J. Phys. Chem. 1993,97, 11887-1 1900
11887
Vibrational Analysis of Biliverdin Dimethyl Ester Kurt Smit, Jorg Matysik, Peter Hildebrandt,' and Franz Mark Max-Planck-Institut f i r Strahlenchemie, Postfach 101365, 0-45413 Miilheim an der Ruhr, Fed. Rep. Germany Received: June 25, 1993'
The Fourier-transform resonance Raman and infrared spectra of biliverdin dimethyl ester and the isotopomer deuterated at the pyrrole nitrogens were measured in the solid state and in CC14 solution. A vibrational analysis of the spectra is presented. The force field was obtained on the basis of the semiempirical AM1 method by a two-step procedure. First, scaled AM1 force fields for fragments of the tetrapyrrole system were developed according to Pulay's scaling method (Pulay, P.; Fogarasi, G.; Pongor, G.; Boggs, J. E.; Vargha, A. J . Am. Chem. SOC.1983,105,7037). These force fields were checked against those from ab-initio Hartree-Fock calculations. The scaling factors optimized for the fragments were used as initial parameters for the vibrational analysis of biliverdin dimethyl ester. They were refined in the second step by using both the frequencies and the infrared and resonance Raman intensities as criteria. The resonance Raman intensities were estimated according to the model introduced by Peticolas and co-workers (Peticolas, W. L.; Strommen, D. P.; Lakshminarayanan, V. J. Chem. Phys. 1980, 73, 4185). The accuracy of the normal mode analysis was better than 20 cm-l which along with the evaluated intensities allowed for a unique assignment of most of the observed bands. It was found that most of the vibrational modes are localized in the individual pyrrole rings and the adjacent methine bridges.
Introduction Linear tetrapyrroles constitute the chromophoric centers in different photoreceptor proteins. Phytochrome is an example of such a chromoprotein. It is responsible for a variety of photomorphogenicprocesses in higher plants.' The underlying molecular reactions are still not sufficiently known. Since a crystal structureof phytochrome is not available, spectroscopictechniques are the most important sources of structural information. Among them, resonance Raman (RR) spectroscopy holds promise to contribute significantly to the elucidation of the conformation of the active &en2-' A large number of spectroscopicstudies have thereforebeencamedout with phytochrome as wellas withvarious model compounds.211 However, a reliablevibrationalassignment, which is a prerequisite for extracting structural information from the spectra, is still missing. In an attempt to fill this gap, we analyzed thevibrational spectra of biliverdin dimethyl ester (BVE) for which detailed structural data are available.12 Hence, this compound may serve as an appropriate starting point for the vibrational analysis of linear tetrapyrrolesin general. For a normal mode analysisof molecules of that size, generally empirical approaches based on valence bond or (modified) Urey-Bradley force fields have been employed.13-18 Numerous studies have been carried out on cyclic tetrapyrroles, i.e., porphyrins and related compounds.13 Among them, the most detailed vibrational characterization of metalloporphyrin complexes has been reported by Spiro's group.1618 This work was based on the RR and IR spectra of various isotopomers constituting a large set of experimental data. This allowed for developing a self-consistent force field satisfactorily predicting the frequencies and isotopic shifts in the spectra of various porphyrin derivatives. The vibrational assignment is facilitated by the high symmetry (046) of porphyrins so that RRand IR-active modes can be sorted out. Tetrapyrrolemacrocycles including a reduced pyrrole ring (Le., chlorin derivatives) have lower symmetry, so all modes are potentially both RR and IR active. In addition, less spectral data of isotopomers are available. Under these conditions a higher intrinsic accuracy of the normal mode analysis is required, so quantum-mechanical calculations appear to be the only alternative.I3 e
To whom correspondence should be addressed. Abstract published in Aduance ACS Abstracts, October IS, 1993.
In several studies the quantum mechanical consistent force field (QCFF) approach, introduced by Warshel and Karplus,l9 has been utilized to calculate the vibrational frequencies of porphyrins and chlorins.13 Margulies and Toporowiczmemployed this method to analyze the RR spectrum of BVE. However, the resulting frequencies may be in error by 100 cm-1,21 ruling out unambiguous assignments for a molecule such as BVE which possesses 243 normal modes. Grossjean et al.z2 have used the MNDO method to calculate the force field of the retinal chromophore in bacteriorhodopsin. These authors used a global scaling procedure by introducing "spectroscopic masses" in order to compensate for the systematic errors in the MNDO approximations. Such an approach can thus effectively compete with empirical studiesl4J5which are based on a large set of experimental data. The present work is also based on a semiempirical approach, but we have used the AM1 method23 for calculating the force field since AM1 is a distinct improvement over MND0.24 Moreover, instead of using scaling factors for the G matrix as in ref 22, we have scaled the F matrix. This promises to be a more accurate approach since it allows for correcting systematic errors in a mode-specific way. The determination of the scaling factors followed the procedure introduced by Pulay et al.21 In a first step, we checked this approach for smaller molecules (Le., BVE fragments) by comparing the results obtained by AM1 with those from ab-initio Hartree-Fock (HF) calculations. In this way, scaling factors were obtained which served as the initial parameter set for the calculations of BVE itself. Even this improved quantum-mechanicalapproach does not yield unique assignments if only the frequencies are considered. Hence, IR and RR intensities were also calculated, the latter being approximated following a procedure introduced by Peticolas and co-workers.25 The calculated spectral parameters were compared with the experimental IR and RR data for a further refinement of the scaling factors. To the best of our knowledge, this is the first approach in which the scaling factors in a normal mode analysis are optimized based not only on vibrational frequencies but also on IR and RR intensities. The final set of calculated data leads to a straightforward vibrational assignment for most of the observed bands. Thecapabilities and limitations of this approach are discussed.
0022-365419312097-11887%04.00/0 0 1993 American Chemical Society
11888 The Journal of Physical Chemistry, Vol. 97, No. 46, 1993
Materials and Methods FT-IR spectra were measured with an IFS-66 spectrometer (Bruker). For NIR-FT-Raman measurements, this spectrometer was connected with a Raman module (Bruker, FRA-106). The 1064-nm line of a Nd:YAG laser was used for excitation. The samples were deposited in a melting capillary, and the scattered light was collected in a 180' backscattering geometry. Details of the equipment and the sample arrangement are described el~ewhere.~~,~~ BVE was isolated and purified according to Lehner et a1.28 The FT-Raman spectra were measured directly either from the solid sample, from solutions in CC14,or from suspensionsin H20 or D20. The solid-state spectrum (boxcar apodization and a zero-filling factor of 8) exhibits a higher resolution with a 0.1cm-1 increment per data point as compared to the solution and suspension spectra (four-term Blackman-Harris apodizationand a zero-filling factor of 2) with a 0.9-cm-1 increment per data point. The four-term Blackman-Harris apodization function yielded a broadening of the bands by -6 cm-I. The IR spectra were measured either in KBr pellets or in CC14solutions. In the latter case, the D/H exchange of the pyrrole N-H protons was achieved by repeated suspension in D 2 0 after pelleting. The resulting sample was dried and suspended in D20-saturated CC4. The spectra were analyzed by a band-fittingprogram to determine the spectral parameters of overlapping bands. The accuracy of the frequency determination strongly depended on the quality and resolution of the measured spectra. For example, for all the bands displayed in the RR spectrum of solid BVE in Figure 2B the standard deviation was fO.l cm-' for the frequencies and f3.8% for the intensities. The~correspondingvalues for the IR spectrum (Figure 2C) were f0.3 cm-l and *lo%, respectively, for the strong bands, but significantly worse for the weaker ones which exhibit relative intensities below 5. In the more crowded spectral regions below 1500 cm-I (cf. Figures 6 and 7), the accuracy was ca. f 1 cm-l and f 15%for most of the bands with relative intensities above 5 but a factor of ca. 3 lower for the weaker ones, in particular in the IR spectra. In those cases where the same modes appeared in both the RR and the IR spectra, we tried to obtain a consistent fit by using the same frequencies ( f l cm-1) to simulate the measured spectra. For the semiempirical and the ab-initio calculations, we used the program packages MOPACZ4and TURBOMOLE,29 respectively. The normal mode analysis and the calculations of the RR and IR intensitieswere carried out with programs developed in our laboratory.30 The calculations are described in detail in the following section.
Results and Discussion Force Field Calculations and Normal Made Analysis. The normal mode analysis was carried out within the harmonic approximation; i.e., anharmonic effects were neglected. The intrinsic errors, which are associated with the harmonic approximation as well as with systematic deficiencies of the AM1 force field approach, were partly compensated by multiplying the force constants with scaling factors which minimize the difference between the calculated frequencies and intensities and the correspondingexperimentalvalues. The scalingprocedure chosen was introduced by Pulay and co-workers.21 An element& of the force constant matrix, expressed in internal coordinates according to Pulay's convention,31 is multiplied by the geometric mean (sisj)llz of the scaling factors si and sj which are associated with the internal coordinates i andj, respectively. In matrix formulation, this is expressed by eq 1
p' = S1/2.F.S1/2
(1)
where F is the unscaled force constant matrix calculated either ab-initioor byusingAM1,Sisadiagonalmatrixwiththediagonal
Smit et al. elements being the scaling factors, and is the scaled force constant matrix. The scaling factors are characteristic for the individual internal coordinates to which they refer and should be. similar for molecules which include the same internal coordinates in similar chemical environments. We have followed a two-step procedure for determining the minimum number of scalingfactors to be used and their numerical values. In the first step, we have optimized the scaling factors for some small molecules which altogether possess the structural elements and functional groups of BVE. In the second step, the resulting set of scaling factors for these fragments was used as starting values for a further refinement in BVE itself. Using this two-step procedure, the quality of the scaled force field could be checked on well-known systems. In this way we could largely avoid the risk of getting lost in local minima upon progressing through the multidimensional parameter space. We have chosen pyrrole, maleimide, aceticacid, and ethene as fragments of BVE. For these molecules, structural and spectral data are available?*+ and, in addition, the quality of the present approach and the resulting vibrational assignments can be checked by comparison with the results of ab-initio calculations reported by other groups and obtained in the present work. For pyrrole, we carried out abinitio H F calculations with the basis sets 4-21G and 6-31G using both the experimentally determined and the calculated (optimized) molecular geometry. In each case, the vibrational assignment is identical with that obtained from the AM1 calculation provided that the original set of scaling factors as used by Xie et al.32was enlarged by adopting different scaling factors for the c=C- and C-C stretching coordinates. The accuracy of the AM 1 approach, as judged from the standard deviation of the calculated from the experimental frequencies, was slightly worse (f14 cm-l) than that for the ab-initio calculations ( f 5 cm-l). Our vibrational assignments agree with those recently reported by Kofranek et al.,33 who obtained a fit of frequencies with a somewhat larger standard deviation (f9 cm-l) using a MIDI-4 basis set. These assignments are corroborated by more elaborate abinitio calculations which include electron correlation effects.34 On the other hand, some frequencies have been differently assigned by Xie et al.32 who used the same scaling factors for both the C = C and C-C stretching coordinates. For maleimide, the scaled AM1 and 4-21G ab-initio H F force fields gave identical vibrational assignments but slightly larger standard deviations between the calculated and experimental frequencies40 for the AM1 force field (19 vs 5 cm-1). There was also a good agreement with the ab-initio results of Csaszfrr et a1.,40 with some minor exceptions which are discussed in detail elsewhere.30 The force field of acetic acid was determined by including also the deuterated isotopomers. The AM1 and ab-initio 4-21G HF calculations yielded identical assignments which also agree with the ab-initio H F results obtained with a 4-31G basis as reported by Williams and Lowrey.44 For this molecule, the standard deviation was better in the AM1 approach (f9cm-1) than in the ab-initio calculations (f18 cm-1). Only for the C-C torsional motion was a large discrepancy found between the experimental and the AM1 calculated frequency. While the C - C torsion is observed at 93 cm-l (taken from ref 44), a value close to zero is obtained by AM1. This failure of the AM1 method, however, does not influence our assignments of the BVE spectra since the frequencies are too low to be observed in the IR and RR spectra. Also for ethene45s46identical assignments were obtained from AM1 and ab-initio 4-21G HF calculations. This molecule was used to determine the scaling factors for the C - C stretching and sp2angle deformation coordinates of the methine bridges and the vinyl groups in BVE. The comparison of the results for the BVE fragments clearly demonstrates that the semiempirical AM 1 calculations and the ab-initio 4-21G H F calculations yield force fields of comparable
Vibrational Analysis of Biliverdin Dimethyl Ester
The Journal of Physical Chemistry, Vol. 97, No. 46, 1993 11889
TABLE I: Optimized Scaling Factors for the Internal Coordinates of BVE coordinatea C-C str (ring A,C;D) C-C str (ring B) C-C str (ring-methyl, -prop) C-C str (ring-methine
-vinyl) C-C str (prop) C;=C str (ring A,C;D;
scaling factor
scaling factor
0.6851 0.5942 0.7502
coordinatP methyl asym def methyl rock methylene def (prop)
0.7585
C = O def (ring A;D)
1.0054
0.8692 0.5758
C = O rock (prop) C-O def (prop)
1,0874 0.7504
0.9108 0.9526 0.8167 0.8556 0.7884 0.7159 0.6738 0.6174 0.8721 0.9658 0.9960 0.9875
ring def (ring A,D) ring def (ring B) ring def (ring C)
0.8579 0.8830 0.8429 1.1171 1.0373 0.7509 1.1974 1.2242 1.1805 1.3804 1.1805 1.2065
1.0517 0.8421 1.0091
vinyl)
C==Cstr (ring B) C-N str (ring A;D) C-N str (ring B) C-N str (ring C) C=N str (ring C) C-O str (prop) C 4 str (prop) C 4 str (ring A;D) C-H str N-H str N-H def (ring A,D) N-H def (ring B)
C = O oop (ring A;D) C - 0 oop (prop) C-Hoop N-H oop (ring A,D) N-H oop (ring B) Ring tors (ring A,D) Ring tors (ring B) Ring tors (ring C) C = C tors (methine; vinyl)
ring-C (bend; oop; 0.9600 C-O tors (prop) 1.2476 tors) methyl sym def 0.9226 a Bend, bending; sym def, asym def, symmetric and asymmetric deformation;oop, out-of-planebending;prop, propionic ester group; rock, rocking;str, stretching; tors, torsion;labeling of the atoms refers to Figure 1. For the definition of the internal coordinates, see ref 31. quality, justifying the use of AM1 to calculate the force field of BVE itself. Further details of the calculations on the fragments of BVE are discussed elsewhere.30 Calculation of the Raman Intensities. For a molecule as large as BVE, an assignment of thevibrationalbands which is exclusively based on the vibrational frequenciesdoes not lead to unambiguous results. Hence, we calculated the relative IR and Raman intensities so that the respective IR- and Raman-silent modes could be sorted out for the comparison between the experimental band frequencies and the calculated data. The evaluation of the IR intensities is straightforward since they can immediately be obtained from the derivativesof the dipole moment with respect to thenuclearcoordinates. The computationof Raman intensities is by far more complicated. The following approximations were made. The FT-Raman spectra were measured with NIR excitation which is shifted from the lowest electronic transition of BVE (-650 nm).47 A recent FT-Raman study of phytochrome has revealed that the energy of 1064 nm is still sufficient to yield an appreciable (pre)resonance enhancement of the Raman bands of the protein-bound tetrapyrr~le.~ This is also the case for the FT-Raman spectrumof BVE, which isdominated by strong bands in the range between 1550 and 1650 cm-l (cf. Table I). In this region, one expects modes including predominantly stretching vibrations of the tetrapyrrole skeleton. On the other hand, bands in the region of the C-H stretching vibrations at -2900 cm-1 are very weak. Under nonresonant conditions,however, the skeleton stretching vibrations exhibit a weaker Raman activity than the C-H stretching modes.48 Resonance enhancement only occurs for those modes which include molecular coordinates differing in the ground and excited state (A-term mechanism) or for modes which are effective in vibroniccoupling (B-term mechanism).49qm Since the 650-nm absorption band of BVE is due to a a ?r* transition of the tetrapyrrole ring system, modes including, in particular, C=C(C-C) and C=N(C-N) stretches are expected to be resonance enhanced over modes such as the C-H stretching vibrations which do not satisfy the requirements of either an A-term or B-term mechanism. Hence, RR rather than Raman intensities must be calculated.
-
Figure 1. Structural formula of BVE.
The evaluation of RR intensities requires knowledge of the potential energy surfaces of the excited state(s) involved. In particular for larger molecules such as BVE, such calculations are extremely time-consuming and are currently limited by the availablecomputercapacities. Hence, we have chosen a simplified approach introduced by the Peticolas group,Z5.51.52 which is based on the assumption that the RR spectrum is dominated by A-term scattering. This appears to be a reasonable approximation since the electronictransition is strongly allowed and is separated from the second one by as much as 10000 ~ m - l . ' ~ Assuming that the vibrational frequencies in the ground and excited state are the same, the RR intensity Zjof the normal mode j depends on the displacements of the normal coordinates in the ground and electronicallyexcited state. For small displacements (AQ), this relationship is expressed by eq 2
Ij = KjAQ;u;
(2) where uj is the vibrational frequency of the normal mode.5*95*Kj is given by eq 3
B
Kj = [('GM
- ue,.c)z + rZ1 [('GM
-
+
+ rZ1
(3)
where UGM is the frequency of the electronic (0-0) transition under consideration and B represents a proportionality factor. 'I is a damping constant for which an empirical value of 1000cm-1 is adopted.25 In order to correlate the determination of the RR intensities with the normal mode analysis, it is necessary to transform AQj into the displacement of the internal coordinates, AR,via Wilson's L matrix53 according to eq 4 (4) where underlined letters denotevectorial quantities. Combination of eq 4 and eq 2 yields eq 5
Lagant et al.25 restricted the evaluation of AR to stretching coordinates which were assumed to be proportional to the change in the bond order Abk between the ground and the electronically excited state (cf. ref 54). Within this assumption,eq 6 is obtained:
where ck is a proportionality constant, relating the bond length Rk with the corresponding bond order bk. ck varies between 0.180 for C-C and C-N bonds and 0.214 for C-O bonds.% The bond orders in the ground and excited state were calculated by the CNDO/S method using the parameters from refs 55 and 56. For the excited state, a configuration interaction calculation limited to the energetically lowest 500 singly excited codigurations was performed. It is necessary to emphasize that Peticolas'
Smit et al.
11890 The Journal of Physical Chemistry, Vol. 97, No. 46, 1993
TABLE II: Calculated and Observed Frequencies and Intensities of BVE(H) between 3500 and 1330 cm-1' observed calculated mode
Y
v4 I
3491-3432 3002-2797 1738 1735 1700
~ 4 2
1696
YI-Y~
u4-u38 ~ 3 9
ua
~ 7 9 ~, 8 o
1629 1616 1594 1590 1581 1535 1525 1521 1506 1479 1476 1453 1452 1440 1438 1437 1434 1430 1425 1421 1420 1418 1414 1413 1413 1413 1409 1403 1402 1401 1401, 1400 1398 1395 1392 1391
Y8 1
1380
Y43 Y4.i
v45 UM
Y47
Y40 v49 ~ 5 0 Y51 0 2 Y53 Y54 Y55 US6 ~ 5 7 ,us8 Y59 YM)
Y61 Y62 Y63 YM Y65 Y66 ~ 6 7 Y68 Y69 Y70
Vl Y72 Y73 ~74,~75 ~ 7 6 Y77 Y78
~ g r ~ g 41378-1374 Y83 Vg6,Y87 Y88 ug9
YW
1371 1368, 1367 1363 1347 1338
IR
I(IR) 3.0 45.0 4.4 53.8 100.0
I(RR) 0.2 0.2 0.8 7.3
3020-2800 1737 1743 1706
46.0
1.3
1685
-
21.7 4.5 43.2 46.8 30.4 2.9 4.5 2.2 0.7 0.2 4.6 76.2 20.3 3.6 6.5 5.0 1.5 5.2 0.3 0.3 1.4 0.3 1.4 3.1 2.2 12.4 12.4 2.2 1.6 1.6 2.4 1.6 8.5 2.4 0.2
2.0 52.8 100.0 0.5 0.9 0.6 6.4 0.4 5.7 0.3 6.4 53.8 11.2 1.4 1.2 10.6 1.3 2.0 0.1 0.0 0.0 0.2 1.0 5.7 0.3 0.2 0.2 0.0 0.0 0.0 0.5
2.4 3.3
0.0
8.1 17.7 9.3 14.3 8.0
Y
-
1661 1638 1625 1616
-
1593 1585 1575 1550 1532 1514 1499 1491 1469 1459 1447 1436
-
1417 1405 -
RR I(IR) 50 23 52 100
Y
2970-2820 -
I(RR) 10.0 -
-
1698.6
5.8
1669.0
0.7
1637.1 1622.9 1616.7 1606.8 1593.0 1583.2 1532.8 1499.2 1469.3 1457.2 1448.0 1438.0 1429.8 1418.6 1402.2
3.2 27.9 12.6 40.3 100.0 24.5 7.0 16.3 64.6 6.7 7.3 22.6 8.7
str C a 4 (D) 47%; str Ca=O (A) 15%
24 6 2 6 8
13 19 7 0.5 3 1 1 1 2 9
-
9 20 -
-
8 10 -
-
-
-
-
5.6 8.7
-
-
-
-
11 -
1384.0 -
25.5 -
1.1
-
-
1378.0
2.4
0.1 0.0 1.6 0.2 0.1
1362 1350 -
-
-
15
1363.5 1342.1
0.0
2.9 1.9 0.0
-
1386 -
-
8
-
--
PEDb& str N-H (A,B;D) 100% str C-H (all groups) 100% str C=O ( p r o w ) 4 6 % str C 4 (prop-B) 36% str C=O (prop-B) 46% str C=O ( p r o w ) 36% str C , 4 (A) 48%; str Ca=O (D) 16%
-
-
6.1
-
5.6
str C,=N (C) 64% str C,(B)-methine 26% str Cb-Ci,@) 22% str C,-C, (B) 28%; str Ca(B)-methine 20% str C,-N (A) 26%; str C.-N (D) 15% str Ca-N (D) 24%; str C,(D)-methine 14% str Cb(D)-Vinyl 31%; str Cb-CY (D) 28% str Cb-CY (C) 42%; str Cb(C)-methyl 19% str cb-cy (A) 30%; str Cb(A)-vinyl37% str C,-N (B) 25% str C = C (vinyl-A) 21%; str Cb-CV (A) 18% str C,(C)-methine 24% str C = C (vinyl-D) 24%; sym def = C H I (vinyl-D) 21% asym d e r -CH3 (B) 31%; rock C-H (methine-AB) 16% sym def CH3 (prop-B p r o w ) 80% asym def CH,(C) 2296, rock C-H (methine-CD) 18% rock C-H (methine-AB) 21% asym def CH3 (B) 26% asym def CH3 (B) 77% asym d e r CHI (C) 69% asym def CH,(A) 48% sym def = C H I (vinyl-A) 20% wag C,H2 ( p r o w ) 26% asym d e r CHI (D) 49% asym d e r CHI (D) 2 1 % wag C.H2 (prop-B) 15% asym d e r CH3 (A) 90% asym def CH3 (D) 79% bend N-H (A) 39% scis CoH2 (prop-B) 45% bend N-H (D) 21% asym d e r CH3 ( p r o w ) 27% asym d e r CH3 (prop-B; p r o w ) 32% scis CpH2 ( p r o w ) 57%; asym def CH3 (C) 21% rock C-H (methine-BC) 12% rock C-H (methine-BC) 1 4 % bend N-H (D) 14% asym def CH3 (prop-B; p r o w ) 6 5 % asym d e r CH3 (prop-B; p r o w ) 24% scis C,Hz (prop-B) 2 8 % scis C,H2 ( p r o w ) 25% sym def CH3 (B;C) 35%; scis C,H2 (prop-B; p r o w ) 27% sym def CH3 (A) 33%; bend N-H (B) 14% sym def CH3 (A;D) 61% scis C,H2 ( p r o w ) 32%; wag C B H(~p r o w ) 19% wag C,H2 (prop-B) 29%; wag CoHz (prop-B) 16% rock C,H (vinyl-D) 18% sym def =CH2 (vinyl-D) 16%; str C-N (D) 18%
-
-
-
-
-
0 Frequencies are given in cm-1; relative IR and RR intensities refer to the modes Y41 and ~ 4 5 ,respectively. Only the dominant contributions of the PED are listed. Modes with similar PED are summarized in one entry. In these cases the intensities refer to the sum of all modes involved while the PED represent average values. C scis, scissoring; wag, wagging. Further abbreviations are given in the footnotes of Table I.
approach can predict RR intensities only for modes involving C-0, C-N, and C-C stretching vibrations. Hence, for internal coordinatesother than bond lengths, the corresponding Ck values were set equal to zero. This implies that the calculation of the RR intensities is only possible for those normal modes which include high contributions from the stretching vibrations within t h e tetrapyrrole. A s shown below, for many modes which include only minor contributions from these stretching vibrations only very small RR intensities (
