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Relaxation Processes in Photochemical Reactions
Relaxation Processes in Photochemical Reactions. An Electron Spin Echo Study of Chemically Induced Spin Orientation’ David C. Doetschman Department of Chemistry, State University of New York at Binghamton, Binghamton, New York 1390 1 (Received February 2, 1976)
Following a short historical introduction which traces the paper’s subject back to early work of Kasha and others, electron spin echo experiments on the photochemically induced spin orientation in triplet diphenylmethylene are reviewed. The remainder is an interpretation of the highly preferential photochemical population of one of the triplet sublevels, an interpretation in which the photochemically excited reaction product relaxes via an intersystem crossing.
1. Introduction
This work, like so much else, has its origin in Lewis and Kasha’s early work on the phosphorescence of organic molecule$ which established the triplet character of the emitting state. Lewis, Calvin, and Kasha’s subsequent photomagnetism experiments3 together with other efforts eventually led to the successful application of EPR to photoexcited triplet molecules.4 Since then interest has turned to the dynamic photophysical processes which are set in motion by photoexcitation. Kasha recognized that there are prominent pathways of molecular excitation which seem to stand out from the many processes imaginable.5 The spin-orbit coupling selection rules were identified which govern intersystem crossing as well as the triplet decay to the ground state.6-8 The triplet spin substate preferences of these pathways often generate remarkable nonthermal population distributions in the triplet sublevels when the temperature is low enough to retard thermal equili b r a t i ~ n .Moreover, ~ the spin substate selectivity may be predicted with spin-orbit coupling theory in which only one center atomic integrals are retained.6-s The presence of large nonthermal population differences among the triplet sublevels, which are often called spin polarizations or orientations, have led to the use of new magnetic resonance techniques. Two examples are the microwave induced phosphorescence effectsgJOand the spin echo methods.11J2 A by-product of these techniques is the ability to easily monitor moderately fast changes in the triplet sublevel populations. For example, with spin echoes a time resolution of a few microseconds in solids at low temperatures is possible.l2 First to be described will be some recent experiments1 on a photochemical reaction for which electron spin echo techniques were borrowed from earlier photophysical work. Then an interpretation of the photochemistry results will be presented, also in terms of what has been learned about photoexcitation and decay processes.
2. Photochemically Induced Triplet Electron Spin Orientation Experiments Recent electron spin echo experiments‘ reveal an orientation of the electron spin in the ground triplet state of diphenylmethylene (DPM) which is induced by the photolysis of diphenyldiazomethane (DPDAM). See Figure 1. The DPDAM is the dopant in an appropriate single crystal l 1 0 s t ~ which ~ J ~ is in an X-band microwave cavity in a magnetic field and at T 1.2 K. The crystal is photolyzed with a pulsed N
T- 1.2K
337 nm 8 nsec; 6mJoule
PHOTOLYSIS
LASER
MICROWAVES ECHO
n n&
EQUILIBRIUM
TIME --t.
Flgure 1. Experimental sequence in the two pulse spin echo detection of the triplet spin orientation in diphenylmethylene which is induced by photolyzing diphenyldiazomethane with a N2 laser pulse.
Nz laser. A somewhat idealized experimental sequence, shown in Figure 1, is the laser flash, followed by a pair of resonant microwave pulses and the subsequent spin echo. The echo intensity is a measure of the population difference between two of the DPM triplet sublevels. The time scale must, of course, be less than the spin-lattice relaxation times, which are all found to be greater than 3 ms.l After the DPM spins have reached thermal equilibrium, a reference experiment is done without the laser flash. In practice it is necessary to use several laser flashes, to make minor spin-lattice relaxation corrections, and to subtract the echo intensity of the residual DPM which is inevitably left behind from previous experiments. The echo intensity I , in the photolysis experiment is proportional to the difference A p in the relative populating rates of the two triplet sublevels connected by the microwaves. The reference intensity I , at thermal equilibrium is proportional to the relative Boltzmann population difference Ab, a quantity which is readily calculated. Here relative means to all three triplet sublevels. So A p may be determined from the experiment through AP = Up/Ie)Ab
(1)
A p may as well be expressed in terms of the populating rates p x ,p y rp z of the sublevels in zero field, as in The Journal of Physical Chemistry, Vol. 80,No. 20, 1976
David C. Doetschman
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I I 30-
I I
t,* 0 ,I
3?+$,-
20-
0-.so
-
I
I
I
Figure 2. Diphenyldiazomethane and diphenylmethylene energy level diagrams which are juxtaposed according to a lower limit for the endothermicity of the diphenyldiazomethane photodissociation (see text) when zero N2 excitation is assumed. The wavy lines indicate the proposed relaxation
scheme in the reaction and the numbers adjacent are quantum yields. The dotted lines connect the states which may be strongly coupled by spin-orbit interaction. The relative populating rates of the diphenylmethylene ground triplet sublevels are indicated numerically and with arrows of proportionate length.
Ap = AC, 2p,
+ AC, 2py+ AC, 2pz
(2)
The numbers denoted by the AC2’s depend on the transformation between the DPM spin functions in the magnetic field of the experiment and in zero field. Thus the p,, p y , p , may be determined from three or more Ap measurements a t distinct fields. In DPM there are altogether four different Am = fl X-band transitions for fields along the principal axes. Experiments on the four lines show that pr is at least 0.93. Only upper limits are established for p , and p z . The relative rates are indicated in Figure 2 on the “blow up” of the DPM triplet level. Insofar as the echo experiments could determine, the appearance of the spin oriented triplet after the laser flash is instantaneous. 3. Interpretation
The photochemical processes to be examined are displayed in the adapted Jablonski diagram, Figure 2. The laser excites the DPDAM to a singlet state from which dissociation occurs with the relatively high quantum yield indicated.13 When the lower singlet is excited, the quantum yield is much smaller,13 a fact which suggests that intersystem crossing from l m * DPDAM before dissociation is not appreciable. The reaction is endothermic but the dissociation energy is not known and the difference shown in Figure 2 is a reasonable lower limit.l5 Also, no direct spectroscopic information exists for the bracketed DPM singlet states. These low lying states derive from single and double occupancy of the two nearly degenerate methylene-like orbitals which are singly occupied in the ground triplet state. The events which take place may be cast in familiar photophysical terms. There is a photo(chemica1) excitation step followed eventually by an intersystem crossing to a (chemically) metastable triplet. Return to the reactant ground state presumably is inhibited by diffusion of the “hot” N2 away from the DPM in the crystal. There are two interrelated questions about these processes which can be partially answered, namely, why there is so great a spin preference for the Y substate of triplet DPM and what the pathway is by which excitation goes from lm*DPDAM The Journal of Physical Chemistv, Vol. 80, No. 24 1976
to the DPM triplet? In the slightly bent prototype methylene CH2 the two nearly degenerate triplet orbitals are essentially the carbon p, and the sp, hybrid. Herzberg’s diazomethane photolysis experiments16 and theoretical calculations of the CH2 electronic stated7 suggest that the doubly occupied sp, methylene singlet is first formed and then converts to the ground triplet. One center spin-orbit coupling between these two states clearly involves matrix elements of the y orbital angular momentum component. Consequently the Y spin sublevel of the triplet is singlet contaminated7 and is expected to be the recipient in intersystem crossing. It is no surprise to find the strong Y selectivity reflected in DPM. However, the 93% preference seems too good because it is known14b that approximately 40% of the DPM triplet electron spin does not even reside on the central carbon atom! So any explanation of the high preference must also take into account the delocalization of the DPM wave functions onto the phenyl rings. The DPM bend angle 0 about the central carbon atom is only 16” 14b so the molecule has approximately Dz symmetry. Reasonable methylene-like DPM orbitals dx and d2 will belong to the representations B3 and B1 of the D2 group. The representations of the four two electron configurations in these orbitals are given in Table I. Only spin-orbit coupling between the Y sublevel of the triplet Bz and the singlet A1 states is symmetry allowed and the matrix elements are the same to both A1 states. So ’in the D2 approximation symmetry fully accounts for the spin selectivity. Symmetry, however, does not reveal the relative contributions of coupling on the rings and on the central carbon atom nor how the coupling varies with the angle 4 of phenyl ring twist from coplanarity. See Figure 3. It is clear from magnetic resonance studies of the DPM triplet state that electron delocalization into the u system of the phenyl rings is very small.14b In a T approximation for the phenyl rings, the molecular orbitals d,, d2 contain only the ring carbon p orbitals directed normal to the ring planes. All one center integrals of orbital angular momentum on the ring carbons, which appear in the spin-orbit coupling matrix element between 4, and dz,
Relaxation Processes in PhotochemicalReactions
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TABLE I: Representations to Which the Two-Electron Configuration in the & and & Diphenylmethylene Orbitals Belong for Molecular Symmetries Dz and CZ Representation
DZ
Configuration
'& l&
3'
1
CZ
Triplet
l'
will t,herefore vanish. In other words, no appreciable spinorbit coupling contribution from the rings is expected. Higuchi's simple orbital@ in Flgure 3. The diphenylmethylene molecule. The axis system, the carbon atom numbering scheme, and the bend (8) and twist (4)angles are illustrated.
- pn5 - pnw + pn7 + Pn7OI (4) conform to this approximation and lead to the twist angular dependence of the central carbon spin-orbit coupling matrix element given in
+
4
(5)
d 4 0 9 sin2 24 where unity represents the element between two orthogonal p orbitals. The actual DPM twist angle 4 = 54" is close to the angle for which the element is minimum. DPM actually has C2 symmetry and c $ ~ and 4z can be modified for the bend 8 and for sp, hybridization on the central carbon atom. The orbitals now belong to representations B and A of C2. The representations of the two electron configurations in C2 are also given in Table I. Spin-orbit mixing of the singlets A is now formally symmetry forbidden only with the Z spin state of triplet B. However, within the x approximation for the rings there can still be no ring contribution to mixing with the X substate. Moreover, sp, hybridization on the central carbon atom can lead to no X mixing either. The angular dependence of the central carbon spin-orbit coupling on both 0 and 4 is given in
4 cos1I228 (6) d ( 4 6 sin2 4)[2(1 cos 28) 6 cos2 4 cos 281 again relative to the element between two orthogonal p, orbitals. One concludes that very high Y substate selectivity is a result of the nearly complete dominance of spin-orbit coupling by the central C atom, a dominance which arises because the u delocalization in the ring system is small. One also predicts the selectivity to be quite insensitive to molecular geometry so long as G delocalization remains negligible. The experiments are consistent with triplet coupling to one or both of the singlets indicated by the dotted lines in Figure 2 and with intersystem crossing from among the bracketed singlets. It is unlikely that other x-type DPM singlets lie lower than the observed 37r +X14a which is well above the excitation of the reactant. Herzberg's experiments and evidence from the chemical reactivity of methylene derivatives in general both point to the transient existence of singlet methylenes before crossing to the triplet. The pathway for relaxation in the photochemical reaction in Figure 2 is a scheme which is consistent with the experi-
+
+
-
+
mental information currently available. Time-resolved optical absorption experiments on DPDAM and DPM could provide a crucial test of the scheme. Similar spin echo experiments on methylenes with different geometries are planned to test the spin-orbit coupling mode, in particular, the predicted insensitivity to molecular geometry. References a n d Notes (1) The experiments reviewed here were performed in collaboration with B. J. Botter, J. Schmidt, and J. H. van der Waals at the Center for the Study of Excited States of Molecules, Huygens Laboratories, The University of Leiden, Leiden, The Netherlands. The detailed description of the experiments will be published elsewhere. (2)G.N. Lewis and M. Kasha, J. Am. Chem. SOC., 66,2100(1944);67,994
(1945). (3)G.N. Lewis, M. Calvin, and M. Kasha, J. Chem. Phys., 17,804 (1949). (4)C. A. Hutchison, Jr., and B. W. Mangum, J. Chem. Phys., 34, 908 (1961). (5)M. Kasha, Radiat. Res., Suppl. 2,243 (1960). (6)D. S.McClure, J. Chem. Phys., 17,665 (1949);20, 682 (1952). (7)J. H. van der Waals and M. S.deGroot in "The Triplet State", A. B. Zahlan, Ed., Cambridge University Press, London, 1967,p 101. (8)W. S. Veeman and J. H. van der Waals, Mol. Phys., 18,63(1970). (9)M. Sharnoff, J. Chem. Phys., 46,3263 (1967). (IO) J. Schmidt, D. A. Antheunis, and J. H. van der Waals, Mol. Phys., 22, 1 (1971). (11) J. Schmidt, Chem. Phys. Lett, 14,411 (1972). (12)B. J. Botter, D. C. Doetschman, J. Schmidt, and J. H. van der Waals, Mol. Phys., 30,609 (1975). (13)D. C. Doetschman and C. A. Hutchison, Jr., J. Chem. Phys., 56, 3964 (1972). (14)(a)G.Closs. C. A. Hutchison, Jr., and B. E. Kohler, J. Chem. Phys., 44,413 (1966);(b) C. A. Hutchison, Jr., and B. E. Kohler, ibid., 51,3327 (1969). (15)That DPM may be formed by excitation to 'na" DPDAMi3 indicates that
34x'4z'DPM lies to lower energy. The DPM ground state has been placed
2000 cm-' lower than the activation energy for CHzNz pyrolysis, to the authors knowledge the lowest conceivable indicator of the reaction endothermicity. More reliable indicators such as bond energy estimates and methylene excess energy measurements in CH2N2 photolysis all point to a considerably higher endothermicity. (16)G. Herzberg, Proc. R. SOC.London, Ser. A, 262,291(1961);Can. J. Phys., 39, 151 1 (1961);"Molecular Spectra and Molecular Structure, 111, Electronic Spectra and Electronic Structure of Polyatomic Molecules", Van Nostrand, New York, N.Y., 1966,p 492;G.Herzberg and J. W. C. Johns, J. Chem. Phys., 54,2276 (1971). (17)J. F. Harrison and L. C. Allen, J. Am. Chem. SOC., 91,807 (1969). (18)J. Higuchi, J. Chem. Phys., 38, 1237 (1963).
Discussion M. W. WINDSOR.What is the energy of the optical transition (from lowest triplet ground state to higher triplet) in diphenylmethy-
lene?
D. C. DOETSCHMAN. The difference between that ground triplet and the excited triplet is the lowest optical absorption band which lies at 4500 A, I believe. The absorption spectrum of diphenylmethylene has been observed by Hutchison and Kohler. With our lower limits that places that level well above the energy that we put into the system in the first place. The Journal of Physical Chemistry, Vol. 80, No. 20, 1976
