J . Phys. Chem. 1994, 98, 8813-8816
8813
Molecular Orientation and Structure of the Transition Moments of Porphyrin Derivatives with Various Symmetries Zygmunt Gryczynski, Roberto Paolesse, Kevin M. Smith, and Enrico Bucci' Department of Biochemistry, University of Maryland Medical School, 108 North Greene Street, Baltimore, Maryland 21 201, and Department of Chemistry, University of California at Davis, Davis, California 95616 Received: March 29, 1994; In Final Form: June 15, 1994"
In order to determine the anisotropy in the absorption transition moments of hemes we measured the visible and UV linear dichroism of the high-symmetry porphyrin derivatives cu,&y,6-tetraphenylsulfonicporphyrin (D4hsymmetry), deuterohemin I11 (iron deuteroporphyrin I11 chloride; CZ,symmetry), and protohemin I11 (iron protoporphyrin I11 chloride; C2, symmetry) in stretched poly(viny1 alcohol) films in the 250-700-nm region. Their linear dichroism was analyzed by using either a "circular absorber" model or a linear absorption oscillator model. For a,P,y,6-tetraphenylsulfonicporphyrin with 4-fold symmetry the absorption anisotropy was found to be wavelength independent as for a circular absorber. Deutero- and protohemin I11 with Ch symmetry had a wavelength-dependent dichroism, indicating the linear type of the allowed transition moments. As expected from theoretical calculation the transitions most affected by peripheral substituents were the relatively weak Q, L, and N bands. Linear dichroism with very similar characteristics was reported earlier by us for native protohemin I X (iron protoporphyrin IX chloride) derivatives (Gryczynski et al. Photochem. Photobiol. 1993, 58, 492). It appears that the absorption of hemes should be considered as a simple combination of linear oscillators. The linear character of heme transition moments is what regulates the radiationless tryptophanheme interactions. R
Introduction
I
Metalloporphyrin complexes are some of the most used chromophores as probes of structure-function in proteins. The large number of spectroscopic applications utilizing the heme absorption to study ligand binding processes, and hemoprotein structure and dynamics, underscore the importance of investigating the details of the electronic structure of the hemes. In particular, detailed knowledge of the structure and directions of the heme electronic transition moments are necessary for the interpretation of circular dichroism data and radiationless energytransfer process in metalloporphyrin-protein compiexes.'J Recently, we showed the relevance of the polarization of the transition moment in the near-UV heme absorption band to radiationless energy transfer from excited tryptophan~.~ Porphin has the symmetry of the perfect square plate, which belongs to the point group D4h.4 The classic free electron or LCAO molecular orbital model" properly describes the frequencies and intensities of its s-electronic transitions. These theoretical calculations predict that for such a planar system, with 4-fold symmetry, the allowed transitions are polarized parallel to the main symmetry axes in the plane of the molecule. The linear character of the electronic transition of porphin has been amply demonstrated by fluorescence polari~ation,~ fluorescence in Shpolski-typematrixes,ls14and Fourier-transform spectroscopy in noble gas matrixes.I5 The questions may be posed whether this linearity survives in the presence of metal substitutions, which would degenerate the electronic orbitals in the center of the porphin ring and what effect peripheral substituents may have on the electronic transitions. Our recent investigation of the linear dichroism of various protohemin IX derivatives16 is consistent with a linear type of heme electronic transitions and shows a better polarization separation of the electronic transitions in the near-UV region. Also, it is well-known that the presence of magnesium in the
* Address correspondence to this author at the University of Maryland Medical School. Abstract published in Advance ACS Absrracrs, August 1, 1994.
R R
R
Figure 1. Structures of a,&y,6-tetraphenylsulfonicporphyrin (top) and of protohemin I11 (1) and deuterohemin I11 (2).
porphyrin ring of chlorophylls does not produce degeneration of the electronic transitions and well-defined linear transition moments are observed.17-20 However, experimental data of polarized absorption in the visible and Soret regions, in single crystals of myoglobin and hemoglobin,21-23 were interpreted as consistent with a planar degeneration of the main absorption bands of the heme moiety. As a consequence,the heme absorption transitions were interpreted as a circular absorber for linearly polarized light. The complex structure of the electronic transitions in porphyrin derivativesdeserves more detailed exploration, and this controversy must be clarified. To shed light on this problem, in this paper we present a comparative study of the linear dichroism of highsymmetry porphyrin derivatives, so as to investigate the effect of symmetry changes on the structure of the transition moments and orientational properties of porphyrins, in stretched PVA [poly(vinyl alcohol)] films. We measured the linear dichroism of a,B,y,b-tetraphenylsulfonic porphyrin (D4h symmetry), deuterohemin I11 (Cb symmetry), and protohemin I11 (Cbsymmetry) (Figure l), and we
0022-365419412098-8813%04.50/0 0 1994 American Chemical Society
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The Journal of Physical Chemistry, Vol. 98, No. 35, 1994
'I
Gryczynski et al.
/=
-0251 - Q
-050
4 Figure 2. Laboratory-fixed (X,Y,Z) and the molecule-fixed ( x y , z ) coordinate system. The orientation of the molecule is specified by_angles wx, wy, w2. The orientation of the absorption transition moment A in the molecular plane is described by the angle p.
Figure 3. Orientation triangle showing the positions determined by the Saupe parameters for a,8,y,6-tetraphenylsulfonicporphyrin ( O ) , protohemin I11 (U), and deuterohemin 111 (0).
can be expressed by27,28
K(X) = 'I3LDr= S,, cos2cp + Syysin2 cp
(4)
developed a simple theoretical model for the circular absorber, described by Eaton et al.21-24 On this basis, we madecomparative analyses of the data in terms of either a circular absorber or a linear oscillator model. BasicTheory. Let us consider a planar molecule with associated fixed orthogonal coordinates (x,y,z)in a laboratory system with fixed orthogonal coordinates (X,Y,Z), where the orientation direction (in our case the stretching of PVA films) is along the Z axis (Figure 2). The orientation of an assembly of identical molecules is characterized by the orientation tensor (cos wi cos w j ) (ij= x,y,z). The cos wi denotes the direction cosine of the angle between the ith axis of the molecules and the direction of the orientation. In Figure 2, & . represents the absorption vector which lays on the molecular plane and makes the angle cp with the z axis of the molecular coordinates system. The observed absorption anisotropy K(X) as a function of the wavelength X is given by25J6
Using eq 4, it is possible to compute the range of variability of the absorption anisotropy -0.5 C K C 1.O. Also it implies a strong dependence of the linear dichroism on the wavelength of observation, Le., the orientation of the transition moment of the band there observed. The Saupe orientation parameters will position the molecule inside the classic orientation triangle, depending on the shape of the molecule and its interaction with the orienting medium. The presence of a circular absorber implies a continuous distribution of absorption vectors A around the x axis of the molecular coordinates perpendicular to the molecular plane.21-24Jo Therefore ( ( cos2cp) ) and ( (sin2 cp) ) in eq 2 are averaged around thexaxis,giving( (cos2cp)) = ( (sin2q))= '/2,andtheabsorption anisotropy becomes
where All and A L are the absorptions parallel and perpendicular to the orientation direction at the given wavelength X and A = AI! 2AI is the total absorbance. The absorption anisotropy, K(X), is related to the dichroic ratio by Rd = A I I / A=~( 2 K + 1)/(1 - K ) and to the reduced linear dichroism by LDr = 3(A/l - AL)/(Al+ , 2AL) = 3K. The absorption anisotropy has been chosen for describing absorption properties in oriented systems because of its convenient additivity over the contributions of several components.25,26 For planar porphyrin systems only transition moments laying in the molecular plane are considered here. In the general case, following the Matsuoko and Norden pr0cedure2~328absorption anisotropy can be expressed by
It is interesting to note that, in this case, the absorption anisotropy is independent of the wavelength of observation and is a function only of the two orientation parameters Syyand S,,. This yields a constant value of the observed absorption anisotropy across the absorption spectrum, which has a much more restricted range: 0 IK I0.25. Also, in this case the orientation parameters computed from eq 5 locate the molecule on the "disklike" edge of the orientation triangle (Figure 3 ) , independently from the shape of the molecule. This would produce the paradox that even rodlike molecules in linear dichroism measurements would behave as having disklike shapes in the orientation triangle. For high-symmetry porphyrin structures (D,,,), as discussed above, the absorption bands are produced by two orthogonal linear transitions, polarized along the main symmetry axes. The symmetry also implies that they have equal intensity. The additivity of absorption anisotropy implies that the resultant anisotropy is the sum of the anisotropies of the two components,26 therefore at any given wavelength X we have
+
K ( X )= ( 3 / 2 ( ~w~Y )~-2'/,)(sin2
cp)
+
(3/,(cos
w z )-
I/,)(cos2
cp)
(2)
where cp is the angle between A and the z molecular axis and wy and w, are the angles between the molecular y and z axes and the stretching direction Z of the film (Figure 2); ((cos ai) ) denotes an average value of the cosine of the angle between the ith axis and the stretching direction and is related to the Saupe molecular orientation parameters Sii27,29 by
For linear oscillators ( (cos2 p) ) = cos2 cp and ( ( sin2 c p ) ) = sin2 cp. If the molecular system (x,y,z) is the diagonal system with the axes labeled so that the Saupe orientation parameters fulfill the condition S,, IS,, L S,,, the absorption anisotropy K
where a,(X) and 4 X ) are the relative contributions of two orthogonal transitions to the absorption spectra (al(X) + q ( X ) = 1). Substituting in (4) we have
It should be noted that, when the two orthogonal transitions have equal intensity, we have q ( X ) = az(X) = l / 2 , and eq 7 becomes identical to eq 5, as derived for a circular absorber. Therefore the linear dichroism becomes wavelength independent, and the measured anisotropy places the molecule on the disklike edge of the orientation triangle as in the case of a circular absorber. It should be stressed that eq 5 is valid for porphyrins with any
Linearity of Heme Transitions
The Journal of Physical Chemistry, Vol. 98, No. 35, 1994 8815
symmetry, when the absorption includes two mutually orthogonal transitions of equal contributions. In consequence, the theory shows that in oriented systems linear dichroism and the Saupeorientation parameters cannot distinguish between circular absorbers and porphyrins with 041, symmetry molecular skeletons. It also shows that porphyrins have wavelength-dependent dichroism, which displaces the molecule away from the disklike edge in the orientation triangle, if, and only if, they have a linear structure.
Materials and Methods Synthesis of Symmetrical Heme Derivatives. Deuteroporphyrin I11 and protoporphyrin I11 dimethyl esters were synthesized by cyclization of the corresponding apbiladiene dihydrobromides, using copper(I1) acetate to promote the ring c l o s ~ r e . ~In~the .~~ case of protoporphyrin I11 dimethyl ester, 2-chloroethyl groups were used as precursors of the vinyl substituents.33.34 The corresponding hemins were obtained by iron insertion and ester hydrolysis, following literature procedures.35 Film Preparationand Measurements. PVA films were prepared from 15% aqueous solutions. The various hemin derivatives were dissolved in a minimum amount of 0.1 N NaOH and added to the PVA solution prewarmed at 350 K. The mixture was poured into Petri dishes to form thin liquid layers. These were rapidly dried a t 330-340 K. The short time of drying (15-20 min) a t high temperature and the dilution prevented the formation of aggregates. The most homogeneous films were used for the measurements. The films were slowly stretched about 5-fold a t 360 K. Drying at high temperatures did not affect the plasticity of the PVA films.16 In order to obtain films containing CO-protohemin I11 and CO-deuterohemin 111, stretched films were immersed in a water solutions of dithionite and equilibrated with CO at atmospheric pressure, in a closed container. Within 150-200 min, the ferric forms were quantitatively transformed into CO-ferrous derivatives. The films were rapidly dried under a CO atmosphere and the completion of the reaction was controlled spectrophotometrically. It should be stressed that, as already noted for protohemin IX,16 CO-derivatives in PVA films were very stable and the absorption spectrum of these films remained unchanged for weeks, at room temperature, exposed to air. Spectrophotometric measurements were performed with an AVIV 14DS spectrophotometer. Linear dichroism was measured by placing a Glan polarizer in front of the sample inside the instrument. The absorption of the sample was corrected for a baseline obtained with empty films, then calibrated for its thickness. Results The parallel (All) and perpendicular ( A l ) absorption components of a,@,y,&tetraphenylsulfonicporphin and of the various derivatives of deutero- and protohemin I11 are shown in Figure 4. Their resulting absorption anisotropies are also illustrated there. They were obtained upon a 5-fold stretching of the films resulting in a stretching ratio R, = 1 1.2. As already reported,16 the dehydration produced by embedding in PVA films sharpened and increased the maximum intensity of the various absorption bands. As anticipated by the theoretical calculations for D4h symmetry molecules, the absorption anisotropy of a,@,y,&tetraphenylsulfonic porphyrin was wavelength independent with a value close to 0.16, corresponding to a dichroic ratio Rd = 1.5. This value, compared to that anticipated for a perfectly axially oriented system (K= 0.25),indicates a significant orientation of the system. Also, both the flat spectrum and the very small scattering of the data imply the absence of instrumental artifacts, which would distort the data. Instead, the anisotropies of the deutero- and protohemin I11 were strongly wavelength dependent, changing from a value near
WAVELEHGTH I mm I
Figure 4. Starting from the top, from left to the right, down: absorbance components and anisotropy of a,j3,y,&tetraphenylsulfonicporphyrin, carbonmonoxyprotoheminIX (redrawn from Gryczynski et al., 1993b), fcmc dcuterohemin 111, carbonmonoxydeuterohemin 111, ferric protohemin 111, and carbonmonoxyprotohemin 111.
0.27 a t long wavelength to a value near -0.01 in the near-UV and
UV regions (the corresponding dichroic ratio Rd varied from 2.1 to 0.99). Figure 3 shows the positions of the molecular shape of the various porphyrinsinside theorientation triangle. As anticipated, a,@,y,&tetraphenylsulfonicporphyrin (D4h symmetry) is on the edge for disklike shapes. The shapes of the Cbsymmetry deuteroand protohemin I11 are shifted toward the rodlike edge, being located in the center of the orientation triangle.
Discussion For a h e a r oscillator, with D4h symmetry, eq 4 anticipates a wavelength-independent dichroism, which, in a perfectly oriented system, should give an absorption anisotropy near K = 0.25 and a dichroic ratio near & = 2.0. In very good agreement with the theory, a,B,y,btetraphenylsulfonicporphyrin showed a wavelengthindependent anisotropy near K = 0.16 and a dichroic ratio near & = 1SO. A small dip of absorption anisotropy can be observed in the blue edge of the Soret band. This probably was the contribution of out-of-plane transitions, consistent with data obtained by Fisher et al.36for tetraphenylporphyrin in stretched polyethylene films. As expected, its shape is disklike in the orientation triangle. The dichroism of deutero- and protohemin I11 shown in Figure 4 is very interesting. The presence of the iron and the symmetrical position of the peripheral substituents confer to these porphyrins the C , symmetry. This affects the orientation of the molecular frame for which the preferential orientation axis becomes the a-y meso-axis of the porphyrin ring. This is the Cb symmetry axis, which orients along the stretching direction (i.e., the z axis of the molecular frame) shown in Figure 2. The observed absorption anisotropy changed from near K = 0, for the UV and near-UV absorption regions, to values above K = 0.27 for the wavelength in thevisible region. This indicated that the presence of the iron and of the peripheral substituents produced a splitting of the orthogonal linear transitions of the porphyrin and modified their relative intensity. The computed orientation parameters of deutero- and protohemin I11 were very similar and positioned in thecenter of theorientation triangle, closer to the edge that defines linear shapes (Figure 3). Figure 4 also shows the dichroic behavior of protohemin IX, which was discussed in a previous paper,I6 and is included here
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The Journal of Physical Chemistry, Vol. 98, No. 35, 1994
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for comparison. Together with the other spectra it clearly shows was positioned near 60’ from the a--y meso-axis of the porphyrin that dichroism of hemins is sensitive to the nature and symmetry This electronic transition dipole is the one responsible of the peripheral substitutions. As previously discussed, the for the radiationless energy transfer from the excited trypspectrum of protohemin IX shows a clearly distinct dichroic band t o p h a n ~ . ~Therefore, - ~ ~ , ~ ~ in computing the Forster orientation in the 300-380-nm region of the spectrum. This is the absorption parameters for this phenomenon, the linear structure of the heme band responsible for radiationless transfer from t r y p t ~ p h a n s , ~ , ’ ~ transition moments cannot be ignored. in hemoproteins. The wavelength dependence of the dichroism confirms the Acknowledgment. This work was supported in part by Grants theoretical calculations of Weiss et al.’ for metal porphyrins with HL-22252 (K.M.S.), HL-13164, and HL-48517 (E.B.) and by peripheral substituents. In fact, the most affected bands were in the Center of Fluorescence Spectroscopy HL-08 119. Computer the visible, Soret, and near-UV regions, corresponding to the time and facilities were supported in part by the computer network weak Q, L, and N bands identified by Weiss et aL7 The high of the University of Maryland. R.P.acknowledges the support value of the anisotropy in the visible and red part of the Soret of a research fellowship from Consiglio Nazionaledelle Richerche bands, where the transitions are vertically polarized, and the low (Italy). value of anisotropy in the near-UV and UV region of the spectrum, where the transitions are horizontally polarized, result from the References and Notes linear-in-plane structure of the electronic transition moments of (1) Hsu, M.; Woody, R. J. Am. Chem. SOC.1971, 93, 3515. the hemins. It should be noted that the anisotropy of protohemin (2) Hochstrasser, R. M.; Negus, D. K. Proc. Natl. Acad. Sci. U.S.A. IX (Le., natural heme),I6 in the near-UV region between 300 and 1984.81, 4399. 380 nm, is consistent with the presence of a well-resolved single (3) Gryczynski, 2.; Fronticelli, C.; Tenenholz, T.; Bucci, E. Biophys. J. 1993, 65, 1951. transition moment, which is responsible for the radiationless energy (4) As noted by Gouterman and Stryer (J.Chem. Phys. 1962,37,2260), transfer from tryptophan.3J0 in free-base porphin the two central hydrogens lower the symmetry of the In our measurements, out-of-plane transitions did not seem to system to &,+,without consequences regarding the orientational behavior of the molecule. contribute significantly. They belong to n-ir transitions, which (5) Simpson, W. T . J. Chem. Phys. 1949, 17, 1218. are generally much weaker than the ir-ir transitions, mostly (6) Gouterman, M. J. Mol. Spectrosc. 1961, 6, 138. responsible for the dichroism of the system. Extensive research (7) Weiss, C.; Kobayashi, H.; Gouterman. M. J. Mol. Specfrosc. 1965, and theoretical considerations do not support large increases of 16, 415. their strength due to the presence of metals and other (8) Knop, J. V.; Knop, A. Z. Naturforsch. 1970, 25, 1720. s ~ b s t i t u e n t s .Also, ~ ~ ~in axially oriented systems, they would (9) Gouterman, M.; Stryer, L. J. Chem. Phys. 1962, 37, 2260. (10) Voelker, S.; Macfarlane, R. M. J. Chem. Phys. 1980, 73, 4476. lower the anisotropy, producing dips in the spectrum, as reported (11) Voelker, S.; Macfarlane, R. M. Chem. Phys. Lett. 1979, 61, 421. by Fisher et al.36 We have noticed a small dip in the blue side (12) Gladkov, L. L.;Gradyushko, A. T.; Shulga, A. M.;Solovyov, K. N.; of the Soret region for the anisotropy of a,P,y,G-tetraphenylStarukhin, S. J. Mol. Struct. 1978, 47, 463. sulfonic porphyrin. If it was due to out-of-plane transitions, it (13) Gradyushko, T.; Solov’ev, K. N.; Starukhin, A. S . J. Mol. Strucr. would indicate their small intensities and their locations in the 1977, 40, 469. (14) Even, U.; Jortner, J.; Berkovitch-Yellin, 2. Can. J. Chem. 1985, 63, absorption spectrum. 2073. Therefore, we can safely interpret the dichroism of deutero(15) Radziszewski, J. G.; Waluk, J.; Michl, J. J. Mol. Spectrosc. 1990, and protohemin I11 as a combination of linear electronic transitions 140, 373. in the visible band (Q), red part of the Soret band (L), and near(16) Gryczynski, Z.; Bucci, E.; Kusba, J. Photochem. Photobiol. 1993, 58, 492. UV (N) absorption bands. (17) van Gurp, M.; van Ginkel, G.; Levine, Y. K. Biochim. Biophys. Acta It is interesting to note that for porphyrins in general, when 1989, 973,405. the orthogonal transitions have equal oscillator strength, eqs 7 (1 8) van Gurp, M.; van der Heide, V.; Verhagen, J.; Piters, T.; van Ginkel, and 5 become identical, producing a wavelength-independent G.; Levine, Y. K. Photochem. Phofobiol. 1989, 49, 663. (19) Fragata, M.; Norden, B.; Kurucsev, T. Photochem. Photobiol. 1988, anisotropy, similar to that for a circular absorber. In this case, 47, 133. considering that orientation can never be perfect, even if the (20) Bauman, D.; Wrobel, D. Biophys. Chem. 1980, 12, 83. oscillator strength of the two orthogonal components is slightly (21) Eaton, W. A.; Hochstrasser, R. M. J. Chem. Phys. 1967, 46, 2533. different, it would be difficult to distinguish between “circular” (22) Eaton, W. A.; Hochstrasser, R. M. J. Chem. Phys. 1968, 49, 985. and linear geometries of transition moments. This is probably (23) Eaton, W. A.; Hofrichter, J. Methods Enzymol. 1981, 76, 175. Hofrichter, J.; Eaton, W. A. Annu. Reu. Biophys. Bioeng. 1976, 5, 5 11. at the origin of the circular absorber interpretation for the data (24) Ansari, A.; Colleen, M.; Henry, E. R.; Hofrichter, J.; Eaton, W. A. obtained from crystals of myoglobin and h e m o g l ~ b i n .We ~ ~ ~ ~ ~ Biophys. J. 1993, 64, 852. want to stress that a combination of linear polarizations with (25) Kawski. A.; Grvczvnski, 2. Z . Naturforsch. 1987. 42a. 617. . . different orientations, as it is found in the center of the Soret (26) Kawski, A.; Gryczynski, 2.;Gryczynsii, I.; KuSba, J: Z . iafurforsch. 1992, 47a, 471. bandI6 and in the visible absorption spectrum of hemoglobin and (27) Matsuoka, Y.; Norden, B. Chem. Phys. Left.1982, 85, 302. myoglobin, may also mimic the presence of a circular absorber. (28) Matsuoka, Y.; Norden, B. J. Phys. Chem. 1983, 87, 220. Moreover, in the crystals of hemoglobin and myoglobin, the (29) Saupe, A. Mol. Cryst. 1966, I , 527. absorpion of the protein prevented the use of data obtained in the (30) Gryczynski, Z.;Tenenholz, T.; Bucci, E. Biophys. J. 1992,63,648. UV regions, therefore limiting the amount of information (31) Clezy, P. S.; Liepa, A. Aust. J. Chem. 1971, 24, 1027. available. (32) Almeida, J. A. P. B.; Kenner, G. W.; Rimmer, J.; Smith, K. M. Tetrahedron 1976, 32, 1793. We could not find in the literature a theoretical formalism for (33) Cavaleiro, J.A.S.;Gonsalves,A. M.;d’A,R.;Kenner,G. W.;Smith, quantum mechanical treatment of circular absorbers. Therefore K. M. J. Chem. Soc.. Perkin Trans. 1973, I, 2471. the circular absorber model has to be interpreted as an average (34) Smith, K. M.; Parish, D. W.; Inouye, W. S. J. Org. Chem. 1986,51, of linear dipole electronic transitions, whose overlapping bands 666. make it difficult, if not impossible, to identify (them) individually (35) Smith, K. M.; Fujinari, E. M.; Langry, K. C.; Parish, D. W.; Tabba, H . D. J. Am. Chem. SOC.1983, 105, 6638. in their orientation on the porphyring ring. This approximation (36) Fischer, N.; Goldammer, E. V.; Pelzl, J. J. Mol. Srruct. 1979, 56, is especially useful, and necessary, for interpreting data obtained 95. in both the Soret and most of the visible regions of the absorption (37) Michl, J.; Thulstrup, E. Spectroscopy with polarized light; VHS Publisher, Inc.: New York, 1986. spectrum, where multiple overlapping absorption bands are (38) Davidson, A.; Gouterman, M.; Johansson, Y. L.; Larson, R.; Norden, present. B.; Sundbom, M. Act. Chem. Scand. 1972, 26, 840. This, however, is not the case for the near-UV region of the (39) Gale, R.; Peacock, R. D.; Samori, B. Chem. Phys. Lett. 1976, 37, heme absorption, where we have demonstrated the presence of 430. a well-resolved single absorption band, whose linear transition (40) Waluk, J.; Thulstrup, E. W. Chem. Phys. Lett. 1986, 123, 102.
