J . Phys. Chem. 1988, 92, 997-1003 will ellable the approach to be extended to systems in which the rotational correlation time is from 10 to 100 times greater, permitting experiments on larger complexes and in more viscous environments. This extension will permit systems of real biological interest to be investigated. If experimental evidence is found that rigid limit parameters are temperature dependent, part of our knowledge of biologically active copper complexes based on analysis of frozen solution
997
spectra would have to be revised.
Acknowledgment. This work was supported by N I H Grant G M 35472 (U.S.A.) and by C N R Grant 85.00256.02 (Italy). Thanks for useful discussions are due to W. E. Antholine (National Biomedical ESR Center, Milwaukee, WI), M. Bacci, and P. Moretti (lRoE-CNR* Italy)* Registry No. Cu2+KTS, 19976-05-7;Cu2+KTSM2,19976-18-2.
Photoexcited Triplets and Structural Properties of Slngle Crystals of the trans-Stilbene-I ,2,4,5Tetracyanobenzene ( 1:2) Complex G . Agostini, C. Corvaja,* G . Giacometti, L. Pasimeni, Department of Physical Chemistry, University of Padova, 351 31 Padoua, Italy
and D. A. Clemente Department of Biology, University of Lecce, Monteroni di Lecce, Italy (Received: May 26, 1987; In Final Form: September 17, 19871
The 1:2 trans-stilbene (TSB)-l,2,4,5-tetracyanobenzene (TCNB) charge-transfer crystal is triclinic, space group Pi,and the lattice parameters are a = 7.577 (2) A, b = 12.703 (3) A, c = 7.287 (2) A, a = 93.03 (2)O, @ = 94.56 (2)O, y = 99.44 (2)?. The structure consists of a 1:2 adduct in which each of the benzene rings of TSB is overlapped by a TCNB molecule with slightly alternated interplanar spacings of 3.40 and 3.42 A. The stilbene molecule exhibits orientational disorder similar to that found in other stilbene structures. EPR spectra of excited X-traps in the triplet state are detected and principal directions of their ZFS tensor have been determined. The triplet excitation resides almost completely on the TSB molecule. The analysis of the orientation dependence of the optical electron polarization (OEP)allows one to establish that the TCNB molecule is involved in the populating process of the triplet excitation. It is also ascertained that selective decay from the spin sublevels of the triplet occurs, with an in-plane ZFS principal direction most active.
1. Introduction
The electronic properties of the lowest triplet state of transstilbene (TI state) are still poorly known although the cis-trans photoisomeriza$ion reaction has been extensively investigated. 1,2 This is because of its short lifetime and its nonphosphorescent character. In a previous work3 we have studied the EPR spectra of single crystals of the 1:2 CT complex of TSB with TCNB and we have obtained the zero-field splitting (ZFS) parameters D and E of its lowest triplet state. In a C T complex t h e , Z F S parameters depend on the C T character which can be inferred from the comparison of D with the corresponding value of the triplet state of the donor, usually the only one involved in the lowest triplet of the CT complexes formed with TCNB. Because of the lack of data on the TSB triplet we made a tentative use of ZFS parameters of p-toluene triplet4 by considering the fact that each aromatic ring of the TSB molecule was expected to be bonded to one TCNB molecule in the 1:2 complex. We obtained a guess of 36% for the C T character. Recently the EPR spectra of T, together with its ZFS paramthe triplet state being generated either eters have been in a glassy medium at 77 K2 or by photosensitization in a micellar aggregate.5 The D and E values are remarkably close to our data, (1) Arai, T.; Sakuragi, H.; Tokumaru, K . Bull. Chem. Soc. Jpn. 1982,55, 2204 and references therein. (2) Yagi, M. Chem. Phys. Lett. 1986, 124, 459. (3) Agostini, G.; Corvaja, C.; Giacometti, G.; Pasimeni, L. Chem. Phys. 1984, 85, 421. (4) Vergragt, Ph. J.; van der Waals, J. H. Chem. Phys. Lett. 1974.26, 305. (5) Murai, H.; Yamamoto, Y.; l’Haya, Y. J. Chem. Phys. Lett. 1986, 129, 201.
0022-3654/88/2092-0997$01.50/0
indicating that the TSB-(TCNBh complex has a rather low (3%) C T character provided that stilbene in the T1state, populated by the photosensitization of TSB in micellar or glassy aggregate, is in the trans-planar form.5 In this case, all the EPR data obtained for the C T complex can be safely transferred to the TSB T1state like the orientation of the ZFS principal axes which cannot be obtained from spectra in unoriented media. The aim of this paper is to extend the previous studies with the scope of determining the orientations of the principal directions of the ZFS tensor with respect to the TSB molecule and to elucidate in detail the properties of OEP carried by the EPR lines. Especially, the angular dependence of OEP will be examined when the magnetic field Bo is rotated with respect to the crystal. To accomplish the investigation the crystal structure of TSB-(TCNB)2 was needed and it has been determined by the X-ray diffraction method. In weak donor-acceptor complexes the lowest excited singlet state SI is a charge-transfer (CT) state. Intersystem crossing (ISC) from the latter populates the lowest triplet T, which may be of quite different C T character depending on the particular pair of partners. In a large series of complexes of TCNB with different donors ISC to the three sublevels of the lowest triplet state occurs always with relative populating rates that are equal to those occurring in pure TCNB molecule even when the triplet wave function 3 kompicx = a31Cdonor + b3rC/,,ptor + c 3 h is localized almost exclusively on the donor molecule ( a = 1).6-9 (6) Pasimeni, L.; Guella, G.; Corvaja, C. Chem. Phys. Lett. 1981,84, 466. (7) Pasimeni, L.; Corvaja, C.; Clemente, D. A. Mol. Cryst. Liq. cryst. 1984, 104, 231.
0 1988 American Chemical Society
998 The Journal of Physical Chemistry, Vol. 92, No. 4, 1988
Agostini et al.
...
TABLE I: Atomic Coordinates" and Anisotropic Thermal Parameters (Vi,. X lo') in the Form e ~ p [ - 2 r ~ ( U , ~ b+~ a *+~ 2UI2bka*b* + ...)I
Atomic Coordinates
xlb
xla
0.0587 (4) -0.0466 (35) 0.0578 (3) 0.2117 (3) 0.3676 (4) 0.4773 (33) 0.3696 (3) 0.2140 (3) 0.0815 0.1414 -0.0080 0.0857 0.1933 0.3732 0.4455
(6) (41) (24) (4) (4) (4) (4)
xla
z/c
0.2212 0.1783 0.3282 0.3918 0.3496 0.3951 0.2436 0.1790
(2) (21) (2) (2) (2) (20) (2) (2)
0.1309 0.0686 0.1820 0.2726 0.3057 0.3575 0.2519 0.1669
(4) (35) (3) (3) (4) (32) (3) (3)
0.0116 -0.0497 0.0506 0.2160 0.3095 0.3094 0.2158
(4) (25) (12) (4) (4) (4) (4)
0.5391 0.5291 0.5291 0.6448 0.7244 0.7824 0.7608
(6) (41) (20) (7) (7) (7) (7)
(b) In trans-Stilbene 0.79 C(7) 0.79 C(2) 0.21 HC(3) 0.79 HC(4) 0.79 HC(5) 0.79 HC(6) 0.79 HC(7)
xlb
z/c
occupn factor
0.2072 0.2054 -0.0999 -0.2212 0.2188 0.2270 0.5332 0.6633
(3) (4) (4) (3) (4) (3) (4) (3)
0.5001 (2) 0.5843 (2) 0.3755 (2 0.4148 (2) 0.0674 (2) -0.0202 (2) 0.2004 (2) 0.1679 (2)
0.3393 (4) 0.3989 (4) 0.1387 (4) 0.1012 (4) 0.1197 (4) 0.0877 (4) 0.2835 (4) 0.3056 (4)
1.0
0.3380 0.1580 -0.0536 0.1373 0.4565 0.5848 0.3940
(4) (4) (4) (4) (4) (4) (4)
0.1223 (4) 0.1224 (4) 0.2160 (4) 0.3819 (4) 0.3818 (4) 0.2157 (4) 0.0498 (4)
0.6813 (7) 0.6232 (7) 0.5999 (7) 0.7411 (7) 0.8440 (7) 0.8057 (7) 0.6645 (7)
0.79 0.79 0.79 0.79 0.79 0.79 0.79
AnisotroDic Thermal Parameters In TCNB 461 (16) 681 (87) 429 (1 4) 465 (15) 421 (15) 564 (75) 436 (14) 487 (15) 459 (16) 753 (18) 513 (17) 589 (16) 528 (17) 753 (18) 536 (17) 599 (17)
500 (17)
495 (16)
-16 (13)
-6 (13)
16 (13)
497 (10)
467 (15) 426 (1 5 ) 500 (17)
460 (1 5) 460 (15) 545 (17)
12 (12) -14 (12) -25 (1 3)
0 (11) 12 (12) -14 (12)
73 (11) 57 (12) 27 (13)
455 (9) 456 (9) 500 (10)
(16) (14) (18) (17) (16) (17) (18) (16) (17) (17)
504 (16) 482 (16) 639 (19) 1072 (23) 618 (19) 1014 (22) 586 (18) 902 (20) 658 (19) 1089 (23)
34 (12) 9 (11) -37 (14) -178 (15) -18 (13) 22 (15) -13 (14) -76 (14) 10 (14) 61 (15)
616 (25)
626 (26)
644 692 596 700 705 622
436 485 518 561 668 670
483 418 547 575 481 690 527 517 502 710
39 72 -50 -56 -52 -148 54 71 25 22
(12) (12) (13) (1 6) (14) (15) (13) (14) (14) (15)
87 (12) 58 (12) 67 (13) 118 (14) 42 (13) 172 (14) 56 (14) 92 (13) 80 (14) 233 (14)
473 464 559 815 550 770 552 730 569 788
50 (19)
182 (25)
611 (15)
57 34 39 37 27 4
-22 (30) 104 (23) 67 (27) 5 (30) 136 (27) 6 (28)
591 613 608 633 693 682
(9) (9) (10) (12) (1 1) (12) (10) (12) (1 1) (11)
In trans-Stilbene 623 (23) 873 (105) 473 (30) 656 (35) 656 (31) 695 (38) 602 (32) 711 (32) 711 (44) 712 (106) 720 (107) 662 (101) 861 (122) 833 (119)
(33) (50) (29) (32) (48) (30)
(25) (27) (25) (28) (30) (32)
108 (21) 85 54 45 49 83 70
(18) (26) (20) (20) (28) (24)
(22) (18) (25) (22) (21) (27)
(17) (23) (20) (19) (22) (22)
HC(1') represents the hydrogen atom bonded to i-th carbon atom.
This does not mean, of course, that ISC occurs through an intermediate acceptor triplet but that ISC is dominated by spin-orbit coupling (SOC) matrix elements typical of the acceptor component of the wave function. A typical example of this behavior is given by the lowest triplet state of the anthracene (A)-TCNB complex where the ZFS parameters are those of anthracene while the TCNB molecule is responsible for ISC. The latter result was obtained from the analysis of the angular dependence of OEP carried by the A-TCNB lowest triplet state.6 The same method is applied here to get information on the spin selectivity in the populating and decay processes of the T, state in the TSB-(TCNB), complex. 2. Experimental Section 2.1. Crystal Preparation and EPR Experiments. TSB (Ega (8) Erdle, E.; Mohwald, H.Chem. Phys. 1979, 315, 283. (9) Agostini, G.; Corvaja, C.; Giacometti, G.;Pasimeni, L.; Clemente, D. A.; Bandoli, G. Mol. Crysf. Liq. Crysf. 1986, 141, 165.
Chemie) was purified by sublimation. TCNB was synthesized from pyromellitic dianhydride (Ega Chemie) according to the method described in the literature.I0 It was then purified by crystallization from ethyl acetate. Molar amounts of donor and acceptor (1 :2) were dissolved in spectroscopically pure acetone (Merck, UVASOL) and the solvent was slowly evaporated. The orange crystals grow mainly along c and have an average size of 1 X 3 X 10 mm3 with a well-developed (100) face. In the EPR measurements crystals mounted on a lucite rod were rotated inside the microwave cavity of the EPR spectrometer (Brucker E R 200D SRC). Irradiation was performed by a high-pressure Osram HBO 500-W mercury lamp. Light was filtered through a solution of CuS0,.5H20 (50 g/L) with transmission wavelength range 320 < A < 600 nm and conveyed through a light pipe into the cavity equipped with optical access. 2.2. X-ray Experiments. A well-formed transparent yellow crystal was glued to a thin glass fibre, coated with a clear acrylate (10) Lawton, E. A,; McRitchie, D. D. J. Org. Chem. 1956, 2 4 , 26.
Properties of the trans-Stilbene-TCNB Complex
The Journal of Physical Chemistry, Vol. 92, No. 4. 1988 999
Figure 1.
adhesive and mounted on a goniometer head. The dimensions of the prismatic crystal were approximately 0.1 5 X 0.20 X 0.25 mm3. The crystal was transferred to a STOE diffractometer (graphite-monochromatized Mo Ka radiation); cell constants, determined at 20 'C by least-squares calculation on the basis of 27 symmetry-related reflections (18' I 2 0 I38'), are a = 7.577 (2) A, b = 12.703 (3) A, c = 7.287 (2) A, a = 93.03 (2)', p = 94.56 (2)', y = 99.44 (2)'. Crystal system: triclinic, space group: PT (No. 2), pcalcd = 1.29 g cm-3 for a (1:2) CT complex pcxptl= 1.30 g cm-3 (density was determined by flotation in a carbon tetrachloride/benzene mixture). A 0 - 28 scan was used up to 0 = 25'. The scan width was 1.2' while the minimum and maximum scan speed was 0.O5-0.1O0/s. Three reflections, used as standards and measured every hour, showed no variation in intensity. Of the 2412 reflections measured 1551 had Fo > 5a(Fo) and were considered observed. Peak counts were corrected for background to yield the net integrated intensity I . Lorentz and polarization corrections were applied, but absorption was neglected ( p = 0.76 cm-I); the overall isotropic temperature factor B = 3.6 A2 and the scale factor K = 0.172 were calculated by least-squares fit to a Wilson plot.
3. Results 3.1. Crystal Structure. Initial fractional coordinates for all the 21 non-hydrogen atoms were obtained by using the direct methods program EEES incorporated in SHELX-76 package," in which only the reflections with E 11.4 were processed. (This process of phase determination was conducted with some difficulty because a first attempt to solve the molecular structure done by another X-ray data set, collected from another crystal, failed to give the solution by direct methods. Moreover, some crystals show cell parameters that are apparently different from those reported here. These difficulties are probably due to twinning, a phenomenon observed in our previous EPR measurements. Full matrix least-squares isotropic refinement of the coordinates (11)Sheldrick, G.M.s ~ ~ ~ x -Program 76, for Crystal Structure Defermination; Cambridge University: Cambridge, U.K., 1976.
TABLE II: Selected Bond Lengths (A) and Angles (deg) with Estimated Standard Deviations in (A) Bond Lengths
C(1)-C(1)' C(1)B-C(1)B' C(l)-C(2) C(8)-C(9) C(8)-C(13) C(9)-C(10) C(l0)-C(l1) C(l1)-C(12) C(12)-C(13) C(9)-C(15) C(8)-HC(8)
In trans-Stilbenec 1.299 (6) C(l)B-C(2) 1.518 (16) 1.360 (22) C(1)-HC(1) 0.97 (4) 1.509 (7) In TCNB C(15)-N(2) 1.137 (4) 1.391 (4) 1.383 (4) C(lO)-C(14) 1.441 (4) 1.400 (3) C(14)-N(1) 1.135 (4) 1.385 (4) C(12)-C(17) 1.443 (4) 1.385 (4) C(17)-N(4) 1.133 (4) 1.400 (3) ( 13)-C(16) 1.448 (4) 1.444 (4) C(16)-N(3) 1.138 (4) 0.96(3) C(1 1)-HC(11) 0.97 (3)
(B)Angles In tram-Stilbene HC(l)-C(l)-C(2) 113.0 (2) C(2)-C(1)B-C(1)B' C(2)-C(l)-C(l)' 121.7 (2) In TCNB C(9)-C(8)-C(13) 119.4 (2) C(12)-C(13)-C(8) C(lO)-C(14)-N(l) C(8)-C(9)-C(IO) 120.2 (2) C(9)-C(lO)-C(ll) 120.1 (2) C(9)-C(15)-N(2) C(l0)-C(l1)-C(l2) 119.7 (2) C(13)-C(16)-N(3) C(ll)-C(l2)-C(l3) 120.1 (2) C(12)4(17)-N(4)
113.4 (2)
120.4 (2) 177.2 (3) 177.9 (3) 177.6 (3) 178.5 (3)
'Primed label denotes atom at -x, -y, -2 + 1. bC(l)Bis the ethylenic carbon atom of trans-stilbene related by disorder to C(1). the C-C bond distances in phenyl ring of trans-stilbene were fixed to 1.395 8, as well as the C-H distances were fixed to 1.080 8, (see text). (function minimized Cw(k(FoI- (FCl)*,unit weight to each reflection and with introduction of rigid-body refinement of the benzene ring of trans-stilbene) led to R( C(k(Fo(- IFCI)/Ck(Fo() = 0.12 for the 155 1 observed reflections. The constraint on the molecular geometry of the benzene ring proved to be useful when severe disorder was present; we always maintained this constraint in all the refinements performed with the exception of the last cycles. At this stage of refinement, examination of a difference
Agostini et al.
1000 The Journal of Physical Chemistry, Vol. 92, No. 4, 1988
TABLE III: Equations of Weighted Least-Squares Planes in the Form AX + BY + CZ = D , Where X, Y , Z Are Orthogonal Coordinates Obtained through the Orthogonalization Matrix la,b cos 7 , c cos Bl0,b sin 7 , -c sin B cos alO,O,c sin B sin al
plane:
+
(1) 0.3070 (94)X 0.3278 (93)Y - 0.9835 (45)Z = -3.41 14 (46), disordered trans-stilbene (2) 0.3219 (9)X + 0.3243 (9)Y - 0.8895 (5)Z = 0.0065 (40). TCNB
dihedral angles (deg) between planes: (1)-(2) = 0.82 (0.12)
deviations from the planes: plane (1): C(1), -0.032 (5); C(l)B, -0.037 (15) plane (2): c(8),-0.002 (3)*, C(9), 0.012 (2)*; C(10), -0.012 (2)*; C(11), 0.000 (3)*; C(12), 0.011 (2)*; C(13), -0.011 (2)*; C(14), -0.108 (3); N(1), -0.232 (3); C(15), 0.082 (3); N(2), 0.174 (3); C(16), -0.057 (3); N(3), -0.117 (3); C(17), 0.048 (3); N(4), 0.106 (3)
"Deviations for atoms defining the planes are marked with asterisks. TABLE I V Some Relevant Contacts in Molecular Packing" HC(8) N(3)i') 2.41 (2) HC(3) N(l)(O 2.95 HC(8) N(4)ib) 2.89 (3) HC(4) N(2)(0 2.73 HC(l1) N(l)(') 2.84 (2) HC(5) N(2)(*) 2.92 HC(11) N(2)(d) 3.05 (3) HC(7) N(4)iC) 2.75 HC(1) N(4)(e) 2.56 (3)
1,
4
(1) (1) (1) (1)
a Superscripts refer to the following equivalent positions relative to x, y , z : (a)-x,-y,-z;(b)-1 + x,y,z;(c) 1 - x , 1 - y , I - z ; ( d ) 1 x , y, z; (e) 1 - x , -y, 1 - z; (f) -x, 1 - y, 1 - 2; (g) 1 + x, y, 1 + z.
+
electron density map showed, without doubt, that there are six peaks forming a regular hexagon approximately midway between the carbon atoms of the benzene ring of trans-stilbene, varying in intensity from 0.71 to 1.14 e/A3, along with the position for the eight hydrogen atoms. Moreover, the model showed a short central double bond C ( l)-C( 1)' (for primed labels see Table 11) of 1.22 A that is typical of a disordered trans-stilbene molecule positioned on an inversion The six regular peaks were interpreted as due to a disorder of the benzene ring of trans-stilbene; then this benzene ring was divided in two benzene rings (A and B) with normalized fractions fA andfB. Then, using always the rigid-body approximation, an anisotropic refinement was carried out on all the atomic parameters (including isotropic hydrogen atoms) already found. The values OffA and fB of the carbon atoms of ring A and B were refined but their thermal parameters where fixed at B = 3.6 (the value found for the overall isotropic temperature factor). The resulting values werefA = 0.79 and fB = 0.21. Further rigid-body refinements on anisotropic thermal and positional parameters, with fA and fB fixed at the values already found, lowered R to R = 0.038. We present coordinates (Table I) selected bond lengths and angles (Table 11),weighted least-squares planes (Table III), relevant contacts (Table IV), and Fo/Fctables from this refinement for complex A and for the ethylenic bond of complex B. The constituent molecules of the trans-stilbene-l,2,4,5-tetracyanobenzene (1:2) molecular complex are nearly planar; a benzene ring of trans-stilbene is overlapped by a TCNB molecule with an average interplanar spacing of 3.41 f 0.01 8, and a dihedral angle of 0.82O f 0.12O. This interplanar spacing of 3.41 A is close to the spacing of 3.44 A found in the diphenylacetylene-TCNB complex.' Since the other benzene ring of trans-stilbene is overlapped by another TCNB molecule, the molecular complex is formed by one trans-stilbene molecule and two TCNB molecules and constitutes the complete unit as shown in Figure 1. The stacks are formed with a TCNB molecule alternated with a benzene ring of one TSB molecule in infinite columns along the c axis; the interplanar spacing between one half of trans-stilbene and TCNB molecule is slightly alternated with shorter (3.40 %.) and longer (3.42 A) spacings. In Figure 2 a projection of the stacked molecules viewed along the normal to the plane of the two differently oriented (A and B) TSB.molecules is represented. (12) (a) Finder, C. J.; Newton, M. G.;Allinger, N. L. Acta Crystallogr. Sect. B 1974, B30.411. (b) Bemstein, J. Acfa Crystallogr.Sect. B 1975, B31, 1268. ( c ) Hoekstra, A.; Meertens, P.;Vos, A. Acta Crystallogr. Sect. B 1975, B31, 2813. (d) Bar, I.; Bernstein, J. Acta Crystallogr. Sect. B 1978, 834, 3438. (e) Bernstein, J.; Bar, I.; Christensen, A. Acta Crystallogr., Secr. B 1976, B32, 1609. (0 Valle, G.; Busetti, V.; Galiazzo, G. Cryst. Struct. Commun. 1981, 10, 861.
I
.'.. . I
Figure 2. Schematic representation of the two centrosymmetric TSB
molecules in the disordered TSB-(TCNB)2 crystal viewed along the normal to the plane of disordered TSB. In-plane ZFS principal directions are drawn. Data of Table I are used for ethylenic fragments. The relative orientation of the donor and acceptor molecules in each TSB-(TCNB)2 is very similar to that of diphenylacetylene-TCNB as reported in Figure 4 of ref 7, with one NC
CN
'c=c /
/ \ moiety of the acceptor TCNB molecule placed in the middle of the benzene ring of the donor molecule. The crystal packing is shown in Figure 1 and the shortest contacts are reported in Table IV. The principal feature is that the packing is controlled by C-H - - - N 4 - contacts, especially when the hydrogen atoms involved are HC(8), HC(11), and HC(1). These hydrogen atoms are in fact very positively charged, being part of TCNB (a strong electron acceptor) or, as HC( I ) , of the acidic part of trans-stilbene. 3.2. EPR Spectra and ZFS Principal Directions. EPR spectra of the illuminated TSB-(TCNB)* crystal have been already reported3 and their assignment to a triplet trap was shown. They allowed us to determine ZFS parameters and principal directions of the fine tensor with respect to the a*b*c frame where c is the crystallographic axis of stacking. The b* axis normal to c is contained in the more developed face (100) of the crystal while the a* axis is taken perpendicular to the b*c plane. In order to relate the principal directions of the ZFS tensor of the TSB-(TCNB)2 complex to its molecular moieties we make use of the atomic coordinates of the donor and the acceptor molecules reported in Table I. First, we find the orthogonal transformation that allows one to express the axes of the abc frame in terms of those (xD,yD, zD) centered on the TSB molecule in orientation A (see Figure 2) with the zD axis perpendicular to the molecular plane and the xD axis coincident with the ethylenic bond. Details of the calculation are reported in the Appendix. With the aid of the numerical results reported in Table V we find that
The Journal of Physical Chemistry, Vol. 92, No.4,I988
Properties of the trans-Stilbene-TCNB Complex
1001
TABLE V direction cosines
ZFS
eigenvectors
Xn
Vn
Zn
XA
YA
ZA
X
-0.8188 0.5743 0.0041
-0.5740 -0.8161 -0.0679
0.0358 0.0584 -0.9973
0.8446 -0.5 3 5 5 -0.0050
-0.5350 -0.8401 -0.0692
-0.0358 0.0554 -0.9978
Y Z
the ethylenic bond of TSB forms an angle of 35.2O with the x principal direction of the ZFS tensor associated to the X = -308 M H z eigenvalue3 as shown in Figure 2. By applying a similar calculation we have determined the orientations of the ZFS principal directions with respect to the symmetry axes (xA,y,, zA)of the TCNB molecules of the complex (see Appendix). Direction cosines are reported in Table V. We find that the ZFS principal direction y forms an angle of 32.6O with the molecular axis passing through the CH bonds of TCNB as shown in Figure 3.
Y P
f
xh
4. Discussion
As shown in Figure 1 the crystal structure of the TSB-(TCNB)2 complex consists of stacks of donor and acceptor molecules with the TCNB components overlapped with the benzene rings of the TSB molecules. Donor and acceptor molecules are arranged in an alternating sequence with average interplanar spacing of 3.41
V'
t-lk
A.
The final refinement in the crystal structure determination revealed the presence of crystal disorder which resembles that found in crystals of trans-stilbene-like molecules.12b,c,f The TSB-(TCNB)2 crystal contains two complexes A and B (in the ratio 4:l)that differ for the TSB orientation in the crystal (cf. Figure 2). In both species the TCNB molecules occupy the same positions in the unit cell and the TSB molecules have the same inversion center. So, the crystal stacks are composed of columns of A and B complexes organized in sequences
...BAAAAAAAABBBBAAAAAAAA ... Microclusters of A and B complexes seem to alternate perfectly oriented with respect to each other over microscopic sequences. At the AB boundaries, crystal defects are present with two TSB-(TCNB)2 complexes that have donor molecules differently oriented in the crystal. A behavior of this kind has been found recently in crystals of ( ~ y r e n e ) , P F ~ . ' ~ When the crystal is irradiated with visible light and the triplet state is formed, the excited state moves along the stack within the segment of equivalent sites. At the ends of a sequence the distorted lattice sites act presumably as traps (X traps) of the mobile excitation. EPR spectra from X traps are in fact detected in this crystal with unresolved hyperfine structure responsible for the large line width, although ODMR experiments gave evidence that triplet excitons are surely produced in the photoexcitation of the crystaL3 Thus, the triplet mobile excitation is efficiently trapped in this system favored by the characteristics of the crystal structure. The ZFS parameters measured in single crystals of the TSB-(TCNB)2 complex ( D = 0.1007cm-' and E = 0.0233 cm-l) are quite close to those recently obtained for TSB in a frozen micellar aggregate5 ( D = 0.105cm-' and E = 0.024cm-'). Since the only contribution to the ZFS parameters is expected to come from the donor triplet, the acceptor one being much higher in energy, this fact indicates that the C T character of TI is only a few percent (3%). From EPR spectra only one pair of lines is observed (spectra of two sites are actually seen but are due to twinning) and this can occur either when triplet excitation is shared on the two TSB molecules of an AB dimer or when it resides on the same TSB molecule (A or B) of the defect. The first possibility is ruled out by the fact that the ZFS principal axes do not represent symmetry axes of the AB dimer as shown in Figure 2. The ZFS parameters of the TI state of TSB indicate that the triplet wave function is (13) Schatzle, A.; von Schlitz, J. U.; Wolf, H.C. Muter. Sci. 1984, X , 235.
Figure 3. Projection of the TSB-(TCNB)2 complex in the A orientation along the normal to the TCNB molecules. The in-plane ZFS principal axes and the symmetry axes of TCNB are drawn together with the angle formed between the two frames.
delocalized over the ethylene and the "toluene-like" fragments of the molecule. The assignment of the triplet excitation on the defect of the TSB molecule in the orientation A is strongly supported by the alignment of the ZFS principal axes. Particularly, t h e y principal direction lies almost parallel to the line that connects the centers of the benzene rings of TSB with the inversion center in the orientation A. Therefore, the same crystal site (A molecule of TSB) is excited in the trap regardless to which microcluster (A or B) produces originally the mobile excitation. The method of generating locally excited triplet states by means of the optical excitation of weak C T complexes appears to be very attractive when the locally excited states either on the donor or on the acceptor molecule are inefficient in inducing ISC. In C T complexes of TCNB we have always found that the acceptor molecule is responsible for efficient ISC while the triplet excitation may reside almost completely on the donor molecule as in the A-TCNB crystal.6 The same mechanism of triplet population is assumed to operate in the TSB-(TCNB)2 crystaL3 When the triplet exciton is first produced by optical excitation, the highly selective initial population of the triplet sublevels of the triplet state is preserved due to the short lifetime of the excitation, which is comparable with the spin-lattice relaxation time among the triplet sublevels, and produces a large amount of stationary optical spin polarization. If all the crystal sites are magnetically equivalent, optical electron polarization (OEP) carried by the exciton is directly transferred onto the spin sublevels of the trap. Instead, if the exciton is originated within a microcluster of B donor molecules, the slight misalignment between ZFS principal axes of the exciton and the trap should be taken into account. However, we have discounted this minor effect in the calculation of OEP of the trap as excitation of sites B is less favorable in our crystal (ratio of A over B 4:l). Assuming that the energy-transfer rate from exciton to trap is fast enough with respect to the spin-lattice relaxation time of the exciton, the populating rate constants of the trap are in the same ratios as those of the exciton. The presence of OEP in the trap gives rise to the observed
1002 The Journal of Physical Chemistry, Vol. 92, No. 4, 1988 1
I
-
1
Figure 4. Calculated values of I+ when Bo is rotated in the a*b* plane (a = 0, Bollas) of the TS-(TCNB)2 crystal. I+ is calculated by the populating rate constants of TCNB,Zomisalignment of 3 3 O around z . Different sets of decay rate constants are used: (a) k,:k,:k, = 0.l:l:O.l; (b) k,:k,:k, = 1:O.l:O.l; (c) k,:k,:k, = 1:l:l. Wis set equal to (k, + k , ) / 3 . Arrows indicate experimental orientations at which the EPR signal changes its phase with the accuracy of f 1’.
special effects on the phases of its EPR signal when the magnetic field Bo is rotated with respect to the crystal. The intensity of the EPR line for the 10) I+) triplet transition (Z+) has the expression
-
I+ = cb(n+ - no)
(1)
where c is a scaling factor dependent on the experimental conditions while b represents the transition probability. The steady-state populations ni of eq 1 are obtained by solving the following set of kinetic equations (under the condition Ai = 0) n+ = (-k+ - 2W)n+ Welno + We2n..+ P+n,
+
no = Wn++ (-ko - “(1 + el))no+ Weln- + Pons ti- = Wn+
+ Wno+ (-k- - W(el + e2))n- + P n ,
(2)
where W = l/jT1 is the frequency of spin-lattice relaxation, n, is the steady-state population of the excited singlet state and e, = exp(-jg@/kT). The populating rate constants P, (i = +, 0, -) in the presence of magnetic field appearing in eq 2 are related to those at zero field through an expression
Pi = ClCiu12 P,
i=
+, 0, -; u = x, y , z
(3)
U
where the coefficients Ci, express the eigenfunctions of the full spin Hamiltonian in terms of those of the fine-structure interaction. An analogous relation holds for the decay rate constants. Equation 3 implies that the populating axes coincide with those of the ZFS principal direction~.’~J~ However, as shown in Figure 4, this is not the case of the TSB-(TCNB), crystal and equation 3 must be replaced
Pi = CIC\,12Pu a
Agostini et al.
i=
+, 0, -;
(Y
=
xA,
yA, Z A
(4)
where the coefficients Pi,represent the spin Hamiltonian eigenvectors projected on the frame of the independent channels of the populating process (xA,yA, zA) (in our case the symmetry axes of the TCNB molecule). The main consequence is that even when Bo is rotated in a ZFS principal plane asymmetries in the values of I+ may appear. In particular, if I+ changes sign in that plane, the orientations at which this occurs are not longer symmetrical with respect to the ZFS principal axes of that plane. The effect of noncoincidence of the (x, y , z ) and (xA,yA, frames is manifested also when EPR measurements are carried in a frame different from the ZFS one. However, in such a case the amount of the misalignment is obtained from a detailed analysis of the angular dependence of Z+. Measurements of the sign of Z+ in the TS-(TCNB), more
zA)
(14) Podgoretskii, M. I.; Khrustalev, D. A. Sov. Phys. Uspekhi 1975, 6, 154. (15) Schadee, R.A.; Schmidt, J.; Van der Waals, J. H. Chem. Phys. Lett. 1976, 41, 435. (16) Corvaja, C.; Pasimeni, L. Chem.Phys. Letf. 1982, 88,347.
0 /
Figure 5. Calculated values of I+ when Bo is rotated in the a*b*(A), b*c(B), and ca*(C) planes. Parameters used are the same as those of Figure 5 with the choice of k,:k,:k, = 0.1:l:O.l.
accurate than those reported in ref 3, when the magnetic field is rotated in the a*b*, b*c, and cu* planes, have allowed a precise comparison with the calculated values of I+. Our previous calculation~~ were performed by assuming an isotropic decay process. Even with such a crude model we have shown a misalignment between the (x, y , z ) and (xA, y A , zA) frames consisting of a rotation of about 20” around the z = zA axis. When the misalignment angle of 33” obtained from the crystal structure determination is used, the comparison of the calculated values of Z+ with the experimental signal phases gets worse. Then, we have removed the assumption of isotropic decay. The latter is suitable for excitons that deactivate by trapping or by a triplet-triplet annihilation process which is almost independent of the Zeeman level,”J* but spin selectivity in the decay rate constants of triplet sublevels of a trap is well estab1i~hed.l~Another quantity that enters the calculation of I+ is the spin-lattice relaxation frequency Wwhose value is not known in this system. However, if W is large compared to all k,, the steady-state population of the triplet sublevels is close to the Boltzmann distribution and the OEP is destroyed. On the other hand, we have noted that there is no change in the angles at which polarity reversal of the calculated Z+ values occurs for Wvaried up to 10 times larger than all k,. In the calculations reported in Figures 4 and 5 , Wis taken equal to the average decay rate constant ( k , + k, + k , ) / 3 . In Figure 4 we report the results of the calculated values of I+ when Bo lies in the a*b* plane showing definitely that the decay rate constants of the ZFS spin sublevels of the TS-(TCNB)2 triplet are anisotropic, with the y principal axis parallel to the long in-plane axis of TSB most active. A complete account of experimental and calculated values of I+ with Boin the u*b*, b*c, and ca* planes is reported in Figure 5. In conclusion, we have shown in this paper that the crystal structure of the TSB-(TCNB)2 complex consists of stacks of donor-acceptor molecules in which TSB is present in two orientations arranged in segments of different length along the stack, a typical case of crystal disorder. Triplet excitons generated by optical excitation are forced to move within those segments and eventually become trapped at the domain walls. The OEP displayed by the TS-(TCNB)* triplet trap is indicative of several peculiarities occurring in C T crystals. Specifically, (i) only the acceptor molecule is involved in the ISC process; (ii) triplet excitation resides mainly on the donor molecule; (iii) the decay process is anisotropic with its most active component along the y principal axis of the ZFS tensor.
Acknowledgment. We thank Prof. A. Dal Negro for providing technical assistance in collecting X-ray data. Use of the diffractometric facilities of Istituto di Mineralogia dell’Universit8 (17) Avakian, P. Pure Appl. Chem. 1974, 37, 1. (18) Johnson, R. C.; Merrifield, R. E.; Avakian, P.; Flippen, R. B. Phys. Rev. Lett. 1967, 19, 285. (19) Hausser, K. H.; Wolf, H. C. Adv. Magn. Reson. 1976, 8, 85. (20) Yagi, M.; Nishi, N.; Kinoshita, M.; Nagakura, S . Mol. Phys. 1978, 35, 111.
Properties of the trans-Stilbene-TCNB Complex di Padova is also acknowledged. This work was supported in part by the Italian National Research Council (CNR) through its "Centro di Studio sugli Stati Molecolari Radicalici ed Eccitati" and in part by the Minister0 delle Pubblica and Istruzione.
Appendix Let us denote with L, and L, the orthogonalization matrices that allow to express the atomic coordinates of Table I in terms of orthogonal coordinates. In L, and L, the crystallographic axes a and c respectively are maintained fixed. Matrix L, is given in the caption of Table 111 and L, is reported in ref 21. We have obtained the orthogonal frame (xo,yo, zo) by applying L, to the crystallographic frame (a, 6, c ) while application of matrix R D transforms (xo,yo, zo) into the system (xD,yD,ZD)fried (21) Rollet, J. S.In Computing Merhods in Crystallography; Rollet, J. S.,Ed.;Pergamon: Oxford, 1965; Chapter 3.
The Journal of Physical Chemistry, Vol. 92, No. 4, 1988 1003 on the TSB donor molecule (in the orientation A) with ZD axis normal to the molecular plane and xDaligned with the ethylenic bond. Matrix U = L,(R&,)-* gives the system of axes (a*, 6*, c) (reference frame of the EPR measurements reported in table I of ref 3) in terms of (xD,y D ,zD). The direction cosines that give the eigenvectors of the ZFS tensor on the latter frame are reported in Table V. An analogous procedure was followed to relate the principal directions of the ZFS tensor to the coordinate system (xA, Y A , zA) fixed on the TCNB acceptor molecule with the two XA and y A axes coinciding with the symmetry in-plane molecular axes CYA passes through the C H bonds). Let RA be the orthogonal matrix that transforms (xo, yo, zo) into (XA,yA, ZA) and U' = L&LJ1 the transformation that connects the axes (a*, 6*, c) to the molecular symmetry frame (xA,y,, zA) of TCNB. With respect to the latter frame the principal directions of the ZFS tensor are expressed by the direction cosines reported in Table V. Registry
NO. 1:2 (TSB)-(TCNB), 90176-70-8.
