Electronic structure of multilayered and multistepped cyclophanes

Journal of Molecular Structure (Theochem), 165 (1988) 163-174 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

ELECTRONIC STRUCTURE OF MULTILAYERED MULTISTEPPED CYCLOPHANES

163

AND

LESZEK CZUCHAJOWSKI and ANTON1 K. WISOR Department of Chemistry, University of Idaho, Moscow, ID 83843 (U.S.A.) (Received 28 March 1987)

ABSTRACT The electronic structure of multilayered, MLP, and multistepped, MSP, cyclophanes containing 2-5 layers and 2-4 steps, respectively, was investigated using the PPP CI-1 method with application of the supermolecule approximation and consideration of o-x polarization and u-x orbital interactions between the bridges and the rings. The electronic excitations were evaluated as a combination of exciton resonance (ER% ) and charge resonance (CR% ) both based on the localization of excitation numbers on given molecular fragments. The transition ascribed to the new (when compared with 2L) long wavelength absorption band in 3L localized on the inner ring was influenced by the deformation and substituent effects, but transannular interactions were predominant, CR% =53. These interactions increased with the attachment of every new benzene ring. The transfer from the inner ring(s) to the outer rings prevailed over the opposite trend. CR% values were 15-20% greater for MLP than MSP, pointing to the differences in transannular interactions.

INTRODUCTION

Unlike the double-layered cyclophanes, such as [ 2.21 paracyclophane, the electronic structure of multilayered [l] and multistepped [ 21 cyclophanes have been discussed in a limited number of papers [ 2a,3,4]. The research has mainly focussed on obtaining a good agreement of the calculated energy of transition values with the experimental data. By reaching this agreement, the applicability of the formalism used was proven, although attention was also paid to the transannular interactions, which are so characteristic of the cyclophanes. A few years ago, we began applying the excitation indices calculated on the basis of the transition density matrix [5,6] in order to elucidate the electronic structure of heterophanes [ 71. The “localization of excitation numbers” and the exciton and charge resonance numbers appeared to be useful in the description of the localization of excitation on certain molecular fragments and the extent and direction of transannular interactions. This encouraged us to apply this approach to the more complicated structures of multilayered cy0166-1280/88/$03.50

0 1988 Elsevier Science Publishers B.V.

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clophanes, ( MLP) and multistepped cyclophanes ( MSP) . The latter series of compounds has never been treated theoretically, even in a simplistic approach. THEORETICAL TREATMENT

The cyclophanes under consideration represent the double-, triple-, quadruple- and quintuple-layered paracyclophanes denoted respectively as 2L, 3L, 4L and 5L, and the double-, triple- and quadruple-stepped metacyclophanes, denoted as 2S, 3s and 4S, respectively (Fig. 1). The size and complicated character of these compounds necessitates a calculational procedure based on the x-electron theory, commonly used in papers devoted to cyclophanes [ 2a,3,4,8,9]. It has been proved [ lo], however, that any extention beyond this theory improves the description of the n-electron system only to a small degree. It is also of importance that in the framework of the n-electron approximation it becomes possible to consider the o-x polarization [ 111. We expected to achieve this indirectly by adjusting the parameterization. Therefore, we: (1) applied MO theory in the supermolecule approximation [ Ba] ; (2) considered the o-n interaction [ 121 by direct recognition of the presence of ethane bridges; (3) calculated the transition energies and oscillator strengths using the PPP CI-1 method [ 131; and (4) analyzed the electronic transitions by applying the formalism of the transition density matrix [ 61. In the evaluation of the numerical values of particular empirical parameters of the PPP method, the parameterization taken from the CNDO/S method [ 141 was used, where the basic parameters were exclusively one-centered in-

5-L

Fig. 1. Cyclophanes under consideration: (A) multilayered paracyclophanes, (B) multistepped metacyclophanes.

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tegrals. The details involved were the same as those described previously [ 151. The most essential aspect of the treatment applied was the analysis of the excited state using the transition density matrix method [ 51. This method introduces the so-called localization numbers [ 61. The basic magnitude is the localization number LA ( % ) describing the participation of the molecular fragment A in the excitation, which is calculated from the transition density matrix [6a] and expressed as L*=z*+1/2(z*__B+z~_*+...+I*-z++-*)

(I)

where lA is the partial localization number giving the local excitation on the molecular fragment A and 1A _ BP 1B _ AY-* 1A _ ZP 1Z _ A represent the charge-transfer numbers referring to the transfer from A to B,..., Z and from B,..., Z to A fragments. This method when applied to evaluation of the transannular interactions, as in this paper, also gives insight into the details of the electronic structure of molecules, which cannot be defined strictly by the use of the standard SCF-CI approach because of the delocalized character of the MOs. These new possibilities can be particularly well explored when the molecules consist of identical, isolated structural fragments, e.g., A=B. In such a case, e.g., the cyclophanes, the wave function of the excited state is, through the analogy to excimer theory [ 161, either a function of the “exciton resonance” type ER( ?)=1/J2(@A*@n+@A

@n*)

(2)

or of the “charge resonance” type CR(+)=~/J~(~A+~B-~~A-~B+)

(3)

When the orbitals overlap appreciably, as in the A-B dimers, excimeric states appear which represent the linear combination of the ER-type and CR-type states. The sum of the partial localization numbers ZAand ln on the molecular fragments A and B represents the participation of the ER-type states, while the sum of the charge transfer numbers lA__Band ln__Abetween the fragments gives the participation of the CR-type states in the excimeric excited state. This can be generalized to the case of the molecule consisting of a number of fragments, A + B + ... + Z ER%=ZA+Zn+...+Zz

(4)

CR%=ZA_n+1n_A+...+ZA_z+lz_A

(5)

for which ER% + CR% = 100%. The ER% and CR% numbers proposed by us, represent a measure of the transannular interactions in certain types of molecules to which MLP and MSP species belong. The pure electronic treatment, based on the Born-Oppenheimer approximation (BO),is not always applicable to the layered structures: the electronic spectra of such compounds are affected by the vibronic couplings. However, in the case of MLP and MSP a so-called “strong coupling” occurs which, in fact,

166

affects the BO transition energies to only a minor extent. Moreover, when only the energies of transitions, and not their oscillator strengths, are considered, it is possible to incorporate, as we did, the vibronic effects into the n-electron treatment by appropriate parameterization of the resonance integrals between the adjacent layers or steps: this is applicable to the case of strong vibronic coupling. In the case of a weak vibronic coupling, calculation was done directly through the functions of the excited states appearing in eqns. (2) and (3)

[171. RESULTS AND DISCUSSION

Multilayered paracyclophanes The UV absorption spectra of MLP were presented by Otsubo et al. [lb]. In addition to the increase in the number of layers, the spectra of MLP show strong batho- and hyper-chromic effects. These effects are particularly strong in the transformation of a single-layered compound to a double-layered one [ 181. The addition of a consecutive layer results in another large bathochromic shift of the absorption curve of 3L, which remains structureless. These remarkable spectral changes are explained mainly by an increase in the transannular effect as a result of the increase in the region of x-a interactions in 3L with regard to 2L [lb], until now explained only qualitatively by theoretical treatments [ 3,4]. Furthermore the influence of exceptional deformation of the inner benzene ring [ 191, which is twist-shaped [ 201, cannot be neglected. Consecutive increase of the number of rings results in broadening of the absorption curves of 4L and 5L, giving further batho- and hyper-chromic shifts. The results of the present calculations totally reproduced the observed effects (see Table 1). A comparison of the results calculated for 2L with those for the benzene dimer, characterized by inter-ring distances of 3 A, indicates that the better agreement between experimental and calculated values for 2L is due to the consideration of the real structure of this double-layered cyclophane and of the boat conformation of its rings [ 211. The influence of the deformation effect is generally reflected in a lowering of the energies for all transitions, in particular for those which originate from the l’& ( cx band) and llB1, (p band) transitions in benzene (see Fig. 2). A similar tendency is observed for [ n] paracyclophanes for which the bands shift insignificantly, but gradually, toward longer wavelengths as the number of methylene groups in the chain is decreased so that the benzene ring becomes more and more strained and finally takes the boat shape as in 2L [ 221. A comparison of the indices of excitation shows that, as a result of the deformation of benzene rings, the transannular interactions increase in the long-wavelength transitions. As ex-

167 TABLE 1 Calculated and observed [ 4,181 electronic transitions in multi-layered paracyclophanes Symmetry

Calculated

Observedb

I(nm)

1 (nm)

f

Double-layered paracyclophane, 2L 1’Bzg ((Y) 337.5 0 305’sh l’B1, (a)a 331.1 0 llBsp (PI 294.5 0 l’B*, (PI” 274.2 0 llBsu (a) 283.6 0.057 286” l’B,” (a)* 273.8 0.000 2lB*, (8) 249.2 0 2lB3, (P’) 243.0 0 llEl, (/3/3’)” 274.2 0 11B2” (PI 236.2 0 120 244”’ sh l'&"@)" 226.4 0:ooo 2lB3” (P) 211.7 0.267 225’” 2lB,” (P’) 208.7 0.219 l’E,, (PB’)” 207.3 0.553

Quadruple-layeredparacyclophane, 4L 1’B 382.0 0.002 2lB 362.5 0.005 3lB 343.7 0.026 339’ 4lB 332.9 0.002 5lB 308.9 0.003 6lB 299.0 0.046 297” 7’B 288.8 0.013 8’B 284.6 0.017 9lB 274.8 0.001 1O’B 264.3 0.094 11’B 261.3 0.055 260’” 12lB 259.2 0.016 13lB 245.5 0.097 14lB 239.0 0.000 15lB 235.0 0.121 230”’

Symmetry f

Calculated

Observedb

1 (nm)

I (nm)

f

Triple-layered paracyclophane, 3L 1’B (a) 377.4 0.000 1’Bzu (a)’ 375.2 0.000 2lB (~1 342.0 0.003 347’ l’B1, (P)’ 315.4 0.000 313.6 0.034 0.007 3lB (a) l’Bt, (a)= 309.6 0 4’B (P) 305.2 0.002 QB (P’) 277.2 0.000 l’El” (p/Y)” 315.4 0.000 299.2 0.015 294” 0.105 5lB ((Y) 21Bz,(a)c 280.5 0.000 0.760 7lB (P) 269.0 0.016 I’B,, (P)” 263.1 0 258”’ 8lB (P) 254.4 0.106 21B1,~) 234.9 0.007 9lB (B) 252.8 0.007 10IB (8’) 243.5 0.009 l’EI, (/Ifi’)” 248.7 0 1l’B (P) 230.3 0.277 0.005 12lB (p’) 220.8 0.227 235’” 21El, (p/3’)= 216.0 0.563

f

0.004

0.034 Quintuple-layered paracyclophane, 5L 1’B 381.9 0.008 3lB 354.2 0.033 339’ 9lB 286.5 0.056 297” 16lB 251.3 0.114 260”’ 0.099 201B 237.0 0.474 230”’

0.004

0.028

0.067

0.194

0.005 0.034 0.099 0.329

0.329

*Benzene dimer. bSuperscripts I-IV denote band number. “Benzene trimer.

petted, the greatest increase occurs in the llBzU (p) transition, CR%=40 for the dimer, and CR%=50 for the 2L species. The most interesting effects, however, are observed in the analysis of 3L species. For the sake of comparison, the benzene trimer is considered to represent a simple model of 3L. The behavior of the transition energies of singlet excited states in the trimer was investigated as a function of the inter-ring distance; the outer rings (B ) were simultaneously brought toward the inner

168

ring (A) from the distance of 4-2.5 A (Fig. 2). heavy lines in Fig. 2 [ l’& (a), l’B1, (p) , l’&, a high degree of localization of excitation in the nance of “charge transfers” from the outer rings, the reverse “transfers” lA>21nand1~_s
The transitions denoted by (/?/?‘)I are characterized by inner ring, A, and the domiB, to the inner ring, A, over

(6)

The remaining transitions represent the same transitions as in the benzene dimer [ 8~1. Contrary to the transitions described above, they are characterized by a high degree of localization of excitation on the outer rings, B, and constant localization of excitation, or no excitation, on the inner ring A, independent of the inter-ring distances. In addition, the “charge transfers” from the inner ring, A, to the outer rings, B, predominate over the reverse “transfers” lA<21s andlA--B)lB_-A

(7)

EIU

lB.P’) 50

BlU (P)

B2u [Cd

Fig. 2. Dependency of transition energies (cm-‘) trimer.

on the inter-ring distances (A) in the benzene

170

to be connected with the 2lB (p) transitions at 342.0 nm because of the nonzero value of the oscillator strength for this transition, f=O.OOS.This transition shifts bathochromically in going from the benzene trimer to 3L, and the shift is greater than the corresponding shift connected with the transition to 2L, described above. The substituent effect is of some importance [ 231, but first the influence of the deformation of the inner ring, which takes the twist-shape [ 201, should be considered. This motion is inferred from the comparison of UV spectra of [ 8][ 81 paracyclophane and [ 81 paracyclophane [ 241. The former compound, in which the benzene ring is twist shaped, shows absorption at a higher wavelength than the latter, which is characterized by the boat conformation. The role of the deformation effect in the 2lB (p) state is meaningful, although the transannular interactions are large, as indicated by the sum of the numbers of “charge transfer”. However, the sum of “charge transfer” numbers does not alter in going from the benzene trimer (CR%=54) to 3L (CR%=53). Equal distribution of transannular interactions over the entire molecule ( ZA_-B= ZB_*) also characterizes this state. All other meaningful states in 3L originate from 2L. The calculations show that for the second, consecutive, broad absorption band near 290 nm, three transitions can be ascribed to the excited states 3lB (a), +!?B (a), and 7lB (p) . The second transition is shifted bathochromically with regard to the analogous 11B3, (a) transition in 2L, which is in ageement with experiment [ 41. The presence of three transitions explains the increased intensity of the band as compared with 2L. The transitions of the next absorption bands at 258 nm and 235 nm can be ascribed to the excited states 8lB (p), lllB (8) , and 12lB (j3’). These transitions are also shifted bathochromically when compared with the transitions in 2L [ 181. All transitions under consideration for 3L show larger transannular interactions than the corresponding ones in 2L (greater CR% for 3L) (see Fig. 3)) pointing to an increase in the transannular effect when the benzene ring becomes attached to the 2L system. This increase is also influenced by the deformation effect which is evident from a comparison of the numbers of excitations for benzene trimer and 3L. The calculated values for 4L (Table 1) correlate well with the experimental data [ 41. The bathochromic shift of the longest wavelength absorption to the excited state 1’B is limited to only 5 nm. This value confirms the tendency of these shifts to decrease with an increase in the number of layers particularly in moving from 3L to 4L [ lb] ) . The analysis of numbers of excitation for the four longest wavelength transitions to the states llB, 2lB, 3lB and 4lB indicates, as previously, localization of excitation on the inner rings (see Fig. 3). Therefore addition of another ring changes the properties of the long wavelength absorption to only a small degree. All the above considerations can be applied to 5L (see Table 1 and Fig. 3). However, it can be stated that, in general: (i) no further bathochromic shift of the longest wavelength transition takes place; (ii) the excitation at the long wavelength transitions becomes localized to the highest degree on the inner-

171

most ring and to a smaller degree on the remaining inner rings; and (iii) a further increases of transannular interactions takes place. Multistepped metacyclophunes Metacyclophanes show weaker transannular interactions than paracyclophanes because of the smaller overlap of the n-electron clouds of the benzene rings. Accordingly, the changes in the electron spectra of MSP are less significant than are those in MLP spectra. The differences in the spectra of the compounds belonging to the MSP series are similar to those appearing in the spectra of MLP. The most remarkable changes occur in moving from 1,3dimethylbenzene to 2s. The UV spectrum of 2s shows two absorption bands in the long wavelength region: (i) a weak, structureless band near 280 nm [ 2,251 (originating from the (Y band of benzene) , and (ii) a new broad band, 225-250 nm [ 21. The disappearance of the fine structure is explained by the deformation effect, while the appearance of the new band reflects the transannular effect. Increasing the number of “steps” by one, 2&3S, results in the largest batho- and hyper-chromic shifts in the absorption curves, but not such large shifts as in the case of 2L+3L. Addition of another step, 3S+4S, changes only the second band, which now becomes an independent band with a distinct maximum at 262 nm [ 2b]. The calculations presented in Table 2 totally confirm the above phenomena. Most of the implications arising from the theoretical treatment of MSP are TABLE 2 Calculated and observed [ 2,251 electronic transitions in multistepped metacyclophanes” Symm.

Calculated l(nml

Observedb f

I(nml

Double-stepped metacyclophane, 2S 272” 0.006 1’A” 274.4 0 l’B, 270.4 240” d sh 0.324 l’B, 236.0

Symm.

Calculated I(nm1

Observedb f

1 (nm)

Quadruple-stepped metacyclophane, 4S 280’ 0.059 l’A, 279.6 0 l’B, 273.2 262” 0.772 1’B” 255.8 0.045 2’A, 253.1

Triple-stepped metacyclophane, 3S 280’ 0.053 l’A, 281.0 0 l’B, 272.7 0.001 2lA, 272.1 252” sh 0.525 1lB” 250.9 “The values calculated for other isomers of 3s and 45 [ 261 do not differ from the values listed. bSuperscripts I and II denote the band number. =f=O.O14 [ 251.

dfzO.1.

172 2s

3s

4s

CR%=35, 55

Fig. 4. Indices of excitation for multistepped metacyclophanes given for the two transitions corresponding to bands I and II in Table 2. For additional information see Fig. 3.

similar to those concerning MLP, already discussed in this paper. In the l’A, state the excitation is localized to the highest degree on the benzene rings which confirms its origin from the llBzu (a) state in benzene. In 2s the localization is equally distributed between both rings, and in 3s and 4s the excitation becomes localized mainly on the inner ring (s ) , as in 3L and 4L. The transannular interactions participate in the llB, state due to the magnitude of the CR% numbers as compared to the corresponding numbers characterizing the l’A, state. Successive addition of new rings to 2s increases these interactions (see Fig. 4). It is interesting to compare the states in MLP and MSP which have common origins, i.e., the llA, and llB, states in MSP and the states in MLP originating from the l’BsU and l’BzU states of 2L. The contribution of transannular interactions to the llA, and llB, states is small and comparable for both states, although their importance gradually increases with the addition of new rings. The structural parameter does not have any essential meaning for these states. The converse situation characterizes the 11B3,and l’& states in which the transannular interactions are the most predominant. The much larger CR% numbers (by 1520%, see Fig. 3 and 4) for MLP, as compared to MSP, are responsible for the influence of structural features on the extent of transannular interactions. CONCLUSION&

The results of the present calculations fit and explain well the spectroscopic properties of the paracyclophanes investigated: i.e., (1) the bathochromic shift

173

on the long wavelength absorption, and (2) the appearance in this region of a new band when the double-layered structure, 2L, is transformed into the triplelayered one, 3L. The decrease in the long wavelength absorption with the addition of every new layer ( 2L+ 3L >> 3L+4L > 4L+ 5L) is reflected in the calculations of the longest wavelength electron transitions. The calculated bathochromic shift for 2L-+3L is 40 nm, as compared with an experimental value of 42 nm. Addition of the fourth and fifth layers results in calculated shifts of 5 nm and < 1 nm, respectively. The fact that the new, longest wavelength band appearing in 3L originates from the addition of a new layer to 2L is confirmed by the finding that the corresponding electron transition to the 2lB (p) excited state is localized on the inner ring; the latter phenomenon is proven, in turn, by the highest degree of the excitation of that ring amounting to 35%. Also in this transition, the deformation effect, connected with the twist-shape of the inner ring, is of reasonable importance. The substantial value of CR%=53 points to the participation of the transannular effect, which is uniformly distributed over the entire molecule, IA-n = ln+,. Similar conclusions concern the 4L and 5L cyclophanes. The localization of the long-wavelength transitions on the inner rings originates from the deformation of these rings. The increase of transannular interactions in all electron transitions occurs with the addition of each new layer. The largest spectral differences occur between 2s and 3s metacyclophanes and are reflected in the calculated values. MSP species show weaker transannular interactions than MLP species due to the different way in which the layers are stacked. The conclusions reached here are based on the transition density matrix analysis of the excited states [ 7,151, demonstrating the usefulness of this method.

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