J. Phys. Chem. 1983, 87, 3829-3836
pled to CH motions of the methylenic groups in the cyclobutene ring. Thus, a more likely explanation for the result is (2) that energy initially introduced into the cyclobutene ring by overtone excitation is transferred between the two rings before any significant amount of reaction (> k,'(O-O), k,'(O-O)
(1)
for the 3Bluassignment, and
k,'(O-O)
>> k,'(O-0), k,'(O-O)
essence of this model is outlined as follows: (i) The pure spin Born-Oppenheimer adiabatic wave functions20 are taken as a basis set, and only the first term in the expansion of the resolvent operator is considered. Thus, we consider only the spin-orbit coupling between the initial and final vibronic states. (ii) This matrix element of the spin-orbit coupling is expanded into the Herzberg-Teller series. (iii) In this expansion, only those terms which involve one-center spin-orbit coupling are retained. Once all plausible mechanisms are selected according to the above procedures, the following criteria are used in order to select the important mechanisms. First, the most important criterion is the order of the Herzberg-Teller expansion. That is, the mechanisms starting from the zeroth-order term are more important than the mechanisms starting from the first-order term regardless of the other factors. Similarly, the first-order term is more important than the second-order term. Second, comparison among the mechanisms of the same order in the Herzberg-Teller expansion may be made in view of the energy denominator criterion. The important mechanisms selected according to the above criteria are as follows for the two alternative assignments: (a)
3 ~ i uassignment
T,:
second order in the Herzberg-Teller expansion
T,
(19) Metz, F.; Friedrich, S.;Hohlneicher, G . Chem. Phys. Lett. 1972, 16, 353. Metz, F. Ibid. 1973, 22, 186.
( II II*)
IB 3 u( fl r*
' A (G )
3 B l u ( ~ ~ * ) l b 3 E Z 0 (* n)--~ (01A p ( G ) T,:
3 ~ 1 u ( I I I I * ) (- 1 ) I A , ( ~ ~ * ) & ' A , ( G )
B
3B l u ( r r*)
,
(oII*) 2' A ( G 1
(b)
3B2,
T,:
second order i n !he Herzberg-Teller expansion
Tu:
3BZu(rr*)-!!-!-
(2)
for the 3B2uassignment. That is, in either assignment, the radiative rate constant of one sublevel emission greatly surpasses those of the other two sublevel emissions. The experimental results conform to either of the assignments, and the qualitative analysis discussed above cannot discriminate between the two alternative assignments. We shall consequently examine them in a somewhat more quantitative manner. We compare the mechanisms of the most radiative sublevel emissions in the two assignments. The mechanism of the T, emission from the 3Blustate involves the perturbation of na* states. On the other hand, the mechanism of the T, emission from the 3B, state involves only UT*perturbing states, and in this respect the mechanism is identical with that of hydrocarbon phosphorescence. In view of the fact that phenazine phosphoresces more intensely than anthracene, the contribution of na* perturbing states is quite clear. Thus, the 3Bluassignment is more likely. Further support of this assignment may be obtained from the analysis of the nonradiative decay rate constants. We have shown in our previous papers1-8that the nonradiative transitions from the triplet sublevels are quite satisfactorily predicted, at least qualitatively, by a simple theoretical model originally proposed by Metz.lg The
: 3B
3B2,
T,:
assignment
(WII*)
3B2,(rr*)"'
'A,(nr*)*'A,(G)
vlb 3 E 2 q ( f l ~ )""A, *
( G)
1E3u(or*)A1A9(G)
3 ~ 2 (us r r * ) * 3 ~ l q ( o n
* 1- ( 1 )
1A , ( G )
Thus, in either of the assignments, the nonradiative decay rate constants are expected to be in the order of kyn' > 12,"' > k,"'. It might therefore appear, a t first glance, that analysis of the nonradiative decay rate constants is not helpful to the assignment. However, if we compare the mechanisms of radiative and nonradiative transitions simultaneously, the ambiguity is removed in the following manner. In the 3Bluassignment the sublevel which decays most efficiently in the radiative path should decay most efficiently also in the nonradiative path. In the 3B2uassignment, on the other hand, a sublevel which decays less efficiently in the radiative path should decay most efficiently in the nonradiative path. The experimental results shown in Table I are in conformity with the 3Bluassignment. This conclusion agrees with the assignment of Clarke and Hochstrasser21based on their Zeeman analysis. D. Identification of the Sublevels. Once the lowest triplet state is identified as 3B1u(aa*),then it is straightforwardly concluded that the sublevel which decays most efficiently in both the radiative and nonradiative transi(20) For notation, see: Azumi, T.; Matsuzaki, K. Photochem. Photobiol. 1977, 25, 315. (21) Clarke, R. H.; Hochstrasser, R. M. J . Chem. Phys. 1967,47, 1915.
3834
The Journal of Physical Chemistry, Vol. 87,No. 20, 1983
Asano et al.
TABLE 11: Radiative Rate Constant Ratios Determined by the MIDP Method for Individual Vibronic Bands in the Site I Phosphorescence of Phenazine in a Phenanthrene Host vibrational assignment
band
0-0 0-248 0-285 0-411 0-491 0-608 0-714 0-872 0-904
b,,
h,, ag
b,,, b,,(248) a, b,, b, ? ag,311) t big(491)
X
kxr/kv" 0.0016 ?: 0.0004 0.052 i 0.017 0.019 2 0.008 0.0020 i 0.0010 2 0.0068 i- 0.0030 0.0036 i 0.0020 0.023 i 0.011 0.035 f 0.024 0.013 i 0.007
kzrlkvr 0.019 i 0.010 0.037 i 0.050 0.043 i 0.030 0.024 F 0.015 0.048 i- 0.030 0.019 i 0.010 0.039 i 0.020 0.18 t 0.11 0.046 i 0.030
tions (i.e., the sublevel tentatively referred to as T,) should be T,. The assignments of the other sublevels are somewhat complicated. Comparison of the radiative rate constants does not yield unambiguous assignments. For, in this case, one has to compare the mechanism involving three-center spin-orbit coupling with the mechanism involving the breakdown of the selection rule (that is, intensity gain due to slight molecular distortion). It is not, however, a priori clear which of the mechanisms is more important. We then examine the nonradiative decays. As is discussed above, the nonradiative decay rate constant should be the smallest for the T, sublevel in either of the assignments. Consequently, it is most reasonable to identify T, as T,. The remaining sublevel T, is then automatically assigned as T,. It has been proved, in this way, that the zero-field experiments alone lead to the assignments that are identical with those of Grivet and Lhoste.ls The final conclusion is also supported by the theoretical expectation that the out-of-plane sublevel (i.e., T,) should be energetically far apart from the two in-plane sublevels. The final assignments are indicated also in Table I. E. Radiative Rate Constant Ratios for Individual Vibronic Bands and the Sublevel Phosphorescence Spectra. The radiative rate constant ratios determined for individual vibronic bands by the MIDP method are shown in Table 11. The experimental results are reasonably accurate for the k,'/ky' ratios. However, the accuracy is somewhat less for the k;/k,' ratios; this is due to the small population of the T, sublevel and to the low microwave power a t frequencies below 1 GHz. As Table I1 shows, of the three radiative rate constants, k,' is significantly larger than the others for any vibronic band. Therefore, the phosphorescence spectrum obtained by the ordinary method may essentially be regarded as the T, spectrum. The AM-PMDR spectrum shown in Figure 3b represents the dispersion of k;-k,' with respect to wavelength. Since k,' is significantly smaller than k,' at any vibronic bands, the spectrum may be regarded as the T, spectrum of site I in good approximation. The T, spectrum may also be obtained if the excitaton is made by a pulsed light, since, by doing so, practically only the T, sublevel is populated. The spectrum thus obtained is identical with the AMPMDR spectrum except that some bands due to site I1 are overlapped. With the aid of the T, phosphorescence specrum thus obtained and the radiative rate constant ratios, the T, and T, spectra are constructed. By this procedure, however, only the peak heights of the vibronic bands are determined, and thus band shapes are unknown. The sublevel phosphorescence spectra thus determined are schematically shown in Figure 5, where the relative radiative rate con-
Flgure 5. Schematic representation of the sublevel phosphorescence spectra of phenazine in phenanthrene determined at 1.2 K. The ordinate represents the relative radiative rate constants of individual vibronic bands with respect to the 0-0 band of'the T, phosphorescence. The vibrational frequencies and the assignments are also indicated. Only the spectra for site I emission are shown.
stants of vibronic bands are represented by vertical bars. In terms of the relative radiative rate constants of all vibronic bands, we are able to calculate the radiative rate constant ratios for the entire band envelope. The results are as follows:
Ck,'(O-v)/Ck,'(O-v)
= 0.004
(3)
Y
Y
Ck,'(O-v) / Ck,'(O-u) = 0.02 U
(4)
U
These ratios should be regarded as the radiative rate constant ratios determined for unmonochromatized phosphorescence providing the sensitivity of the detector is wavelength independent. In reality, the sensitivity of all photomultiplier tubes is wavelength dependent. However, the above ratios should roughly correspond t o the ratios determined by Antheunis et a1.I6 The kzr/k3' ratio of 0.02 reported by these authors is close to the ratio determined above. However, their k,'/k; ratio of 0.02 significantly differs from the ratio determined above. The source of the discrepancy is unknown at present. We surmise that the large ratio determined by Antheunis et al. may likely be connected to an adverse effect in a biphenyl host as its complicated spectrum (Figure 1) might suggest. F. Analysis of t h e Mechanisms of t h e Radiative Transitions for Vibronic Bands as a Guide to Vibrational Assignments. In this section, we analyze the mechanisms of radiative transitions for vibronic bands. By doing so we try to examine if such analysis leads us to correct vibrational assignments. The radiative rate constants for vibronic bands may be expressed in terms of the second-order perturbation theory in which spin-orbit coupling and vibronic coupling are treated as perturbation. In examining the mechanisms we made the following assumptions. First, the TI state is assumed to be expressed as the single configuration in which an electron is promoted from a BZgT molecular orbital to a BBuT* molecular orbital. Namely, configurational mixing to TI is neglected. Second, spin-orbit coupling and vibronic coupling operators are assumed to be expressed as the sum of one-electron operators. We then adopt the criteria that we have discussed in section 3C. The important mechanisms thus selected are shown in Figure 6 for vibronic bands involving gerade
Phosphorescent Spin Sublevels of Phenazine
I
Tx
The Journal of Physical Chemistry, Vol. 87, No. 20, 1983 3835
1
TY
I
~~
Tz forbidden
b2g
I
forbidden
Flgure 6. Mechanisms of radiative transitions for vibronic bands. The bands are classified according to the sublevels and symmetries of the vibrational species. The coupling is Indicated by the following notations: (1) spin-orbit coupllng involving one-center integrals; (3) spin-orbit coupling involving three-center integrals; (vib) vibronic coupling; (-) dipole coupling. 'A,(G) denotes the ground state. For further details see ref 5.
vibrations. Coupling of ungerade vibrations is not considered since it does not provide allowded character. In exactly the same manner as we have discussed for the 0-0 band, we can estimate the radiative rate constants for individual types of vibronic bands which are classified according to the symmetries of the vibrational species. By examining Figure 6 in rows, we predict that the radiative rate constants are in the following orders: ag: k,' >> kXr,k,' (5)
> k,' > k,' b2,: k,' > k,' > k,' blg: k,'
b3g: k,'
> k,', k,'
(6)
in this respect it is like an ag band. At the same time, however, the band appears quite intensely also in the T, spectrum, and in this respect it is more like a big band. The observed kx'/k,' ratio is larger than the ratios of ag bands and is smaller than those of the blg bands. These observations lead us to conclude that the band is composed of two energetically close and unseparated bands, one of which being an ap band and the other being a blg band. We next try to estimate the contribution of each component. We assume that the radiative rate constant ratio for the ag component is the same as that of the 0-0 band. That is
(7) (8)
kx'(ag)/k,'(ag) = 0.0016
(12)
Similarly, we assume that the ratio for the blg component is identical with that of the 0-774-cm-' blg band. That is
For all vibronic bands except those involving b, vibrations, k,' is expected to be the largest. The k,'/k; and k,'/k,' ratios, however, should be smaller in ap bands as compared with blg and b, bands. We next examine the mechanisms in Figure 6 in columns. For individual sublevel spectra, the radiative rate constants are expected to be in the following manner: (9) T,: bl, > ag > hg,hg
The experimentally determined ratio should be expressed as
T,: ag > big, bZg > hg
(10)
k,'(ag)/kXr(blg)= 0.22
(15)
(11)
kyr(ag)/kyr(blg) = 3.1
(16)
T,: big, b2g
> agr bg
We are now prepared to examine individual vibronic bands. First, we examine the 0-411- and 0-608-~m-~ bands. These bands appear quite intensely in the T, spectrum. Further, the k;/k,' and k:/k; ratios are BS small as those of the 0-0 band. These observations clearly indicate that the bands are ascribed to the coupling of ag vibrations. We next examine the 0-248- and 0-774-cm-' bands. They appear quite intensely in the T, spectrum. the kXT/k,' and kL'/k,' ratios are larger than those of the 0-0 band. In view of these observations we assign the bands as due to blg vibrations. The 0-285-cm-l band is characterized by the relatively large k,T/k,' and k,'/k,' ratios as compared to the 0-0 band. In this respect the band should be ascribed to either blg or b2g vibration. The intensity of the band in the T, spectrum is smaller than those of the two blg bands assigned above. From these observations, the band is more likely to be attributed to a b2gvibration. The behavior of the 0-491-cm-' band is somewhat odd. The band appears quite intensity in the Tyspectrum, and
kx'(big)/k,'(bIg) = 0.023
[k,'(ag)
+ k,'(b1,)1/[k,'(ag)
+ ky'(blg)l = 0.0068
(13)
(14)
These expressions yield the following results:
Thus, in the T, spectrum, more than 4 / 5 of the intensity comes from the blg component. In the T!, spectrum, on the other hand, nearly 3/4 of the intensity is due to the ag component. A question remains as to the source of the component. We surmise that two quanta of the 248-cm blg vibrations are responsible for this band. The 0-904-cm-' band is assigned as the combinational bands involving the 491-cm-' bl, and 411-cm-' ag vibrations. No band from other sources appears to be overlapped. As is expected, the radiative rate constant ratio is close to those of the other b,, bands. Finally, we examine the 0-872-cm-l band. The kXr/kyT ratio is close to those of blg and bZgbands. Further, the intensity in the T, spectrum is small. Thus, at first glance, the band appears to be due to a b2gvibration. However, we note that the k,'/k,' ratio is significantly larger than the ratios of other bands. The b2gassignment is therefore somewhat questionable. The band for which we may expect a large k,'/k,' ratio is only a b, band. However, we have estimated in the above discussion that k,' should be
3
3836 The Journal of Physical Chemistry, Vol. 87, No. 20, 1983
smaller than k;. That the k;/ k; ratio is somewhat smaller than unity is not easily understood. In view of this odd feature we reexamine the radiative mechanisms of. b3g bands. In the above discussion we have assumed that the "forbidden" Tyemission should be less emissive than the T, emission. However, the mechanism of the T, emission is associated with large enegy denominators and small transition moment, which diminish the effect of one-center spin-orbit coupling. Therefore, k,' may well be larger than kzr. Especially, if the molecule is distorted along a b3 coordinate, the originally forbidden Ty emission should gain significant intensity. In view of the above discussion we attribute the 0-872-cm-' band to a b,, vibration rather than to a b, vibration. Ikegami et al.15 assigned this band as a combinational band involving the 248-cm-' bl, vibration and the 608-cm-' a, vibration. However, if that be the case, the radiative rate constant ratio would have to be identical with those of the 0-248-cm-' band. The k Z r / k ; ratios are greatly different from these bands. Our b, assignment is in accord with the vibrational assignment given by Durnick and Wait22in terms of Raman spectroscopy. We have thus completed the analysis of the vibrational structures. The results of our analysis are also indicated in Figure 5 and in Table 11. G. Comparison between One-Center and Three-Center Spin-Orbit Coupling. In the above discussion, we have always assumed that the mechanism involving one-center spin-orbit coupling is significantly more important than the mechanism involving three-center spin-orbit coupling. We now try to examine the validity of this assumption by analyzing the radiative rate constants for the T, and T, phosphorescence at the 0-0band. As is discussed above, the 0-0 band of the T, emission is due to a mechanism involving the three-center spin-orbit coupling between 3(r7r*) and '(m*), whereas the 0-0 band of the T4.emission is due to a mechanism involving one-center spin-orbit coupling between 3(x7r*) and '(n7r*). Thus, in exactly the same manner as we have examined for quinoxaline, we are able to estimate the relative importance of the one-center to three-center spin-orbit coupling. The relevant, radiative rate constant ratio is expressed as
- =I
k,'(O-O) k,'(O-O)
(3Biu(7r7r*)lH,,l'B2u(7rr*))
X ( 3Blu(~~*)JH,,11B3u(n7r*) )
( 'B2,,(.rr.lr*)lerl'Ag(G))
ll
E['B,,,(nr*)] - E[3B1u(7rr*)]
('B,,(nr*)lerl'A,(G) ) E['Bz,,(*T*)I - E[3B1u(***)l = 0.0016
(17)
where E denotes the state energy. In the above expression we assume that only one perturbing state is important in individual emission. In terms of the energies and the transition dipole moments pertaining to the 'BzU(a**)and lB,,(na*) states given by Perkampus and K ~ r t U mand ~~ H o c h s t r a s ~ e rrespectively, ,~~ we obtain
Asano et al.
Namely, the sum of more than lo3 three-center terms amounts to only 0.004 of the sum of two one-center terms. Thus, the contribution from three-center spin-orbit coupling may well be neglected to a good approximation. The three-center to one-center ratio of 0.004 determined above is smaller than the ratio obtained for quinoxaline by 1 order of magnitude. Since the ratio is not expected to vary so significantly with molecules, either one of the results should be erroneous. In view of the expectation that slight molecular deformation to nonplanarity introduces a one-center term in the 3(7r7r*)-'(7r7r*) spin-orbit coupling, the larger three-center to one-center ratio found for quinoxaline is likely to be due to such geometrical distortion. The ratio determined in this paper is regarded as more authentic for planar molecules. Further, the above analysis suggests that the planarity of the phenazine molecule is preserved quite rigorously. H. Molecular Distortion in the Triplet State. As is discussed above, the 0-0 band of the T,spectrum, which is expected to be forbidden in the D2h point group, is observed to some extent. Similar breakdown of the selection rule is observed also for b, bands in the T, spectrum and b3, bands in the Tyspectrum. These observations suggest that the molecule in the triplet state is distorted from the D2h symmetry. We now try to determine along which direction the distortion takes place. In the preceding section, we have suggested that the planarity of the molecule is preserved quite rigorously. Therefore, the distortion should take place only along an in-plane vibrational coordinate. Since all the vibronic bands are satisfactorily interpreted in terms of gerade vibrations, distortion along an ungerade vibrational coordinate is unlikely. On these grounds we conclude that the molecule is distorted along a b3g coordinate. This conclusion well accounts for the unexpectedly large radiative rate constant for the 0-872 cm-' in the Tyspectrum. We finally try to understand what makes the molecule distorted along a bSgcoordinate. In order to estimate the effect of pseudo-Jahn-Teller interaction, we try to determine the locations of upper triplet states. The second triplet state, 3B2u(7r7r*),has not been observed experimentally. We have therefore made a CNDO calculation which was developed for the aid of predicting excited-state energies by Hayashi and Nakajima.25 In this calculation, the 3 B 2 u ( ~state ~ * ) is predicted to lie only -300 cm-' above the lowest triplet state, 3 B l u ( ~ ~ *Thus, ). the pseudoJahn-Teller distortion along a bSgcoordinate is expected to take place quite efficiently. The third project state, ,B3"(n7r*),on the other hand, is predicted to lie -5000 cm-' above T,; this prediction agrees with the experimental26 energy gap. In view of the large energy gap, the distortion along the out-of-plane b2gcoordinate is unlikely to take place. Our conclusion is thus well accounted for in terms of the available knowledge on the upper triplet state energies. Acknowledgment. We thank Professors T. Nakajima, M. Ito, and N. Mikami of this Department for stimulating discussions. Registry No. Phenazine, 92-82-0; phenanthrene, 85-01-8. ~~~
(22) Durnick, T. J.; Wait, S. C., Jr. J.Mol. Spectrosc. 1972, 42, 211. (23) Perkampus, H.H.; Kortum, K. 2. Phys. Chem. (Frankfurt am Main) 1967, 56, 73.
(24) Hochstrasser, R. M. J . Chem. Phys. 1962, 36, 1808. (25) Hayashi, T.; Nakajima, T. Bull. Chem. SOC.Jpn. 1975, 48, 980. The parameters for the nitrogen atom were determined by Hayashi (Dissertation, 1975) as follows: Us, = -62.0 eV, Up, = -60.0 eV, and BAo = 23 eV. (26) Mikami, N.; Ito, M. Bull. Chem. SOC.J p n . 1972, 45, 992.
