flC,C,) > f(C,N) > f(C,C,). This trend is consistent with that of Nip.** However, there are some significant changes of
4214 The Journal of Physical Chemistry. Vol. 95, No. I I, 1991 force constant from NIP to H2P. For example,f(C,C,) is reduced by -0.7 mdyn/A, corresponding to the experimentallyobserved bond length increase of about 0.02 A at 1.38 A (Table IV). All 1-2 (or i-i 1) stretchstretch interactions (type I of Figure 3) and stretch-bend interactions (type 11) are less than or about equal to 10% of the geometrical means of their diagonal force constants. 1-3 stretchstretch (or i-i 2) have values less than or about equal to 5% of the geometrical means of their diagonal force constants. It has been noticed in the previous force field calculation of N i p that the 1-3 stretch interactions are not necessarily negative in sign, as they are in benzene. It was argued that this is likely due to the polycyclic aromatic structure of MP, which provides more than one competing delocalization pathway. This argument is supported by the recent ab initio force field calculation for naphthalene2cand purine nucleic acid bases.2h 1-4 (or i-i 3) stretchstretch interactions (type IV) were all set zero values in NiP force field calculation in order to reduce the number of parameters. However, extensive work on benzene force field," including both empiricalzsand ab initid approaches, has shown that 1-4 interactions should not be neglected. They sometimes have values comparable to those of the 1-3 or even 1-2 interactions. Therefore, we have tested the importance of 1-4 interaction forces along the ?r skeleton. We find that certain 1-4 stretchstretch interactions are indeed important for porphine; these are the C,Cm-CdCmtinteractions across the pyrrole ring. This will be discussed in the mode assignment section. Bend-bend interactions between angle coordinates sharing two common atoms (type VI) and one common atom (type VII) were also systematically examined in this study. Their values are found to be very important in accurate description of pyrrole internal deformation and collective rotation and translation of pyrrole ring as a rigid unit. These force constants will be discussed when related modes are assigned in the following section. Assignment of Fundamentals. The calculated frequencies for natural abundance H2Pand its d2,d,, d,, dI2,and I5N2isotopomers are given in Table VI. The experimental frequencies listed there are taken from resonance Raman, IR, polarized IR, and highresolution luminescence spectra reported in the literature.11J*v26*27 The assignment of fundamentals to their major local coordinates is given in Table VII. About 270 observed frequencies are assigned with an average deviation of 1 1.5 cm-'. Special attention is paid to the reproduction of the isotopic shifts. This is a better criterion for the relative accuracy of normal modes than the frequency matching. Although the majority of the bands assigned here is in agreement with those in ref 1 la, the detailed normalmodes composition is quite different as implicitly indicated by very different force fields of the two works. We will discuss this in more details below. I . Symmetric and asymmetric CaCmstretching modes (v3,va, v3g.,b and ul0, ~ 1 9 V378.b): , There are eight c,cmstretching modes
Li and Zgierski
-
+
+
'" Vna(
b2, ) : 1616.0 CM-'
Vsb(
.,'
bg, ) ; 1596.0 CM-I
+
(25) (a) Ozkabak, A. G.; Goodman, L. J. Chem. Phys. 1987, 87, 2564-2582. (b) Duinker, J. C.; Mills, 1. M. Spectrochim. Acra 1968, 24A, 417-435. (c) Painter, P. C.; Snyder, R. W.Spectrochim. Acra 1980, 36A, 337-339. (d) See ref 2. especially 2a and 2g. (26) (a) Gladkov, L. L.; Gradyushko, A. T.; Shulga, A. M.; Solovyov, K. N.; Starukhin, A. S.J . Mol. Srrucr. 1978,45,267-305. (b) Ibid. 1978,47, 463-493. (c) benofontova, N. M.; Gradyushko. A. T.; Solovyov, K. N.; Starukhin, A. S.;Shulga. A. M.J . Appl. Specrrmc. (Engl. Trawl.) 1976, 25, 872-876. (d) Ibid. 197625,1398-1404. (e) Bykovskaya, L. A.; Gradyushko,
A. T.; Penonov, R. I.; Romanovsky. Y. V.; Solovyov, K. N.; Starukhin, A. S.;Shulga, A. M.J. Appl. Specrrosc. (Engl. Trawl.) 1978, 29, 1510-1518. (f) Arabci. S. M.; Shkirman, S.F.; Solovyev, K. N.; Yegorova, G. D. Specrrosc. Lett. 1977. IO,677-697. (s) Arabei, S.M.;Solovyov, K. N.; Shkirman. S.F.; Egorova, G. D. J. Appl. Spectrosc. (Engl. Trawl.) 1978,30,657-663. (h) Gradyushko, A. T.; Solovyov, K. N.; Starvkhin, A. S.Opr. Specrrosc. (Engl. Trans/.) 1976,40,267-271. (i) Gradyurhko, A. T.; Solovyov, K. N.; Starukhin, A. S.!bid. 1977,43, 37-41. 6)Gradyushko, A. T.; Solovyov, K. N.; Starukhin, A. S.;Shulga. A. M. Izu. Akad. Nauk SSSR, Ser. Fiz. 197s. 39, 1938-1943. (27) (a) Verma, A. L.; Bernstein, H.J. Biochcm. Biophys. Res. Commun. 1974, 57, 255-262. (b) Plus, R.; Lutz, M. Specrrosc. Lerr. 1974, 7, 73-84, 133-145. (c) Kim, B. F.; Bohandy, J. J. Mol. Specrrosc. 1978.73. 332-343. (d) Kim, B. F.; Bohandy, J.; Jen, C . K. Specrrochim. Acra 1974, 30A, 2031-2040. (e) Volker, S.; Macfarlane. R. M.J . Chem. Phys. 1980, 73, 4467-4482.
b v3 ( a g ) : 1421.0 CM-I
V,,,(
bzu ) : 1492.0 CM-'
V3eb(
bgu ) : 1437.0 CM-I
Figure 5. (a) Calculated Cartesian displacements of asymmetric C,C, stretchings via, vi9, and uj7,,,, Note that for vIo and v37,, the main amplitude is localized on C,C,C, triatom bridge, while for uI9 and u37b and C,C, bonds attached to pyrrole-like ring possess much larger amplitude than the C,C, bonds connected to pyrrolenine-like ring. For the purpose of clarity, the atomic displacements in this and all following figures are multiplied by a factor of 10. (b) Calculated Cartesian displacements of symmetric C,C, stretchings v,, ua, and u%,. Note that the C&, stretch coordinates are mixed with the symmetric C,C, stretchings; this is more evident if one compares this figure with Figure 6. expected for both MP and H2P. In MP, they are grouped into two sets according to whether they are symmetric (19,va, v3+J or asymmetric (vIo,~ 1 9 vnab) , with respect to the C2,axis passing through the opposite C, atoms. In H2P, the C2,axis is lost due t o symmetry reduction to D2h, and therefore it is probably more appropriate to use in-phase (symmetric) and out-of-phase (asymmetric) combination of the two adjacent CaC, stretchings
The Journal of Physical Chemistry, Vol. 95, No. 11, 1991 4275
Porphine Force Field
TABLE M u,
HlP expt calc
1610 1546 1493 1425 1360 1353 1182 1063 1063 988 952 736 723 309 157
A("N2)C PED6 pyr-H pyr (a) Observed and Calculated a, Fundamental Frequencies (cm-I) 0 3309 7 (99) 9 3095 5 (96j 0 0 3095 5' (96) 0 0 3041 6 (99) 0 0 1611 2 (36), 2' (36) 0 0 1542 I' (37), 13' (9). 1 (13) 0 0 1512 1 (30), 13 (a), 1' (31) 0 0 1421 2 (la), 2' (14), 1 (24) 0 y..,> : 'E' .',k.,,, . ....! ......i,, ,.
:
,;*...,
I
*..e: .
.'* -4
,
.?
,
,
,.
~
..+....',..
.'
,,I._.
i......pJ.,q .....:, , : ,..... . *,,.. ,
;
C
J
:
.2
'.
.
p.. ....4,. ?.
,,.%.....
*
&,,.
'...*..y .. ,
j
-"
;'*-
.A.._.:'
i
...... (* :
\...A.
jt,, i,,,:4
7
......,.. ,-., '.
,i.....'
,p., '
,
I
. ;
1'
Figure 8. Same as Figure 5 , but for pyrrole symmetric half-ring stretching modes u4, uI2, ~4l,,b Note that u4 and u12 have mode compositions very similar to those calculated for Da NiP in ref 8a even though the symmetry is 2-fold lower in HzP than in Nip. ~41,,b split in a way similar to that for u,,,,b but with ~ 4 1 ,dominated by the stretching of the pyrrolenine-like rings and Y4lb by the pyrrole-like rings. and ~ 4 I b(bu) modes are assigned to the observed IR bands at 1351 band and 1370an-',respectively. GS have assigned the 1350-~m-~ to both u41aand ~41bThis has been shown to be incorrect by recent polarized IR absorption spectroscopy by Michl and co-workers,l& which shows that 1351-cm-I band is of b,, polarization only. Eigenvectors of the four HIP symmetric half-nng stretching modes and the calculated frequencies are given in Figure 8. Calculated u4 and uI2for HIP have characters very similar to those of their counterparts in Their total displacement amplitudes are shared among the symmetric half-ring stretch of all four pyrrole rings (Figure 8). Their sensitivities to the ISNsubstitution at two types of pyrroles do not differ very much (Table 6). However, the splitting of ~ 4 occurs 1 in HIP in such a way that u41a and u4lb are dominated by the symmetric half-ring stretching of only one of the two types of pyrroles (Figure 8). Therefore, ~ 4 is1dom~ inated by the stretch of pyrrolenine-like rings and is more sensitive to its I5Nsubstitution; ~ 4 l is b mainly localized on the pyrrole-like rings and sensitive only to its 15Nlabeling (Table VI). 5. Pyrrole asymmetric hau-ring stretching modes ( ~ 2 2 , ~30, V&,b): Pyrrole asymmetric half-ring stretches are at much lower frequency, 1000 cm''. They are assigned to the observed vibronic bands (fine structure fluorescence) at 1005 (b Y ~ and ~ ) 976 cm-' (b,#, and IR bands at 986 (bh, vM), ant990 cm-' (bkr u,&), respectively. Calculated frequencies and eigenvectors are given in Figure 9. All asymmetric half-ring stretches have large displacing amplitudes on the pyrrole nitrogen atoms, as in MP. They all show very large ISNisotope shifts (>lo an-', Table VI). u2, and uW have some N-H in-plane bending component due to mixing with the 6(NH) bend coordinate in the same symmetry block. As a result, the skeletal amplitudes of Y~~ is shared by uII (1 138 an-')and 4(NH) (1226 cm-')modes, as will be shown later. The localization of the displacement amplitude on only one type of pyrroles is also very clear from Figure 9. 6. Pyrrole breathing modes ( p a , uIS,u47&b): Pyrrole breathing modes are concerted in-phase stretchings of all bonds within pyrrole (except C& which is very much a localized coordinate), as illustrated in Figure 2. They are assigned to the observed Raman bands at 988 (as, u6), 952 cm-I (as, v I 5 )and IR bands at 949 (bur uq7,). and 968 cm-'(bluru47b). respectively. Calculated frequencies and eigenvectors are given in Figure 10. It can be
-
V4,,( b3, ) : 1012.0 CM-'
J
Figure 9. Same as Figure 5, but for pyrrole asymmetric half-ring stretching modes vu, Y ~ and , v h b . This group of modes have large displacements on N atoms, similar to those calculated for Nip'* therefore, they are expected to show large I5N/l4Nisotope shifts (- 10 cm-'). Another common feature of this group of modes is that they all are slightly mixed with a certain amount of H in-plane (N-H, C,-H, and C,-H) deformations, resulting in the loss of displacements at C, atoms to H in-plane deformation modes (see text for discussion). v,
:
t,.
*-i
? ...I......*..
I
J'..
uIs( a g ) : 956.0 C M - ~
( a g ) : 971.0C M - ~
v,(Cu) > v,(Zn) > v,(H2-) where i = 10,19,37. The frequency lowering of the asymmetric C,C, mode in above order cannot be due to the d-T* back bonding since this effect would result in the H2Phaving the highest frequency asymmetric C,C, modes, which contradicts the observation. The shape of the accepting T* orbital (Figure 19) calculated for porphine dianion, predicts that d-r* back bonding would cause an overall reduction of the ?r-bond order of the C,C, bond and therefore a decrease of its frequency. C,C, bond shortening induced by metal coordination (X-ray diffraction data of Table IV) is consistent with a C,C, frequency increase from H2P to MP but inconsistent with the d-r* back-bonding picture. We noticed that although the whole inner 16-membered ring contracts upon metal coordination, the NC, bond length increases while the C,C, bond shortens. This fact seems to indicate that bond polarization effect due to the u donation upon M-N bond formation plays a major role in the C,C, bond order change from H2P to MP and not the d l r * back bonding since the latter effect would result in the increase of both NC, and C,C, bond lengths. The shortening of C,C, bonds upon metal coordination as listed in Table IV is also inconsistent with the picture of d-?r* back bonding. However, if the back-bonding overlap between metal d,, and the X component of the e,* orbital only affects the ?r bond strength of the two pyrroles (and their directly attached C,C,
4284
Li and Zgierski
The Journal of Physical Chemistry, Vol. 95, No. 11, I991
v, ( a lg ) : 378.0
CM-~
V ,8 ( big ) : 245.0
V W ( e,,) : 413.0 CM-'
*.
,
'.+..."., ;
:
.......... 4~., , .......... I
.
....i ..".,. ...
--e -
-
&
-
~~
TYpc I
CM-'
e u ) : 261.0
V,(
TABLE I X Commrisoa of Force Fields for H,P rrrd M P this work and ref 8a Gladkov and Solo~yov~I',~ force cOnstb HzP NiP HzP CUP 7.932 6.821'(6.821) 7.273 5.67 (5.67) 5.64 7.474 (7.474) 6.889 5.32 (5.32) 5.27 6.981 (6.093) 6.058 1.12 (1.12) 1.37 1.402 (1.402) 1.550 1.67 (1.67) 1 .SO 1.402 (1.402) 1.550 1.447 1.67 (1.67) 1.53 1.55 (1.55) 0.78 (0.78) 0.83 0.673 (0.673) 0.463 0.78 (0.78) 0.83 0.673 (0.673) 0.463 1.41 1.45 1.309 1 S74
CM-'
0.56 (0.50) 0.40 0.37 (0.48) 0.40 (0.44) 0.43 (0.57) 0.43 (0.53)
.
', u 3......... -,
.
.'
'y
j , &...d'
i
,,
,A........ "7'
: I,
Type 11
: ~
. ......... .
0.30 (0.30) 0.25 0.10 (0.20) 0.30 0.20 (0.20) 0.10 0.20 (0.30) 0.25 0.25 (0.15) 0.10 0.15 (0.10) 0.25 0.20 (0.20) 0.10 0.15 (0.20) 0.25 0.25 (0.30) 0.25 0.23 (0.25) 0.25
+-u
Figure 20. Calculatedh Cartesian displacements of (hindered) pyrrole translational modes of D,,, Nip, us, u18, and vm All displacements are multiplied by a factor of 10. Compare with Figure 14 to see the effect of the M-N bonds.
bonds) on X axis (Figure I), and the overlap between dw and the Y component of the e * orbital only affects the two pyrroles (and their directly attach4 C,C, bonds) on Y axis, then the observed bond length changes from H2Pto MP (Table IV) can be accounted for by the back-bonding picture: C,C, and C,C, bonds shorten upon metal coordination because of their bonding character in the e,* orbital, and C,C, and C,N bonds elongate due to their antibonding character in the e,* orbital. The metal size dependence of the asymmetric C,C, frequencies is similar to the core-size effect found for many other metalloporphyrin~.~~ Symmetric C,C, and C&, modes were also used as core-size markers in those studies. The high-frequency modes of H2P and MP, other than ul0, ~ 1 9 ,and u3?, do not show the consistent trend to the metal size probably due to the mixing of C,C, stretch with symmetric C,C, stretch as discussed above. A second group of metal-sensitive modes is concerned with the d-r* back bonding. It is expected that upon metal coordination some porphine skeletal bonds would be weakened due to this effect. Therefore certain modes are expected to shift down in frequency when going from H2P to MP. Figure 19 gives one component of the e, r* accepting orbital (other component can be obtained by rotating Figure 19 by a angle of 90O). The phasing of this orbital implies that (a) C,C, and C,C, related modes decrease their frequenciesas the result of the d a * back bonding because the overall bond order of the C,C, and C,C, bonds should be reduced by the d a * back bonding, although some of the bonding character and antibonding character cancel each other between (33)(a) Spaulding, L. D.; Chang, C. C.; Yu, N. T.; Felton, R. H. J . Am. Chem. Soc. 1975,97,2517-2525. (b) Huong, P. V.; Pommier, J. C. C. R. Acad. Sci., Ser. C lW7, 285, 519. (c) Scholler, D.M.; Hoffman, B. M. J. Am. Chrm. Soc. lW9,101, 1655-1662. (d) Stong, J. D.; Spiro, T. G.; Kubaska, R. J.; Shupack, S.I. J . Raman Sprctrosc. 1980, 5, 312-314. (e) Spiro, T. G.;Stong, J. D.; Stein, P. J. J . Am. Chrm. Soc. 1979, 101, 2648-2655. (f) Choi, S.;Spiro, T. G.; Langry, K. C.; Smith, K. M.; Budd, L. D.;LaMar, G. N. J. Am. Chrm. Soc. 1982,101, 4345-4351. (8) Parthasarathi, N.; Hansen, C.; Yamaguchi, s.;Spiro, T. S.J . Am. Chrm. Soc. 1987,109,3865-3871and references therein. (h) Spiro, T.G.; Li, X. Y. In Biological Applicationrof Ramon Spectroscopy;Spiro, T. G., Ed.; 1988;Vol. 3, Chapter 1, pp 1-37. (i) Oterling. W.A.; Salehi, A.; Chung, Y. C.; Leroi, G. E.; Chang, C. K.; Babcock, G. T. J . Phys. Chrm. 1987,91,5887-5898. Sarma, Y. A. Spectrochim. Acta 1989. ISA, 649-652. (k) Shelnutt, J. A.; Alston, K.; Ho. J.-Y.; Yu, N.-T.; Yamamoto, T.; Rifkind, J. M. Biochemistry 1986, 25, 620-627. (I) Kim, D.;Su,Y. 0.;Spiro, T.G. Inorg. Chrm. 1986. 25. 3988-3993.
u)
0.45 0.30 0.30 0.40 0.45 0.45
0.706 (0.706) 0.490 0.590 (0.590) 0.590 (0.590) 0.967 (0.967) 0.706 (0.706)
0.508 0.768 0.791 0.791 1.035 0.508
1.513 (1.513) 0.285 (0.285) 0.285 (0.285) 0.464 (0.464) 1.513 (1.513) 1.513 (1.513) 0.294 (0.294) 1.513 (1.513) 1.513 (1.513) 0.294 (0.294)
0.825 0.119 0.119 0.538 0.825 0.538 0.424 0.825 0.825 0.424
Type 111
cRcB-cncm
-0.2 (-0.3) CPCB-NC, 0.20 (0.25) C L - N C , (trans) 0.20 (-0.20) C,Ci-NC;(cis) ' -0.15 (-0.20j CnCm-CaC, -0.10 (0.15) cacRcncB 0.12 (-0.14) 0.14 (0.20) C,CB-NC,
-0.35 0.00(0.00) 0.20 -0.898 (-0.898) -0.10 -0,3671-0.367) -0.10 -0.367 (-0.367j? -0.10 0.00 (0.00) 0.20 -1.127 (-1.127) 0.20 -0.843 (-0.843)
0.00 -0.6575 -0.426 -0).426? 0.00 -0.636 -0.536
OStretch and stretch-stretch interactions are in units of mdyn/l(; stretch-bend interactions, mdyn/rad; bend and bend-bend interactions, mdyn A/rad2. Gladkov and Solovyov's force constants are converted to above units according to factors given in ref 1 1 . Values in parentheses are for deprotonated pyrroles. Only diagonal force constants and first three types of interactions in Figure 2 are given; see Table V for a complete list of other types of interactions.
two components of the e orbital; (b) for concerted pyrrole ring stretches, the d a * back %onding has a much larger effect on the symmetric half-ring stretch modes than on other modes due to the match of the phase. Indeed, the systematic down shifts of the pyrrole symmetric half-ring stretchings (v4, u12, u41r,b) going from NiP to ZnP (Table VIII) is consistent with the weakening of the NC, bonds caused the by d a * back bonding. This effect will be discussed further in conjunction with the oxidation-state marker mode later. A third group of metal-sensitive modes is the low-frequency collective rotation and translation of pyrrole rings hindered by methine bridges. They experience additional hindrance from the M-N bonds upon metal coordination. In these modes, where pyrroles move like structureless units, the main forces that determine their frequencies are these hindrances. For H2P, it is the methine bridge deformation force, whereas for MP it is the methine deformation plus MN stretch and NMN deformation forces. Therefore, these modes all have higher frequencies in MP than in H2P (Table VIII). For different metal ions, stronger M-N bonds result in higher frequencies. It follows from Table VI11 that the MN bond strength has the order of NiN > CuN > ZnN and the modes that are responsive to MN strength have the following order: u,(Ni) > u,(Cu) > u,(Zn) > ui(H2P)
The Journal of Physical Chemistry, Vol. 95, No. 11, 1991 42885
Porphine Force Field V a ( 8 % ) : 419.0 CM-l
V33(
ba):424.0
CM-'
Figure 21. Same as Figure 20, but for (hindered) pyrrole rotational modes v2,, uj3, and v,~. Compare with Figure 13 to see the effect of the M-N bonds.
to the spin-state and ligation-state change.33Normal-coordinate analysis"" shows that the skeletal modes that are sensitive to the core size are mainly of C,C, or C&@stretching characters in the frequency region 1450-1650 cm-'. The observed inverse correlation between the core size and frequency was suggested to arise from the weakening of the C,C, *-bond strength caused by the increase of methine bridge angle during core e x p a n ~ i o n . ' ~ - ~ ~ W a r ~ h e calculated l~~ the core-size dependence of skeletal frequencies and found that the reduction of the C,C, bond order due to an increase of its bond length is responsible for most of the frequency down shift. It was also concludedm that the pyrrole tilting due to the out-of-plane displacement of metal ion plays a much smaller role than the in-plane core expansion in the observed inverse correlation. Choi et have noticed that the sensitivity of a particular band to the core size is approximately correlated to the extent of the involvement of C,C, stretching character in the empirically determined normal mode.9 This has been taken as a supporting point for the force constant change of the C,C, bond during the core expansion and accompanied frequency decrease. Sarma33jhas recently checked the validity of the idea by calculating the core-size dependence of the high-frequency modes by progressive decrease of C,C, stretching force constant obtained from a Uray-Bradley force field. Although he reproduced the basic trend of the observed core-size correlation," the relative slope of the calculated correlation does not fit the observed Several problems arise if one takes the weakening of the C,C, bond as the only or even main cause of the core-size effect. First, according to the high-quality normal-mode analysis and force field calculation,8 if a change of the C,C, force were the only source of the observed core-size effect, the slopes of the frequency-core size relationships for the sensitive modes should bew
where i = 8 , 18, 25, 35, 49, 50, 53. This order is consistent with the earlier IR study of MP by VI0 = Y37 > Y3 * Y28 >> v2 = = v38 (1) Ogoshi et a].'" The calculated frequencies and Cartesian displacements for the pyrrole collective motions in NiP are given in for a pyrrole-substituted porphyrin such as pctaethylporphyrin Figures 20 and 21 The effect of the Ni-N bonds on a specific (OEP) and protoporphyrin (PP) and mode can be visualized by comparing Figures 20 and 21 with their UIO c Y l g ~ 3 > 7 ~ 2 > 8 ~2 = ~3 > u I I (2) correspondents in H2P, Figures 14 and 13, respectively. The effect of metal coordination on the H2P skeletal force for a meso-substituted porphyrin such as tetraphenylporphyrin constants is not very big (Table IX), so that the change of the (TPP). The above order is determined by the nature of the modes H2P force field upon metal coordination can be viewed as a and their sensitivity to the C,C, stretching force constants.8 perturbation, which does not significantly alter the composition Experimentally observed sl0pes~~8 for MTPP complexes are of the skeletal normal modes. The largest change of the stretching consistent with the above order but not for PP and OEP comforce constant is that of the C,C, bond, a decrease of -0.7 p l e ~ e s . ~To ~ gresolve this controversy, we call the attention to the mdyn/A from NiP to HIP, which corresponds to a 10%change. following three facts: (a) For a given metalloporphyrin such as The average change of the C,C, force constants is about 0.25 NiOEP or NiPP, the frequency shift caused by "pure" spin-state mdyn/A, or 4% of the original value. There are also some slight ~ h a n g e ~is~ consistent k' with the above-mentionedtrend derived changes of bending and interaction force constants, which are listed from the normal-mode analysis, that is, the sensitivity of the in Table IX. high-frequency skeletal modes to the spin-state change is such On the Structural Marker Modes. It has been found, via that Aulo = AuI9,and Au2 = AuI1,the former pair being more extensive RR studies of heme model compounds and hemeproteins, sensitive to the spin-state change than the latter pair; (b) NiOEP that heme skeletal modes in the frequency region 1350-1650 cm-I can form two isomorphic structures with different core sizes for are sensitive to heme properties such as the core size of the T ring, a given spin state. In this complex, the frequency shifts caused the oxidation state, spin state, and ligation state of the central by the core contraction via pyrrole tilting are similar to the effect metal ion.I3J4 For example, u4 is sensitive to the oxidation state of the core expansion observed in the core-size correlation. Pyrrole of metal ion and to the electron population of the T* orbital. Thus, tilt-induced frequency shifts have a similar trend as in point a, it is often called the oxidation-state marker. v2 and u3 are rethat is, Aulo = Aq9, Au3 = Au2?.and Au2 = Avll. However, the sponsive to the ligation-state and spin-state changes and are usually latter two pairs of modes have similar shifts, which is inconsistent referred to as the spin-state markers. The structural origin of these marker modes has been constantly discussed in the l i t e r a t ~ r e . ' ~ * ~ ~with the picture that the change of the C,C, force constant is the only or even the dominant factor. Pyrrole tilting causes also With the help of the detailed normal-mode analysis of free-base an apparent decrease of the C&@force constant. This is consistent porphine, metalloporphine, and metalloporphyrins with various with the X-ray diffraction studies of the two NiOEP complexesperiperal substituents, the sensitivity of a given normal mode to in which it was found that C,C, bond experiences significant a specific structural parameters such as core size, oxidation state, weakening due to the increase of its bond length; (c) the third and spin state of metal ion can now be understood at a much better important fact arises from the present comparison study of the level. Two types'of the most important marker modes will be metal versus free-base porphyrins. Going from MP to HIP or discussed below. going from a metal-dictated core size to an optimized free-base Marker modes for core size, spin state, and ligation state of core size, the frequency shift for the modes of similar nature is metal ion: For a given metal ion, its spin state, ligation state, and very different. For example, vIo shifts down by about 40 cm-' ionic radius are not independent parameters. The change of its ligation state, for example, is always accompanied by a change of its spin state and its effective ionic radius. Therefore, the (34) (a) Warshel, A. Proc. Narl. Acad. Sei. U.S.A.1977.74, 1789-1793. core-size (or size of the metal ion) marker modes are also sensitive (b) Warshel, A. Annu. Rev. Elophys. Eioeng. 1977, 6, 273-300.
Li and Zgierski
4286 The Journal of Physical Chemistry, Vol. 95, No. 11, 1991 for Pyrole, HIP, HaOEP, d NIOEP
TABLE X C~mpuirOaot
H P
pyrrold word
ri
Pi
ri
c8c8 CaC,
1.417 1.382 1.370
0.48 0.61 0.41
1.365 (1.345) 1.431 (1.452) 1.380 (1.376) 1.387 (1.376)
CaN
c,cm
HzOEPd Pi 0.75 (0.925) 0.27 (0.14) 0.34 (0.37) 0.575 (0.66)
NiOEP
ri
Pi
ri
Pi
1.373 (1.353) 1.438 (1.462) 1.367 (1.364) 1.388 (1.393)
0.68 (0.85) 0.225 (0.08) 0.43 (0.45) 0.57 (0.53)
1.346 1.443 1.376 1.371
0.92 0.19 0.37 0.70
OExperimental *-bond orders are calculated according to Pauling's formula from refs 38a,b. ri = experimental bond length; p = calculated *-bond order. bGeometry data from ref 2Ob. 'Geometry data from ref 20a; values in parentheses are for the deprotonated pyrroles. jGeometry data from ref 2Od. eGeometry data from ref 2Oe. I N atom has inherent smaller size than C atom. The correction is made to N by 0.04 A, the value from ref 38c. The same value can be estimated by taking average of the differences between benzene C=C (1.395 A) and pyridine C=N (1.338 A), and between benzene C = C and pyrrole C-N (1.370 A) bond lengths.
-
from NiP to HIP but ~ 1 shifts 9 only by 10 cm-I. In this case, it is not only the change of the C,C, force constant but also changes of the interaction forces between C,C, and nearby coordinates that dictate the magnitude of the core-size correlation. The three facts listed above indicate that the core-size correlation and spin-state sensitivity are not simple structural effects caused by the change of C,C, force constant only. With a consistent and a high-quality force field in hand, we can now systematically study this effect in more detail. The related results will be published separately" Marker modesfor oxidation states of metal ion and for electron population in A* accepting orbital: Up to now, the only oxidation-state marker mode has been assigned as v,.13J4 It shifts down 10-15 cm-' from Fe(II1) to Fe(I1) p o r ~ h y r i n . ~This ~ , ' ~mode is also found to be sensitive to the electron population in the e A* orbital. It shifts down significantly upon the reduction o t t h e porphyrin A ring (A anion).36 It was described as a N-C, stretching mode by Abe et aL9 and was argued that its oxidation-state sensitivity comes from the in-phase stretching of all the N-C, bonds in a gorphyrin-breathing-like motion. Later, a systematic analysis of metalloporphyrin normal modes showed that v, is basically a pyrrole symmetric half-ring stretching with not only the N-C, character but also a significant amount of the C,C, character. Therefore, its sensitivity to the oxidation-state change and to the electron population of the e8 A* orbital is a result of the vibration of the whole porphyrin ring whose phase happens to be consistent with the A-bond-order change caused by A back bonding and/or direct population of e, ?r* orbital. In the same sense, v4 should not necessarily be the only mode that is sensitive to the oxidation state and the electron population of the e8* orbital; all other symmetric half-ring stretchings and pyrrole breathings should also show similar effect. Indeed, when we examine the available RR and IR of metalloporphyrin A anion, which is formed by a direct population of the e, orbital with one or two electrons, we find that the modes that show the largest down shifts (35) (a) Mashiko. T.; Reed,C. A.; Haller, K. J.; Sheidt, W. R. Inorg. Chem. 1984,23, 3129. (b) Ciurli, S.; Gambarotta, S.; Floriani, C.; ChiesiVilla, A.; Guastini, C. Angew. Chem., Inr. Ed. Engl. 1986,25, 553-554 and references therein. (36) (a) Ksenofontova, N.M.; Maslov, V. G.; Sidrov, A. N.; Bobovich, Ya. S. Opt. Specrrmc. 1976,40,462-465. (b) Gurinovich, G. P.; Gurinovich, I. F.; Ksenofontova. N. M.;Terekhov, S.N. J. Appl. Spectrmc. (Engl. Trawl.) 1985,43,758-763. (c) Gurinovich, G. P.; Gurinovich, I. F.; Ivashin, N.V.; Sinyakov, 0 . N.; Shulga. A. M.; Terekhov, S. N.; Filatw, I. V. J. Mol. Srrcr. 1988, 172, 317-343. (d) Yamaguchi, H.; Soeta, A.; Toeda, H.; Itoh, K. J . Elecrroanal. Chem. 1983, 159,347-359. (e) Donohoe, R. J.; Atamian, M.; Bocian, D. F. J . Am. Chem. Soc. 1987,109,5593-5599. (f) Atamian, M.; Donohoe, R. J.; Linfsey, J. S.; W a n , D. F. J . Phys. Chem. 1989, 93, 2236-2243. (g) Teraoka. J.; Hashimoto, S.;Sugimoto, H.; Mori, M.; Kitagawa, T. J . Am. Chem. Soc. 1987, 109, 180-184. (37) (a) Ivashin, N. V.; Gurinovich, I. F.; Gurinovich. 1. F.; Gurinovich, G. P. J . Appl. Specrrosc. 1975,23,1026-1030. (b) Ivashin, N. V.; Gurinovich, 1. F. J. Appl. Spectmc. 1978,28,309-313. (c) Ivashm, N. V.; Tcrekt~ov, S. N.; Gurinovich, 1. F. J . Appl. Spectmc. (Engl. Trawl.)1979.30, 197-201. (d) Ivashin, N. V.; Terekhov, S. N.;Gurinovich, I. F.; Sivchik, V. V. J . Appl. Specrrmc. (Engl. Trawl.) 1981,31,95-102. (e) Ivashin, N.V.; Gurinovich, 1. F. J. Appl. Specrrosc. (Engl. Tranrl.) 1984, 40, 563-568. (38) (a) Cuickshank, D. W. J.; Sparks, R. D.Proc. R.Soc. London 1960, 2584270-285. (b) Cuickshank, D. W. J. Tetrahedron 1962.17, 155-161. (c) Huheey, J. E. Inorganic Chemistry, 2nd ed.; Harper & Row: New York, 1978; pp 232-233. (d) Fleischer. E. B.; Miller, C. K.; Webb, L. E. J. Am. Chem. Soc. 1964,86, 2342-2347.
upon the formation of A anion are the pyrrole symmetric half-ring stretchings and pyrrole breathings. This is consistent with the increase of N-C, bond lengths upon the formation of A anion, as observed in the X-ray crystallographic study.35 F. Comparison with Previous Work. The empirical force field for H2P has been reported before."*j9 Bohandy and Kim (BK)39 published a force field to account for the observed frequencies of natural-abundance H2Pfrom luminescence, IR, and RR spectra. The BK force field is quite crude since the selection of force constants was not restrained by the isotope sensitivity test of each normal mode. This is especially important if the empirical approach is to be adopted to a large molecule such as HIP. Their force constants for NC, and C,C, bonds are especially not reliable in our opinion. Gladkov and Solovyov (GS) and co-workers have studied H2P vibrational properties from both experimental and theoretical Their extensive effort can be recognized by their numerous publications in the Their work on H2P was summarized and updated recently in ref Ila, in which a complete list of valence force constants and calculated frequencies for H2P fundamentals are presented. Although a detailed nature of the normal modes and force field of H2P is not discussed in comparison with those of MP, their work does represent hitherto the most thorough study of HIP fundamental normal modes of the ground electronic state. The differences between our force field and GS's for MP was noticed and briefly discussed previously.8 In Table IX we list force fields for both H2P and MP from two independent works: our force field for H2Pand NIP and GS's force field for H2Pand CUP. As can be seen from Table IX, there are several significant differences between the two sets of force fields. First, we notice that most of the principle stretching and interaction force constants have much larger values in GS's force fields for both H2P and MP than those in our force fields. Some of their interaction force constants are 5-10 times larger than our corresponding values. Our experience is that the overestimation of the diagonal force constant always requires larger values of interaction force constants to balance the effect. Therefore, a proper choice and restraint on the values of diagonal force constants, especially stretch force constants, are very important. The criterion in our choice of the stretch force constants is that they have to scale properly with respect to their bond orders which, in turn, are determined by experimental bond lengths. It has been shown that the bond order of a C-C bond can be quite precisely evaluated from the experimental bond lengths by using the Pauling formula or vise versa.38 In Table X, we list the *-bond orders evaluated from the experimental bond lengths and Pauling formula3*for pyrrole, H2P, H20EP, and NiOEP. A comparison of Tables IX and X shows that our stretch force constants do scale properly with respect to their bond orders and bond lengths, whereas those of GS's do not. The second difference is that, despite very large values, GS's 1-3 (or i-i 2) stretchstretch interaction force constants were all restrained to be negative in sign or given zero values (e&, C&,&,C, interactions), whereas we do not have such restraints. Although it has been established for benzene molecule that 1-3
+
(39) Bohandy, J.; Kim, B. F. Spectrochim. Acra 1980, 36A, 463-466. (40)Li, X. Y.; Zgierski, M. 2.. results to be published.
Porphine Force Field interactions have negative values, a recent ab initio force constant calculation for naphthalene& and purine nucleic acid bases2h reveals that the 1-3 interactions are not necessarily negative in sign for these two molecules, especially those 1-3 interactions that involve two separate rings. This is consistent with the physical picture of the molecular structure of polycyclic aromatic rings where a multipath exists for *-electron delocalization and stabilization. The 1-3 interactions of GS for C,C,-C,C, and C,CB-C,N are of too large magnitude in our opinion. The third difference between two sets of the force fields is that we include the interactions between stretch and bend coordinates sharing one common atom, and 1-4 (i-i + 3) stretchstretch interactions. These interactions, although of very small values (
