DFT study on Raman spectra of Fe(II)-porphin

Density functional theory (DFT) quantum-chemical calculations of Raman spectra of Fe(II)-porphin in a quintet (ground) state were performed. Spin-unrestricted UB3LYP functional with the 6-311G basis was used for geometry optimization and Raman calculation. All active modes of Raman spectra were analyzed in detail. It was noted that the insertion of Fe(II) ion into porphin leads to the considerable changes in frequencies and intensities for those vibrational modes which involve nitrogen atoms displacement. The Raman depolarization ratio for plane polarized incident light is discussed.

Introduction.The iron ion with the (+2) degree of oxidation plays an important role in chemistry of hemproteins, in binding of oxygen and its activation in particular.Fe(II)-porphin (Fe(II)P) may exist either in high-spin (S = 2), or low-spin (S = 0) state, or in a state with interim spin (S = 1), where S is a quantum number of the total spin.The DFT quantum-chemical calculations of spin states of Fe(II)-porphin molecule were performed as in [1] with subsequent determination of relationship between a spin and stereochemistry of Fe(II)-porphin which is of great importance for understanding biological functions of hemproteins.It was noted that the quintet (Q) state with a quantum number S = 2 is the main ground state of Fe(II)P molecule.
The data on the force field of vibrations of all atoms in Fe(II)-porphin molecule are necessary to reveal mechanisms of catalytic processes, occurring with participation of these and related molecules, as vibrational frequencies determine the energy transfer and reaction capacity of hemoproteins in the interaction with ligands as well as in the enzymatic reactions of cytochrome P450, for which Fe(II)P is a simple model.DFT was used to calculate infrared (IR) spectrum of absorption and Raman spectra of a free-base porphin (H 2 P) in [2,3], and IR-spectrum of Fe(II)-porphin in different spin states -in [4].
The current work deals with DFT quantum-chemical calculations ofRaman spectra of Fe(II)-porphin in the quintet (ground) state.Special attention is paid to the analysis of form of vibrational modes which belong to various types of symmetry.
In case of the Fe(II)P molecule with high symmetry (D 2h ), the normal vibrations active in Raman spectra are prohibited in IR-spectrum, and vice versa, the intense IR-bands are absent in Raman spectra.Therefore, this work devoted to the theory of Raman spectra of Fe(II)P is a supplement to the work [4], where vibrations, active inRaman spectra, were not considered.
It is especially important to determine force constants for the out-of-plane vibrations of Fe ion, dependent on the balance of attractions and repulsions due to conjugation of the 4p p (Fe)-and a 2u (porphin) orbitals as well as the antibinding 3d x y 2 2 -(Fe) and 2p(N)-combinations of orbitals.The issue of changes in strength of chemical bonds depending on p-delocalization, d-p-conjugation, and spin of Fe ion is yet to be clarified.These questions are essential for understanding enzyme activity of cytochromes and hemoproteins.
Investigations of molecular vibrational spectra using quantum-chemical calculations have recently become more popular [1][2][3][4][5][6][7][8][9][10].Frequencies of the IR spectrum of Fe(II)P were calculated by Kozlowski et alt.[5] using DFT B3LYP method with the 6-31G basis set, however, only several normal modes of the low-frequency vibrations were presented and discussed.The majority of frequency assignments in Raman spectra of cytochromes and metalloporphyrins were made on the basis of empiric rules and fitting [11][12][13].Therefore, the authors consider the calculations of Fe-porphyrins spectra on the ground of consistent theoretical approach to be quite urgent and timely.
Ma te ri als and Meth ods.The DFT method [6,14] was used in this work to per form cal cu la tions of the opti mized ge om e try and Raman spec tra of the Fe(II)P mol e cule at the B3LYP level of the ory (three-pa ram eter hybride ex change-cor re la tion func tional of Becke-Lee-Yang-Parr ap proach [6]) with the 6-311G ba sis set [14,15] us ing GAUSSIAN 03 soft ware package [15].Fre quen cies were ob tained by an a lyt i cal calcu la tions of the Hessian ma trix for the equi lib rium geom e try, optimized in different spin states.
IR and Raman spectra of four-coordinated Fe(II)-porphin have not been studied in experiments due to chemical instability of Fe(II)P depending on fast oxidation [16].There are data on resonance Raman spectra of five-and six-coordinated derivatives of Fe(II)-octaethylporphyrin (FeOEP), namely, Fe(OEP)Br, [Fe(OEP)(dimethyl sulfoxide) 2 ]ClO 4 , Fe(OEP)(imidazol) 2 [7,11] etc.It was shown for fiveand six-coordinated metalloporphyrins [11] that vibrations of metal-axial ligand bonds do not blend with vibrations of macrocycle.Therefore, it is possible to compare corresponding Raman and IR bands of FeP to spectra of Fe(OEP) derivatives.We consider it critical to clarify IR and Raman spectra of idealized FeP structures in different spin states and degrees of Fe oxidation, comparing results of calculations of vibrations of FeP to analogous results for free-base porphin (H 2 P) and zink-porphin (ZnP), reliable assignment of IR and Raman spectra as well as all non-active vibrations for which have already been obtained on the basis of rather accurate DFT calculations for the ground singlet state of these molecules [3,[8][9][10].This is the only way to decipher vibrational spectra of actual hemproteins and to determine dependence of frequencies and force fields on spin and degree of the Fe ion oxidation.
Though calculations of normal vibrations of metalloporphyrins on the basis of empirical force fields [12,13] provide many assignments for in-plane modes and specify a number of regularities in IR and Raman spectra without analysis of their intensities, they can not provide a definite answer to abovementioned questions, that can be solved only by direct DFT calculation.
Results and Discussion.The Fe(II)P molecule in the quintet state possesses the D 2h symmetry, but its structure is similar to the D 4h symmetry, which this molecule has in the singlet (S) and triplet (T) states.The D 4h point group has two kinds of symmetry -A 1g and B 1g , which correspond to A g -one irreducible representation in the D 2h group.Vibrations of this type of the Fe(II)P molecule in the quintet state correlate with two types of symmetry -A 1g and B 1g in the S-and T-states in the D 4h point group, thus they have different polarization.The lines in Raman spectra with 0< r<3/4, are called polarized [17].The polarization degree is high (e.g.r = 0.11) only for those vibrations of the A g -type in the Fe(II)P molecule in quintet state, which correlate with A 1g vibrations in the D 4h group (see Table 1 in [4]).These data are important for band assignment in Raman spectra and their comparative analysis for all hemproteins.
Numeration of atoms and the choice of axes in Fe(II)P molecule (Oz axis is perpendicular to the molecular plane) are shown in Fig. 1.We used traditional marking system: carbon atoms in a-positions -C a , in b-positions -C b , in mezo-positions of macrocycle -C m , mezo-atoms of hydrogen, located close to bridge carbon atoms, correspond to Greek letters a, b, g, d.Atoms of pyrrole rings II and IV are indicated with prime symbols (C a ', C b ').Calculations showed that in the quintet state of the Fe(II)P molecule all atoms are located in one plane with simultaneous in-plane deformation of the molecule (compared to the singlet and triplet states) and its symmetry decreases from D 4h to D 2h [1].Electronic state of spin quintet has 5 B 2g symmetry.
Calculated bond distances, presented in Fig. 1, show that if a molecule rotates around the Oz axis in 90°, the bond distances differ from the initial ones, which testifies to decrease the symmetry to D 2h .
The Fe(II)P molecule has 37 atoms and 105 internal freedom degrees.If axes are selected as in Fig. 1 [4].Raman spec tra of Fe(II)P, cal cu lated in the cur rent work, has 51 nor mal vi bra tions: 18 vi brations of a g sym me try, 17 -b 1g sym me try, 8 -b 2g , and 8b 3g sym me try.Cal cu lated fre quen cies and forms of normal vi bra tions, ac tive in Raman spec tra of Fe(II)P, are pre sented in Ta ble, which also gives com par i son with Raman spec tra of H 2 P (all fre quen cies of nor mal vi brations are real).Fig. 2 pres ents calculated Raman spectra of Fe(II)P.
Mo lec u lar sym me try does not change in the course of for ma tion of Fe(II)P in the quin tet state from porphin, since there is no align ment of geo met ri cal param e ters of pyrrole frag ments, ob served in metallocomplex Fe(II)P (Fig. 1).Raman spec tra of Fe(II)P, com pared to that of H 2 P, will not con tain vi brational modes, de ter mined by va lence vi bra tions of the N-H bond in H 2 P (n calc = 3584 cm -1 ) and deformational NH-vi bra tions (n calc = 610 and 1261 cm -1 ).
The high-frequency region of Raman spectra.We predicted a number of very intense Raman bands in high-frequency region which are determined by CH-vibrations (Table).This range of porphyrin spectra has not been studied in experiments, as it is covered by scattering due to CH-or OH-vibrations.However, it provides a lot of interesting information if a proper assignment is available.Frequencies (n, cm -1 ) and intensities (I, & A 4 /a.m.u.) of normal vibrations in Raman spectra of Fe(II)-porphin and free-base porphin, calculated by the B3LYP/6-311G method.n as (C a -N) + n as (C a' -N), twisting and deformation of rings (², ²²²out-of-phase, II, ²V -out-of-phase There are three vibrational modes of a g -and three modes of b 1g -symmetry of high intensity in the range of 3100-3250 cm -1 in Raman spectra of Fe(II)P, calculated in our work (Fig. 2  A 4 /a.m.u.), vibrations of C b -H and C b' -H bonds occur in the out-of-phase fashion; the calculated depolarization ratio is rather high (r = 0.740).InRaman spectra this band should be depolarized.In the D 4h point group of the ZnP molecule this mode corresponds to the b 1g symmetry with the similar frequency and intensity [3,8].In H 2 P this mode corresponds to vibration of C b -H bonds in non-protonated rings; our calculated data show that it has lower frequency, but almost two times higher intensity (Table ).Next to intense band (102, 105) in Raman spectra of Fe(II)P there are two groups of closely-located bands (94, 97, and 98, 100).Bands (100 and 98) at 3223 and 3222 cm -1 form a weak shoulder (Fig. 2), they correspond to asymmetrical vibrations of C b -H and have b 1g symmetry type in D 2h group.Modes a 2g and b 2g in a more symmetrical D 4h group correspond to them, respectively.The first one is prohibited in Raman spectra of ZnP molecule [3,8], but it becomes strongly allowed in Fe(II)P molecule (I = & A 4 /a.m.u.).The analysis of these bands in the fine-structure Raman spectra of Fe(II)P crystals could be a reliable criterion in determination of structural deviations from the D 4h symmetry.
Vibrational mode 97 with a g symmetry is highly polarized (r = 0.132).It is determined by vibrations of the C m -H bonds in methine bridges, occurring in one phase in the Fe(II)P molecule.The present calculations suggest that position of this vibrational mode in the spectrum and its intensity are not affected by introduction of the Fe 2+ ion into coordination centre of the molecule.Band 94, the degenerate analogue, is depolarized and less intense.
Intermediate region of Raman spectra.Middle part of Raman spectra of porphins was thoroughly investigated in experiments.We predicted a group of vibrational modes of a g symmetry and low-intensity mode 92 of b 1g symmetry in the range of 1500-1650 cm -1 frequencies in Raman spectra.Mode 93 is mainly determined by asymmetrical stretching motions of C m -C bonds of methine bridges and related deformational vibrations of C m H.These vibrations have a large amplitude, they occur in one phase in positions a, b, g, and d.In Raman spectra of H 2 P this type of vibrations corresponds to frequency of 1643 cm -1 and intensity of 203.4 & A 4 /a.m.u., close to values for Fe(II)P (1650 cm -1 and 195.9 & A 4 /a.m.u.).In experimental Raman spectra of H 2 P this band is observed at 1609 cm -1 [2,18], and in fluorescence spectrum -at 1614 cm -1 [19].The ratio of n exper /n calc for this vibrational mode of H 2 P and many other modes, equal to »0.98, allowed correcting the majority of frequencies, calculated for Fe(II)P in interim range of Raman spectra.
To take into account systematic errors in the course of frequency calculation for the stretching motions of C-H bonds (in the high-frequency range) we introduced the scaling factor 0.96, vibrational frequencies in the range of 145-756 cm -1 were corrected by the introduction of scaling factor 0.99 (n corr is a corrected frequency value).Asymmetric stretching motion C m -C gives a depolarized band inRaman spectra (calculated r = 0.659), found experimentally in Raman spectra of a number of FeOEP derivatives [11].Its shift to the range of lower frequencies correlates with the increase of the Fe-N distance in complexes.
Polarized bands of Raman spectra, revealed in the range of 1475-1510 cm -1 for a number of FeOEP derivatives, were assigned by Kitagawa et al. [11] to the totally symmetrical C m -C stretching motion.Our data prove that polarized mode 89 Fe(II)P (r = 0.110) really includes the n s (C m -C) vibration, but the main contribution into this mode is made by stretching ) and C a -N (C a' -N), occurring in all pyrrole ring in one phase (n calc = 1578 cm -1 , n corr = 1546 cm -1 ).InRaman spectra of H 2 P molecule, the 89 mode of Fe(II)P corresponds to mode 91 [3] with a higher frequency (n calc = 1590 cm -1 ) and with less intensity (Table ).
Similar to the mode 89, the mode 86 with calculated frequency of 1523 cm -1 consists of vibrations of C b -C b bond (C b' -C b' ) and symmetrical vibrations of C a -N (C a' -N), but vibrations in the II and IV pyrrole rings are in the out-of-phase fashion to vibrations in the I and III pyrrole rings.According to calculations, this mode has depolarization character (r = 0.733), therefore, it will correlate with the b 1g vibrations in the D 4h group.The amplitude of vibrations of the C a' -N bonds in Fe(II)P is considerably smaller than that of C a -N.The calculated intensity for this mode (405.3 & A 4 /a.m.u.) in Fe(II)P has the highest value in the observed range of frequencies; as for H 2 P, the same regularity is observed with smaller differences in Raman intensities.
We also predicted three vibrational modes of a g symmetry in the range of 1300-1500 cm -1 , but they are less intense (Fig. 2, Table ).Polarized (r = 0.145) mode 82 (n calc = 1457 cm -1 , I = 95.A 4 /a.m.u.)Like mode 82, it belongs to stretching motions of pyrrole rings bonds, but vibrations in rings II and IV take place in out-of-phase to I and III.In this mode stretching motions are mingled with deformational vibrations of C m H groups of methine bridges of large amplitude.According to calculations, the last band a g in this spectral range (mode 76, n calc = 1360 cm -1 ) may be described as stretching motions of C a -N and C a -C b , taking place in one phase in all pyrrole rings, with strong displacement of C a (C a' ) and N atoms, simultaneous deformation of pyrrole rings and considerable bending motions of C a C m C a' and CC m H, which, in its turn, conditions movement of C m H-groups with a large amplitude.
Calculated depolarization ratio (r = 0.195) is much smaller than that for H 2 P (r = 0.444), i.e. in Fe(II)P this type of vibrations is more polarized due to the fact that deviations from the D 4h symmetry of the Fe(II)P molecule are not so significant as those for H 2 P, telling considerably on the latter.Vibrations of b 1g -type (except mode 77) in this range are of extremely low intensity (Table ) which differs considerably from the behaviour of these vibrations in H 2 P molecule.
Five vibrational modes of a g symmetry should be observed in Raman spectra in the range of frequencies of 950-1200 cm -1 .The main contribution into mode 69 (n calc = 1196 cm -1 ) is made by rocking motions of C m H-groups.There are also vibrations of Fe-N bonds without displacement of Fe atom in this mode.It is noteworthy that displacement of Fe atom is completely absent in vibrations in Raman spectra, as it violated symmetry of inversion (these vibrations are assigned to ungerade type; they may be active only in IR spectrum).Mode 89 is depolarized (r = 0.745), therefore, this type of vibrations in D 4h group will correlate with b 1g mode of symmetry.The main contribution into polarized (r = 0.109) mode 65 (n calc = 1107 cm -1 ) is made by rocking motions of C b H and C b' H groups; its calculated intensity is not very high (9.The last intense band in this range (about 1020 cm -1 ) is conditioned by overlapping of modes 55, 56, 60 (Fig. 2).Analysis of the data in Table shows that these modes are rather selective regarding Fe(II) ion, it is especially true about polarized mode 60 (r = 0.125), whose frequency is displaced -17 cm -1 in H 2 P, and 57 cm -1 in ZnP.
The main input into mode 60 is made by symmetrical stretching motions of C a -C b and Fe-N 33(34)  with strong displacement of atoms of N 33(34) and C b H-groups.Similar vibrations are observed in rings II and IV, but their amplitude is smaller.Corresponding mode in H 2 P molecule is observed in non-resonance Raman spectra at 987 cm -1 , while in resonance Raman spectra, phosphorescence and fluorescence spectra it is close IR range at the wavelength of 1064 nm [8].Quasi-degenerate low-intense modes 8 and 10 (211 and 216 cm -1 ), 23 and 24 (442 and 444 cm -1 ) are conditioned by out-of-plane twisting of pyrrole rings.
The most intense band in low-frequency range of Raman spectra of Fe(II)P is that of strongly polarized (r = 0.117) mode 18 of a g symmetry (n calc = 370 cm -1 , I = 99.9 & A 4 /a.m.u.).This mode is conditioned by stretching motions of Fe-N bonds in one phase which causes pulsation (breathing) of the whole macrocycle.Vibration n 18 remains as a very intense polarized band in Raman spectra in all metalloporphyrins, calculated by us: ZnP (373 cm -1 ) and MgP (364 cm -1 ) [3].Stretching motions of Fe-N bonds out-of-phase form depolarized and less intense band of a g -symmetry in Raman spectra at 216 cm -1 (mode 9, I = 27.1 & A 4 /a.m.u.).This mode correlates with vibration of b 1g symmetry in D 4h group.Vibrations n 18 and n 9 include Fe-N bonds, therefore, their frequencies are strongly displaced compared to Raman spectra of H 2 P ( 60 cm -1 to the region of high frequencies).
Conclusions.The performed calculations proved reliability of the DFT B3LYP/6-311G method in prediction of frequencies of active vibrations in Raman spectra of free-base porphin and metalloporphyrins.Forms of vibrations in Raman spectra remain unchanged during formation of the Fe(II)P complex from the porphin molecule (only the NH-vibration bands vanish); considerable changes are mainly observed in frequencies and (or) intensities of those vibrational modes in case if there is strong displacement of nitrogen atoms during vibrations (modes 6, 9, 18, 55, 56, 60, 75, 77, 78, etc).Comparison of data for the H 2 P and Fe(II)P molecules allowed prediction of a new weak band at 158 cm -1 in Raman spectra of Fe(II) porphin.As this vibrational mode has contribution of NFeN, FeNC a deformational vibrations, it should be very sensitive to the structure of Fe-porphyrin, its spin, and oxidation degree as well as to dynamics of energy transfer in enzymatic reactions.Correction of the calculated vibration frequencies ofRaman spectra of Fe(II)P was performed on the basis of the ratio of experimental values of frequencies to theoretical ones, calculated for porphin molecule.Calculated depolarization parameters for the plane-polarized incident light allowed symmetry prediction of active vibrations in Raman spectra of metalloporphyrins with the D 4h point group, which is important for assignments in their Raman spectra.
The possibility of applying the methods of quantum mechanics regarding large molecules to simulate vibrational spectra is of great importance to the vibrational spectroscopy.It is possible that in the near future the theoretical methods would be as important for vibrational spectroscopy as the experimental ones.Investigation in the sphere of spectroscopy of porphins, performed by present work, proves the DFT method to be promising in simulation of vibrational spectra of hemproteins.
The work is financially supported by the state foundation of fundamental research (DFFD, F26.5/008).

Fig. 1 .Fig. 2 .Fen
Fig.1.Indication of atoms and the choice of axes in the Fe(II)-porphin molecule in the quintet state (bond distances are presented in & A) s (Fe -N 33(34) ) + n s (Fe -N35(36) ) -out-of-phase + n s (C a -N) (² and ²²² -in one phase) + n s (C a' -N) (²² and ²V -out-of-phase), pulsation of rings + d(ÐÑNC) + r(C m Í) + r(C b Í) + r(C b' -plane.g s (C b' Í),deformation of rings in the envelope form (II and IVout-of-phase)+g(C m Í)-in one phase in a and b, and out-of-phase with g and d positions -plane.g s (C b Í), de for ma tion of rings in the en ve lope form (I and IIIout-of-phase)+g(C m Í)-in one phase in a and d, and out-of-phase with b and g po si b C a N, Ñ a C b C b , Ñ b' C a' N, Ñ a' C b' C b' ), twisting and deformation of rings + t(C m Í) + t(C b Í) + t(C b'

nnn
-plane.g(C m Í) -in one phase in a and d, and out-of-phase with b and g positions + g s (C b Í) (² and ²²² -out-of-phase) + g as (C b' Í) (II and IV -in one phase-plane.g(C m Í) -in one phase in a and b, and out-of-phase with g and d positions + g s (C b' Í) (²I and ²V -out-of-phase) + g as (C b Í) (I and III -in one phase) -plane.g as (C b' Í) (II and IV -in one phase) + g(C m Í) -in one phase in a and d, and out-of-phase with b and g positions + g s (C b Í) (² and ²²²out-of-phase) -plane.g s (C b' Í) (II and IV -out-of-phase) + g(C m Í) -in one phase in a and b, and out-of-phase with g and d positions + g as (C b Í) (² and ²²² -in one phase) s (Fe -N 35(36) ) + n s (C a' -C b' ) (II and IV -in one phase) + n s (C a -C b ) (I and IIIin o ne phase) + d(ÐÑ a' C b ' Í, Ñ b ' C b ' ) + n as (C a -N) (I and III -out-of-phase) + n as (C a' -N) (II and IVout-of-phase), strong displacement of N atoms, twisting of rings + t(C b Í)+ t(C b' as (C a' -N) and n as (C a' -C b' ) (II and IV-out-of-phase) + n as (C a -N) and n as (C a -C b ) (I and III-out-of-phase), twisting of rings + d(ÐÑ a C b Í, Ñ a' C b' Í) + t(C b Í) + t(C b' s (Fe -N 33(34) ) + n s (C a -C b ) (I and III -in one phase), pulsation of rings + d(ÐÑ a C b Í, Ñ b C b Í) + n s (Fe -N 35(36) ) + n s (C a' -C b' ) (II and IV) b Í) + r(C b' Í) + n(C b -C b ) (I and III -in one phase) + n(C b' -C b' ) (II and IV -in one phase, but out-of-phase with I and III) b Í) + r(C b' Í) + n(C b -C b ) and n(C b' -C b' ) -in one phase + d(ÐÑC b Í, ÑC b' Í), pulsation of rings in one phase 1107 as (C a -N) and n as (C a -C b ) (I and III -out-of-phase) + n as (C a' -N) and n as (C a' -C b' ) (II and IV -out-of-phase), deformation of rings + r(ÑÍ) m Í) + n s (C a' -N) and n s (C a' -C b' ) (II and IV -in one phase) + n s (Fe -N 33(34) ) + n s (Fe -N 35(36) ) -out-of-phase + n s (C a -N) and n s (C a -C b ) (I and III -in one phase, but out-of-phase with II and IV) + d(ÐÑC m as (C a' -N) and n as (C a' -C b' ) (II and IV -out-of-phase) + t(C b' Í) + n as (C a -N) and n as (C a -C b ) (I and III -out-of-phase) + t(C b Í) + d(ÐÑC m Ñ, ÑC b Í) + n s (C m -C a ) b Í) + t(C b' Í) + n as (C a' -N) and n as (C a' -C b' ) (II and IV -out-of-phase) + n as (C a -N) and n as (C a -C b ) (I and III -out-of-phase), twisting of rings + d(C m Í) -in one phase in a and g, and out-of-phase with b and d positions + d(ÐÑC m Í) s (C a -N) and n s (C a' -N) -in one phase + n s (C a -C b ) and n s (C a' -C b' ) -in one phase + d(ÐC a C m C a' , ÑC m Í), deformation of rings, d(C m H)

nnnnnn
b Í) + t(C b' Í) + n as (C a -N) and n as (C a -C b )(I and III -out-of-phase) + n as (C a' -N) and n as (C a' -C b' ) (II and IV -out-of-phase), asymmetrical twisting of rings + d (C m Ím Í) + n(C b -C b ) and n s (C a -N) (I and III -in one phase) + n(C b' -C b' ) and n s (C a' -N) (II and IV -in one phase, but in the out-of-phase fashion with I and III), pulsation of the I and III rings, and II and IV -in the out-of-phase fashion in respect to the former.b -C b ) and n s (C a -N) (I and III -in one phase) + n(C b' -C b' ) and n s (C a' -N) (II and IV -in one phase), pulsation of rings + d(ÐÑNC) + n s (C m -C) as (C a -C b ) and n as (C a -N) (I and III -out-of-phase) + n as (C a' -C b' ) and n as (C a' -N) (II and IV -out-of-phase), twisting of rings with deformation + t(C b Í) + t(C b' Í) + n s (C-C m a ) and n s (C-C m g ) -in one phase, but out-of-phase with n s (C-C m b ) and n s (C-C m b -C b ) and n s (C a -N) (I and III -in one phase) + t(C b Í) + t(C b' Í) + n(C b' -C b' ) and n s (C a' -N) (II and IV -in one phase, but out-of-phase with I and III), pulsation of rings 1523 b -C b ) and n s (C a -N) (I and III -in one phase) + n(C b' -C b' ) and n s (C a' -N) (II and IV -in one phase, and in one phase with I and III), + n s (C m -C) + d(ÐÑNC) + t(C b Í) + t(C b' as (C m -C) + d(C m Í) -in one phase in a and g, and out-of-phase with b and g positions + n as (C a' -C b' ) (II and IV -out-of-phase) + n as (C a -C b ) (I and IIIout-of-phase), rocking of rings 1609 as (C m -C) + d(C m Í) -in one phase + d(ÐÑNC) + n s (C a -C b ) (I and III -in one phase) + n s (C a' -C b' ) (II and IV -in one phase, but out-of-phase with I and III), pulsation of rings I and III, out-of-phase with II and IV m a -Í) and n(C m g -Í) -in one phase and out-of-phase with n(C m bas (C b -Í) (I and III -out-of-phase) + n as (C b' -Í) (II and IV -out-of-phase in out-of-phase with I and III) as (C b -Í) (I and III -out-of-phase) + n as (C b' -Í) (II and IV -out-of-phase and in one phase with I and III) as (C b -Í) (I and III -in one phase) + n s (C b' -Í) (II and IV -in one phase, but out-of-phase with I and III) s (C b -Í)+ n s (C b' -Í) -in one phase 3247 Stretching motions (n): n s -symmetrical; n as -asymmetrical.Deformational vibrations: d(Ð) -change in valency angle; t -twisting; r -rocking; d(CH) -in-plane vibration of CH-groups; g(CH) -out-of-plane vibration of CH-groups C b -H motions occur only in protonated pyrrole rings.In the close-lying vibrational mode 102 of the Fe(II)P molecule (n calc = 3246 cm -1 , I = 331.1 &

8 &
A 4 /a.m.u.) consists of stretching motions of C b -C b (C b' -C b' ) and C a -N (C a' -N), occurring in one phase in all pyrrole rings, and of symmetrical vibrations of C m -C bonds in one phase in all methine bridges.The amplitude of vibrations of C a -N bonds is less than that of C a' -N, while values for C b -C b are higher that those for C b' -C b' .Similar regularity was noted in the corresponding mode of H 2 P. Depolarized band (r = 0.733), calculated at 1417 cm -1 (mode 80) is more intense (I = 186.5 &

1 &
A 4 /a.m.u.).In H 2 P molecule vibrations r(C b H) in the corresponding mode take place only in protonated pyrrole rings.Similar to mode 65, mode 64 (n calc = 1102 cm -1 , I = 4.2 & A 4 /a.m.u.) has a large contribution of vibrations of r(C b H) and r(C b' H), and stretching motions of C b -C b and C b' -C b' bonds out-of-phase, which results in considerable depolarization of mode in Raman spectra (r = 0.582).Therefore, mode 65 in metalloporphyrins of the D 4h symmetry group should correlate with the corresponding mode of the a 1g symmetry, and mode 64 -with b 1g .However, comparison to the calculated Raman spectra of ZnP molecule showed that the mode 65 in Fe(II)P correlates with the low-intensity mode b 1g in ZnP.The reason of polarization of mode 65 is not clear.This is the only deviation from the simple symmetry rules in Raman spectra for metalloporphyrins of the D 4h -and D 2h -type, found by us while comparing calculations of ZnP, Fe(II)P, and H 2 P molecules.Though intensity of this band in Raman spectra is not high, it deserves special investigation.
, in the D 2h -symmetry 105 normal vibrations are distributed in the symmetry types as follows: 18a g , 17b 1g , 8b 2g , 8b 3g , 8a u , 10b 1u , 18b 2u , 18b 3u , where a g , b 1g , b 3u , and b 2u -are plane vibrations, while b 3g , b 2g , a u , and b 1u are out-of-plane vibrations.Sym me try vi bra tions of the b 1u , b 2u , and b 3u types are al lowed in the IR spec trum, sim u lated by us and analysed in Ref.
, Table).The most intense mode 105 (n calc = 3247 cm -1 , I = 1038.8& A 4 /a.m.u.) is determined by symmetrical stretching motions C b -H and C b' -H, Í) + t(C b' Í) + n as (C a' -N) and n as (C a' -C b' ) (II and IV -out-of-phase) + n as (C a -N) + n as (C a -C b ) (I and III -out-of-phase), twisting of rings + n as (C-C m )