J . Phj~s.Chem. 1986. 90, 1534-1537
1534
. > t
Ln
Y t
Mi 1
I
200
600
400
,
800
1000
nB
1200
illi
1400
1600
11
(cm-l)
Figure 2. Raman scattering by 2,2’-cyanine chloride excited by 568-nm radiation in a metallic silver colloidal suspension. Concentration of dye M and laser power ca. 100 mW. The intensity of the central ca. feature of the triplet corresponds to 194 121 counts/s.
result consider the argument, for large N, small in general. An expansion of the cotangent term yields ECot2 [ak/2(N k
4N’ 1 + l ) ] = -E----a2 /=1(21- 1 ) 2
(23)
where on the left-hand side of eq 2 3 the sum is over odd values of k from 1 to N, and on the right-hand side we have set k = (21 - 1). The value L on the right-hand side is ( N 1)/2 and can be extended to infinity without introduction of much error due to the small contribution of the cotangent term. The resultant sum has the value a2/8, giving eq 23 the approximate value of M/2. W e thus determine that the B” term acquires a factor of magnitude N reflecting the summation over exciton states. Upon squaring, as require_d by eq 14 to calculate Raman intensity, one gets the factor MN times other terms which are general in the as mentioned earlier, is the Raman intensity expression. number of scattering centers (Le., aggregates), and hence, Nhr represents the number of molecules that scatter radiation. The additional factor of N thus represents an inherent enhancement factor due to the formation of an aggregate containing N molecules.
+
m,
Other avenues for enhancement are suggested by eq 2 1. For example, a resonance is implicitly indicated when the laser frequency (uo) approaches the aggregate absorption at u,. Also, the energy separation between the first excited electronic state and another higher excited electron state, if sufficiently small, can technically lead to an enhancement. However, since the nearest electronic states to the normal a* excited state are usually u* states, it is required for a totally symmetric ground state, for an allowed coupling between the u and a states, that the symmetry species of the direct product r, X I?, contain the totally symmetric representation. This cannot be the case, and coupling between the first excited state and the u* states are not expected (for a totally symmetric ground) in this a p p r o x i m a t i ~ n .Thus, ~ ~ the summation over s in eq 21 excludes u-type states. For a nontotally symmetric ground state the above prohibition is not applicable and the energy spacing between first excited state and o-type states can appear in the denominator leading to a possible resonance in the enhancement. Raman scattering selection rules also are extracted easily from eq 21. For the various modes, within the harmonic oscillator approximation, we see that all Raman bands should be fundamentals. We also note, similar to the findings of A l b r e ~ h tthat ,~~ and [M,],,: can be zero if B”is to be neither h,,s“ nor [M,]o,lo nonzero. Thus states 1 and s must both be electric dipole allowed transitions. Further, based on the definition of Herzberg-Teller correction term h” as aH/dQ,, and assuming a totally symmetric ground state, the customary Raman selection rules result where the symmetry species of the allowed normal modes of vibration must belong to a t least one of the direct product species of the rr2.Q, rJz, or r12). Cartesian coordinates (specifically, rx2,rxq, Figures 1 and 2 show representative spectra of 2,2’-cyanine taken a t two excitation frequencies (488 and 568 nm). The J-aggregate absorption for this molecule occurs at ca. 570 nm and a significant increase of those Raman bands, earlier identified as associated with aggregate formation (see ref 18-20). is observed upon excitation under the aggregate envelope as opposed to excitation a t 488 nm. The resultant enhancement depends both on quenching of fluorescence and enhancement of scattering due to the presence of vibro-excitonic states. Detailed presentation of Raman excitation spectra and discussion in terms of the equations we have developed will await a later publication.
Acknowledgment. Funding for this research from the National Science Foundation under grants No. PRM-2811023 and RII8305241 is gratefully acknowledged.
Fourier Transform Infrared Spectra of the 2v2 and v 2 4- v4 Bands of PH, T. Tipton: J.-I. Choe, and S. G . Kukolich* Department of Chemistry, University of Arizona, Tucson, Arizona 85721 (Receiued: August 16, 1985)
The lowest-lying overtone ( 2 4 and combination (u2 + u4) bands of phosphine have been investigated for the first time with a Fourier transform spectrometer with 0.01-cm-* resolution. A least-squares fit which includes Coriolis coupling parameters has been performed on both bands simultaneously. The resulting constants fit 400 transitions with a standard deviation of 0.05 cm-I. Rotational parameters for the excited states and vibrational frequencies are obtained from the analysis.
Introduction Infrared spectra of PH, were obtained with the Fourier transform spectrometer constructed by Jim Brault and co-workers a t the National Solar Observatory a t Kitt Peak. Arizona.
The range from 1900 to 2500 cm-’ of the phosphine spectrum is expected to contain the 2% u2 + u4, 2u4, v i , and v3 bands. The V I and ~3 fundamentals are well-characterizedl but the remaining three bands have not been analyzed previously although they have
Department of Chemistry, University of Florida,
( 1 ) A. Baldacci, V . M. Devi, and K. N . Rao, J . Mol. Spectrosc., 81, 179-206 (1980).
‘Present address: Gainsville. FL.
0022-3654/86/2090-1534$0l.50/0
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 8, 1986 1535
FTIR Spectra of PH3 been observed.1i2 The present paper focuses on the two lowest-frequency bands of the above group: 2v2 and v2 + v4. The assignment of the 2v4 band has been postponed for the present because there is a high density of lines in the region where it is expected to be located. The four fundamental bands of phosphine have recently been analyzedii3by a model which accurately characterizes the Coriolis interactions between nearby E-type and A-type vibrational states. The v2 vibration is A-type symmetry and v4 is E-type symmetry. The same type of analysis is used here to fit the 2v2 and v2 v4 bands. Both the 2v2 and v 2 + v4 bands lie in a wavenumber range (1900-2100 cm-l) in which phosphine has been observed in the spectrum of Jupiter’s a t m o ~ p h e r e . ~A. ~discussion of the astrophysical importance of phosphine has been given by Larson et al., The investigation of overtone and combination bands of phosphine has been very limited. Maki et aL5 performed leastsquares fits on the 3v2 and 4v2 - v2 bands in an unsuccessful effort to detect inversion splitting. A subsequent theoretical study6 indicated that the inversion splitting is much too small to be measured by conventional infrared spectroscopy. Bernard and Oka’ measured the A1-A2 splittings in the 3v2, 4v2, and 4v2 - v 2 states but did not undertake any band-fitting analyses.
+
Experimental Section The experiment was performed with the Fourier transform spectrometer and 6-m multipass white cell at the National Solar Observatory a t Kitt Peak. The White cell was filled with approximately 0.1 torr of PH,. The spectrum was obtained broad band (1800-7000 cm-l) by using 64 passes of the infrared beam and 14 madded scans. The resolution was 0.01 cm-l for the region that was analyzed. Calibration was obtained from the 1-0 band of C O using the standard frequencies given by Guelachvili8 along with a +0.0004-cm-’ correction determined by Jennings and B r a ~ l t . ~ The spectrometer was equipped with a folded Michelson interferometer with a total internal path of approximately 12 m from input to output. The path inside the spectrometer was evacuated to 20 mtorr. The beamsplitter was CaF,, and the detector was InSb at liquid nitrogen temperature. The IR source was a 450-W GE dryer igniter functioning as a glower. The estimated signal-to-noise ratio was -500. The 10-m external path between the White cell and the spectrometer was purged with dry nitrogen evaporated from a liquid nitrogen dewar containing a 100-W heater. Impurity lines due to H 2 0 were observed in our spectra but did not cause problems in the ranges which we assigned. It was easy to distinguish the sharp lines in the cell and wide lines due to H 2 0 outside from the PH, lines. The line centers were determined by taking the average of the peak position (relative minimum) and the second derivative. The estimated precision of line frequency measurements was about f0.00004 cm-I by using the formula of half-width/(S/N X absorbance). The accuracy of line centers was estimated to be about f0.0005 cm-’. Results The data base consists of 400 transitions: 312 for the v2 v4 band and 88 for the much weaker 2v2 band. Both of these bands lie in a relatively sparse region of the phosphine spectrum. Ro-
+
(2) H. P. Larson, R. R. Treffers, and U. Fink, Astrophys. J., 211, 972-979 (1977). (3) G. Tarrago, M. Dang-Nhu, and A. Goldman, J . Mol. Specfrosc., 88, 311-322 (1981). (4) V . Kunde, R. Hanel, W. Maguire, D. Gautier, J. P. Baluteau, and A. Marten, Astrophys. J., 263, 443-467 (1982). (5) A. G. Maki, R. L. Sams, and W. B. Olson, J . Chem. Phys., 58, 4502-4512 (1973). (6) V . Spirko and D. Papousek, Mol. Phys., 36, 791-796 (1978). (7) P. Bernard and T. Oka, J . Mol. Spectrosc., 75, 181-196 (1979). (8) G . Guelachvili, J . Mol. Spectrosc., 75, 251-269 (1979). (9) D. E. Jennings and J. W. Brault, J . Mol. Spectrosc., 102, 265-272 (1983).
TABLE I: Spectroscopic Constants for the 2u2 and u2 + Phosphine constant VO(22) B(22) W2) o‘(22) dK(22) @(22) HJ(22,24) HJJK(22,24) LJJJK(22,24) r3(22,24) &‘:(22,24) 6 $
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. 1. J "Column headings are observed frequency, observed frequency - calculated frequency X IO4, I , symmetry, J and K for the upper state, and J and K for the lower state. The set of signs chosen for the coupling constants is arbitrary3 since these cannot be determined from the data. The abbreviations 22 and 24 are used to denote the 2u2 and u2 u4 states, respectively. A listing of all measured transitions is given in Table 11. The following information is provided for each line: (1) the observed frequency in cm-' units; (2) the difference between the observed and calculated frequencies in cm-' units; (3) the [-doubling constant; (4) the symmetry of the upper level; and ( 5 ) J f , K', J", and K". Blended (A,, A,) doublets are denoted by the abbreviation "A". The two frequencies that are marked with an asterisk were affected by an anomalous perturbation and were not used in the fit. The standard deviation of the fit (0.05 cm-'1 was found to be large compared to the estimated accuracy of the line measurements (0.0005 cm-I). This is to be expected since the 2u2 and
+
u2 + u4 states were nearby 2u4, u,, and u3 states. It should be noted that the inclusion of the Coriolis coupling parameters shown in eq 1-3 produces a dramatic improvement in the fits of the 2 v 2 and u2 + u4 states. Therefore, it appears that these two states interact much more with each other than with the 2u4, u , , and u3 states. A summary of selected data involving the u, and u4 modes of phosphine is given in Table 111. The vibrational dependence of the rotational C constants is found to be well-described by the formula' C, = (constant) - azc( u 2 + 1/2) - a 4 c ( ~+47,) (4)
On the other hand, the reported B constants are not accurately deperturbed and cannot be fit with a parameters.
1537
J . Phys. Chem. 1986, 90, 1537-1540 TABLE 111: Selected Constants (cm-') for the v2 and u4 Normal Modes of PHj" state B C VO ref ground 4.452418 3.919014 2 4.45018 4.2392 4.0354 4.46625 4.2973
y2
2v2 3~2 y4
u2
+ v4
3.94436 3.9687 3.9913 3.89550 3.9232
992.130 1972.55 2940.772 1118.313 2108.05
"Derived constants (cm-I): c~~~ = (-2.44 f 0.07) f 0.02) X
u :
2
present work 5 2
present work X
CY;
= (2.2
= 998.2 f 0.2: X22 = -6.0 f 0.1.
The vibrational frequencies for the v2 mode are well described by the relation GO(v2) = ~ 2 + X ~ 2 2~~ 2 ~2
spectra at higher pressure to get more data for these bands, especially the 2v2 band. Additional analysis of the present spectra may yield assignments for the 2v4 band, and thereby aid astronomers. It would also permit a simultaneous fit of the five-band system: 2v2,v2 + v4, 2v4, v l , and v 3 .
Acknowledgment. The support of the National Science Foundation is gratefully acknowledged. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. Technical assistance from Rob Hubbard and Jeremy Wagner was greatly appreciated. We thank J. W. Brault for the development of an outstanding spectrometer" and for helpful discussions on this research. Registry No. PH,, 7803-51-2.
The results obtained for aZC, adc,w:, and X 2 , are given in Table 111.
Conclusion The present study is intended as a preliminary analysis of the 2v2 and v2 u4 bands. It would be desirable to obtain additional
+
(17) J. W. Brault, 'Solar Fourier Transform Spectroscopy", 1978, Osseruarioni e Memorie dell' Osseruatorio Astrofisico di Arcetri, Proceedings of the JOSO Workshop, Vol. 106, G. Godoli, G. Noci, and A. Righini, Ed., pp 33-50.
Electron Spin Resonance in the 4EuState of Copper Porphine and the 'E, State of Platinum Porphine in n-Octane and n-Decane Crystals W. A. J. A. van der Peel,+ A. M. Nuijs, and J. H. van der Waals* Huygens Laboratorium, University of Leiden, Leiden, The Netherlands (Received: August 26, 1985)
The directions of the spin axes for the phosphorescent state of PtP (3E,) and CUP (4E,) incorporated in n-octane and n-decane single crystals are obtained. It is concluded that the Jahn-Teller active mode has b,, symmetry for CUP and b2gfor PtP. For CUP the EPR signals can be fitted with an effective Hamiltonian containing electron spin operators only. For PtP a larger Hamiltonian has to be used which is spanned by the six-dimensional spin-orbital basis of the 3E, state in the crystal field.
1. Introduction In a previous paper' we have shown that in the metastable triplet state of palladium porphine (PdP), with the loss of effective DZh symmetry, a host-dependent difference occurs in the orientation of the in-plane orbital axes (E, 7 ) determined in a phosphorescence Zeeman experiment, and the in-plane spin axes (&, qs) obtained by EPR. Recently the metastable luminescent states of two other porphines, namely copper porphine (CUP) and platinum porphine (PtP), have been studied by Zeeman ~ p e c t r o s c o p y . ~From ~ ~ these studies the directions of the orbital axes and estimates of the parameters in the spin Hamiltonian were obtained. Here we report an EPR study on these two porphines to (1) locate the spin axes, and by comparing these with the orbital axes, obtain an idea about the symmetry of the active mode and strength of the Jahn-Teller coupling; (2) determine some of the zero-field splitting parameters of the Hamiltonian with greater precision than previously determined from the Zeeman experiments. In discussing the multiplet structure of the metastable triplet and quartet states of metalloporphines it has become customary to start with a 2(2S 1)-dimensional spin-orbital basis spanning the 'E, or 4E, multiplet, with S = 1 for PtP3and S = 3/2 for The total spin of 'I2 in the metastable state of CUParises from the unpaired (3d) electron on the Cu nucleus, which has only a weak exchange interaction with the *-electron system of the porphine ring. As a result, the metastable triplet state yields a
+
Present address: Philips Research Laboratories, 5600 JA Eindhoven, The Netherlands.
0022-3654/86/2090-1537$01 .50/0
doublet and a q ~ a r t e > the t , ~ latter being the lowest in energy and separated from the doublet by a few hundred cm-1.294 The Hamiltonian accounting for the multiplet splitting in an external magnetic field B is of the form The term ?YCF represents the crystal field splitting, 7fss the spinspin interaction, 7fLs the spin-orbit interaction, and the last two terms the Zeeman interaction. Besides the familiar spin-Zeeman interaction 7fBSthere is an orbital Zeeman interaction 7fBLthat describes the coupling of the external field to the magnetic moment which arises from the orbital angular momentum A. When the two orbital wave functions of the 2SflEustate are written in real form as It) and 17) (as in the previous paper'), then the nonvanishing matrix elements of P t B L are off-diagonal in these orbital functions and diagonal in the spin Here pBis the Bohr magneton and B, the component of the applied ~
~~
~~~
~~
~~
~
~
~
~~
(1) van der Poel, W. A. J. A,; Nuijs, A. M.; Noort, M.; van der Waals, J. H. J . Phys. Chem. 1982, 86, 5191. (2) van Dorp, W. G.; Canters, G. W.; van der Waals, J. H. Chem. Phys. Left. 1975, 35, 450. van Dijk, N.; Noort, M.; van der Waals, J. H. Mol. Phys. 1981, 44, 891. (3) van Dijk, N.; Noort, M.: Volker, S.;Canters, G. W.; van der Waals, J. H. Chem. Phys. Lett. 1980, 71, 415. (4) Ake, R. L.; Gouterman, M. Theor. Chim.Acta 1969, IS, 20.
0 1986 American Chemical Society
