Photochemical cis-trans isomerization of s-trans-1,3-pentadiene. A theoretical study

CHEMICAL PHYSICS LETTERS

Volume 5 1, number 3

PHOTOCHEMICAL A THEORETICAL 1. BARALDI,

US-TRANS

ISOMERIZATION

1 November 1977

OF s-TRAM-1,3_PENTADIENE.

STUDY

M.C. BRUNI, F. MOMICCHIOLI

Istituto di ChimicaFisica. Gkiversit; di Modena. 41100 Modena, Italy

J- LANGLET Laboratoirede Biochimie Tht?orique.Institut de Biologic Physico-Chimique, 75005 Paris,France

and J.P. MALRIEU Laboratoirede Physique Quantique. UniversitgPaul Sabatier. 310 77 Toulouse-Cedex, France Received 19 April 1977 Revised manuscript received 26 July 1977

The cis-trans photoisomerization pathway of the s-trans-1,3-pentadiene is investigated on the basis of excited state potential curves calculated using the CIPSI method in the excitonic (PCILO type) scheme. It is shown that both direct and sensitized excitation of either isomer are followed by equiprobable formation of two allyImethylcne intermediates, one of which can lead to isomerization, while the other undergoes radiationless decay to the starting geometrical isomer_ In the triplet state TI the intermediates are separated by rather low potential barriers. This suggests the occurrence of rapid interconversion of the biradical intermediates at room temperature and explains the relatively high efficiency of the sensitized 1,3-pentadiene photoisomerization.

1. Introduction Electronic transitions and cis-mzrzs photoisomerism of polyenes have been the subject of many studies in the last few years. On the one hand, detailed spectroscopic measurements [l-S] and quantum-mechanical calculations [6-91 have been carried out in the attempt to ascertain the nature of the lowest Franck-Condon excited states- On the other hand, the structures of the photoisomerization intermediates have been investigated by measuring the photoreaction quantum yields [ 10,l l] and calculating the electronic potential surfaces [ 12-141 which describe the photochemical rearrangements*. The latter subject, that is the study of the photoreaction mechanisms in terms of the features of the potential surfaces, has already been treated by us, taking photoisomerism in stilbene [17,18] and

styrene [ 191 as an example. With this note, we undertake a similar investigation on the photochemistry of polyenes, and start with the cis-tram photoisomerization of dienes. In particular, we shall analyze in detail the case of s-mm-1,3-pentadiene which exists in the two conformations:

( trans

) &

( cis

1 c

* Furthermore, a model for the dynamic description of cistrans photoisomerization of conjugated polyenes has been recently developed [IS]. For the dynamical aspects of photoisomerization in unsaturated hydrocarbons see also ref. [I61 493

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The available experimental data on the c&tram photoisomerization of 1,3-pentadiene indicate clearly that direct and sensitized photoconversions proceed independently [IO] (via S, and T, , respectively), but they are insuffkient to establish in detail the pathway of the two reactions. A mechanism involving formation of allylmethylene intermediates has been suggested [lOJO] by a&logy with the well defined case of 2,4-hexadiene [IO,2 1,22]_ The proposed scheme is: t

d

-

c

ff

;

\

c

/

-2

‘=_.__--

(1)

--

(31

I f

/ t

(2) \

1 c

c

In short, excitation (both direct and sensitized) of any of the two isomers should be followed by rotation about either terminal double bond. So, two different excited

allylmethylene

biradicals

should

be

formed, one of which (3) can lead to isomerization, while the other {(l) from t, and (2) from c} relaxes into the starting isomer*. According to this scheme, the striking difference between the quantum yieIds of the direct photoisomerization (I$++ = &+c = 0.1) [IO] and thase of the sensitized photoreaction (O,,, t Qt+c = 1) [10,20] may be due to preferential formation of “non-reacting” (I), (2) and “reacting” (3) intermediates in S, and T, , respectively. An ahernative explanation is that in T, the “non-reacting” intermediates can undergo efficient conversion into the “reacting” one, while in S, they cannot. What follows represents a theoretical test of these hypotheses.

2. Calculation

(101.

procedure

The calcuIations were carried out within the CIPSI 1261 method in a PCILO 127,281 type version, and adopting the CND0/2 parametrization [29] *. This calculation technique has been already used to study excited state conformations of styrene [ 19 ] , propiophenone I3 I ] , benzaldehyde (321 and butadiene [337. Briefly, it is an iterative configuration interaction procedure, in which the basis set consists of Slater determinants built with fully-localized bond orbitaIs. In stage zero a proper starting subset is chosen, and the determinants to be added at each subsequent stage are selected according to a perturbative criterium. So, multiconfigurational zero-order wavefunctions zre obtained, whose adequacy is tested by calculating the second-order correction of the energy. In the present paper, the iterative CI processes were especially devised to obtain the “best” zeroorder descriptions for the lowest excited n~1~*states and their evolution through the rotaticn about terminal double bonds. In practice, three-stage processes were carried out and the resulting zero-order wavefunctions included mono-, di- and t&excited determinants involving both 7~and CTbonding and antibonding orbit& (in addition to ;: quad&excited deterrninant and the ground state determinant). The 0-n coupiing, which is very important in twisted configurations [ 191, is described essentially in terms of monoand di-excited determinants, involving the ‘IT(and n*) orbital localized on the rotating bond and the nearestneighbour o (and o*) orbitals. Bond angles and bond lengths of the diene chain were chosen as follows: L CCC, L CCH and L HCH = 120°, R,H = 1.1 a, R,, = 1.46 a (central bond) and R cc = 1.34 fi (terminal double bonds). For the methyl group we adopted the geometry given in ref. [34]_ In general, ah of these parameters were kept constant during internal rotations. In a few cases the influence of CC bond stretch on the excited state potential energy

* Formation of cyclopropylmethylene intermediates (already postulated for the direct valence photoisomcrization of acyclic 1,3-dicncs [23,24] ) provides an alternative interpretation of the experimental data concerning the direct photoconversion [ 10,24,25] _However, this mechanism is regarded as less likely than the allylmethylene mechanism

1 November 1977

was also tested.

* It is important to remind that the basic CNDO hypothesis (i.e. the negIect of the differential overlap) becomes less crude when inserted into the PCILO scheme [27,28] _Thus, PCILO type calculation procedures should predict both geome*Jc parameters and force constants more correctly than the CNDO/Z method. At least, this is true as Far as the conformations of conjugated systems are concerned (381.

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CHEMICAL PHYSICS LEmERS

3. Results and discussion Before studying the excited state relaxation mechanism in 1,3-pentadiene it is necessary to point out what we know about the electronic states of transbutadiene, which is the obvious reference system. The main characteristics, derived from some preliminary calculations as well as from a previous CIPSI-PCILO study [33] can be summarized as follows: (i) The potential curves for the rotation of only one double bond in the lowest-lying triplet (Tl) and singlet (S1) excited states of butadiene have a marked energy minimum in the perpendicular configuration [33] *. These findings agree with previous calculations, both semi-empirical [15,35,36] and ab initie [14], and suggest that allylmethylene biradicals are very likely intermediates in photochemical stereoisomerization of 1,3-dienes. (ii) Rotation at both double bonds with formation of a common 1,4-biradical intermediate. initially proposed to explain the quantum yields of the sensitized 2,4-hexadiene photoisomerization [lo], appears to be unfavoured. In fact, some trial CIPSI-PCILO calculations for the symmetrical twisting at both ends of the molecule indicated that the 1 ,4-biradical geometry does not correspond to a minimum in either S, or Tl potential surfacez. Recent ab initio [ 141 and MINDO-type [ 1 S] calculations on butadiene support our results. (iii) The existence of a symmetry forbidden (’ Ag) state below the first IB,, (S1) state of planar butadiene is doubtful. Actuelly, the “hidden state” (IA,) observed by some authors in diphenylpolyenes [ 1,37, 381 and calculated by Karplus et al. in several linear polyenes [6,7], is the second excited singlet in our loo-determinant calculation on butadiene [33] (and keeps higher than the lBU state throughout the rotation about one double bond)_ Considerable extension of the CI (186 determinants) [39] did not produce significant effects on the relative ordering of the I$

*The iterative CI procedure led to wavefunctions including 100 determinants. The zero-order potential curves were not

sensibly different from those obtained after second-order energy correction. $ This conclusion has only qualitative value, in that the zcroorder results (obtained with a 216-determinant calculation)

converged poorly.

1 November 1977

and IB,, states? _ Thus, failing any real experimental evidence, we assume that no “hidden states” are involved in the direct photoisomerization of acyclic 1,3-dienes. According to the foregoing points, the theoretical investigation on the cis-frans photoisomerism of 1,3pentadiene can be focused on formation and interconversion of allylmethylene intermediates in the states T1 and S1 (corresponding to the lowest-lying 3B, and IB, states of butadiene). 1.

Formatiorl of the allylmethylene intermediates

In dealing with this problem we first assumed that the methyl group does not affect appreciably the potential energy curves which describe twisting at the opposite end of the diene. In other words, we assumed that the potential curves for the rotation of the Cl -Cz bond in 1,3-pentadiene (both tram and cis) are “the same” as those obtained for the rotation of one double bond in butadiene. Then, we expressly calculated the potential curves for the rotation about the C3-C, bond. Fig. 1 shows the results obtained for the ground state (So), the lowest-lying triplet (T1) and singlet (S,) excited states and the “double excited” s$a_l,eS (primarily represented by the determinant ( Rz !?)*. In the perpendicular the states So, T, ,S1 and configuration (‘5~2n2-~$Oo)* S* (two by two ‘$degenerate”) describe the biradical siruation which occurs owing to breaking of 7r2 bond [40] _ In particular, So and T, have essentially covalent character, while S, and S* correspond to highly polarized structures of the type M-A* (M = methyl-

? The reliability of the ‘Bu-‘Ag

ordering was also tested by carrying out a CIPSI-PCILO calculation for a structure having the double and single bonds reversed relative to the ground state geometry. This bond length inversion is expetted to greatly stabilize the ‘Ag state on account of the significant bond order changes associated with the transition from the ground state [7,8]. In fact, the zero-order calculation (186 determinants) favoured the ‘A -lB, sequence, but second-order corrections restored t g e tBu-‘Ag ordering. * ~2 and P$ are the n bonding and antibonding orbit& lo&ized on the rotating bond, ~1 and rrt being the 5~orbitals localized on the other double bond. * w L and w2 indicate the rotation angles about C, -C2 and C3 -Ca bonds, respectively.

495

1 November 1977

CHEMICAL PHYSICS LETTERS

Volume 5 1, number 3

180

0

cis

Hans

0

brans

90

180

cis

@eg Fig. 1. Potential curves for the lowest electronic states of 1,3-pentadiene,

C3-C4

double bond. o Singlet states;

l

as functions of the angle of rotation (wz) around the triplet state. (a) Zero-order energies; (b) second-order corrected energies.

ene, A = allyl) and

M+A-, respectively*. The zero-order potential energies (fig. la), obtained with a 116-determinant calculation, and the second-order corrected energies (fig. 1b) appear to be consistent, except for the relative ordering of the states S, and S”. This remaining ambiguity will be removed later on by larger CI calculations_ However, fig. 1 shows clearly that the twisted conformations correspond to marked minima in both T, and S, potential energy surfaces. The curves reported in fig. 1 and those obtained for twisting of C, -C, bond [33] are very similar and indeed they are indistinguishable as far as the features of the excited state relaxation are concerned. In other words, the planar excited states of both tram- and cis-1,3-pentadiene are expected to decay with the same probability into the “reacting” (3) and the “non-reacting” [( 1) from tram (2) from cis] allylmethylene intermediates. This occurs in both T, and S1 states, and hence the striking difference in efficiency between sensitized and direct &-tram photoisomerization of 1.3-pentadiene

should originate in the interconversion intermediates. 2. Interconversion

of the allyhnethylene

process of the

intermediates

In order to verify the final hypothesis of the previous section, we calculated the excited state potential curves for an interconversion coordinate (e), through which the out-of-plane distortion is transferred from one end of the molecule to the other. Precisely, 8 was chosen as to minimize non-bonded interactions and corresponds to the (simultaneous) rotation of Cl -C2 and C,-C4 bonds in the same direction. The zeroorder results obtained by diagonaiization of matrices including 200 determinants are given in fig. 2 for the first two triplets (T, and T2) and the lowest excited singlet (S1). In both T, a& S, the three intermediates correspond to three non-equivalent minima of the potential energy*. The “reacting” intermediate (3) appears to be energetically preferred, but the high * In T1 the energy minima correspond to RZ* states “local-

* At o = 90”, the more important configurations in S1 and S* wavefunctions are @($), o(tz $) and $0 &round state determinant, monoexcitation prevailing in S 1 and diexcitation in s*. 496

ized” on Cl-C2 (0 = Go, 180’) or C3-C4 (19s 90”) bonds. Thus, the energy maxima located at 0 = 45’, 135O represent avoided curve crossings involving migration of the excitation [ 19,411 from one end of the diene to the other. The contrary occurs in Tz _

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5 I, number

1 November 1977

CHEMICAL PHYSICS LETTERS

3

(i) in the lowest triplet

the potential

barriers

hinder-

ing intermediate

interconversions are rather low if compared with those existing in S, , (ii) the activation energies of the conversions (1) --* (3) and (2) + (3) are lower than those of the opposite processes. These findings suggest that in the state T, the *‘non-reacting” intermediates [( 1) and (2)] may undergo relaxation into the “reacting” intermediate (3) at moderately high temperatures, thus explaining the rather high efficiency of the sensitized cis-tram photoconver-

180

90 .* ,I*

*

C”,

-. ,*r +-F

CH3

B/de9 Fig. 2. Zero-order potential energy curves describing the in-

terconversion of the al~y~methyieneintermediates in the lowest-lying e&cited states. o Singlet state; l triplet states.

sion* . Such a mechanism is not possible for the direct photoreaction, as in the state S, the short nonradiative lifetime and the very high activation energies combine to obstruct interconversion_ The results of figs. 2 and 3 need some criticism with regard to the fact that no allowance was made for any further geometrical deformation during rotation about double bonds. Let us consqder first the interconversion potential curve of the state S, _ The three energy minima correspond to the following polar structures*:

barriers which separate (I) and (2) from (3) seem to exclude any appreciable intermediate interconversion_ Nevertheless, the second-order corrections calculated for five values of 0 (0”, 45”, 90”, 135”, 180”) led to a different qualitative interpretation. Indeed, the potential energy diagram obtained after second-order ~rturbation energy correction (fig_ 3) indicates that:

I +0.38

+0.06

(3) L

1

90

2-

_*

1.

e/de9

3-F

- - ==-cv3

Fig. 3. Second-order corrected energies obtained for five values of 0, corresponding to minima and maxima of the interconversion potential functions. Dotted lines represent reasonable potential curves connecting the intermediates in the lowest triplet end singlet excited states.

1 Actually, the calculated barriers to interconversion in the state Tt (= 14 kc&mole) appear to be largely overestimated if compared with those determined by Saltiel et al. [22] for the analogous processes occurring in sensitized cis-trans photoisomerization of 2,4-hcxadiene (a 3 kcal/ mole). This overestimation may be imputed to the approximations of our calculation procedure, e.g. CNDO parameters, as well as to other factors which will bc discussed shortly. * The net charges of the four diene carbon atoms were obtained by the zeroarder ~vavefunctions. The twisted bond is markedly polarized fespecialiy for fl) and <2)], but deIocaiization of the net charge in the ally1 fragment is rather small. The reliability of such charge distributions, which cast dpubt on the occurrence of very high dipole moments in twisted excited singlets of polyenes [ 121, is extensively discussed in ref. [ 331.

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CHEMICAL PHYSICS LETTERS

(1) and (2) are of the type M-A+ while (3) is a M+A- type state*- This is due to the methyl substituent which stabilizes the positive centers [ 133 , thus removing the “degeneracy” between M-A* and M+A- states. The effect is larger in (3) according to the larger net charge at the positive center, and this explains the relative energies of the three intermediates- On the other hand, Bruckmann and Salem [ 131 have recently shown that M-A+ and M+A- states are stabilized to a different extent by pyramidalization at the negative centers_ In particular pyramidalization of the C, site in (1) and (2) is more effective than pyramidalization of the C3 site in (3), and hence the energy of (1) and (2) might be equal to (or lower than) that of (3). This possible event corroborates our interpretation, since it further reduces the probability of (1) + (3) and (2) + (3) conversions in the state S, . As for the state T,, recent ab initio calculations [13] have pointed out that the twisted triplet of butadiene does not undergo pyramidalization, but is sensibly stabilized by prolongation of the rotated bond. On the other hand, the form symmetrically rotated at 45” at both ends of the molecule is even more stabilized by simultaneous prolongation of the rotated bonds [13]. In this view, the potential barriers separating (1) and (2) from (3) in T1 state of 1,3pentadiene might be substantially lower than those indicated in fig. 3. In view of the importance of the latter point we carried out some CIPSI-PCILO zero-order calculations to estimate the influence of CC bond stretch on the interconversion barriers in the state T, _ In practice, a rough optimization of the CC bond lengths was Performed at 8 = 0’ and 4S” (fig. 2) for the state T, (by the same 200 X 200 CI) and the following geometries were obtained: Clearly,

* The corresponding wavefunction$hye

the pre$o$nant

weight on the configurations @(“r zr) and @(z

z),

re-

spectively. Thus they are real S’&?ttes and the “St” potential curve of figs- 2 and 3 must be understood as the lowest tying adiabatic pathway connecting the singlet intermediates.

498

CH,3

4-7 3

1.36

1.40

--_

4 '

1.48

1

a

As expected, the triplet stabilization induced by rearrangement of the CC bond disrances was found to be much higher at 8 = 4S” than at 8 = 0”, the barrier to the (1) + (3) conversion being reduced from 2.14 to 1.22 eV (at the zero order)- This result is in keeping with that of ref. [13] and supports the idea that sensitized cis-tram photoisomerization of 1,3_pentadiene involves interconversion of the allyImethylene intermediates_

4. Conclusions In the present work detailed CIPSI-PCILO calculations have been carried out in order to assess the mechanism of the cis-tram photoisomerization in sfans-1,3_pentadiene_ The results can be outlined with the help of a tribedral diagram (fig. 4), which emphasizes the excited-state relaxation pathway. Fig. 4 represents the region of the D-QRSisomer without specifying the nature of the excited state (S1 or T1). Let us assume that at a given time 1,3-pentadiene, say tram, is prepared in the planar conformation of the excited state (A in fig. 4). Then, the system will undergo rapid vibrational relaxation to the energy minima B and C, corresponding to configurations twisted about C!,+ (wl = 90”) and C,-C4 (w2 = 90°) bonds, i In this case only CaC3 and C&4 bond distances were optimized, while the length of the C!tCa twisted bond was assumed to be equal to that calculated by Buenker et al. 1421 for the CC bond of (twisted) ethylene in the lowestlying triplet state (L-48 18).

Volume 5 1, number 3

CHEMICAL PHYSICS LETTERS

1 November 1977

Nazionale delle Ricerche (Rome)_ We thank V. BonaEicKouteckjr and S. Ishimaru for making their results available prior to publication_

References 11) B.S. Hudson and B-E. Kohler, Chem. Phys. Letters 14 (1972) 299; J. Chem. Phys. 59 (1973) 4984. [2] R.L. Christensen and B.E. Kohler, Photochem. Photobiol. 18 (1973) 293. [3] R.M. Gavin Jr., S. Risemberg and S.A. Rice, J. Chem.

Phys. 58 (1973) 3160. [4] 0-A. Mosher, W.M. Flicker and A. Kuppcrmann, J. Chem. Phys. 59 (1973) 6502. 151 P.M. Johnson, J. Chem. Phys. 64 (1976) 4638. 161 K. Schulten and M. Karplus, Chem. Phys. Letters 14

L x

(1972)

CHa

Fig. 4. Trihcdral diagram representing the proposed photoisomerization pathway of 1,3-pentadiene in the frans isomer region. A wholly similar d&ram can be drawn for the region of the cis isomer.

respectively. The two species are formed with the same probability, since the paths AB and AC are aImost equivalent, but only the species C can undergo isomerization. Thus, the trarzs -+ eis isomerization efficiency is expected to be low, unless the B + C conversion is fast enough to compete with decay of B to the starting diene, as well as with the opposite conversion C + B. This really happens in the triplet manifold at room temperature in virtue of long lifetimes of the intermediates and rather low activation energy (a few kilocalories) of the process B -+ C (E,,,(C -+ B) being somewhat higher). None of these conditions occurs in the singlet manifold, and this explains the low efficiency of the direct photoconversion. A stimulating prediction of the above photoisomerization pathway is that the quantum yields of the sensitized reaction should be dependent on temperature and solvent viscosity, as experimentally found by Saitiel et al. for the corresponding process of 2,4-hexadiene 1221-

Acknowledgement This work was supported by a fund of Cons&ho

305.

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[3_8] S. Diner. J-P_ Malrieu. F_ Jordan and M. Gilbert, Theoret. Chim. Acta 15 (1969) 100. 1291 J.A. Pople and G.A. Segal, J. Chem. Phys. 44 (1966) 3289. 1301 D. Perahia and A. Pullman, Chem. Phys. Letters 19 (1973) 73. [31] J. Langlct and P. Gacoin, Theoret. Chim. Acta 42 (1976) 293. [32] J. ianglet and P. Gacoin, Theoret. Chim. Acta, to be published. [33] hi-C. Bruni, J.P. Daudey, J. Langlet, J.P. Malrieu and F. Momicchioli, 3. Am. Chem. Sot. 99 (1977) 3587. [34] D.R. Lide Jr. and D. Christensen, J. Chcm. Phys. 35 (1961) 1374.

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[35] E-M. Evleth, Chem. Phys. Letters 3 (1969) 122. [36] NC. Baird and R-M. West, J. Am. Chem. Sot. 93 (1971) 4427. [37] R-L. Swofford and WM. McClain, J. Chem. Phys. 59 (1973) 5740. [38] G.R. Holtom and W.M. McClain, Chem. Phys. Letters 44 (1976) 436. [39] MC. Bruni, F. Momicchioli and I. Baraldi, unpublished results. [40] L. Salem and C. Rowland, Angew. Chem. Intern. Ed. 11 (1972) 92. [41] L. Salem, Science 191 (1976) 822. [42] R-J. Buenker, SD. Peyerimhoff and H.L. Hsu, Chem. Phys. Letters

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