Triplet State Resonance Raman and Absorption Spectroscopy of a

Sep 1, 1994 - Triplet State Z/E-Photoisomerizations of Polyenes: A Comparison of ab Initio and Density Functional Methods. Maria Brink, Helene Jonson,...
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J. Phys. Chem. 1994, 98, 9437-9445

9437

Triplet State Resonance Raman and Absorption Spectroscopy of a Configurationally Locked (2)-Hexatriene: 1,2-Divinylcyclopentene Annemarie ten Wolde and Harry J. C. Jacobs* Leiden Institute of Chemistry, Leiden University, P. 0. Box 9502, NL-2300 RA Leiden, The Netherlands

Frans W. Langkilde,? Krzysztof Bajdor,* and Robert Wilbrandt' Department of Environmental Science and Technology, Risb National Laboratory, DK-4000 Roskilde, Denmark

Fabrizia Negri, Francesco Zerbetto, and Giorgio Orland? Dipartimento di Chimica "G.Ciamician ", University of Bologna, I-40126 Bologna, Italy Received: April 14, 1994; In Final Form: July 7, 1994@

1,2-Divinylcyclopentene (DVCP-do) and its terminally tetradeuterated isotopomer (DVCP-d4) are studied as models for (Z)-1,3,5-hexatriene locked with respect to torsion around the central C-C bond. Preresonance Raman (DVCP-do) and resonance Raman (DVCP-d4) spectra of the ground state and time-resolved resonance Raman and absorption spectra and kinetics of the lowest excited triplet state of both isotopomers are reported. The observed spectra are compared with results from theoretical calculations. Optimized geometries, vibrational frequencies, and resonance Raman intensities are calculated for SOand T1 by both a b initio and semiempirical (QCFFPI) methods. The triplet lifetime of DVCP-do is found to be 3.4 p, a factor of 17 longer than for (3-1,3,5-hexatriene, demonstrating the importance of torsional motion around the central C-C bond in the deactivation of 1,3,5-hexatriene. Terminal deuteration prolongs the triplet lifetime even further, which seems to indicate that deactivation in DVCP occurs through a vibration involving the terminal hydrogen atoms. Furthermore, a comparison of T I resonance Raman spectra of different (2)-1,3,5-hexatrienes leads to the suggestion of the existence of a marker band around 1273 cm-l characteristic for the presence of the planar Z conformation of hexatrienes in the T I state.

I. Introduction

2'

The isomerization around the C=C bond in polyenes has been subject to extensive study because of its importance in both chemistry and biology. For alkyl-substituted 1,3,5-hexatrienes it has been shown that the principle of nonequilibration of excited rotamers (NEER)'$* is valid in both the SI and T1 The NEER principle states that the geometry around C-C bonds that are formally single in the ground state is preserved after excitation. In contrast, torsion around the central formally double bond is observed in both the SIand T1 states. It is interesting, therefore, to investigate the excited state properties of a hexatriene in which this torsional motion is restricted by "locking" the central C=C bond. This will not only block the chemical deactivation route (En-isomerization) but possibly also affect the nonradiative return to the ground state. In (a-hexatriene the desired locking can be achieved by incorporating the central double bond in a small ring as in 1,2divinylcyclopentene (DVCP-do). We have recently synthesized this compound and its terminally tetradeuterated isotopomer (DVCP-d4) and investigated their ground state conformations and some singlet excited state proper tie^.^^^^ In principle for both compounds three rotameric forms (whether or not planar) can be envisaged, Z z , cZt, and CZC,but with 'H-NMR nuclear Overhauser enhancement spectroscopy it was found that, as expected, in the ground state the two isotopomers exist predominantly (>95%) in the tZt form (Figure l).9910 At variance with unlocked hexatrienes, DVCP-do and -d4 prove to Present address: Astra Hassle AB, S-43183 Molndal, Sweden.

* Present address: Industrial Chemistry Research Institute, ul. Rydygiera

+

8, 01-793 Warszawa, Poland. Abstract published in Advance ACS Abstracts, August 15, 1994. @

2'

1'

3'

4'

D , 2"

4

3'

1'

4' D

1

4"

5v3 4

Figure 1. Molecular structure and atom numbering of 1,2-divinylcyclopentene-do and -da (tZt conformation).

be photostable under oxygen-free conditions and to show fluorescence in solution (& = 0.01 at room temperature). In this paper we report a study of the ground and triplet state properties of DVCP-do and -d4. First, the ground state preresonance (DVCP-do) and resonance (DVCP-d4) Raman spectra are presented. Then, we present the T1 resonance Raman (RR) and TI-T, absorption spectra of DVCP-do and -d4. as well as their triplet state decay kinetics. The experimental results are compared with those for (Z)-1,3,5-hexatriene (ZHT)6,7,11and (2)-3-methyl-1,3,5-hexatriene (Z-3-MHT)s and with theoretical QCFFPI and ab initio calculations. 11. Experimental Methods

A. Materials. The syntheses of the trienes have been described in detail elsewhere?JO No impurities were detected by GC, but the DVCP-d4 sample contained some partially deuterated triene (DVCP-do, -dl, -&,and -d3) according to GCMS (d4-incorporation: 76 & 10%). Prior to the addition of triene the solvents were purged with Ar for more than 35 min. The solutions were prepared and transferred to sample cells under an Ar atmosphere. For the RR and absorption spectra

0022-3654/94/2098-9437$04.50/0 0 1994 American Chemical Society

9438 J. Phys. Chem., Vol. 98, No. 38, 1994 solvents were used as received: acetonitrile (Merck, LiChrosolv), acetonitrile-d3(Fluka, puriss., 299.8% D or Fluka, purum, '99% D), methanol (Merck, p.a.), and acetone (Merck, p.a.). B. Raman Measurements. The ground state Raman spectra were recorded with preresonance excitation at 3 15 nm (DVCPdo) or with resonance excitation at 266 nm (DVCP-d4). The time-resolved TI RR spectra were obtained at room temperature as described b e f ~ r e . ~ ,The ~ J ~triplet state of the triene was produced by exciting acetone as sensitizer with a pump pulse from an excimer laser (Lambda Physik EMG 102E) at 308 nm (ca. 5 mJlpulse at the sample). The RR spectrum of the triene T1 state was obtained with the second harmonic at 315 nm from a Nd:YAG pumped dye laser (Quantel) as probe pulse (ca. 2 mJ/pulse at the sample). Both lasers were pulsed at 5 Hz with pulse lengths of 10-15 ns, pump-probe time delays ranging from 60 ns to 1 ps. The triplet state RR spectra were obtained by subtraction procedures. The sample was contained in a spinning cylindrical Suprasil cell with 26 mm inner diameter and 6 mm inner height. The detection system has been described in detail b e f ~ r e . ~ - ~ J l Scattered Raman light was dispersed in a single-grating spectrometer (f= 600 mm, 2400 grooves/mm). A polarization scrambler was placed in front of the spectrometer. An intensified photodiode array (OSMA IRY-700 from Spectroscopy Instruments) with 700 active channels was used." The chemical composition of the solutions was monitored by ground state UV absorption spectroscopy before and after the experiments, in order to detect possible photo-oxidation during the experiments. C. Absorption Measurements. The procedures used in the time-resolved UV absorption measurements have been described in detail before." The sample was irradiated with a pulse from the excimer laser at 308 nm, with a pulse energy of ca. 20 mJ at the sample. The triplet-triplet absorption at 320 nm was measured at right angles with respect to the laser beam with a pulsed Xe lamp, a monochromator (spectral bandpass 8 nm) placed after the cell, and a photomultiplier (RCA IP28) coupled to a digital storage oscilloscope (LeCroy 9450). The absorbance at 308 nm from the acetone sensitizer was ca. 1 per cm. The preparation of sample cells and the geometry of the set-up were as decribed before." Like for the Raman measurements, the chemical composition of the solutions was monitored by ground state UV absorption spectroscopy before and after the experiments.

Ten Wolde et al. respect to the HOMO-LUMO reference determinant in the zz* space were considered. The CI space includes 33 zz* determinants. The calculations on singlet states were also based on a CI, by including 9 singly excited and 45 doubly excited configurations in the mc* space. The semiempirical QCFFPI model, despite its modest requirements of computational resources, has been shown to be reliable in describing conjugated and aromatic and hence it provides a good first level of description. The modeling of RR spectra is performed by assuming that the Franck-Condon (FC) mechanism provides the dominant intensity contribution to the observed vibrational bands. This is reasonable since in our experiment the exciting laser is in resonance with an intense T1 T, (or SO S,) transition and thus a very minor role is left to a vibronic coupling mechanism. The evaluation of the Franck-Condon integrals is performed by associating a harmonic oscillator to each totally symmetric normal mode. In the absence of normal mode rotation and frequency change upon electronic excitation, the displacement parameter Bi of a given totally symmetric mode furnishes a measure of its Franck-Condon activity in the RR ~ p e c t r u m . ~ ~ - ~ ' The Bi parameter, which is associated with the difference of the equilibrium geometries of the two states involved in the RR experiment, is defined as

-

Bi = 0.172& (x, - x,).&*L~ where vi (cm-') and L, are the ith vibrational frequency and normal mode in the state under study (SO and T1 in our case), M is the matrix of atomic masses (in amu), and XI,~0 are the Cartesian coordinate vectors (in A) defining the equilibrium structure of the two electronic states involved in the transition. The required equilibrium geometries for TI, T, and SO,S, were obtained by using the QCFFPI Hamiltonian. The Franck-Condon intensity of a fundamental in the RR spectrum is proportional to the parameter y;, which is given by

y i = 0.5B: The displacement parameters Bi were also obtained at the ab initio level by computing the gradient of the potential energy surface of the resonant electronic state T,(S,) at the equilibrium geometry of the Tl(S.0) state. In this case Bi is given by

(3)

111. Computational Methods Ground state geometries and harmonic vibrational frequencies were calculated by ab initio methods using the Gaussian9212 set of programs and by the semiempirical QCFFPI'3314method, upgraded as described in refs 15-17. Ab initio calculations of the ground state (SO)were performed at the SCF and at the MP218 level, using the 6-31G* atomic basis set. The lowest triplet state was studied using the same 6-31G* basis set at the CIS19 level, that is, expanding the wave function in the space of singly excited configurations with respect to the ground state closed-shell configuration. The vibrational frequencies of SOwere computed at the HF and MP2 levels of theory, while the vibrational frequencies of T1 were obtained at the CIS level. HF and CIS frequencies were scaled by a common factor of 0.9, while the MP2 frequencies were scaled by the factor 0.95. Triplet and singlet states were investigated also by using the QCFFPI Hamiltonian. The calculations on triplet states were performed by the half-electron SCF procedure, followed by a CI treatment in which all singly excited determinants with

-

where f is the Cartesian force vector of the resonant state in atomic units. Since SOand S, were calculated at different levels of accuracy (MP2 and CIS, respectively), in the Bi calculations it is assumed that the MP2 and CIS geometries are both realistic.

IV. Results Ground state Raman experiments were performed with argonsaturated solutions of (1) 0.005 M DVCP-do in n-pentane (preresonance excitation at A = 315 nm) and (2) 0.008 M DVCP-d4 in CD3CN (resonance excitation at A = 266 nm). Triplet state resonance Raman experiments with excitation at A = 315 nm were performed with the following argon-saturated solutions, containing 0.545 M acetone as sensitizer: (1) 0.005 M DVCP-do in CD3CN, (2) 0.005 M DVCP-do in CH3CN, (3) 0.008 M DVCP-d4 in CD3CN, and (4) 0.008 M DVCP-d4 in CH3CN. In the time-resolved absorption measurements the argon-saturated solutions were (1) 0.408 M acetone and 0.005 M DVCP-do in methanol and (2) 0.408 M acetone and 0.002 M DVCP-d4 in methanol.

J. Phys. Chem., Vol. 98, No. 38, 1994 9439

A Configurationally Locked (2)-Hexatriene

A

I

1600 1400 1200 1000 800

LOO

I

400

, B

200

WAVENUMBER(cm-1)

Figure 2. Ground state preresonance Raman spectrum (A) of a solution of DVCP-do in n-pentane. Excitation wavelength is 315 nm. Solvent bands have been subtracted. Calculated spectra for the fZr rotamer: (B, C, and D). (B) calculated (QCFFPI) al vibrational modes and y-factors within the C2" point group for the SO SZ transition; (C) calculated (MP2/6-31G*) a1 vibrational modes and y-factors within the C2" point group for the So Sz transition; (D) calculated (MP2/6-31G*) a' vibrational modes and y-factors within the C, point group for the SO SZ transition.

-

-

-

Product formation was monitored by ground state UV absorption spectroscopy. A new absorption maximum appeared at A = 244 nm after the RR experiments. A product with a

similar W absorption spectrum has been found after irradiation with W light of DVCP-do in the singlet state, possibly a photooxidation product of the t~iene.~JO A. Ground State. Experimental ground state preresonance and resonance Raman spectra are shown in Figures 2 and 3. In Figure 2 the SO spectrum of DVCP-do in n-pentane is shown with 2 = 3 15 nm (preresonance) excitation. In Figure 3 the SO spectrum of DVCP-d4 in CD3CN is shown, with A = 266 nm (resonance) excitation. This wavelength was chosen because the CD3CN in which the deuterated triene had been dissolved contained some fluorescing impurities that disturbed the RR measurements with 315 nm excitation. With excitation at 266 nm, the impurities did not affect the RR results. The observed frequencies are listed in Table 1 and shown in Figures 2 and 3. As discussed above, equilibrium geometries and harmonic vibrational frequencies were computed by both ab initio and semiempirical QCFFPI methods. Optimized bond lengths and angles for the tZt conformer of DVCP in the SO state, as calculated by ab initio methods at the HF/6-31G* and MP2/631G* level of theory, are listed in Table 2. The resulting optimized structure was of C2, symmetry in the conjugated chromophoric part of DVCP, but of lower symmetry (C,) with respect to the (nonplanar) five-membered ring. The energy of the Czv geometry was found to be 162 (389) cm-' above the C, geometry at the HF (MP2) level of calculation. In contrast to this, QCFFPI calculations yielded an almost planar structure after a very slow convergence history indicative of a very flat potential energy surface. The HF and MP2 vibrational frequencies listed in Table 1 were calculated at both the equilibrium (nonplanar) and imposed (planar) geometries. QCFFPI vibrational frequencies computed at the planar geometry are also listed in Table 1 together with y-factors (Le. RR intensities of fundamentals) obtained by using MP2 and QCFFPI parameters. Experimentally, the 266 nm

TABLE 1: Observed and Calculated Frequencies (cm-l), y-Factors, and Assignments of Totally the rzf Rotamer of 1,2-Divinylcyclopentene-doand -dd in the Ground Stat@ DVCP-d4 DVCP-do MP2 HF MP2 MP2 QCFFPI HF HF MP2 HF Cs Cf yi C2v C Z ~ yi obsb Cs CJ yj C2v CZ, yz C2v yi obs' 1615 1680 1605 0.91 1685 1614 0.95 1622 1696 1623 0.72 1700 1628 0.79 1671 2.47 1597 1614 1550 0.29 1618 1560 0.19 1602 0.33 1533 1566 1509 0.05 1570 1516 0.02 1498 1488 0.01 1504 1498 0.01 1498 1489 0.01 1504 1499 0.01 1475 1447 1469 1466 0.02 1469 1467 0.01 1442 1469 1467 0.03 1469 1468 1443 1037 1025 1405 1423 1403 1423 1404 1434 0.12 1037 1037 1024 1383 1318 1337 1311 0.04 1340 1314 0.03 1336 0.49 1323 1337 1308 0.01 1340 1312 1328 1296 1329 1302 0.04 1304 0.15 1302 1319 1289 0.04 1320 1295 0.04 1219 1225 1219 0.15 1217 1225 1220 0.26 1191 1204 0.08 1184 1210 0.29 1191 1202 0.09 1190 1210 0.27 1242 0.12 1046 1030 1047 1032 1025 962 968 898 1006 1005 1039 0.02 883 867 877 0.01 860 866 0.02 1014 1004 1001 961 856 768 686 929 911 923 912 927 894 914 959 896 898 917 844 834 849 0.01 752 751 0.02 787 0.01 837 824 836 0.04 731 724 667 656 0.04 709 703 697 0.11 541 520 67 1 657 638 0.05 591 583 570 0.03 612 620 0.14 605 0.21 590 574 575 0.06 575 584 0.11 506 354 351 0.45 354 351 0.43 410 385 383 0.39 386 384 0.36 443 0.33 355 257 257 262 280 280 166 164 0.03 166 164 181 180 223 0.14 186 180 179 131 156 0.17 133 159 0.35 83 85 0.20 91 93 0.20

Symmetric Normal Modes of

QCFFPI C2v Yi assignmentd 1665 2.06 vCC 1559 0.87 vCC 1475 SUHZ 1443 SUHZ 1045 0.04 sCHz(CD2)

1341 0.33 vCU,rUHz 1300 0.16 rCCH,vCU rUH2, vCC 1242 0.13 vCC,vCU rUHz rCHz(CDz) 930 0.02 rCHz(CDz),vCU wCHz(CDz) 972 0.03 vUU,rUHz 723 0.03 rUH2,vCU rUH2, rCH2 tCHz(CDz), ring def. 590 0.16 GUUU 407 0.45 GCCC wCCHZ 204 0.11 GCCC ring puck rCCCC

a In the HF and MP2 calculations the 6-31G* basis set was used, and frequencies calculated by these methods were scaled down by a factor of 0.9 (HF) or 0.95 (MP2). In n-pentane with excitation at 315 nm. In acetonitrile with excitation at 266 nm. C = conjugated carbon, U = unconjugated carbon, v = stretching, r = rocking, s = scissoring, 6 = bending, r = twisting, w = wagging.

9440 J. Phys. Chem., Vol. 98, No. 38, 1994

Ten Wolde et al.

=g4'

TABLE 2: Calculated Geometries of the tZt Rotamer of 1,2-Divinylcyclopentene-d0in the Ground State and TIand T5 States 2'

1'

4

so HF

HF C2yb

MP2

1.348 8, 1.452 8, 1.364 8, 1.509 8, 1.546 8, 124.1' 126.5" 105.0" 106.6" 111.7" 183.1" 165.7"

1.325 8, 1.467 8, 1.337 8, 1.5128, 1.545 8, 125.0' 126.6' 104.8' 106.3' 112.1" 180.0' 180.0'

0.W

0.0'

1.348 8, 1.452 8, 1.367 8, 1.512 8, 1.536 8, 124.3' 126.6" 103.0" 104.6" 110.6" 180.0' 180.0" l.ld

csa

atoms C(2')C(l') C(1')C(1) C(1)C(2) c(1)c(5) C(5)C(4) C(2')C( 1')C( 1) C(l')C(1)C(2) C(l)C(5)C(4) C(5)C(4)C(3) C(5)C(l)C(2) C(3')C(2)C(1)C(5) C(1')C( 1)C(5)C(4) E (kcaymol)

1.3258, 1.466 8, 1.338 8, 1.5158, 1.5388, 125.1' 126.7" 103.6" 105.1" 111.4" 0.5'

Ts QCFFPI

TI

MP2

C22

QCFFPI

CIS

0.0

QCFFPI

CSa

C2,b

c2vc

1.373 8, 1.394 8, 1.481 8, 1.5128, 1.537 8, 125.8" 126.4' 104.2" 104.7' 108.4" 181.5' 162.3" 39.5'

1.3738, 1.395 8, 1.475 8, 1.510 8, 1.547 8, 125.5' 126.2' 106.5' 107.5' 109.8' 180.0' 180.0' 41.2'

1.398 8, 1.389 8, 1.476 8, 1.489 8, 1.552 8, 124.4' 124.7" 103.8' 109.8' 110.9" 180.0' 180.0' 24.3

C2VC

1.345 8, 1.474 8, 1.360 8, 1.493 8, 1.552 8, 124.0" 125.3' 102.9" 108.0" 112.6" 180.0' 180.0"

CIS

C2VC

1.411 8, 1.434 8, 1.415 8, 1.4898, 1.554 8, 123.4" 124.3" 103.1' 109.1' 111.9" 180.0" 180.0"

118.7

Optimized geometry; planar triene moiety, nonplanar five-ring. Imposed planar triene and planar five-ring geometry. Optimized geometry. Reference energy -348.899 923 au. Reference energy -347.75 1 292 au.

/

,

,

,

1500

, D

I1

1Mx)

1400

1200

1000

800

,

-

600

-

wavelength is in resonance with the first strongly allowed transition of hexatriene, which-according to these calculations-is the SO S 2 transition, the Sz state being predominantly LUMO configuration. described by the HOMO B. Triplet State. Experimental time-resolved T1 RR spectra are shown in Figures 4 and 5. T1 RR spectra of DVCP-do are shown in Figure 4, part A (in CD3CN) and part B (in CH&N), together with the calculated spectra of the tZt rotamer. Excitation energy calculations indicate that in the present experimental study the resonant triplet-triplet transition corresponds to that described p r e v i ~ u s l y for ' ~ (Z)-1,3,5-hexatriene (TI T5). A

-

,

,

,

,

,

,

,

loo0

,

,

,

,

I

500

WAVENUMBER(cm-1)

,

WAVENuMBE R (cm-1) Figure 3. Ground state resonance Raman spectrum (A) of a solution of DVCP-d4 in CH3CN. Excitation wavelength is 266 nm. Solvent bands have been subtracted. Calculated spectra for the tZt rotamer: (B, C, and D) (B) calculated (QCFFPI) al vibrational modes and y-factors within the C2" point group for the SO Sz transition; (C) calculated (MP2/6-31G*) al vibrational modes and y-factors within the C2, point group for the SO S 1 transition; (D) calculated (MP2/6-31G*) a' vibrational modes and y-factors within the C, point group for the SO Sz transition.

-

,

-

-

Figure 4. Observed (A and B) and calculated (C and D) resonance Raman spectra of DVCP-do in the TI state (negative and derivativelike features in spectra A and B are due to artifacts from the subtraction of strong solvent bands): (A) in CD3CN; (B) in CH3CN (excitation wavelength 315 nm, pump-probe time delay 120 ns); (C) calculated (QCFFPI) al vibrational modes and y-factors within the C2" point group for the TI Ts transition;(D) calculated (CIS/6-31G*) a' vibrational modes and y-factors within the C, point group for the TI Ts transition.

-

-

weak experimental band in spectrum B around 1400 cm-' is an artifact of the subtraction procedure, and it is not seen in spectrum A. In Figure 5A the T1 spectrum of DVCP-d4 in CD3CN is shown (the spectrum in CH3CN is essentially the same), and in Figure 5B the spectrum calculated for the tZt rotamer of DVCP-& is presented. Optimized bond lengths and angles of the tZt conformer of DVCP in the T1 state calculated by the ab initio CIS methods and the semiempirical QCFFPI Hamiltonian are reported in Table 2 . Calculated and observed vibrational frequencies and intensities (y-factors) predicted for the RR spectra are listed in Table 3 and shown in Figures 4 and 5. In Figure 6 the resonance Raman spectra of DVCP-do, 3-methyl-l,3,5-hexatriene, and 1,3,5-hexatriene in the TI state are compared.

J. Phys. Chem., Vol. 98, No. 38, 1994 9441

A Configurationally Locked (3-Hexatriene

TABLE 3: Observed and Calculated Resonance Raman Frequencies (cm-l), y-Factors, and Assignments of Totally Symmetric Normal Modes of the tZt Rotamer of 1.2-DivinvlcvcloDentene-doand -da in the Lowest Excited Triplet State DVCP-do DVCP-d4 CIS CIS CIS QCFFPI QCFFPI CIS CIS CIS QCFFPI QCFFPI obsb C, Y~ C2, C2" YI obsb cs Yz C2" C2" Yl assignment' 1535 1514 1.32 1518 1550 0.25 v c c 1545 1541 1.07 1545 1554 0.22 1463 sUH~ 1486 0.06 1489 1499 1503 1490 1499 sUH~ 1456/1436 1466 1465 1439 0.01 1438 1466 0.01 1465 1033 0.05 1468 1002 994 0.18 993 1435 1458 0.20 1457 sCHz(CD2) GUUH 1393 0.15 1331 1337 0.01 1341 1393 0.10 1329 1337 0.04 1341 GCCH 1329 0.08 1278 1269 0.97 1269 1319 0.05 1275 1275 1.17 1273 1199 1261 0.14 1251 vcc 1271 0.07 1254 1231 1245 0.34 1242 1229 0.08 rUH2 1231 1228 0.02 1234 0.16 vcc 1210 1177 1157 0.13 1162 1156 1113 0.03 1112 rUH2 1029 0.03 1110 1031 0.03 1029 0.01 858 0.18 846 922 0.00 999 999 0.03 1003 Hz(CD21 wCH 929 923 943 965 vUU, rUH2 902 908 953 889 0.03 885 vCC, rUHz 824 0.16 840 830 0.16 wCH~ 638 789 vCC, vUU, rCHz 618 693 684 0.02 698 666 710 596 0.10 GUUU 558 584 589 577 625 606 0.08 tCH2 442 533 0.02 403 0.03 GCCC, GCCU 345 0.02 344 436 0.02 390 373 0.02 373 wCCH~ 275 0.02 307 0.03 ring puck., GCCC 171 0.65 217 0.03 179 0.74 171 155 0.12 157 199 0.02 GCCC, 0.0.p. def. 167 butterfly 104 1.00 112 0.80 ~

~

~~

In the CIS calculations the 6-31G* basis set was used, and frequencies calculated by this method were scaled down by a factor of 0.9. In acetonitrile or acetonitrile-& with excitation at 315 nm. C = conjugated carbon, U = unconjugated carbon, v = stretching, s = scissoring, r = rocking, 6 = bending, t = twisting, w = wagging.

1500

loo0

4 WAVENUMBER (cm-1)

1700

,

.

1500

,

,

1300

,

,

,

1100

,

900

Figure 5. Observed (A) and calculated (B and C) resonance Raman spectra of DVCP-d4 in the TI state; (A) in CDXN (excitation wavelength 315 nm, pump-probe time delay 80 ns); (B) calculated (QCFFPI) al vibrational modes and y-factors within the CZ,point group for the TI Ts transition; (C) calculated (CIS/6-31G*) a' vibrational modes and y-factors within the C, point group for the TI Ts transition.

WAVENUMBER(cm-1) Figure 6. Comparison of the resonance Raman spectra of (A) DVCPdo, (B) 3-methyl-l,3,5-hexatriene and (C) 1,3,5-hexatriene in the TI state. Data from 3-methyl-l,3,5-hexatrieneare adapted from ref 8 and from 1,3,5-hexatriene from ref 11.

Sensitized triplet-triplet absorption spectra of ZHT, DVCPdo, and DVCP-d4 in methanol are shown in Figure 7. Only the shape of the absorption spectra, but not the absolute scale, should be compared. Furthermore, it should be noticed that the experimental error in the absorption spectra increases toward low wavelengths. This is due to ground state absorption of the sensitizer (acetone), which made reliable measurements impossible below 315 nm. In Table 4 the triplet state decay kinetics of the trienes are listed. In Figure 8 logarithmic decay curves for DVCP-do, DVCPd4, and ZHT are shown and in Figure 9 we show an Arrhenius

plot of the temperature dependence of the first-order rate constant of triplet decay of DVCP-do. The activation energy E, and preexponential factor A as determined from a fit of the Arrhenius relation, k , = A exp[-E$kr] (4)

-

-

to the experimental data are E, = 2.0 kcaYmol and A = 8.8 x 106 s-1.

V. Discussion

-

For a Raman excitation wavelength in resonance with a T5 in strongly allowed electronic transition ( S O S:! or T1

-

Ten Wolde et al.

9442 J. Phys. Chem., Vol. 98, No. 38, 1994 A 9

ZHT do-DVCP d4-DVCP

m

-a a

a ma

wa m

31 0

330

350

370

390

10.0 3.1 E-3

I

3SE-3

3.9E-3

4.3E-3

4.7E-3

5.1 E-3

WAVELENGTH/nm

Figure 7. Observed time-resolved triplet-triplet absorption spectra of DVCP-do, DVCP-d4, and ZHT in methanol, immediately after excitation of the sensitizer (acetone)with a laser pulse at 308 nm. The absorbance scales for the different species are arbitrary. 0.00

-0.50 I

j

-a-8

-1 .oo

-1 s o

4.OE-6

6.OE-6

1.2E-5

1.6E-5

2.OE-5

TIME (sec)

Figure 8. Logarithmic normalized plot of the triplet decays of DVCPdo, DVCP-d4, and ZHT in methanol at 325 nm. The decays of DVCPdo and ZHT were fitted by an exponential decay (fitted first-order rate constants of 2.9 x lo5 and 4.78 x lo6 s-l, respectively), while the decay of DVCP-d4 is not monoexponential. TABLE 4: Triplet State Decay Kinetics at 325 nm of DVCP-do, DVCP-dd, and ZHT in Methanol hecay

triene ZHT DVCP-do DVCP-d4

of DVCP-do (Figure 2A,B) and the resonance Raman spectrum of DVCP-d4 (Figure 3A,B) with spectra calculated for the tZt rotamer. The geometry optimization performed by HF and MP2 methods leads to a structure with a nonplanar ring of C, symmetry, the C(4) atom protruding from the plane. The stabilization energy of the C, geometry with respect to the C2, geometry is 1.11 kcallmol at the MP2 level. Within the C, point group the total number of 57 normal modes of vibration divides into 30 a' 27 a" vibrations. Upon increase of the symmetry to C2,, these vibrations transform as (19 a1 11 bl) (10 a2 17 b2). If we neglect CH stretches there are 23 totally symmetric vibrations in the C, point group and 14 of them in the C2" point group. We will now attempt the assignment of the observed vibrational spectra by assuming a dominant FC mechanism. This approach is reasonable since intensities in resonance and preresonance Raman spectra are mainly determined by the strongest allowed electronic transitions close to the excitation wavelength. As mentioned in the previous section, calculations indicate that, for the ground state RR spectra presented here, the resonant electronic transition corresponds to the computed SO S2 excitation. As expected, the S2 electronic state is dominated by the n n* HOMO LUMO excitation, which is localized in the polyenic part of the molecule. The latter state correlates exactly with the l'B1 state of unsubstituted hexatriene. In the following discussion we will start by assuming the planar Cz, structure for SOand we will show that a satisfactory interpretation of the spectra is obtained only on the basis of the frequencies and intensities computed for the nonplanar C, geometry. The RR spectra simulated by using molecular parameters computed with the help of semiempirical and ab initio MP2CIS/6-31G* methods are depicted in Figures 2B, 3B and 2C,D, 3C,D. The most intense vibrational band is observed for DVCPdo at 1622 cm-l and assigned to the highest frequency a1 C=C stretching mode with a frequency computed at 1628 cm-l (MP2/ 6-31G*) and 1671 cm-' (QCFFFI). Upon deuteration, this band shifts downward to 1615 cm-', in agreement with calculations which yield 1614 cm-' (MP2). This mode tends to be localized at the central CC bond. The second CC mode is observed at 1597 cm-' and is calculated at 1560 cm-l (MP2) and 1602 cm-' (QCFFPI). This frequency is shifted to 1533 cm-l (by 64 cm-') upon deuteration, in qualitative agreement with the shifts predicted theoretically (44 cm-' (MP2) and 43 cm-' (QCFFPI)). Three totally symmetric CH2 scissoring

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Figure 9. hhenius plot of the decay rate constant of DVCP-do in methanol, corresponding to a preexponential factor of 8.8 x lo6 s-l and an activation energy of 2.0 kcal/mol.

(105 s-l)o 47.8 2.9

t

(Wb

0.21 3.4 7.0

First-order triplet state decay rate constants; for DVCP-d4 the decay is not monoexponential. Triplet state lifetimes. the case of DVCP) RR spectra are dominated by FranckCondon scattering, and the vibrational bands observed with strongest intensity correspond to totally symmetric modes. They can gain intensity by differences in the equilibrium geometries of the two electronic states involved in the transition or by changes in vibrational frequencies. Changes in geometry usually give the dominant contribution. Hence, we shall first attempt to assign the bands observed in the SOand T1 spectra presented above on the basis of the computed totally symmetric frequencies and y-factors, the latter parameters describing the intensity contributions due to geometry changes. A. Ground State. It has been shown p r e v i o ~ s l y ~from *'~ 'H-NMR studies that DVCP exists predominantly as the tZt conformer. In agreement with these experimental observations, the tZt conformer is also found to be the most stable from theoretical QCFFPI calculations. The calculated energies of the cZt and CZCconformers relative to the tZt conformer are 2.5 and 4.3 kcal/mol, respectively. In the following, we therefore compare the observed preresonance Raman spectrum

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A Configurationally Locked (3-Hexatriene modes in the region around 1450 cm-’ are expected. Of these, the one with lowest frequency (observed at 1405 cm-l in DVCPdo and shifted to 1037 cm-l in DVCP-d4) is assigned to the polyenic methylene groups, while the overlapping bands observed in the region 1442- 1450 cm-’ for both isotopomers are assigned to the totally symmetric scissoring modes of the methylene groups of the ring. Bands of medium intensity observed in the region 11901330 cm-’ are shifted little upon deuteration and are assigned to coupled d(CCH) bending and v(C-C) stretching modes. The observed asymmetry of the experimental band at 1318 cm-I in DVCP-do clearly indicates that this band is due to two overlapping bands, as predicted by theory. One totally symmetric CH2 in-plane rocking mode is expected for the polyenic group: it is calculated at 1005 cm-’ (MP2) and 1039 cm-’ (QCFFPI). Clearly, it has to be assigned to the band observed at 1014 cm-l in DVCP-do. The 1005 cm-l frequency is predicted to shift upon deuteration to 866 cm-’ (MP2) and is assigned to the band observed at 883 cm-l in DVCP-d4. It is noticed that relative RR intensities in the whole region 17001000 cm-’ are predicted qualitatively correctly by QCFFPI and MP2 methods. In addition, as indicated in Table 1, in this spectral region very few differences are found between the frequencies computed at the planar CzV and nonplanar C, structures. Below 1000 cm-’, a large number of weak vibrational bands are observed in DVCP-do. Clearly, not all of these can be assigned to totally symmetric modes of the planar Cz, structure. However, all of them can be assigned in terms of a‘ vibrations of a nonplanar structure of C, symmetry, as indicated in Table 1. Thus, we assign the modes observed in DVCP-do at 186, 262,410,591,671,709,844,and 896 cm-I to the a’ frequencies calculated at 179, 280, 383, 570, 638, 697, 849, and 917 cm-’, respectively. The modes observed at 355 and 506 cm-’ may be due to overtones of the 186 cm-’ mode. Their increasing width and decreasing intensity with increasing overtone quantum number are arguments for this assignment. This explanation implies a considerable anharmonicity of this mode. Other weak observed bands may have contributions from overtones and combination bands as well. In conclusion, we find that all the observed bands of the ground state preresonance Raman spectrum of DVCP-do are well described by the theoretical calculations corresponding to the nonplanar C, structure. Also the RR spectrum of DVCP-d4 can be assigned in a satisfactory way, albeit with the notable exception of the band at 1383 cm-’. This band is in the region of CH2 scissoring modes and is therefore tentatively ascribed to the presence of only partially deuterated molecules (terminally deuterated dl- or d2-isotopomers). The most prominent bands in DVCP-do and DVCP-d4 can be assigned to the totally symmetric modes of the planar Czv structure. However, the presence of a few weaker bands that do not find a match among the a1 frequencies strongly suggests that the structure of DVCP is nonplanar (C,), in agreement with the results of the geometry optimization at the ab initio level. Relative intensities calculated by QCFFRI and ab initio methods are qualitatively correct in the region above 1000 cm-’, but somewhat too large in the region below 1000 cm-’. B. Triplet State. The main effect of the cyclopentene ring is to configurationally lock the molecule with respect to torsion around the central C-C bond, i.e. to induce a large barrier along this torsional coordinate on both the SOand T1 potential energy surfaces. Obviously, the modification of the energy surface is most important in the triplet state, since it is known that in the case of ZHT the potential energy surface of the triplet is rather

J. Phys. Chem., Vol. 98, No. 38, I994 9443 flat11J5 and interconversion between the E and Z isomeric species exists. In contrast to this, in the T1 state of DVCP, although a small degree of torsional motion along this coordinate is conceivable, cis-trans isomerization is not possible, and an essentially planar Z equilibrium structure of the chromophoric part of the molecule may be expected. In fact, the polyenic part of the molecule is expected to be very similar to the planar Z isomer of hexatriene. It should be clear from the above discussion that the T1 RR spectrum of pure ZHT is unknown, since ZHT equilibrates with other isomers in T1.697311As a consequence, in the following we will refer to the ZHT RR spectrum as the spectrum of all equilibrating species in TI. As already demonstrated for the ground state, the T1 RR spectrum of DVCP presented here should provide a good representation of the “unknown” spectrum of pure ZHT. However, in spite of the geometrical similarity of the two compounds, substantial differences in their vibrational spectra may appear for two reasons. Firstly, the coupling of the vibrational motions of the polyenic part with those of the ring might change the shape of some of the vibrational normal modes. Secondly, the possibly lower symmetry of DVCP might increase the intensity of vibrations that are forbidden for ZHT. The rate of triplet decay is expected to be slower for DVCP than for ZHT because of the high torsional barrier of the central CC bond in the former. This prevents the molecule from reaching the twisted geometry around the central bond where the energy gap between SO and TI is the smallest, thereby limiting the rate of the radiationless T1 SO transition. Geometry. The electronic configuration of the lowest triplet state of DVCP is characterized by the singly excited HOMO LUMO configuration, in analogy with unsubstituted ZHT.13 The main structural changes upon excitation from the ground to the triplet state as predicted by the calculations are the lengthening of the central C=C bond (1.36 A in SO) to essentially a C-C single bond (1.48 8, in TI) and the similar bond lengths of C(2’)C( 1’) and C( 1’)C( 1) as compared to the alternation of the two bond lengths in SO (see Table 2). The nonconjugated bonds of the cyclopentene ring remain essentially unchanged upon excitation, and in analogy with SO, ab initio calculations predict the nonplanar C,7structure to be more stable than the planar CzV geometry by 1.7 kcal/mol. Geometry changes upon triplet-triplet excitation are also confined to the conjugated hexatriene skeleton of the molecule. These results merely reflect the ?tx* nature of the SO TI and TI T, excitations that are substantially localized on the chromophoric part of the molecule. As a consequence, it is mainly this conjugated moiety that is responsible for the intensities observed in the RR spectra. Absorption Spectra and Decay. In analogy to ZHT a strong triplet-triplet transition is observed for DVCP in the 300-360 nm region (Figure 7). However, the vibrational structure is more pronounced in DVCP than in ZHT, with a band appearing as a shoulder at 335 nm (DVCP-do). Deuteration also influences the triplet-triplet absorption spectrum to some extent. These effects are in agreement with general expectations according to which the spectrum of a less flexible molecule exhibits more pronounced vibrational structure. The decay of the triplet state (Figure 8) is seen to be markedly changed in DVCP as compared to ZHT. While ZHT shows a rather short triplet lifetime of t = 209 ns, this is increased to 3.4 ps for DVCP-do. Hence, an increase in triplet lifetime by a factor of 17 is observed. This clearly demonstrates that torsional motion around the central CC bond is of crucial importance in the deactivation of TI 1,3,5hexatriene. It

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9444 J. Phys. Chem., Vol. 98, No. 38, 1994 supports the view, proposed previously,8 that deactivation of the T1 state occurs at a twisted geometry, in the proximity of 90". At this geometry the energy gap is substantially reduced, the spin-orbit coupling is sizable,23 and therefore an efficient radiationless transition to the ground state can take place. Calculations have shown that TI-SO spinorbit coupling is 0 at the 90" conformation, but increases rapidly for torsional angles only slightly different from 90°.23 The twisting vibration is therefore likely to play a significant role in the intersystem crossing decay. The T1 lifetime in DVCP, although longer than the corresponding lifetime in ZHT, is much shorter than the T1 lifetimes observed in rigid planar aromatic molecules (ca. 1 s)24 and in stilbene at low temperatures (ca. 20 m ~ ) Its . ~lifetime ~ is similar to that of blocked styrene in T1.26 These observations suggest a reduced role for torsional motion about the central CC bond and a possible contribution of C=CH2 twisting in the T1 decay in DVCP. The triplet lifetime in DVCP-d4 is found to be longer than the triplet lifetime in DVCP-do roughly by a factor of 2 (see Table 4). Furthermore, the decay of DVCP-d4 is observed to be not strictly monoexponential. The increase of the lifetime with deuteration of the terminal double bonds indicates that one path of the triplet deactivation in DVCP involves the torsion of C=C terminal bonds and, according to the above discussion, it has the highest transition probability at about the perpendicular geometry (with respect to one of these bonds). Alternative inducing vibrations involving the deuterium atoms (such as CD;! scissoring, CD;! rock, or CD;? wag) are less likely to be active in promoting the triplet decay. The CD stretches, which play an important role in the triplet decay of aromatic compounds through their contributions to the Franck-Condon are unimportant in the case of hexatriene or DVCP, because of the very small energy gap (a few kcallmol) at the twisted geometry. The observed deuterium effect in the T1 lifetime of DVCP suggests that the twisting of terminal C=CH;? bonds provides a path for the triplet deactivation also in hexatriene. However, in the latter compound this path is of minor importance, being overshadowed by the more efficient channel involving the torsion of the central C-C bond. The Arrhenius plot of the triplet decay rate versus UT (Figure 9) leads to an activation energy of 2.0 kcallmol. This energy is larger than in ZHT (0.7 kcal/molll) and should be associated with the energy of the most reactive geometries along the possible twistings of the terminal or central C=C bonds, with respect to the absolute minimum of the triplet energy surface. Therefore, it could be the relative energy of the perpendicular geometry obtained by twisting the terminal C=CH2 bonds. This interpretation is compatible with the fact that the bond order of terminal C=C bonds is larger than that of the central C=C bond. Alternatively, if we assume that twisting around the central C=C bond is the more important channel for the T1 decay, the observed activation energy reflects the energy required in DVCP to twist the central C=C bond to reach a geometry where spinorbit coupling is sizable and the energy gap is sufficiently small. The different preexponential factors A for DVCP (9 x lo6 s-l) and ZHT (19 x lo6 s-l) indicate that the radiationless decay of DVCP is hindered, possibly by a larger singlet-triplet energy gap. Resonance Raman Spectra. Like for the SO state, the vibrational analysis of the T1 RR spectrum will be attempted in the following by assuming the tZt rotamer to give the dominant contribution. As the geometry of the T1 state is markedly different from that of SO, many vibrational modes are

Ten Wolde et al. expected to be rotated in T1 compared to SO and a direct comparison of ground and triplet state spectra cannot be performed. The total number of vibrational bands observed in the T1 state is considerably smaller than for the (pre)resonance Raman spectrum of the ground state. The strongest band (at 1545 cm-l for DVCP-do and 1535 cm-l for DVCP-d4) is assigned to the v(CC) stretching mode calculated at 1545 cm-' (CIS) and 1554 cm-l (QCFFPI) in DVCP-do and at 1518 cm-' (CIS) and 1550 cm-l (QCFFPI) in DVCP-d4. The shoulder observed at 1503 cm-' for DVCP-do is assigned to the scissoring of the apical CH2 group of the ring. The CH2 scissoring mode of the polyenic methylene groups is calculated to have a frequency of 1457 (CIS) and 1468 (QCFFPI) cm-' and is assigned to the band observed at 1435 cm-l in DVCP-do. In DVCP-d4 the same vibration is calculated at 1033 cm-' and tentatively assigned to a weak band at 1002 cm-l. In the 1100-1350 cm-l region, the bands observed at 1329, 1275, and 1231 cm-' in DVCP-do change their frequency and intensity only slightly upon deuteration. The band observed at 1156 cm-l in the do-isotopomer has its counterpart in the 1177 cm-l band in DVCP-d4. Calculated frequencies in this region, especially those obtained by the ab initio method, agree well with the position of the observed bands. Obviously, the agreement of intensities is much less satisfactory. The weak bands observed below 1000 cm-l for DVCP-do are assigned in a straightforward way, as indicated in Table 3. The bands of DVCP-d4 below 1250 cm-l can be assigned tentatively: the intensity distributions according to the CIS and the QCFFPI calculations are not in agreement in this region. Furthermore, some of the bands are attributed to modes that are totally symmetric only in the C, geometry. The proposed assignments are given in Table 3. As noted in the Experimental Methods section, the isotopic purity of the DVCP-d4 sample was only 76 f lo%, with possible other isotopomers being present. This is probably the reason for the presence of the unassigned vibrational bands, in both the ground and T1 states and for the non-monoexponential triplet decay observed with the deuterated sample. In Figure 6 resonance Raman spectra of DVCP-do, ZHT,6,7a11 in the T1 state are compared. and (Z)-3-methyl-1,3,5-hexatriene8 It can be seen that one vibrational band at about 1273 cm-l remains remarkably constant in frequency and intensity from one compound to another, while the changes in most other bands are considerably larger. For the unlocked (Z)-hexatrienes the 1273 cm-' band has been predominantly assigned to a CH rocking vibration of the hydrogens in the 2- and 5-positions, and this band has consistently been attributed8J1 to a species with the Z configuration of the central C-C bond, which may be in equilibrium with the E form (and possibly the P form). In the locked (3-triene DVCP-do the band at 1275 cm-l is assigned to a CCH bending vibration. We suggest that this vibrational band is a marker band for the Z conformation of 1,3,5-trienes in the T1 state. It will be interesting to test this suggestion in experiments with a configurationally locked (E)1,3,5-hexatriene, in which this band should be absent.

VI. Conclusion Time-resolved absorption and resonance Raman studies of the lowest triplet state of 1,2-divinylcyclopentene confirm that deactivation of the T1 state of ZHT occurs through twisting of the central CC bond." We have shown that the SOvibrational activity of the polyenic part of DVCP is very similar to that of the parent ZHT. This supports the assumption that the T1 RR spectrum of DVCP also gives a good representation of the

A Configurationally Locked (2)-Hexatriene spectrum of pure ZHT. We suggest that a marker band around 1273 cm-' in the RR spectra of the triplet state is characteristic of the Z isomeric form of 1,3,5-hexatriene and substituted derivatives. The complete interpretation of the ground state RR spectrum requires the consideration of the nonplanar C, structure.

Acknowledgment. We thank Dr. J. Fenger, Dr. K. B. Hansen, and Mr. E. Engholm Larsen for help with the laser equipment. Grants from the Danish Natural Science Research Council, the Minister0 della h b b l i c a Instruzione of Italy, and NATO (Grant No. 0137/88) are gratefully acknowledged. References and Notes (1) Jacobs, H. I. C.; Havinga, E. Adv. Photochem. 1979, 11, 305. (2) Gielen. J. W. J.: Jacobs. H. J. C.: Havintra. E. Tetrahedron Lett. 1976,375 1. (3) Brouwer, A. M.: Bezemer, L.; Comelisse, J.; Jacobs, H. J. C. Reel. Trav. Chim. Pays-Bas 1987, 106, 613. (4) Brouwer, A. M. Ph.D. Thesis, Leiden, 1987. ( 5 ) Langkilde, F. W.; Jensen, N.-H.; Wilbrandt, R.; Brouwer, A. M.; Jacobs, H. J. C. J. Phys. Chem. 1987, 91, 1029. (6) Langkilde, F. W.; Jensen, N.-H.; Wilbrandt, R. J. Phys. Chem. 1987, 91, 1040. (7) Negri, F.; Orlandi, G.; Brouwer, A. M.; Langkilde, F. W.; M ~ l l e r , S.;Wilbrandt, R. J. Phys. Chem. 1991, 95, 6895. (8) Langkilde, F. W.; Wilbrandt, R.; Brouwer, A. M.; Jacobs, H. J. C.; Negri, F.; Orlandi, G. J. Phys.Chem. 1992, 96, 64. (9) Ten Wolde, A.; Dekkers, H. P. J.M.; Jacobs, H. J. C. Terrahedron 1993, 49, 6045. (10) Ten Wolde, A. Ph. D. Thesis, Leiden, 1994. I

J. Phys. Chem., Vol. 98, No. 38, 1994 9445 (1 1) Langkilde, F. W.; Wilbrandt, R.; Mbller, S . ; Brouwer, A. M.; Negri, F.; Orlandi, G. J. Phys. Chem. 1991, 95, 6884. (12) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M.; Binkley, Y.; Gonzales, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A,; Seeger, R.; Baker, C. F.; Martin, R. L.; Kahn, L. R.; Steward, J. J. P.; Topiol, S . ; Pople, J. A. Gaussian 92; Gaussian Inc.: Pittsburgh, PA, 1990. (13) Warshel, A.; Karplus, M. J. Am. Chem. Soc. 1972, 94, 5612. (14) Warshel, A,; Levitt, M. QCPE No.247, Indiana University, 1974. (15) Negri, F.; Orlandi, G.; Brouwer, A. M.; Langkilde, F. W.; Wilbrandt, R. J. Chem. Phys. 1989, 90, 5944. (16) Negri, F.; Orlandi, G.; Langkilde, F. W.; Wilbrandt, R. J. Chem. Phys. 1990, 92, 4907. (17) Langkilde, F. W.; Bajdor, K.; Wilbrandt, R.; Negri, F.; Zerbetto, F.; Orlandi, G. J. Chem. Phys., in press. (18) M~ller,C.; Plesset, M. S. Phys. Rev. 1934, 46, 618. (19) Foresman, J. B.; Head-Gordon, M.; Pople, J. A,; Frisch, M. J. J. Phys. Chem. 1992, 96, 135. (20) Warshel, A. In Modern Theoretical Chemistly; Segal, A., Ed.; Plenum Press: New York, 1977; Vol. 7, Part A, p 133. (21) Hemley, R. J.; Brooks, B. R.; Karplus, M. J. Chem. Phys. 1986, 85, 6550. (22) Orlandi, G.; Zerbetto, F.; Zgierski, M. Z. Chem. Rev. 1991, 91, 867. (23) Caldwell, R. A,; Carlacci, L.; Doubleday, C. E., Jr.; Furlani, T. R.; King, H. F.; McIver Jr., J. W. J. Am. Chem. Soc. 1988, 110, 6902. (24) Birks, J. B. Photophysics of Aromatic Molecules; Wiley-Interscience: New York, 1970; Chapter 5 , p 142. (25) Heinrich, G.; Holzer, G.; Blume, H.; Schulte-Frohlinde D. 2. Naturforsch. 1970, 25b, 496. (26) Caldwell, R. A.; Jacobs, L. D.; Furlani, T. R.; Nalley, E. A.; Laboy, J. J. Am. Chem. Soc. 1992, 114, 1623. (27) Henry, B. R.; Siebrand, W. In Organic Molecular Photophysics; Birks, J. B., Ed.; J. Wiley & Sons: New York, 1973; Vol. 1, p 153.