J. Phys. Chem. 1995,99, 10159-10165
10159
Analysis of the Intervalence Band in Lutetium Bis(phtha1ocyanine): The System Is Delocalized Zbigniew Gasyna and Paul N. Schatz” Chemistry Department, University of Virginia, Charlottesville, Virginia 22901
Michael E. Boyle* Materials Chemistry Branch, Code 6125, Naval Research Laboratory, Washington, DC 20375-5342 Received: January 11, 1995; In Final Form: April 4, 1999’
The intervalence band (IVB) of LuPc2 has been measured over the temperature range 268-328 K in CDCl3 solution and at 11 K isolated in an Ar matrix. The IVB shows resolved structure and a pronounced temperature dependence in CDC13 solution. The various properties of the IVB are accounted for quite well if it is assumed that the system involves two conformers in equilibrium with an associated AH“ value of about 1000 cm-I. One conformer is assumed to have DM symmetry, and the other is assumed to be slightly distorted. Piepho’s MO treatment of mixed-valence systems is generalized to the case of an unsymmetrical system. The parameters extracted from fits of the IVB clearly indicate that LuPc2 is a delocalized system, i.e., “ P C ~ ~ ~ - ( L U ~ + ) P C ~ . ~ - ” , not “Pc2-(Lu3+)Pc*’-, Pce’-(Lu3+)Pc2-”.
I. Introduction In a recent paper,’ we have analyzed the optical absorption and MCD spectra of LuPc2 isolated in Ar matrices (LuPcz/Ar) in the region between *5OOO and 60 OOO cm-I. This compound is the prototype for the lanthanide bis(phtha1ocyanine)s (LnPc2) which are an unusual class of compounds that exhibit potentially useful electrochromic, semiconducting, and third-order nonlinear optical properties.’ They are sandwich-type compounds with the lanthanide (M3+) 8-fold coordinated to the isoindole nitrogens of the two Pc rings which are staggered at a 5 O to each other (Figure 1). They are also stable free radical systems with formal charges on the two rings which may be represented as Pc2- and Pc’l-. These compounds are examples of organic mixed-valence systems. Thus, if the system were completely localized, one Pc ring would always be Pc2- and the other would always be Pc’l-. We might then represent the molecule as being either Pc2-(Ln3+)Pc’l- or Pc’I-(Ln3+)Pc2-, the electron hole being respectively on the right or left Pc ring. When inter-ring electronic coupling is turned on, a degree of delocalization appears which directly reflects the competition between the interring electronic coupling and the vibronic (electron-phonon) coupling of the electron hole to the Pc’l- ring. Thus, if we hold the nuclei fixed, it requires energy to move the hole off the Pc*l- ring toward the Pc2- ring because the Pc’I- equilibrium bond lengths “want” to readjust to the Pc2- equilibrium values, and vice versa. As the electronic coupling is increased, this process is increasingly facilitated, and eventually the hole spontaneously delocalizes to an intermediate state with both rings electronically and geometrically equivalent. The system is then delocalized and might be represented as PC~.~-,PC’.~-. We have offered detailed assignments’ of the main absorption bands of LuPc2 with particular emphasis on the Q band at 15 600 cm-I, which is quite well resolved at low temperatures. Our interpretation of the spectra supports the view that the LuPc2 system is delocalized since there are a number of distinctive features that cannot be associated with either a Pc’l- or Pc2moiety. Nevertheless, the conclusion that the system is delocalized is indirect and not totally satisfying. Certainly no @
Abstract published in Advance ACS Abstracts, June 1, 1995.
Figure 1. Schematic rendering of the LuPq molecule based on X-ray data.14 The structure of the closely related YPc2 compound in an unsolvated crystal is reported to have exact Da symmetry.“
quantitative statement can be made about the degree of delocalizaiton from these optical spectra alone. In the present paper, we conclude from a direct analysis of the intervalence band (IVB)of LuPc2 in the region between -5000 and 10 OOO cm-I that the system involves an equilibrium between two conformers, both of which are indeed delocalized, though probably to somewhat different extents.
II. Experimental Section Lutetium bis(phtha1ocyanine) (LuPc2) was synthesized by a modified procedure of Kirin et aL2 as reported previously.1 Solutions of LuPc;! were prepared in CDC13 to avoid strong solvent absorption in the near-infrared region (CH stretching combinations and overtones) which is typical for common protonated solvents such as CHC13. The sample was held in a water-jacketed 1 cm cuvette, and the temperature was controlled to fO.1 K using a circulating water-ethylene glycol bath. The procedure for rare-gas matrix deposition has been described previ~usly.~The LuPc2 was sublimed at -450 “C and codeposited with argon onto a cryogenically cooled (-1 1 K) sapphire window mounted in a closed-cycle helium refrigerator (CTICryogenics). Absorption spectra were collected on a Cary 2415 Whishear-IR absorption spectrophotometer. Typical sample absorbances in CDCl3 were between 0.6 and 1.O at the maximum
0022-3654/95/2099- 10159$09.Oo/O 0 1995 American Chemical Society
10160 J. Phys. Chem., Vol. 99, No. 25, 1995
Gasyna et al. occupied by three electrons. Thus our electronic basis states are
with (neglecting overlap),’
6000
7000
8000
9000
laxX,
Energy i c m ‘
where al,(A) designates the D4h HOMO on isolated Pc ring A, etc. The original PKS m ~ d e lemployed ~,~ a single vibrational coordinate (Q-), the antisymmetric combination of a totally symmetric breathing coordinate on each of the mixed-valent centers. It was later recognized by Ondrechen and coworkers9-’ I and by Piepho6.l2that other coordinates become increasingly and ultimately of dominant importance as a system becomes increasingly delocalized. Piepho shows6 that (at least) two vibrational coordinates are expected to be important, namely.
Figure 2. (a) LuPc: intervalence band in CDCI3 solution between 268 and 328 K. (b) LUPCZ intervalence band in an Ar matrix at 11 K with 300 K CDCh solution spectrum for comparison.
of the LuPc2 IVB at -1400 nm, but only much lower absorbances were achievable in Ar (Figure 2b). 111. Results
The near-infrared spectrum of LuPcz in CDC13 at temperatures between 268 and 328 K is shown in Figure 2a; the same band isolated in an Ar matrix at 11 K is presented in Figure 2b (right ordinate scale) along with the same band in CDCI3 at 300 K (left ordinate scale) for comparison. Notable are at least two distinct maxima in the band contour, and truly striking is the pronounced and reversible temperature dependence in CDC13. The integrated band intensity increases markedly with decreasing temperature. Clearly, any acceptable analysis must reasonably account for these observations.
IV. Theoretical Model The general procedure in analyzing an intervalence band is to choose an appropriate theoretical model, make a “best fit” of the band by adjusting parameters, and then use these parameters to deduce the degree of delocalization of the system. We shall follow such a procedure here. However, we will find that our data cannot be fit on the basis of a single intervalence band. Therefore, following the lead of Bocian et al.?,s who studied related porphyrin systems, we postulate that LuPc2 exists in solution in the form of two “conformers” in equilibrium. One conformer is assumed to be a symmetrical mixed-valence dimer (point group D d d , the A B case), and the other conformer is assumed to be slightly distorted (A IB). We follow the MO approach of Piepho6 which we first outline briefly as a prelude to extending it to the unsymmetrical case (A IB). 1. The Starting Model: A = B. We consider a mixedvalence “dimer” containing two “monomeric” units designated A and B. In the symmetrical case, A = B; in the unsymmetrical case, A & B. Following Piepho,6 we consider only the HOMO of each monomer unit. As discussed previously,’ their interaction gives rise to a bonding (irrep bl of D 4 d ) and antibonding (irrep a2 of D 4 d ) MO separated in energy by A and
QA and QB are totally symmetric breathing coordinates of the respective monomers, and QABmeasures the distance between the monomers. For a strongly localized system, vibronic interaction is dominated by Q!? since an optical (vertical) excitation moves an electron from one center to the other, thus exciting Q?, whereas for a strongly delocalized system the vibronic interaction is dominated by QAB,since an optical excitation moves an electron from a bonding to an antibonding orbital, thus exciting QAB. Thus, though the original PKS treatment7 is formally applicable over the entire range of localizatioddelocalization, it becomes increasingly inadequate as systems become more delocalized. (This defect can in fact be removed by expanding the electronic interaction in a power series in QABin which case the PKS model becomes precisely equivalent to the Piepho two-mode m0de1.I~ Putting it another way, when both coordinates are included, the valence bond (PKS) and MO (Piepho) treatments are equivalent). In our application to LuPc2, we will assign no explicit form to Q l ; we only require that it be invariant to the interchange symmetry operation: A B, B A. The total molecular Hamiltonian of the system is written
- -
with
where r and Q respectively designate electronic and massweighted nuclear coordinates, TN(Q)designates the nuclear kinetic energy operator, and Hei includes all other terms. Our zero-order electronic functions (r&(r, Qo) E 4:) satisfy the equation fieI(r3
Qd$Y = q(Qo)$P
(6)
at the ground state nuclear configuration Qo = 0. Our goal is
Intervalence Band in LuPc2
J. Phys. Chem., Vol. 99, No. 25, 1995 10161
to solve the dynamic Schrodinger equation f i ~ v = k Ekvk
(7)
in the presencepf strong vibronic interactions. This is done6-8 by expanding He] in a Taylor series in the nuclear coordinates and expressing y k in the nonadiabatic form,
(aV/aq2)0 which transforms like q2 is correspondingly odd, whereas 4; 63 4; (i # j ) is odd and (aV/aql)owhich transforms like ql is even. Equation 14 is now substituted into eq 9, the X j k ( Q ) are expanded in complete sets of harmonic oscillator functions in ql and q2, Xjk(Q)
L
yk(r*
Q) =
@;Xjk(Q>
so that the Born-Oppenheimer approximation is not made. The solution to eq 7 is then found by solving the following set of coupled equations for the x j k 2
~ [ ( T N@ - Ek)djj, + y j , ( Q > l X j , k ( Q > = 0;
j‘= 1
( j = 1 , 2 ; k = l , 2 , 3 ,...) (9) where L
2
a= 1
and
c~nlrz&nl(ql)
(17)
Xn,(42)
and the expansion coefficients are determined in the usual way by taking scalar products of eq 9. The matrix elements of the resulting secular equations are given in Piepho eq 26.6 The basis in eq 17 is truncated at sufficient size to give acceptable accuracy, transition dipoles are calculated, and the resulting stick spectra are convoluted with Gaussians of a single ad hoc line width to produce the final intervalence band contour.6 When we attempt to fit the IVB of Figure 2 on this basis, we are completely unsuccessful. First, we are not able to reproduce the cleft between the two main components of the band and otherwise obtain a reasonable fit. Second, and even more serious, we are utterly unable to account for the temperature dependence of the band. In fact, our calculated IVB shows virtually no change over the temperature range of Figure 2. Therefore, following Bocian et aL5 we postulate that a second conformer of LuPc2 exists in equilibrium with the first. This postulate is supported by the existence of an isosbestic point at -6800 cm-’ (Figure 2a). We further postulate that this second conformer is somewhat distorted from exact D4d symmetry. For example, it is knowni4that in the solvated crystalline LuPc2CH2Cl:! form, both rings are somewhat puckered, though to different extents, whereas a more recent X-ray studyI5 shows that the closely related compound YPc2 has exact D4d symmetry in the unsolvated (a)crystalline form. It is very likely that the same would be the case for the a form of LUPCZ. 2. Extension to the Unsymmetrical Case (A B). We turn on a small asymmetry factor, so that the two centers are no longer identical. The effect, to first order, is to mix the original MOs (bl, a2); Le., there is a configuration interaction in which new MOs (7, y * ) and new electronic states (+;, 4;) are formed:
+
k:) = (q5;l(a2V/i3Q~)olqf) Transforming to the dimensionless variables
h-’(hva)’”Qa
C
nI,n?=O
(8)
j= 1
qa
=
(13)
At] = h(hva)-1’2(2/2hva)-1z!)
47 = Iy2y*); 4;
= 1YY*2)
(18)
we assume k z ) = kz’ and writting va = (1/2n)&, we obtain
a= 1
CI2
+ c;
= 1;
lCll
>> IC2]
a= I
In the original Piepho treatment6 which is applicable for the symmetrical case (A B), the ground state configuration (Qo = 0) is chosen at the potential minimum so that no linear terms in 41 or q 2 appear in W11 (q), Le., Ai” = A:) = 0. But because of the vibronic coupling, this will not be true in the excited state and in particular 1:’’ t 0. Nevertheless, W22 and W12 contain no linear terms in q2 and 41, respectively:
(4;I(avlaq2),14;)= 0 (i = 1, 2)
(15)
(&(av/aq,),14;) = o (i * j = 1,2)
(16)
This follows since 4; C3 qf has even interchange symmetry and
Using the new (eq 19) basis, we write eq 14 in its most general form:
+
W,,(q)= (1/2)hvlql2 &Aji)hv,q,
+ ( 1/2)hv2q,2+
1/Zilt)hv2q2; i = 1, 2 (20)
+
W,,(q) = W,,(q) = .JZ(hv1A(,’.2)q, hv2A:‘,2’q2) with
We substitute eqs 18 and-19 into eq 21 making use of eqs 15
10162 J. Phys. Chem., Vol. 99, No. 25, 1995
Gasyna et al.
TABLE 1: Intervalence Band Simulation Parameters for LuPcz Conformers I and I1 LuPcdCDC13, 300 K LuPc~/CDC~~, 300 K no constraints AI = AIL,v: = vy, vi = vy I I1 I I1 A/cm-‘ 7218 7217 7 140 7140 A(?) 0.867 1.108 0.826 1.159 I 765 826 792 792 vl/cm-‘ 1.308 1.131 1.319 1.121 #.2)a v?/cm-‘ 970 852 984.8 984.8 R 0 0.031 0 0.0667 hb/cm-I 392 392 410.5 410.5
A;.*’ =
LuPcdAr, 11 K A1 = A,,, vi = vy, vi = vy I
I1
7719 1.006 715 1.336 911.4
7719 1.244 715 0.940 911.4 0.0627 369.6
0
369.6
- ;IpKs/&. Gaussian line width in convolution using F($
and 16. We may eliminate A:’)by a new choice of origin for q1 since eq 16 continues to apply under these circumstances, but the origin for q 2 is not changed. Following BersukerI6 and Piepho,6 we note that (aV/aqa)O is a one-electron operator so that
eq 26, so we merely list the additional terms which arise when A zk B (using the Piepho notation = 4;~,,(q1)~~~(q2)):
Using eqs 2, 3, 18, and 22 and expanding the matrix elements to one-electron terms, the result is
V. Band Fitting Fitting the IVB at a given temperature involves the following. First, it is necessary to estimate values of all the parameters shown in Table 1 plus the mole fraction of the two conformers. Equation 9 is then solved using the expansion in eq 17 and the potential energy matrix elements in eq 25 (with R = 0 for conformer I and R 0 for conformer 11). This yields the vibronic energy levels (Ek) and eigenfunctions (vk)for each conformer. Transition dipole strengths are calculated, and a stick spectrum is constructed, each stick height being proportional to the product of population-weighted dipole strength and transition energy, which is thus directly proportional to absorbance. To simulate a real IVB, each stick is convoluted with a Gaussian whose area is proportional to the stick height and whose ad hoc and adjustable line width is kept the same for every stick. Finally, a comparison is made with experiment by multiplying the calculated IVB of each of the two conformers by its mole fraction and summing. An iterative simplex routine17 is then used to refine these parameters by minimizing the difference between the observed and simulated spectrum. 1. LuPcdCDC13 Data. An example of this procedure in its most general form is shown in Figure 3;the resulting parameters are listed in the first column of Table 1. The fit is seen to be quite good, probably not surprising in view of the large number of parameters used; this represents the best we can expect to do at a single temperature. With this as a guide, we now seek a procedure which is objective, which reduces the number of adjustable parameters, and which attempts to fit the LuPcd CDC13 data over the temperature range 268-328 K (Figure 2). To reduce the number of parameters, we hereafter require that AI = All, v’,= vy, and v21 - v2I1 (I, I1 = conformer I, conformer 11). The rationale for these constraints is as follows. First, there is no obvious indication of the presence of two conformers in the electronic spectrum, particularly in the Q-band region where the relatively sharp band’ (fwhm -200 cm-I) would be expected to reveal such effects if AI and A11 were substantially different.
*
Inspecting eq 23, we observe that
so the final result is
+
W , , = (1/2)qI2hv, (1/2)q2’hv2
-
+ 2&RA:]’2’
q’hv,
When R 0, these equations reduce to the symmetrical case,6 as expected. Thus, we see that the effect of the asymmetry is to introduce one additional parameter ( R ) which has the simultaneous effect of coupling q2 into the diagonal terms and ql into the off-diagonal terms of the potential energy matrix W. Solution of eq 7 is now obtained by diagonalizing the appropriate dynamic matrix. The elements of this matrix for the symmetric case (A B) have already been given by Piepho6
J. Phys. Chem., Vol. 99, No. 25, 1995 10163
Intervalence Band in LuPcz
0.4
J
-
I
0.2
-
0
6000
7000
8000
9000
10000
Energy / c m i Figure 3. Fit of the LuPcdCDCls intervalence band at 300 K with no constraints; for parameters, see first column of Table 1. The sticks show the positions and relative absorbances of the various calculated transitions of conformer I and conformer I1 after each is multiplied by its mole fraction. Second, resonance Raman (RR) studies4q5of the bis(porphyrin) analogues of LuPc2 do not reveal frequency "splittings" attributable to the presence of multiple conformers; thus, we assume v: = vf ( i = 1, 2). The constraint AI = A11 precludes an otherwise plausible alternative fit of the data based on the assumption that one conformer, at relatively low concentration and with R close to zero, is responsible for the 6500 cm-' shoulder and that the other conformer, with R = 0, is primarily responsible for the two main peaks. Preliminary fits on this basis suggest AI and AII values differing by -700 cm-', a difference which seems much too large to reconcile with the optical spectrum. With the above constraints, we repeat the simplex procedure at 300 K; the result is shown in Figure 4a, and the corresponding parameters are listed in the center column of Table 1. The fit to the experimental spectrum is still quite good, though somewhat inferior to that of Figure 3. We now use the Figure 4a fit and the associated parameters as the basis for an objective procedure to fit the temperature dependence of LuPc2/CDCl3 (Figure 2). We vary only the ratio of concentrations of the two conformers holding all the parameters in the center column of Table 1 fixed; we simply vary this ratio at each temperature to minimize the mean-square deviation between simulated and observed spectrum. The results for the extremes of the temperature range are shown in Figure 5. The fits going to lower temperature (from 300 K) are really quite good while those going to higher temperature are less satisfactory. Clearly, these constrained fits over the entire temperature range cannot maintain the quality of a single-temperature fit, but the general trends are in good accord with experiment and certainly support our interpretation. We attribute the lack of quantitative agreement to the simplicity of our treatment which attempts to describe a complex system with a two-mode model. Figure 4b,c shows the theoretical IVB contours of each pure conformer. These emphasize a crucial point in understanding our explanation of the strong IVB temperature dependence, namely, as an asymmetry is introduced, Le., as R deviates from zero for conformer 11, its integrated band intensity decreases relative to (the symmetrical) conformer I-compare parts b and c of Figure 4. Thus, the decreased band intensity as the temperature is raised implies an increase in the concentration of conformer 11. We emphasize that the IVB temperature dependence is reversible and reproducible with an isosbestic point, so it seems very reasonable to assume that an equilibrium
Energy lcm-'
Figure 4. (a) Fit of the LuPcz/CDCls intervalence band at 300 K with constraints; for parameters, see middle column of Table 1. Notation as in Figure 3. (b, c) Corresponding calculated intervalence band for pure conformer I and 11, respectively. A 0.6
0.4
0.2
0
0
Energy /cm' Figure 5. Best fit of intervalence band at 268 and 328 K for the same parameters used in Figure 4. Only the mole fraction of the two conformers has been varied for best fit. exists between the two conformers over the temperature range 268-328 K, namely
I =+ I1
(27)
The equilibrium constant is simply the ratio of concentrations, CII/CI, and since we have determined this ratio at each temperature by our fitting procedure, we estimate A@ for the equilibrium to be about 1000 cm-' (12 kJ/mol); see Figure 6. 2. LuPcdAr Data. The IVB in Ar at e l l K reflects a significantly different system in view of the change in solvent. This is immediately apparent in the e500 cm-' blue shift in going from CDCl3 to Ar (Figure 2). Nevertheless, it is interesting to view this system in the framework of the previous treatment. The blue shift is primarily reflected in the A (electronic coupling) parameter. We thus fit the 11 K LuPcz/
Gasyna et al.
10164 J. Phys. Chem., Vol. 99, No. 25, 1995 0.61
1
0
-0 2
-
-0.4
-
-0.6
-
1
-0.81 3 .O
3.2
3.4
3.6
( I / ~ ) x 1 0 3/ K
3.8
l
Figure 6. Plot of In(CII/CI) versus UT. For each point, the same parameters are used as in Figure 4. The mole fraction of the two conformers has been determined from best fit.
A
dl
-
0.04
-
C,/C,=O.29
0.02 -
-
0.04-
1
I
EXP
11K C,/ C,= 0.3
-
0 6C0 0
7 m
8ooO
9000
loo00
Energy /cm-'
Figure 7. (a) Fit of the LuPc*/Ar intervalence band at 11 K using the constraints and frequencies of the middle column, Table 1, except allowing A, = A2 and the mole fraction to vary. (b) Fit of the intervalence band as in (a), except also allowing vi = v? and vi = v t to vary; for parameters, see right-hand column of Table 1.
Ar band with the same constraints used previously, namely, AI = An and vf = vf' (i = 1, 2 ) , and initially we also hold V I and v2 at their values in CDCl3 solution (Table 1, middle column). The results of this fit are shown in Figure 7a. The fit is quite reasonable in accounting for the main features including the continued growth of the higher energy peak relative to the lower energy shoulder as the temperature decreases. Finally, we can improve the fit further (Figure 7b) if we allow V I and v2 and to vary from their CDC13 values. The parameters for this case are shown in the last column of Table 1. The best fit frequencies in the Ar matrix are both about 9% lower than in CDCl3 solution whereas A is about 11% higher.
VI. LuPcz: Localized or Delocalized? Having obtained model parameters, we are now able to give a quantitative picture (within the context of the model) of the
Figure 8. Probability distribution in 42 space for each conformer (at 300 K) and corresponding potential surfaces. Dashed curves apply to conformer I, and solid curves apply to conformer 11.
degree of delocalization. If the system is localized, then one center is Pc2- and the other is Pc'l-. Under these circumstances, there will be two most probable values of coordinate Q2 or 42 (eq 3), both of the same magnitude (when R = 0) but of opposite sign. Likewise, the corresponding potential surface in 42 space will show two minima with a potential barrier between with maximum at 42 = 0. On the other hand, if the system is delocalized, there will be a single most probable value of q 2 , namely q 2 = 0 (when R = 0), and the accompanying potential surface will have a single minimum at 42 = 0. Thus, the probability distribution in 42 space, P(q2),will give a quantitative picture of the degree of delocalization. If P(q2)has two maxima, the system is localized, and if P(q2) has a single maximum at 42 = 0 (for R = 0), or near 42 = 0 (for R t 0), then the system is delocalized. We thus square the eigenfunction (Yk(r, Q)) of each occupied state, integrate over electronic coordinates ( r ) and 41, multiply by the appropriate Boltzmann population factor and sum over all occupied states. This procedure has been discussed in detail and we simply show our results in Figure 8. We observe for both conformers that P(q2) has a single distinct peak at or near 42 = 0 consistent with the profile of a clearly delocalized system. Likewise, the ground state potential surfaces have a single minimum at or near 42 = 0. Examining Figure 8, we observe that the model predicts that the unsymmetrical conformer is somewhat more delocalized in view of its sharper probability distribution and the greater curvature of its lower potential surface. Consistent with the optical spectrum,' our analysis emphatically supports the view that LUPQ is delocalized, and it suggests that the system is strongly delocalized, i.e., is well beyond the crossover point between a localized and delocalized case.
VII. Conclusions Our analysis definitely supports the view that LuPcz is a strongly delocalized system with a most probable nuclear configuration which makes both rings equivalent ( R = 0) or nearly so ( R f 0). Furthermore, the pronounced temperature dependence of the intervalence band (IVB) is well accounted for by the postulate that LuPc2 exists in CDCl3 solution as an equilibrium between two distinct conformers with an associated A@ of about lo00 cm-'. These conclusions are fully consistent with the analysis of analogous porphyrin systems (LnPor2: Ln = Eu3+, Nd3+, La3+; CePor**+: Por = OEP, TPP, TPnP) by Bocian and co-w~rkers>,~ who have rationalized the temperature dependence of their IVBs in terms of multiple conformations
Intervalence Band in LUPCZ and have shown on the basis of resonance Raman and EPR studies that the hole is delocalized over both porphyrin rings. In view of the close similarity in properties of the various LnPcz, it seems likely that the entire series is delocalized. (It is interesting to note that a recent study of porphyrinphthalocyanine heterosystems indicates that the hole is preferentially localized on the Pc ring.’*) We can only speculate as to the nature of our proposed two conformers, but it is clear from the X-ray diffraction work we cited earlier that the outer periphery of the Pc rings is relatively easily distorted from planarity. Thus, a simple view is that one conformer has exact D4d symmetry (as in the a crystalline phase of Y P C Z ~ and ~ )that the other has some such distortion as in the CH2C12 solvated crystalline form. Again, this is consistent with the suggestion of Bocian and co-workers that, in the analogous Ln(OEP)2 (OEP = octaethylporphyrin), different conformers represent different conformations of the peripheral ethyl group^.^ We also emphasize that our mixed-valence model must be a significant oversimplification since we discuss the vibronic properties of a complex system in terms of two modes. In view of the large number of possible modes of appropriate symmetry in the LuPc2 system, our two modes are best regarded as effective modes each of which undoubtedly represents some sort of weighted average of several modes. In our treatment, no specific form of these modes need be specified; only their interchange symmetry properties are essential. The frequencies of our two modes (Table 1) are in the general range of Pc ring vibrations, the strongest mode in the resonance Raman spectrum’9320being a totally symmetric macrocycle breathing mode at 679 cm-I. Thus, low-frequency vibrations such as the mode assigned to the metal-N stretch at 240 cm-’ and several other low-frequency modes observed in the Raman spectrumI9do not appear to make an important contribution to the IVB contour. This is in marked contrast to the analogous porphyrin systems where Bocian et ~ 1 identify . ~ progressions in modes at -250 and -315 cm-’ for their two conformers. We are not able to suggest a convincing reason for this difference. Perhaps the more rigid structure of the Pc ring relative to the Por ring is a significant factor. On the other hand, if many modes do actually contribute to the IVB contour, it is entirely possible that lowfrequency modes make a much more important contribution than is evident in an effective two-mode treatment. The overall consistency of the IVB features in a drastically different environment (Ar matrix at 11 K), with those in CDCb solution in the room temperature range, lends support to our basic description of the LuPc2 system.
J. Phys. Chem., Vol. 99, No. 25, 1995 10165 Acknowledgment. We are much indebted to Drs. Kosmas Prassides and Alison Marks for a preliminary analysis of the IVB data which established guidelines and limitations on the possible parameters necessary for a description of the system. We also acknowledge very useful discussions with Drs. Kosmas Prassides and Bryce E. Williamson. This work was supported by the National Science Foundation under Grants NSF CHE8902456 and CHE9207886. M.E.B. gratefully acknowledges partial support for this work from the Office of Naval Research. References and Notes (1) VanCott, T. C.; Gasyna, 2.; Schatz, P. N.; Boyle, M. E. J . Phys. Chem. 1995, 99, 4820-4830 and references therein. (2) Kirin, I . S.; Moskalev, P. N.; Makashev, Y. A. Russ. J. Inorg. Chem. 1965, 10, 1065-1066. (3) Rose, J.; Smith, D.; Williamson, B. E.; Schatz, P. N.; O’Brien, M. C. M. J . Phys. Chem. 1986, 90, 2608-2615. (4) Donohoe, R. J.; Duchowski, J. K.; Bocian, D. F. J . Am. Chem. SOC.1988, 110, 6119-6124. (5) Duchowski, J. K.; Bocian, D. F. J . Am. Chem. SOC. 1990, 112, 3312-3318. (6) Piepho, S . B. J . Am. Chem. SOC.1988, 110, 6319-6326. (7) Piepho, S. B.; Krausz, E. R.; Schatz, P. N. J . Am. Chem. SOC.1978, 100, 2996-3005. (8) Wong, K. Y.; Schatz, P. N. Prog. Inorg. Chem. 1981, 28, 369449. (9) KO, J.; Zhang, L.-T.; Ondrechen, M. J. J . Am. Chem. SOC.1986, 108, 1712-1713. (10) Zhang, L.-T.; KO,J.; Ondrechen, M. J. J . Am. Chem. SOC.1987, 109, 1666-1671 and references therein. (11) Ondrechen, M. J.; KO,J.; Zhang, L.-T. J. Am. Chem. SOC.1987, 109, 1672-1676 and references therein. (12) Piepho, S. B. J . Am. Chem. SOC.1990, 112, 4197-4206. (13) Schatz, P. N. In Mixed Valency Systems: Applications in Chemistry, Physics and Biology; Kluwer: Dordrecht, 1991; pp 7-28. (14) De Cian, A,; Moussavi, M.; Fischer, J.; Weiss, R. Inorg. Chem. 1985, 24, 3162-3167. (15) Paillaud, J. L.; Drillon, M.; DeCian, A,; Fischer, J.; Weiss, R.; Villeneuve, G. Phys. Rev. Lett. 1991, 67, 244-247. (16) Bersuker, I. B. The Jahn-Teller Effect and Vibronic Interactions in Modern Chemistry; Plenum: New York, 1984. (17) Press, W. H.;Elannery, B. P.; Teukolsky, S . A,; Vetterling, W. T. Numerical Recipes; Cambridge University Press: Cambridge, 1986; pp 289-293. (18) Tran-Thi, T.-H.; Mattioli, T. A,; Chabach, D.; De Cian, A,; Weiss, R. J. Phys. Chem. 1994, 98, 8279-8288. (19) Aroca, R.; Clavijo, R. E.; Jennings, C. A.; Kovacs, G. J.; Duff, J. M.; Loutfy, R. 0. Spectrochim. Acta 1989, 45A, 957-962. (20) Battisti, D.; Tomilova, L.; Aroca, R. Chem. Mater. 1992, 4 , 1323- 1328. JP950160A
