertz s calculations, we believe that upon excitation the positive charge of the chromophore is displaced from the benzothiazole moiety to the substituent in the p-position of styryl part of molecule. Basing on this, one can suggest that the molecules under the study can exist only in two mesomeric forms (Chart 2, parts A and B). In the ground state, the mesomeric form represented by structure A is predominant, but upon excitation, predominant becomes the mesomeric form represented by structure B [13,23]. The calculated values of the cavity radius for HC 1 16 are in the range of Å. This value is rather small compared to the molecular length of HC dyes which are about Å. Basing on the Koti and co-workers studies on the photophysics of some styryl thiazolo quinoxaline dyes [19] we tried to comprehence the possible meaning of the small theoretically calculated values of cavity radius for HC dyes, by correlating their values with the charge distribution in the ground and excited state of HC 1 dye. From the theoretical calculations it was deducted that the major changes in net atomic charges occur only on few atoms of the dye in the vicinity of the styryl bond. Chart 3 shows the charge distribution on the styryl bond atoms for ground and excited state (in braces). Large changes (>0.12) in the value of the net charge were observed for the atoms that are shown in bold. Therefore, it is reasonable to expect that this part of molecule plays a dominant role in the solvation dynamics because of the large changes in atomic charges. Interestingly, the length of this part of the molecule was found to be 4.2 Å, which is very close to the calculated value of cavity radius. In the next step we compared the method discussed above with the method applied by Ghazy for the determination of the difference between the dipole moment of the first excited state and the dipole moment of the ground state applied for coumarin and rhodamine dyes [2]. For these purpose we applied Eqs. (1) and (9) (12). Figs. 6 and 7 show the dependence g = (g ε ν dν) 1/2 value on (2n 2 2)/(2n 2 + 1) solvent function for HC 3, HC 4, HC 5, HC 8, HC 12 and HC 14, in different solvents. From the plots of obtained linear relationship and basing on the Eq. (12) the value α/a 3 for hemicyanine dyes under the study were found and their polarizabilities α were obtained. These values are complied in Table 2. Chart 2. Chart 3. Net charges on the atoms of the styryl group and near styryl group atoms, bond distances and angles in the ground state for HC1. The values of net charge on the atoms in the excited state are given in brackets.

7 530 J. Kabatc et al. / Spectrochimica Acta Part A 63 (2006) Fig. 6. The dependence of g = (g ε ν dν) 1/2 value on (2n 2 2)/(2n 2 +1) solvent function for HC 3, HC 4, HC 5 in different solvents. Error bars equal ±2%. Fig. 7. The dependence of g = (g ε ν dν) 1/2 value on (2n 2 2)/(2n 2 +1) solvent function for HC 8, HC 12, HC 14 in different solvents. Error bars equal ±5%. Fig. 8. The value of Stokes shift as a function of f(ε, n) for HC 1, HC 8 and HC 14 in different solvents. Error bars equal ±2%. Figs. 8 and 9 show the relationship between Stokes shift and f(ε, n). The plots show the linear correlation. From the slope of these correlations the difference between the dipole moments of the excited and ground states for tested dyes were calculated and listed in Table 2. Basing on these data one can conclude that results obtained according to method 2 are in good correlation with those obtained using method 1. From Table 2 it is also evident that the difference between the excited and ground state dipole moments are in the range from 1 to 7 D. The value of the excited singlet state dipole moments ranges from 5 to 15 D. Inspection of the data in Tables 1 and 2 reveal that for all dye molecules under investigation, the changes in the dipole moments on the electronic excitation are rather small. This suggests that the emission of these dyes originate from states, which although are more polar than ground state, are probably similar to the locally excited states (FC excited state, see Scheme 1). Table 2 The values of α/a 3, α and µ = µ e µ g for some hemicyanine dyes tested Molecule α/a 3 α (cm 3 ) µ g (D) µ e (D) µ (D) HC HC HC HC HC HC HC HC HC HC HC HC HC HC HC Fig. 9. The value of Stokes shift as a function of f(ε, n) for HC 2, HC 9 and HC 12 in different solvents. Error bars equal ±5%.

8 J. Kabatc et al. / Spectrochimica Acta Part A 63 (2006) It should also be noted that the model used to derive Eqs. (1) and (2) is based on a point dipole in a spherical cavity. Most organic fluorescent molecules for which these equations are applied are neither point dipoles nor spherical in shape. A realistic model of the solvent structure around the molecular dipole is very complex and the simple model such as the used to obtain Eqs. (1) and (2) are only approximations. Alternative realistic models are necessary [19]. 4. Conclusions The estimation of the ground and excited state dipole moments of dye molecules is important because it controls the tunability of dye emission energy as a function of solvent polarity. In the present paper we described the measurements of the ground and excited state dipole moment values for 15 3-ethyl-2-(p-substituted styryl)benzothiazolium iodides. The ground state dipole moments of tested dye molecules were calculated using quantum chemical calculations. The dipole moments of the excited state for HC 1 16 were obtained using calculated value of µ g and the value of (µ e /µ g ). It may be noted that the all estimated values of µ g and µ e for all dyes tested are different. This can be attributed to the structural difference between these molecules. The higher dipole moments in the first electronically excited state indicates that the observed absorption band for these molecules can be attributed to * transition. This observation is in good agreement with those described in literature. Acknowledgements This work was supported by the State Committee for Scientific Research (KBN) (grant no. 3 T09B ). We are very much indebted to Politechnika Gdańska (TASK) for providing programs and computer time. Borys Ośmiałowski gratefully acknowledges receipt of a Fellowship from the Foundation for Polish Science (FNP). References [1] C. Porter, P. Suppan, Trans. Faraday Soc. 61 (1965) [2] R. Ghazy, S.A. Azim, M. Shaheen, F. El-Mekawey, Spectrochim. Acta Part A 60 (2004) [3] S.R. Inamdar, Y.F. Nadaf, B.G. Mulimani, J. Mol. Structure (Teochem) 624 (2003) [4] E. Lippert, Z. Naturforsch 10A (1955) 541. [5] B. Koutek, Collect. Czech. Chem. Commun. 43 (1978) [6] N. Mataga, Y. Kaifu, M. Koizumi, Bull. Chem. Soc., Jpn. 29 (1956) 465. [7] P. Suppan, J. Mol. Spectrosc. 30 (1969) 17. [8] H. Beens, H. Knibbe, A. Weller, J. Chem. Phys. 47 (1967) [9] S.J. Sheng, M.A. El-Sayed, Chem. Phys. 20 (1977) 61. [10] P. Cyril, S.A. Maged, J.J. Aaron, B. Michaela, T. Alphonse, C. Lamine, Spectrosc. Lett. 27 (1994) 439. [11] A. Kawski, Z. Naturforsch. 54A (1991) 379. [12] A. Kawski, B. Kukliński, P. Bojarski, Z. Naturforsch. 56A (2001) 407. [13] K. Binnemans, C. Bex, A. Venard, H. De Leebeeck, C. Görller- Walrand, J. Molec. Liq. 83 (1999) [14] L. Bilot, A. Kawski, Z. Naturforsch. 17A (1962) 621. [15] N.G. Bakshiev, Opt. Spectrosc. (USSR) 16 (1964) 821. [16] P. Chamma, CR. Viallet, Hebd. Seane. Acad. Sci. Ser France 270 (1970) [17] V.K. Sharma, P.D. Saharo, N. Sharma, R.C. Rastogi, S.K. Ghoshal, D. Mohan, Spectrochim. Acta Part A 59 (2003) [18] A. Kawski, J.F. Rabek (Eds.), Progress in Photochemistry and Photophysics, vol. 5, CRS Press, Boca Raton, 1992, pp [19] S.R. Koti, B. Bhattacharjee, N.S. Haram, R. Das, N. Periasamy, N.D. Sonawane, D.W. Rangnekar, J. Photochem. Photobiol. A: Chem. 137 (2000) [20] A. Mishra, G.B. Behera, M.M.G. Krishna, N. Periasamy, J. Lumin. 92 (2001) [21] B. Jędrzejewska, J. Kabatc, M. Pietrzak, J. Pączkowski, Dyes Pigments 58 (2003) [22] Gaussian 98, Revision A.11.4, 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, N. Rega, P. Salvador, J.J. Dannenberg, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, 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, 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, [23] P. Fromherz, J. Phys. Chem. 99 (1995) 7188.