~~~~~~~~~~~~* Maria 6.Bruni, and Ivan istituio tii Chirnica Fisica, Universita di Modena, 41 100 Modena, Italy (Received July 7, 1972) Pubiication
C O S ! ~assisted by
Consiglio Nazionaie delle Ricerche (Roma)
intranioiecis!ar reasons were sought for the deviation of absorption and emission spectra of polyphenyls from i;he mirror image relation. As a working hypothesis it vvas supposed that the differences between fluorescence spectra originate in the excitation of the twisting mode of interannular bonds. Curves of the potential energy as a function of the dihedral angle between phenyl rings were obtained. for t,he ground state and the lowest singlet excited states by using semiempirical calculation procedurm. A polynomial approximation was adopted for the potential functions so that vibrational energies and wave functions could be calculated simply by expanding the wave functions in a harmonic oscillator basis set fly this technique, Franck-Condo3 distributions were obtained for both absorption and emisriioa. The contours of the distributions enabled us to explain both the fine structure of fluorescence spech a and the structureless long-wavelength uv bands in polyphenyis. ~
I. ~~~~~~~~~i~~ The comparison between absorption and fluorescence spectrsi and their deparferre from the mirror image rela"cion provides important information about the relative locations of the iowest excited states of a molecule and the shape of the potential energy surfaces, thus helping the theoreticiain t o elucidate the energy decay mechanisms~ If aromatic molecules are consideredl it is found that the mirror image relation between absorption and emission curves is I~etterretained by single aromatic systems ( e . g . , benzene, anthracene, naphthacene, etc.), while molecules where a few aromatic systems are connected to one another essentially by single bonds generally show fluorescence spectra ~lshichare quite different from absorption spectri:. IFolyphsnyls are typical examples of the latter type of molecule. I n Figure I we have reported absorption and fluosescence speclra of the first two t e r m of the polyphenyl series, i.p.> biphenyl and p-terphenyl., together with those of 4-.viny4F1iphenyl.The most evident difference betwe::n absorption ~indemission spectra is that the fordiffiise, while the latter show mer appear to Ine co~~ipleteAy a well-resolved vibrational structure. In the present w3rk we attempt a theoretical interpretation uf this experiinentai fact. The paper consists of two parts. Bn the first part, the Correlation between the lowest singlet excited states of he molecules in Figure 1 is stated so as to single G i r t the electronic state from which the emission originates and the vibrational mode to which the spacing of the fine stru.cture has to be assigned in each case. :in the si:cond part, energy potential curves correspondiing to a Isw-Beq~.ancyvibrational mode, namely, the twisting of' the interanrrula.r bonds, are obtained for the ground state and the lowest excited states, and finally distributions of transition probability are calculated for bot,h emission and absorption. It is on this basis that the difference betweeri the shape of the absorption bands and nce bands in polyphenyls will be dissigirra d t h e
~~~~~~~~~
As the first step in explaining the spectra reported in
Figure 1, we must state, in each case, whether the emisaion originates from the same singlet excited state that is chiefly responsible for the absorption intensity or not. To this end we carried out a correlation between the lowest singlet excited states of the molecules in question using a PPP calculation procedure for the treatment of T electrons. Alternant hydrocarbon simplifications2 were adopted, and the configuration mixing was extended to include all the singly excited configurations. Two-electron repulsion integrals ( * y p q ) were calculated according to PariserParr proeedure,3 and molecular geometries were chosen as follows: Rcc = 1.397 i% in the rings, Rcc = 1.50'7 A between the rings,4,5 and Rcc = 1.46 and 1.34 A for the essential single and essential double bond, respectively, in the vinyl group. The corresponding elements of the core matrix hold -2.30, -:1.44, -1.76, and -2.95 eV, the first being arbitrarily fixed and the others derived according to the relationship HpqC = KEPq-B, previously used by one of US.^ Bond angles were assumed equal to 120" and, in this model calculation, the dihedral angle between the planes of the phen.yi rings was equal to zero. The results are reported in Figure 2 where the excited states are labeled according to their syanmetry properties ( D Z hpoint group). Figure 2 suggests that in biphenyl the state, while in p-teremission originates from the ,&!1 ~ 1A, tranphenyl the fluorescence (.F) is due to t . 1 lBzu IA., transitions skion. On the ctlzer hand, the 1BaL, (short-axis polarized) are very weak and they are hidden zU '.A, transitjons (long-axis polarized), which provide almost all the intensity o f the absorption band in ~i~he~~yl, both biphenyl and p-terpheny!, In 4 - ~ ~ r i ~ y ~ ~ where the excited states can be easily correlated with those of the other niolecules by analyzing the GI coefficient^,^.^ the situation i s similar bo that of p-t.erpliien:yS,'except for the energy difference between .the two lowest excited states, which is very small. In conclusion, n direct com-
-
d--
-
(1) I . 8 . Berlmari, "Handbook of Fluorescence Spectra of Ararnatic Molecules," Academic Press, New York, R! Y,, 1965, ( 2 ) H. Pariser, J , Chorn. Phys.. 24,250 (1956). ( 3 ) 3 . Pariser and FI. G. Parr, 1.Chem. Phys., 24, '767 (1953). (4) J. Trotter, Acfa C:rysta:/ogr., 1 4 , 1135 (198; j . (5) A . Hargreaves arid S. H.Rizvi, Acta Crystaliogi'., I S , 365 (1962). (6) F. Momicchioli and A. Rastelli. J. Mol. Spoctrosc., 23,310 (1967) (7) F. Nioriiicchioli and A. Rasteili, J. Chem. Scc B, 7353 (1970). The Journal of Physicai Chemistry Voi 76, No. 26. 1972
F. Momicchioli. M. C. Bruni, and I . Baraldi
3984
1.0
0.5
108
-
0
iLi
104
102
1.0
.\2 C aJ
. C
0.5
--.ro 0
2 0
1.0
0.5
0
soooii
35600
30bOO
25000
wavenumber (em-')
ure 1. Solution
and fluorescence spectra of biphenyl, 4vinylbiphenyl, and p-terphenyl (from the top downward) reported LN
Cyclohexane was the solvent and the spectra were recorded at room temperature. The wave numbers of the exciting radiations for the emission spectra were -39,410 cm-' for biphenyl and 33,000 ciii - far 4-vinylbiphenyl and p-terphenyl. frorn ref 1 .
parison betweew! the absorption and emission curves reported in Figure i can only be made for p-terphenyl. and 4-viny!bipheny13 while in biphenyl the two transitions involve different excitied states. This interpretation is supported by some experimental facts. First of all, we refer to the comparisonlJ< between the natural fluorescence lifetime ( ~ 0 ~derived ) from the intepated intensity of the absorption band (e.g., by using F'orster's formulag) and that obtained by the Atitionship rom = T / Q , where T is the measured decay time and Q is the quantum yield. In Table I, where the v d u e s of 7 o m and roc are reported from r e f I. and 8, it is evident that a good agreement between measured and "ccalcula.ted" natural lifetime is found only for p-terphenyl. The strong discordance between ram and roc in biphenyl clearly indicates thet the emission does not originate from the same excited level that is responsible for the absorption band.8 In the case of 4vinylbiphenyl the fairly short dlxay time agrees with our prediction (Figure 2) cancerzing the level responsible for emission, and the relatively low quantum yield might be due to internal quenching caused by the closely lying excited level. Furthix evidence for the resuits of Figure 2 is forthcoming from the spacings of t,he vibrational peaks in the emission spectra. These spacings are -,IO00 cm-1 in biphenyl and 1300 cm- 1 in 4vinylbiphenyX and p-terphenyi, and t h y
-
The Journa! of Phv?ica/ Chemistry, Voi. 76. No. 26, 1972
L
igure 2. Correlation among the lowest singlet excited states of biphenyl, 4..vinylbiphenyl, and p-terphenyi in their planar configurations. Energies are given relative to the ground state. The excited stat& involved i n the emission ( F j are indicated and they can be directly correlated with those corresponding to the shortand long-axis ( 1 1 ) polarized uv transitions. axis (1)
most likely correspond to the ring breathing vibration and to the central bond stretching vibratiorn,10-12 respectively. As a consequence, if our predictions are right (Figure 2 ) , the 1B3u -* 1A, transition must be coupled with the ring breathing vibration and the lBzu l4, transition with the central bond stretching vibration. This condition can be qualitatively checked within our calculation scheme; if a 'r bond order-bond length relationship13 is used to estimate the Length of the interannular bond in IA,, %au, and lBzu states of biphenyl it i s found (see Table I P 4 ) that in state the bond in question is nearly unchanged with respect to IA, state, while in 1 much shorter ( a similar trend also occurs in 4-vinylbiphenyl and p-terphenyl). Thus, in and states, the minima of the potential energy curves corresponding to the stretching mode o f the interannular bond are far apart, and hence the which originates from involves excitation of t the observed progressi vinylbiphenyl and p-terphenyl.
-
III. Shape of the E Since the electronic states resporisibie for the emission and absorption bands of Figure 1 have been identified, it remains to be seen why the transitions lead to completely diffuse uv bands in contrast with. the corresponding fluorescence bands (1 zU I&), which exhibit a marked progression in the inter-rings bond stretching mode. Here we will a t t e k p t a completely intramolecular interpretation. The working hypothesis is that the difference between the distribution of transition probabihty of absorption (*Bzu lip,) and that of emission can be caused by the excitation of a low-frequency
-
-
-
-
(81 I . B. Rerlman and 5. J. Steinaraber, J. Ghen;. P h y s . , 43, 2140 (1965). (9) Ih. Forster, "Fluoreszenz Organischer Vevbindungen," Vandenhoeck und Ruprecht, Gottingen, 1951, 13 158. i l O l D. Steele and E. R. Liooincott. J. Mo!. Soestrosc.. 6. 238 (19611. i l l j G . Zerbi and Sl Sandion,, Specirochim.'Acia, 24,463(1968). (12) A. L, Len and C. H. Ting, J, C!,in. Cliem. Soc. /Taipei), 17, 1 4 (1970). (43) K. Nishimoto and L. S. Forster, Theor. Chim. 4cia, 4 , '55 (1966) (14) E. F. McCoy and I . G. Ross, Aust. .j.Chom.. 35,573 (1962).
3985
Figure 3. Potential energy curves for the twisting mode of the interannular bonds of biphenyi, 4-vinyibiphenyl, and p-terphenyl. In the latter rriolecule only the symmetrical rotation of the outside phenyls is considered. The ground state (So) 2nd t h e two lowest singlet excited states (SIand Sz8)are analyzed. The energy zero is arbitrarily assigned to the minimum of the graund state curve.
LE I: Measured di-orn) and "Calculated" sbrrral ~~$~~~~~~
(1-0~)
Reported in Ref 1 and 8
Molecules
r. riseca
ob
ram, nsec'
roc,nsecd
Biphenyl .l-VinylbiphenyI p-Terphenyi
IELO 2.6 c.95
0 18
88.9
2.87
0.61 0.93
1.51
4.3 1.02
1.43
*
a Decay time. Quarituin yield, rom = r / O . Computed from the iqregratod inlensity of 'the absorption band by using Forster's i o r m ~ l a . ~
rders and Length Changes of the 110of 1 5 in the ~Lowest~Electronic ~ Electronic state
T bond ordera
'A,
0.?921
'B3u
0.2445
'iB2L!
0.3775
~
~
AR. Ab -0.009 -0.033
a Corrections or! h o l d orders due lo configuration interaction have been included (see Appendix I \ (of ref '14). Bond lengths are calculated by tho relationship R,, = . .517-0.18/pq13 (where, , / is the bond order) and At? valiies are r'eierred io the ground slate 'Ag.
vibrational mode, :amely, the twisting of t,he interannular bonds. To test this hypothesis, curves of the potential energy as a function of the dihedral angle ( 4 ) between the planes of the phenyl rings will be obtained first. Then the potential curvcs of both the ground and the excited states will be used b calculate Franck-Condon factors for emission and absorpt,ion, and, on this basis, an interpretation of the diEerence between near-uv and fluorescence spectra will be proposed. Potential Errei-gy Biggrams for the Twisting Mode of h t e r a n n i d a r Bonds. The calculation procedure used here was first proposed by Fischer-Hja1marsl5 and recently
adopted by us to study the internai rotations of'cr,w-diphenylpolyenes.16 Briefly, the potent,ial energy is evaluated, for each value of the angle of twist, a5 a sum of three the core repulsion enerterms, the ?r electron energy (ET), gy (Ec"), and the nonbonded interaction energy ( E " ) .The calculation procedure of the first term ( E T )ir; that outlined in the previous section (for the core integrals of the interannular bonds a cosine dependence on the angle of twist was assumed, Le., N@ I' El02 cos 4 ) . The ( E c c ) term was calculated according to a formula proposed by Dewar and Klopmanl7 in the PNDO procedure. The theoretical reasons, as well as 4he practicai convenience for the use of ~ in ?T ~calculations:18 have been disc~ssedelsethis~ recipe where.16 919 All the interactions between nonbonded ztoms (HH, He,and CC) were included in the stmic interaction energy (E,,) and were evaluated using both the formula and the parameters suggested by Allinger, el n1.20 The potential energy diagrams thus obtained are reported in Figure 3. In p-terphenyl we limited ourselves to analyzing a vibrational mode where the outside phenyls (15) I . Fischer-lijalmars, Tetrahedron, 13, .I805 (1963). (16) F. Monicchioli. I. Baraldi, and M. C. Bruni (part 1 ) ; I . Baraldi, F. Momicchioli and M. C. Btuni (part 2 ) , 2. Chem. SOC.. faraday Trans. 2, 68, '1555. 1571 (1972). ( 1 7 ) M . J . S. Dewar and G . Klopman, J , Am& So transitions (Figure 3). ?‘&e “b~3st”values of the parameters u1 for the potential functions were obtained by means of a least-squares plio~edure. T h e results are reported in Figure 4. ’The same potential f~~rnctions were adopted for b0l;h biphenyl and 4vinylbjphenyl on accournt of the great similarity bet3ween the corresponding potential curves (see Figure 3) amd according to the qualitative character of our calculation. The coni.parisoiz of the curves in Figure 4 with the corresponding curves in Figure 3 shows that the pofycomia? approxini;;tioris fit t t o bottom and the walls of the potential functions lairsy ell^ especially as regards the So states (in th.e Sf:stata of bipherryl arid 4-vinylbiphenyl the very low ba reproduced, and hence this ::xcit.ed be planar in our calculation). 7‘he we of h e poiynomial approximation is certainiy coiwenient i,ri that it makes easy the calculation of Fraiick-Cantion factors, but there is the objection that it may affect t i e res~lltsurr:.ess the tion seems to apply potential. well is very deep. This o particularly in .the case of the gro~uidstate C U K V ~ S of biphenyl and 4-viiaylbiphenyl, where the barrier at, 4 z 90” i s rather low (4.2 kcal/moi). On the other harid, the fre-
+
oretical reports on conforinat,ion and. inter12511 rotacicm of biphenyl, the potential curve:; repor~;ed in Figure 3 pro’bably represent a good compromise and add weight t o ail the prevjsioris of the previcxis sixtion En particular, Figure 3 clearly shows that in a-.c.ir!yPblipherp?i! the .SIstate can cause a deactivation of the Sz stxce, an j.ntr~ru~.d conversion process, and this explains fh.: different \idat: of T~~ with respect to p-terphenyl (see Table I) .?ranch-C’ondon b~,ttoias. In this section the torsioiTa1. pot,ent,ia1 cur corresponding to the electronic states invoi,vvad !.c the emission and absorption processes (Figure 3) are osed to sat up distributions of transition probabiiity, To this end vibrational energies and wave functlorrs must ile first obtained, and then overlap integiais between vikm~tionaiwave functions of the initial and final states must by: catciilated. The method of calculation aciopted liere 1s the simie as recently used by us to study the shape of the “ ~ ~ n j ~ g a t i oband r i ” of the cqo-diphenyip d y e ~ d(see ~ nlsrr ref 33). The basic approximation of this method is +katit e~ipressesthe potential function as a power series (i.t,., ’V(x)= Z l u l x l ) . The matrix. elements of this t,ype of po1:;entlai for ;a harmonic oscillator basis set are known (up eo l 5 8 1 6 , 3 4 ) , and hence the vibrational wave Fxictions v m e expressed as linear combinations of of an arbitrary HO. The problem thus contting up and the diagonalization of a Hamiltonian ma6,rix wlxm?elements are fl,,,, = KnnzK4- H,,” I
a
-
where
Chem. Soc., 90, 5373 (1968). (a) M. J. S . Dewar and A. J. Harget, Prec. Roy. Soc., Ser. A, 315, 44.3 (1970); (b) present work. B. Tinland, T h o r . Chim. Acta, 11, 452 (.ISSb). B. Tinland. J. li4oi. Struct., I, 161 (1969). 0 . Caropen and M. M , Seip, Chem. Phys. i e f f . i 1 , 4 4 5 (1971). A , Rastelli and F. Momicchioli, Bo// Sci, Fac. Chim. ind. Boiogna, 24, 186 (1966). R. Grinter, Ivloi. Phys., 11, 7 (4966) I n the quoted paper the relative positions of l R 2 and ’Bg states are invnrted with iesoect to those found bv us (see Fioure 3 of ref 24 and Figure .3 of the present work). This is drobablydue to the use of a shorter inter-rings:bond distance (1.48 instead of 1.51 p.) that enhance!: the conjugation between the benzene rings and causes a decrease of the ’E2 ’A,, transition energy. Such a reSUN doss not explain the vaiue of r O min biphenyl (see Tabie i ) , and it ShoLJld be relected accordingly. P. J. Wagner, J. Amer. Chern. SOC., 89, 2820 (1967) 1. I-, L.ohr, Jr., J . Amer. Chem. SOC..9 2 , 2210 (1970) E. Weilbroiiner, tis. M. Funthard, and R . Gerdil. Heiv. Chim Acta, 391,I 1 7 1 (195ii). The values Of tlie reduced moments of inertia are 0.075 X g c m 2 for the twisting inode e!‘ biphenyi (and and 0.:?00 X 4-vinyIbi~henyl)and of p-terphenyl, respectively
1241 ,- , A. iniamura and R. Hoffmann. J . A”?.
(25)
(28) (27) (28)
+
The Journai of Physicei Chemistry
\/e/
76. No 26, 7972
F. Momicchioli, M . C. Bruni, and I . Baraldi
3988
BIPHENYL- E m i s s i o n
4-VINYL
v;=o
(Sz-So)
vl'= 2
v; = 0
v;=1
(D
t
0
q v)
I
-
II
1 32000
1 31000
0
I I I I I IIIII II
1f
l
t 4 -VINYL
v;
BIPHENYL - A b s o r p t i o n
vl'= 0
=2
30000
(SpS,)
v;=
vl'= 0
1
0
.;?i 1 '
D
-1-
1-1
- I
-I!
36000
l
35000
o
1 w av e n u m b e r (cm-')
-
Figure 5. Franck-Contlon distributions for the absorption (Sp SO) and the emission (Sp SO) in 4-vinylbiphenyl. Two vibrational modes, namely, the stretching and the twisting of the interannular bond, are considered to be excited. v ( 1 ) " and v(1)' are the quantum nlumbers cf the stretching mode in the ground and the excited state, respectively. On each vertical line we have reported the quantum numbers relative to the transition in the twis?ingmode. +
quency of the twisting mode in biphenyl is extremely low (the value reported in the literature for the crystalline state is 70 cm-1,36 but it is probably lower for the vapor phase3?), and hence the first 15 or 20 levels, as many as are in problem, be accounted for within the approximation adopted here. The Journal of Physical Chemistry, Vol. 76, No. 26, 7972
The Franck-Condon distributions thus obtained were further elaborated in order to emphasize the effect (36) K. Krebs. S . Sandroni, and G. Zerbi, J. Chem. Phys., 40, 3502 (1964).
(37) T. Sekiya, K. Sakamoto, and Y. Watari, Nippon Genshiryoku Kenkyusho Kenkyu Hokoku, J A E R I , No. 1181, 75 (1969).
-
E:
f- t
- /
P
-TE R PHENY 1.- A bsorption ('B
a-'A,)
i/
I
34000
B
i
wavensnt her (cm-') Figure 6. Franck--Cnndon distributions for tails see the caption of F i ~ u r e 5.
the absorption
('B2
+-
brought about b y exci.tution of the twisting mode on each member of the principal progression in the stretching mode of the ~ n t ' ~ ~ ~ nbonds n~.~ (to~ which ar the fine struc' C I ~o k " w in Guoresceiace spectra of 4-vinyibiphenyl and p-t.erphenyil has t o be assigned). Briefly, we calculated distriloi \tione of t,r.ansition probability, the individual tmms of which w e tq,> , A = q i: Q, ,qu( 2 ) ( 2 ) absorption q t i Pv , = yo,ti q v( 2 ) , ( 2 ) emission where q u c ~ , ~ oand 8, are probabilities of individual transitions clue t o excitation of the stretching mode in abI
I
I
I I
I I
' A l ) and the emissiori ( ' 5 2
+
' A , ) in
p-terphenyl, For
further de-
sorption and emission, respectively, and where q u ( 2 i p U ( p ),, are Franck-Condon factors corresponding to excitation of the twisting mode. 'The latter were caleuiabed as described above, whrle the former were derived from the emission spectra (Figure 1). The frequency of the stretching mode was assumed equal to 1275 cm-1 in both the ground ( S O ) and the excited (Sz)states. The resulting distributions of transition probability for absorption and emission of 4vinylbiphenyl and p-terphenyl are reported in Figures 5 and 6, where the probability of each r ~ ~ r ~ a ~ ~ ~ ? ~ ~ n transition has been multiplied by the Bciltzmaagn factor calculated at room temperature. In Figlires 5 arid 6 only The Journal of Physical Chemistry Voi 7E No 26, 7972
F Momicchioii M C
3990
the two principal members of the stretching progression are considered, and for each of them some progressions in the twisting mode are reported. From Figures 5 and 6 it is clear that the contours of Franck-Condon distributions corresponding to emission are very different from those corresponding to absorption. More precisely, the distributions appear to be quite smooth in absor>ption, while sharp peaks are found in emission. In particular, it can be observed that the maximum transition probability value in emission is almost twice that calcuiattld for absorption. The distributions of tramition probability therefore qualitatively justify the different shape of the absorption and fluorescence bands in 4-vinylbiphenyl and p .terphenyl, and they suggest that this difference originates in the excitation of the twisting mode of the interannular bonds. This result depends partly on the general features of the potential curves, but above all on the molecules being twisted in the ground state while being qussiplanar in the excited state. The Franck-Conclon distribution reported in the bottom half of Figure 5 can also be used to explain the blurring of the’ vibrationa! structure in the absorption spectrum of bi1A1 transiphenyl (Figure I ) , which is due to the 1B2 tion. On the other hand, in biphenyl the emission originates from IB3 slats, and hence the properties of the fluorescence spectrum are related to the shape of the corresponding potent al curve (Figure 3). In view of the great similarity between LAl and curves, the twisting vibralA1 and IB3 tion should b e weakly coupled with 1B3 1Aa Iransitions, anti, in consequence, it should not cause any appreciable blurring of the vibrational structure neither in the aktsorption nor in the fluorescence spectrum. In order to carry out ii quantitative check of this prediction, we extended the calculation of Franck-Condon factors to 1A1 artd 1B3 lA1 transitions of biphenyl. For the 1B3 the sake of brevity we limit ourselves t o reporting in Table 111 the values of the transition probabilities corresponding to the principal progressions in the twisting mode both in absorption and in emission (in Table 111 the calculated energies for the twisting vibration in the IA1 and 1B3 states ai-e also reported). The probability appears 0” and 1’ 1” to be greatly concentrated on the 0’ transitions (which tire almost degenerate), and hence the twisting vibration of the interannular bond should not affect Ihe vibrational structure due to excitation of the ringlA1 transitions ’A1 and breathing mode in IB3 of biphenyl. These conclusions provide an explanation for the shape of the fluorescence spectrum of biphenyl (Figure I), while, regarding the corresponding absorption band which I S hidden by the much more intense 1Bz IA1 transition, t h y cannot be directly checked.
IV. Conclusions
-
-
-
-
-
-
-
-
-
The Journal of Physical Chemistry, Voi. 76, No. 26, 1972
In the present work we looked for a simple theoretical scheme to explain why the near-uv spectrum of polyphenyls is completely diffuse in contrast with the fluorescence spectrum where a sharp fine structure is observed (Figure 1). First of all, our SCF-CI calculation, in accordance with the experimental values of the fluorescence natural lifetimes and with the spacings of vibrational peaks in the emission spectra, shows that in the first, biphenyl, term of the polyphenyl series near-uv and fluorescence spectra cannot be directly compared because absorption and emission involve different excited states, the long-wavelength uv band being chiefly due to the long-axis polarIAl), while the fluorescence band ized transition (I82 is ascribable to the short-axis polarized transition IA1) (section 11). In p-terphenyl, as in the 4-vinyl derivative of biphenyl, both absorption and emission are related to the long-axis polarized transition. In these cases we supposed that the peculiar differences between absorption and fluorescence spectra originate in the excitation of the twisting mode of the interannular bonds. This hypothesis was “quantitatively” checked by setting up diagrams of the potential energy as a function of the dihedral angle between phenyl rings and by calculating distributions of transition probability for both absorption and emission. Regarding the potential curves our calculation suggests that in the ground state the molecules in question are twisted (4N 25”), while in the lowest singlet excited state they are quasiplanar. The order of magnitude of the barrier that hinders planarity in the ground state i s of 1 kcal/ mol (quite low with respect to the barrier found a t p = 900). Using these potential curves, Franck-Condon distributions were calculated that show sharp peaks in emission while exhibiting smooth contours in absorption. These results support our working hypothesis, for they show that the well-resolved vibrational structure observed in the fluorescence spectrum of 4-vinylbiphenyl and p-terphenyl, whose spacing (-1300 c m - l ) is ascribable to the interannular bond stretching mode, may be blurred in the absorption spectrum by excitation of the twisting vibration of the interannular bonds. This interpretation also holds for the near-uv spectrum of biphenyl. On the other hand, on account of the great similarity between the potential curves of lAl and 1B3 states, the twisting vibration is not appreciably coupled with 1B3 lA1 transition, and this explains why the vibrational structure, ascribable to exci1000 cm-I), is retation of the ring-breathing mode ( u tained in the fluorescence spectrum o f biphenyl.
-
-
-
Bruni. and I Baraldi
-
+
=
Acknowledgment. This work was supported by a fund of Consiglio Nazionale delle Ricerche (Roma).
