J. CHEM. SOC. FARADAY TRANS., 1994, 90(11), 1479-1486 1479

Configuration Interaction Study of the O,-C,H, Exciplex : Collision-induced Probabilities of Spin-forbidden Radiative and Non-radiative Transitions Boris F. Minaev'? and Vitalina V. Kukueva Cherkassy Engineering and Technological Institute, Cherkassy, 257006, Ukraine Hans Agren Department of Physics and Measurement Technology, Linkoping University, S-58183 Linkoping, Sweden

The collision complex between molecular oxygen and ethene has been studied by configuration interaction calculations, scanning the intermolecular distance in C,, collision symmetry. The calculations give a good explanation for the enhancement of the ethene T, t So and the oxygen A'3A, t X3X; transition probabilities observed by Evans at high oxygen pressure. A number of other oxygen and cooperative transitions are explained and predicted, considering the studied system as a general model for unsaturated hydrocarbon-0, interactions. The intermolecular potentials show negligible complex formation energies for the lower X 3C;, a 'As and b 'Xl states, but exciplex character for higher states. The ethene (m*) excited S, state has a fairly deep minimum and a very strong transition moment to the T, state, which also accounts for the non-radiative quenching of the hydrocarbon fluorescence by molecular oxygen.

Introduction The interaction of molecular oxygen with unsaturated hydro- carbons induces many interesting spectroscopic phenomena. It is well known that the 0, molecule is an efficient fluores- cence and phosphorescence quencher in its ground triplet state (X3Eg-). The quenching has been considered to occur through formation of exciplexes in the encounter complexes. However, these exciplexes have been elusive species, and they have still not been theoretically explored to any appreciable extent. A lot of other photophysical and photochemical effects induced by oxygen are connected with these key species, but also remain to be interpreted.

Theoretically interesting phenomena have been derived from observations of weak transitions in gas mixtures at high O2 press~re.~?' 40 years ago Evans showed that dissolved oxygen strongly induces singlet-triplet (S-T) absorption of aromatic molecules and other unsaturated hydrocarbons (UHC).3 This was the first direct indication of a spin-catalysis phenomenon: the rate of the process was greatly increased by the oxygen catalyst, which enabled the transition to become spin-allowed. The nature of this enhancement has attracted great attention, but has been the subject of controversy for a long time.4-8 The perturbing effect of the triplet ground-state oxygen molecule O2(X3Z;) on the T, t S o absorption spectra of unsaturated hydrocarbons was originally attrib- uted to a spin-orbit coupling perturbation of the UHC triplet state by the inhomogeneous field of the paramagnetic 0 2 ( X 'Xi) species.' This magnetic field perturbation was, however, later taken to be negligibly small in order to explain the observed enhancement of the T, t So t ran~i t ion .~ An ordinary intermolecular interaction was found to be much more important. By introducing the two unpaired electron spins to the collision complex, the 0 2 ( X 'Xi) molecule effec- tively enables the T, + S o transition inside the UHC moiety to become spin-allowed, because both states in the complex become triplets; the united state of the complex (X'X-, T,) provides singlet, triplet and quintet multiplicities.'-' The nature of the T, S o transition enhancement is thus deter-

? Also at: Department of Physics and Measurement Technology, Linkoping University, Sweden.

mined by small admixtures to the united triplet component of the other triplet states of the complex, namely the (%;, S,) state6 and the chargetransfer (CT) ~ t a t e . ~ . ~ The former, so called exchange mechanism, explains the T, c S o transition enhancement as a borrowing of intensity from the very strong S,-So tran~ition,~. ' and the latter accounts for the borrowing of the CT band i n t e n ~ i t y . ~ . ~ Both mechanisms have received much attention in qualitative discussions, but it has been dif- ficult to determine which is the most important, because in a general approach they have the same dependence on inter- molecular overlap.

In addition to the enhancement of the T, e S o transition in UHC molecules, dissolved oxygen induces a number of other spectroscopic and photophysical effects. The appear- ance of a new absorption at shorter wavelengths has been assigned to charge t r a n ~ f e r ~ ' ~ and cooperative transitions (simultaneous TI c S o excitation of the UHC molecule and a IAg t X 'Xg- excitation of oxygen by one q ~ a n t u m ) . ~ For ethene and other UHC molecules with large ionization potentials a new shorter wavelength absorption (280 nm) has been tentatively assigned to the enhanced Herzberg I tran- sition A 'E; t X 3Cg-,2 The presence of molecular oxygen in solution influences drastically the quenching of the S , and TI states by enhancing the intersystem crossing (non-radiative transitions).' The singlet oxygen emission a 'Ag + X 'Eg- which is sensitized by dyes and enhanced by solvents is another type of spectral phenomenon determined by the intermolecular exchange interaction between O2 and UHC molecules.'O~'' The nature of all these effects can be con- sidered by configuration interaction (CI) approaches.

The first CI calculations of the oxygen-UHC complexes were carried out at a semiempirical leve1.12-16 They were sur- prisingly successful and explained an observed intensity enhancement of T-S transitions in 0, and in UHC moieties' at intermolecular distances that were qualitatively consistent with kinetic radii. The INDO/S rnethodl4 cannot reproduce any potential curves and even the MIND0/3 CI approximation gives repulsive potentials for the 0, + C,H, intermolecular interaction.' ' In order to study the oxygen intermolecular spectroscopic effects in more detail, including the proper distance dependence, ab initio CI calculations are presented in this paper.

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1480

-0.681.

-0.682

-0.683 c

% P >

C

-0.684

-0.685

I

-0.686 3 4

R/A

Fig. 1 Intermolecular potential for the X3Xg-, So state of the C2H,-0, system; the 3B, symmetry in the C,, group. -227 E , must be added. [l E , (hartree) w 4.359 75 x lo-'' 5.1

-0.467

S

9 5 -0.461 Q)

Q)

-0.465 4

RIA Fig. 2 Intermolecular potential for the C'X;, So state of the C2H4-02 system; the 'A, symmetry in the C,, group. -227 E , must be added.

J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90

-0.51 6

S

9 > -0.517

C Q)

-0.51 8 4

R/A

Fig. 3 Intermolecular potential for the '(X 3 X i , T,) state

)

of the . ., C 2 H 4 4 2 system; the 'A2 symmetry in the C,, group. -227 E , must be added.

-0.472 1-

-0.486 ! 2 3 4

R /A Fig. 4 Intermolecular potential for the a 'Ag, T, states of the C2H4-02 system; (D) 3A2 and (+) 3B,. -227 Eh must be added.

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J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 1481

-0.44

-0.45

C

9. >

a

-0.46

-0.47 3 4

RIA Fig. 5 Intermolecular potential for the A' 'Au S o and A 'Z:, S o states of the C2H4-02 system; (0) A 'A,,, S o ('A2); (+) A' 'Au, S o ('B,); (W) A 3Z:y S o ('B,). - 227 E , must be added.

-0.30

-0.31

S

9. > g Q,

-0.32

-0.32 3 4

RIA Fig. 6 Intermolecular potential for the X'Z;, S , state of the C,H,-O, system; the 'A, symmetry in the C,, group. -227 E , must be added.

0.05

0.04

0.03 0

h 4t i: 2

0.02

0.01

0.00

Fig. 7 Collision-induced S - S transition dipole moments (in ea,) in the system C , H , 4 , ; (0) b 'Z:, S o ('A,)-a 'Ag, S o ('Al); (+) c 'Xi, S o ('A2)-a '4. So ('B2); (a) '(X 'Xi, T,) ('A2)- 'Agy S o (lB2)

0.08 -

0.06 - 0

3 r' !-

0.04 -

0.02 -

0.00 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2

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1482 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90

Computation From previous semiempirical calculations' ',,' it is known that the C,, symmetry of the ethene-oxygen collision complex is sufficient for the purposes of the present investiga- tion. We have used the same type of collision complex as has been studied before:,' C-C and 0-0 bonds form a regular trapezium (zx plane) where the intermolecular z-axis is per- pendicular to the plane of the ethene molecule (yx). The restricted open-shell Hartree-Fock (ROHF) method, has been applied to the triplet ground-state complex with the standard 6-31G* basis set (valence double-zeta plus a set of d-type polarization functions). 18*' CI calculations account- ing for all single, double, triple and quadruple excitations have been performed in an active space of six occupied and six unoccupied MOs for singlet states. This active space includes lb3, and lb,, (n) ground-state doubly occupied orbitals and lb,, (n*), 3b,,, 3a,, 2b,, and 2b,, empty orbitals of the ethene ground state; molecular oxygen is rep- resented by the ground-state configuration (~,)~(n,)' and by the 30, unoccupied MO. Such a CI is taken into account because it is impossible to reproduce the degeneracy of the 'A, state without all quadruply excited configurations; it gives a wavefunction with ca. 25 OOO configuration state func- tions (CSF). For the triplet states all single and double excita- tions are included together with triple and quadruple excitations for the ng electrons; this corresponds to wavefunc- tions with about 6200 CSFs. Singlet and triplet states of dif- ferent symmetry corresponding to various combinations of locally excited states inside the ethene and oxygen moieties have been calculated, scanning the intermolecular distance from 5 to 2.4 A. A few charge-transfer states were also studied. The computations were carried out with fixed intra- fragment geometrical parameters for 0, and ethene : 40-0) = 1.168 A, r(C=C) = 1.333 A, r(C-H) = 1.085 A, &HCC) = 121.7'. The choice of the CI wavefunction is based on the fulfilment of the following criteria.

(1) Approximate size consistency; our restricted active space wavefunction, with high excitations in a limited set of orbitals, describes the valence correlation well, which is important for open-shell complexes like C2H4 + O,, but neglects a large part of the dynamic correlation. However, only differences of correlation energy at different intermolecu- lar distances are of relevance, and the valence space corre- lation fulfils the size consistency criterion quite well, as shown here.

(2) Reproduction of the degeneracy of the alAg state at large intermolecular distance (R) in the complex.

(3) Reproduction of other properties of the separated adducts such as the Mulliken atomic charges, spin density and the sum of total energies at large R.

(4) Good accordance with experiment2'V2l and with large MCSCF CI calculations22 for the vertical excitation energies of the lower-lying valence excited states of the adducts.

The orbitals used in the extensive CI calculations are the ROHF ground-state orbitals. They have not been reopti- mized for each excited state. We suspect that the effects of orbital reoptimization would be quite small. MCSCF CI cal- culations for the ground triplet and singlet states of the complex at the equilibrium distances show that the popu- lation analysis does not change much. Although the main purpose of this paper is connected with collision-induced transition intensities, we also present the calculated intermo- lecular potentials for different states. The qualitative features of all potentials are reproduced quite well for different sets of CI expansions and in different atomic basis sets (3-21G, 4-31G).23 The results of the above described calculations (6- 31G*) are shown in Fig. 1-8. All calculations have been carried out using the GAMESS programme package.lg

Results and Discussion

Intermolecular Potentials

The potential for the intermolecular interaction in the ground state of the complex X3Zg-, So is shown in Fig. 1. It has a very shallow minimum at intermolecular distance, Re = 3.8 A. The depth of the well, estimated as a difference E(5 A) - E(R,) = D , , is only 0.42 kJ mol-'. The potential curves

for the low-lying singlet states of the complex (a 'Ag and b oxygen states in collision with the ground-state ethene) are quite similar to the curve represented in Fig. 1. The disso- ciation energies are somewhat higher; D, = 0.48 and 0.49 kJ mol- for the a 'A, and b 'El states, respectively. The equi- librium intermolecular distances are only 0.005 A shorter. The complex is extremely weak in all these states and cannot exist at room temperature, so it is better to consider it as a collision complex. This is in qualitative agreement with obser- vations., The next excited singlet state of the complex is pro- duced by the oxygen transition to the clX; state (Fig. 2), which is responsible for the Herzberg I1 band in the near-UV region. The minimum is deeper (D, = 1.42 kJ mol-') and shifted to a shorter distance, Re = 3.5 A. Consequently, this state could be considered as a very weak exciplex (note that the energy scales are different in the figures). The ethene T, excited state (,B,,) interacts with the triplet round-state oxygen without any barrier at a distance of 2.4 1 , the short- est found in this work. The singlet component of this 'double-triplet' state is shown in Fig. 3; approximately the same behaviour is exhibited by the triplet counterpart of this term. The energy diminishes drastically at small distances,

hotochemical activity of the X3Xg-, T, states (at showing R = 2.4 1 the energy is lowed by 0.5 eV). Because vertical transition geometry is used for the T, state of the ethene moiety and no geometry optimization has been performed for the photochemical reaction coordinate, these results have only qualitative meaning. In accordance with the previous MIND0/224 and MIND0/3 CISD it is found that the lV3(X, T,) channels lead to funnels produced by avoided crossings with the ground-states channels (X 'Xi, S o and a 'Ag, So) in the transition-state region for the biradical H,C'-CH2-0,' formation reactions.26 This can explain the 'quasichemical' mechanism of the physical T, state quen- ching, including the energy transfer to the singlet a'Ag oxygen (spin ~atalysis).~ 3926 It follows that the singlet funnel appears at longer distances (R w 1.8 A) than the triplet funnel (R w 1.7 and it could mean that the a 'Ag quantum yield is higher than that of complete quenching. The lowest potential-energy surfaces of both multiplicities (X 'Xi, So and alAg, So) go to the T and S biradicals (Rc4 = 1.4 A) through the activation barriers, which are formed by avoided crossings with the upper states 'v3(X, T,). The funnels appear on the upper potential-energy surfaces and the T, state quen- ching can proceed through these funnels.26 This could be considered as a general mechanism for many hydrocarbons. The singlet reaction path (a 'A,, So) for C2H4 + 0, addition has been studied recently at the MCSCF level,27 supporting the previous semiempirical results about the biradical forma- tion reaction path.'3*24*25 The chemical path that leads to dioxetan is connected with the other component of the a 'A, state, and follows the 'quasibiradical' reaction mechanism. For more details of the 0, reactivity in S and T states see ref. 13. Ab initio calculations on these funnels are now in progress.

The triplet excited ethene, T,, in collision with the singlet oxygen alAg state is described by split potentials, shown in Fig. 4. Both states have shallow minima at large R ; the upper potential has a minimum at R, = 4.05 A (D, = 0.18 kJ mol-') and the lower one has a metastable well at Re = 3.8 A

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(D, = 0.22 kJ mol-'), which goes through the activation barrier (5.32 kJ mol- ') to the photochemical reaction zone.

Quite interesting features are exhibited by the potentials of the A'A, and A3Z: states, which determine the Herzberg I11 and I bands, respectively (Fig. 5, with a larger scale). The A 'A, state is split by intermolecular interaction with the ground state of ethene. The lowest component ('A,) is more stable, D, = 3.38 kJ mol-', having a short intermolecular equilibrium distance, Re = 3.0 A; the potential of the other component is quite similar to that of the A 3 Z i state, D, = 1.5 and 1.28 kJ mol-l, respectively, as well as to the pre- viously described potential of the c 'Xi state.

Singlet excited ethene, S, (n,z*), forms a very stable exci- plex with the ground, triplet-state oxygen. The intermolecular potential (Fig. 6) exhibits a deep minimum, D, = 61 kJ mol-', at a short distance, Re = 2.7 A. This state, X 'Z;, S,, has a large charge-transfer (CT) configuration admixture of the type O,-C,H4+, which also contributes to the X 'Zg-, T, state, although to a lesser extent. All these states as well as the lower components of the A' 'Au, So and a 'Ag, T, states, have 3A, symmetry in the C,, point group of the complex. The CT contributions to these latter states are not so sensi- tive to the intermolecular distance. We have not studied the intermolecular potential of the Schumann-Runge state (B 'Xi) at this level of calculation because it has a much too large vertical excitation energy (> 12 eV). Preliminary CI cal- culations with a small active space (ng , II and n* MOs) in the STO-3G basis set have shown that the. B 'ZC,, So state poten- tial also exhibits a very strong exciplex character, but we cannot discuss its properties because of the crude character of such an approach.

The calculated transition energies for the separated mol- ecules and for the complex are discussed el~ewhere.,~ In summary, the sum of the total energies of the separated mol- ecules and the energy of the complex at a large distance (R = 5 A is considered as a dissociation limit) coincide quite well for many states, the differences are <0.001 eV. The exceptions are given by the doubly excited states in both mol- ecules (a ,Ao and b 'X; oxygen states in contact with the T, ethene and with the triplet component of the X 'Ze-, T, state). The difference with the sum of the energies of the free mol- ecules is of the order of 0.01 eV at large distances. The reason for this discrepancy is obvious; all quadrupole excitations are not taken into account for the triplet states of the complex, while all single and double excitations are included in the same restricted active space for the separated molecules. The calculated vertical transition energies are in reasonable agree- ment with the and theoretical" data. For example, for the T, state of ethene we obtain 4.61 eV, in good accordance with experiment (4.36 ev)." For the alAg and b 'El states we have obtained 0.84 (0.98) and 1.56 (1.63) eV, respectively (where the experimental values are given in parentheses). The energies of the vertical Herzberg transitions are in very good agreement with the best ab initioZ2 results: 5.91 (5.87), 6.07 (6.11) and 6.24 (6.25) eV for the c 'Z;, A' 3Au and A 3Z: states, respectively (where the vertical transition energiesz3 are given in parentheses). The only notable excep- tion is the singlet excited '(n,n*) state of ethene, S,. It is well known that it is necessary to take into account the Rydberg atomic orbitals (AOs) for such but for all other states the 6-31G* basis set employed is quite good for quanti- tative reproduction of the vertical transition energies.

All transitions between states in consideration, except the S,-So transition in the ethene moiety, are forbidden in the system of two noninteracting molecules. Intermolecular inter- action mixes the locally excited, CT and cooperative states, producing non-zero electric dipole probability for all of the formerly forbidden transitions. The collision-induced singlet-

singlet (S-S) transition moments are represented in Fig. 7 and those for the triplet-triplet (T-T) transitions are shown in Fig. 8.

SingletSinglet Transitions in the C2H,-0, System

At large distances (R 9 Re) the most intensive among the S-S transitions turns out to be the c'C;-a 'A, transition in molecular oxygen induced by collision with the So ground- state ethene. This is really one of the most prominent cases of strong emission from oxygen immersed into condensed media.28-30

c'Ci-a 'Ag Transition The c 'CL-a 'Ag transition in the complex with So ethene cor- responds to the 'A,-'B, transition in the C,, group and is polarized along the 0-0 bond (x axis), so it can borrow intensity from the Schumann-Runge system. The a 'Ap state is split into a lower component, 'A,, which is the antiphase combination of the two n,' closed shells, and an upper com- ponent, 'B,, which has an orbital part of the configuration wavefunction (zg,z, ng,J that is very similar to the triplet ground-state orbital f~nct ion. '~ The upper component, lB,, is active in the c 'Ci-a 'Ag transition, while the lower com- ponent, 'A,, is active in forming the blZl-alAe Noxon band. The c-a transition has been observed in absorption and emission;21 its oscillator strength in free 0, is of the order of ca. 13v21 The short-lived c -, a emission from 0, diluted in Ar crystals has been studied for different iso- topes and irradiation condition^.^^.^^ The radiative lifetime of the c 'C; state of 1 6 - 1 8 0 2 in matrices is supposed to be ca. 1 The oxygen complex with ground-state ethene roughly simulates 0, in an Ar matrix, because the nature of the perturbations which induce the transition probability is qualitatively similar. The calculated oscillator strength for the clZ;-alAg transition at the equilibrium distance of the upper state (Re = 3.5 A) is equal to 2.3 x which corre- sponds to the radiative lifetime, z, = 39 ps. At R = 3.8 A the oscillator strength for the c + a absorption is 7.8 x and z, = 0.11 ms. The value z, = 1.1 ms ( f= 7.9 x lo-') appears only at a very large distance, R = 4.6 A. The three to four orders of magnitude enhancement of the c-a transition prob- ability induced by intermolecular interaction with a dia- magnetic species could easily be understood by this calculation. That the observed z, value in Ar matrix is so large can thus be explained as follows. The Ar atoms situated on the opposite sides of the 0, molecule induce the c-a tran- sition moments in opposite directions. In a symmetric static crystal all contributions would cancel each other. The final c 'Ei-a ,Ag transition probability results from non- symmetrical distortion of the crystal and constitutes only a difference of the non-equal contributions from the opposite Ar atoms. Because the distances shorter than Re normally are available for the upper state, the largest contribution to the c 'Zi-a 'Ag transition probability (R = 3.2 A, the left side of the dissociation threshold in Fig. 2) could be used for estima- tion of the lower limit for the z, value in the studied C2H4 + 0, complex; it gives z, = 10 ps.

b 'Z; + a 'Ag Transition The b 'Z: 4 a 'Ag transition, which was firstly observed by Noxon,', is of pure quadrupole nature3,," in free 0, and has a transition probability, A = 0.0017 s-'. 21 In the colli- sion complex the b -, a transition is enhanced even at a large distance; at R = 4.8 A the Einstein coefficient, A = 0.13 s-', is much larger than in the free molecule. Because the equi- librium value (A = 4.6 s-') is of importance, the distances accessible at normal conditions, R = 3.6-3.5 A, would

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provide transition probabilities in the region A = 11.6-18.3 s- ', respectively. So the four-order enhancement is easily pre- dicted for this transition probability. Only one component of the a 'A, state ('A,) is active for the b 'X: -+ a 'Ag transition and provides z polarization. Transitions to the other com- ponents of the alAg state ('B,) are not forbidden (y polarization), but have much smaller probability. The tran- sition moments at R = 3.6 and 3.2 A are equal to 0.0014 and 0.0021 ea,, t respectively; the ratios of the transition prob- abilities for the (B,/A,) components at these distances 0.07 and 0.03, respectively. So we can neglect splitting of the a 'Ag state and consider the b ' E l + a 'A, transition intensity as being determined only by emission to the 'A, component.

Three to six orders of magnitude enhancement of the oxygen b + a transition probability has been observed in the gas phase,33 in rare-gas matrices34 and in organic solu- t i o n ~ . ~ ~ Ethene has not been studied as a perturber in these experiments; however, the calculated A, values are in rea- sonable qualitative agreement with observations for other gases.

Cooperatiue '(X 'Xg-, T,)-(a 'A,, So) Transition Quite unexpected behaviour is predicted for this transition probability. If this transition could be observable in emission it would correspond to cooperative phosphorescence, which is 7900 cm- red shifted in comparison with a 'normal' phos- phorescence of the hydrocarbon molecule. The transition moment is negligible at large distances (R > 4.6 A) and is less than that of the b3C: + a 'A, transition up to R = 3.5 8, (Fig. 7), but at smaller distances it rises rapidly; at R = 2.8 the cooperative transition moment is the largest among all S-S transitions in the collision complex. The radiative life- time at this point is 6 x lo-* s. Because the upper (X 'Xi, T,) state is unstable upon the initiation of the first (not final) step of photochemical oxygen addition to the C-C double bond, as follows from our preliminary discussion (Fig. 3), we cannot obtain any definite conclusion about the possibility of observation of cooperative phosphorescence. The observation is impossible probably because of the very strong com- petition with non-radiative quenching. We should remember the model character of the system with respect to real dyes with T,(nz*) phosphorescent states. From the present calcu- lations and from earlier semiempirical CI calculations' it follows that the '(X "Xi, T,) state potential is attractive up to the transition state of an intermediate biradical formation reaction (Rca x 1.7 A), where an adiabatic transition to the repulsive (a 'A,, So) state occurs. So the physical quenching of the T,(m*) phosphorescent state by molecular oxygen, which is usually accomplished by the intermediate a 'A, state prod~ction,'~ could proceed through such a 'quasichemical' path." Another mechanism of T,(nn*) state quenching is given by long-range (R x 3-4 A) dipole-dipole energy trans- fer from the interaction of collision-induced transition dipole moments [of the b 3X:-a 'Ag and '(X 'Xi, T,)-(a 'Ag, So) transitions], which is accomplished by b state gener- ation.13*" This process is very effective because of large values of these collision-induced transition moments (ca. twice as much in comparison with the previous calculation^'^" ').

On the other hand, observation of the absorption '(X 'Xi, T,) t (a 'A,, So) seems to be easily realized in flash photoly- sis experiments on oxygen-saturation solutions of dyes or even in the gas mixtures studied here. The oscillator strengths for this absorption at the normal accessible distances R = 3.6, 3.4 and 3.2 A, are equal to 2.3 x 7.8 x and

t 1 ea, z 8.478 36 x C m.

2.5 x lo-', respectively, so it should be possible to detect such weak absorptions by modern laser techniques achieving large concentrations of a'A, oxygen. In our studied system the transition energy of 3.7 eV is well separated from other absorptions in this region. For naphthalene, the transition energy would be 1.6 eV and this region is transparent for such observations in the absence of large concentrations of the T,(nn*) state. The blX: t X 3 X , transition is not enhanced by collision and has negligible absorbance. l3

Triplet-Triplet Transitions in the C,H,-O, System

The transitions in the triplet manifold (Fig. 8) of the collision complex can be divided into two groups, transitions from the ground state and transitions from the T,(nz*) ethene excited state which is in contact with the ground-state oxygen. The first group has intensity comparable with that of the S-S transitions, which connect the a 'A, oxygen state with other singlet excitations (note that the scale is different in Fig. 7 and 8). The second group has much more enhanced tran- sition probabilities.

Transition between Excited S , and T, States Special attention must be paid to the collision-induced (X 3Zi, S,) t (X 'Xi, T,) transition. Although the problem of competition between the absorption and non-radiative quen- ching rates cannot be solved now, we stress the huge rise in this transition probability. At the equilibrium distance of the upper exciplex state (Re = 2.7 A) the oscillator strength is 0.08, which is comparable with symmetry-allowed S-S tran- sitions. The (X 'Xi , s,)-(X 'Xg-, T,) transition moment rises so rapidly (0.1 and 0.41 ea, at R = 3.7 and 3.2 A, respectively) that it is impossible to show it on the same scale with other collision-induced transitions; only a part of it is shown in Fig. 8. Even at large distances (R = 4.2 A), where the energy perturbation of both states is negligible, the oscillator strength of the S,-T, transition is as large as 2.5 x lo-', which should be sufficient for observation. The upper and lower states are both of 'A, symmetry and therefore the tran- sition is z polarized (intermolecular direction). Its intensity cannot borrow from the locally excited z-z* transitions but is determined by charge-transfer perturbations. The possi- bility of observing this transition in emission from the ethene molecule is also questionable, because of rotation of the CH, groups, but it should be possible to find such an exciplex emission in aromatic molecules perturbed by oxygen, Picose- cond laser flash photolysis studies of an oxygen-saturated solution of n a ~ h t h a l e n e ~ ~ indicate an exciplex state in which the S, naphthalene combines with an O,(X 'Xi) molecule. Its very fast relaxation to the T, state36 could be understood in terms of our prediction of the unexpectedly strong electron dipole (X'X;, S,)-(X3Ci, T,) transition moment and its dipole-dipole interaction with intramolecular vibrations." This model of electronic relaxation as a dipoldipole energy transfer to intramolecular vibrations has been shown to be quite useful for analysis of non-radiative transitions in oxygen-containing systems.' 5*32

(a'b,, T,) 4 (X 'C;, T,) Emission The next intensive transition from the second group is the oxygen a-X transition induced by collision with the triplet- excited ethene. Its intensity increases rapidly and becomes larger than those of the first group at R > 3.8 A (Fig. 8). The transition has an oscillator strength equal to 6.8 x lo-' at an accessible distance, R = 3.2 A, which is large enough for detection. Because the upper state ('A,) is quite stable upon passing through the photochemical funnel (Fig. 4), we should

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expect the possibility of observing such a transition in emis- sion. The large collision-induced electric dipole moment of this transition could explain the very effective quenching of the a 'A, state by triplet-excited UHC molecules.15 The tran- sition has 'A,-'A, symmetry, it is z polarized and is of CT nature.

Absorption Observed by Evans Among the first group, the transition (X 'Xg-, T,) c (X 'Z;, So) is of great importance and determines the enhancement of the T, t So absorption by the 0, perturbation., The oscil- lator strengths for this absorption are calculated to be 4.5 x 7 x and 2.7 x at the normally acces- sible distances of 3.6, 3.4 and 3.2 A, respectively. The latter distance corresponds to a rather high pressure of oxygen in the 0, + C2H4 gas mixture and determines the more than four order of magnitude enhancement of the vertical T, t So absorption of pure ethene. Spin-orbit coupling calculations predict the oscillator strength for this transition to be of the order of lo-'. 37,38 Such enhancement is in qualitative agree- ment with the observations of Evans.2

The collision-induced absorption in the short wavelength region of the T, +So band, observed by Dijkgraff and Hoijtink7 and attributed to the cooperative (a ,Ag, T,) t (X 'Z;, S o ) transition, is slightly less intense (Fig. 8). This result is also in accordance with ob~ervation.~

Finally, we have a relatively large enhancement of the Herzberg I11 band (A' 'A,, S o ) + (X 'Xi, S o ) to account for. This is a 'A, + 'B, transition, polarized along the x axis. It is of a similar nature to the collision-induced c'C;-a'A, band, but the transition moment is higher (see Fig. 7 and 8). Evans observed this absorption in the 0,-C2H4 gas mixture and assigned it to the Herzberg I transition A 'C,f-X 'Xi. * Our calculations, however, do not support his assignment. The last transition is forbidden in the studied geometry of the complex. For other geometries of collision the Herzberg I transition probability is negligible in comparison with the Herzberg 111 collision-induced transition.' 3*14 This is in accordance with many findings of the UV-induced emission of oxygen in mat rice^^^-'^ and with the enhanced absorption A' 'Au t X 'X,- in pure oxygen at high pressure.2' Evans stressed that ethene enhances this absorption much more than oxygen itself. The oscillator strength of the Herzberg 111 band, (A' 3Au, So) t (X 'Xi, So), is very large in our calcu- lation. At the accessible distances in the ground state, 3.4 and 3.2 A, it is equal to 5 x respectively. The calculated radiative lifetime of the lower component ('A2) of the (A"A,, So) state of the complex at the equilibrium dis- tance (Re = 3 A) is equal to 3.5 ps. This is shorter than the value observed in an Ar matrix, z x 80 ps.28 The reason for this discrepancy is the same as discussed above for the c 'Xi state. The upper component of the (Ar3A,, So) state of the complex (3B,) cannot emit to the ground state (3B2); in this collision geometry the transition is dipole forbidden. The splitting between the components of the (A' 'A,, S o ) state of the complex is 523 cm-' at Re = 3 A; this is larger than the spin-orbit coupling (SOC) induced irregular splitting in the free oxygen molecule (149 cm-').13*39 So in the complex (and perhaps in the matrices) the orbital angular momentum of the A' 'A,, state is effectively quenched. The zero-field splitting (ZFS) of the orbitally non-degenerate 3A2 (A'3A,) state is estimated by the second-order SOC perturbation to be D = -63 cm-', E x 0, where the 0-0 bond direction (x- axis) is the main axis of the ZFS tensor. This means that the t, spin-sublevel is 42 cm-' higher in energy than the t, and t, spin-sublevels. In pure oxygen the lowest R = 3 component of the A' 'Au state is less active in the Herzberg I11 A 'Au t X3Z, band than the upper s2 = 1, 2 c o r n p ~ n e n t s , ' ~ * ~ ~

and

though the whole band is extremely weak (f< In matrices, the emission from the lowest t, and t, spin-sublevels must be observed, though all three spin-sublevels have equal transition probabilities (they are induced by the M,- independent intermolecular interaction, not by SOC).

We can also compare the transition energy shifts on going from the free molecule to the complex or to the Ar matrix. The peak positions of the c 'Ci-a 'A, transition in the Ar crystal shift only slightly to the red of the gas-phase values. The difference between the matrix and gas-phase peak posi- tion for the 5-0 transition of the c + a emission is 49 cm-', in cf. 108 cm- ' for the 0-5 transition of the A' 3Au -+ X 'Xi emission.28 For the C2H4-02 complex the calculated red shift for the vertical c +- a absorption (which could be com- pared with the quoted value) is 66 cm-'. For the correspond- ing A' 3Au + X transition, the calculated red shift, Av = v(R = 5 A) - v(R = 3 A), is 157 cm-', which is of the correct order of magnitude. The intensity of the S,-So tran- sition in ethene in contact with the 02(X3Xg-) molecule is notably diminished. A ca. 10% lower oscillator strength has been obtained at R = 3.4 A.23 This is in accordance with the experimental and semiempirical data. l 4

Conclusions CI calculations on the complex C,H,-O, give a good expla- nation for the strong T, + So and A' 3Au t X 'Z- transition probability enhancements observed by Evans.' We have changed the assignment of the last UV band (260 nm) from the tentative A'X; t X'Z; assignment of Evans. Co- operative absorptions of different types are predicted. The intermolecular potentials show negligible complex formation energies for the lower states, X 3Xg, a 'Ag and b 'c: of the system. The ethene excited 3(nn*) triplet state, T,, reacts with the triplet X oxygen state without barrier. In accordance with previous semiempirical studies," this means that the ','(X, T,) channels lead to a funnel produced by avoided crossings with the ground-state channels (X 'Xi, So and a 'A,, So) in the transition-state region for the biradical H,C'-CH,-O,' formation reaction. This can explain the 'quasichemical' mechanism of the T , state quenching, includ- ing energy transfer to the singlet oxygen (spin-catalysis).' '

A stable exciplex formed by interaction of the singlet excited '(nn*) ethene with the triplet ground-state oxygen is predicted. The exciplex is stabilized because of the large charge-transfer admixture. By the same reasoning, the singlet-triplet transition '(71n*)-'(zn*) in planar ethene in contact with 0 2 ( X 'Zg-) has an enormous probability, compa- rable with that of an allowed singlet-singlet transition. This fact can explain the very fast S, -, T, intersystem crossing in unsaturated hydrocarbons induced by molecular oxygen. (The non-radiative transition is treated by intramolecular energy transfer on vibrations through a collision-induced dipoleaipole interaction. ") These predictions are in accord- ance with recent subnanosecond studies of the naphthalene- oxygen e ~ c i p l e x . ~ ~

Using the studied system as a crude model for the inter- action of oxygen excited states with diamagnetic closed-shell species, the emission of the 0,-containing inert gas matrices can be explained qualitatively in terms of the b 'X; -, a 'Ag, c 'Xi + a lAg and A' 3Au -, X 'Zg- oxygen transitions. The enhancement can be described as a charge-transfer pertur- bation.

References 1 J. B. Birks, Photophysics of Aromatic Molecules, Wiley, New

York, 1970, pp. 301-371,492. 2 D. F. Evans, J . Chem. SOC., 1960,1735.

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Paper 4/00024B; Received 4th January 1994

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