- Email: [email protected]
A normal mode analysis of free base porphin
SpectrochimicaActa, Vol. 36A, pp. 463 to 466 © PergamonPress Ltd., 1981).Printedin Great Britain
0584 8530/80/05(11-046350200/(1
A normal m o d e analysis of free base porphin* J. BOHANDY a n d B. F. K1M Johns Hopkins University, Applied Physics Laboratory, Laurel, MD 20810, U.S.A.
(Received 1 August 1979) A b s l r a ~ - - T h e in-plane vibrational modes of free base porphin have been calculated. The results are compared to high resolution single-site fluorescence spectra and a tentative assignment of some experimental i.r. vibrational frequencies is made. The importance of the peripheral hydrogen atoms in vibronic analyses of porphins is discussed. INTRODUCTION
T h e r e h a v e b e e n several r e c e n t r e p o r t s of n o r m a l coordinate calculations o n m e t a l l o p o r p h y r i n s . OGOSH~, SAITO a n d NAKAMOTO. [1] calculated the e i g h t e e n i n - p l a n e i.r. active E , v i b r a t i o n s of zinc, copper, a n d nickel p o r p h i n in D4h symmetry. ABE, KITAGAWA a n d KYOGOKU [2] r e p o r t e d t h e n o r m a l c o o r d i n a t e s of t h e R a m a n active i n - p l a n e m o d e s of nickel o c t a e t h y l p o r p h i n ( N i O E P ) a n d mesod e u t e r a t e d N i O E P . SUNDER a n d BERNSTEIN [3] p e r f o r m e d n o r m a l c o o r d i n a t e calculations on all of t h e i n - p l a n e A ~ , A2~, Bt~, B2~ a n d E~ v i b r a t i o n s of several c o p p e r p o r p h y r i n s , including C u p o r p h i n (CUP) while S u s l a n d ARD [4] m a d e t h e s a m e calculation for C u P a n d NiP using a different force field. M u c h of this p r e v i o u s w o r k was p r o m p t e d by t h e m a n y r e p o r t s of r e s o n a n c e R a m a n (RR) spectra of h e i n e p r o t e i n s a n d m e t a l l o p o r p h y r i n s . It is m o r e difficult to o b t a i n R R spectra of f l u o r e s c e n t materials such as zinc p o r p h i n a n d free b a s e p o r p h i n (FBP). H o w e v e r , VERMA a n d BERNS~ TEIN [5] o b t a i n e d R R s p e c t r a of F B P using a r o t a t ing cell t e c h n i q u e . T h e lowest f r e q u e n c y m o d e r e p o r t e d was 527 cm t. PLUS a n d L u T z [6] r e p o r t e d excitation spectra of 21 R R b a n d s of F B P in d i m e t h y l f o r m a m i d e b u t s o m e of t h e i r m e a s u r e m e n t s were also b o t h e r e d by fluorescence. In cases such as FBP, w h e r e fluorescence is p r o m i n e n t , t h e optical fluorescence a n d a b s o r p t i o n spectra are p e r h a p s m o r e a p p r o p r i a t e for e x p e r i m e n t a l d e t e r m i n a t i o n s of the r e l e v a n t v i b r a t i o n a l frequencies. Recently, this l a b o r a t o r y p u b l i s h e d the h i g h resolution single site a b s o r p t i o n a n d fluorescence spectra of F B P d o p e d in a n t h r a c e n e ( F B P / A ) [7]. W e r e p o r t ~ere the results of a n o r m a l m o d e calculation of tile i n - p l a n e v i b r a t i o n s of F B P a n d a comp a r i s o n to e x p e r i m e n t a l values of t h e vibrational frequencies.
modified version of c o m p u t e r p r o g r a m s o b t a i n e d f r o m t h e N a t i o n a l R e s e a r c h Council of C a n a d a [9]. F B P has 38 a t o m s a n d t h e classification of t h e p l a n a r m o d e s in D2h s y m m e t r y is 19A~ + 1 8 B ~ + 18B2, + 18B3~. Figure 1 shows t h e 110 i n - p l a n e internal coordinates which were used, including 37 r e d u n d a n t coordinates. A D2h s y m m e t r y matrix was used to facilitate the g r o u p i n g of the frequencies. T a b l e 1 lists t h e F B P structural p a r a m e t e r s of CHEN a n d TULINSKY [10] which were e m p l o y e d in t h e calculation. A valence force field was used a n d the initial values for t h e force c o n s t a n t s were t a k e n to be e q u a l to t h o s e used for c o p p e r p o r p h i n [3], except for the N H s t r e t c h a n d C N H b e n d w h o s e c o n s t a n t s were t a k e n f r o m t h o s e of pyrrole [l 1]. All s t r e t c h s t r e t c h i n t e r a c t i o n c o n s t a n t s not involving a comm o n a t o m , all s t r e t c h - b e n d i n t e r a c t i o n c o n s t a n t s n o t involving a c o m m o n b o n d , a n d all b e n d - b e n d i n t e r a c t i o n s were ignored. T h e C,,,H stretch a n d C ~ H stretch c o n s t a n t s were given the s a m e value. T h e calculated f r e q u e n c i e s were c o m p a r e d to t h e e x p e r i m e n t a l values a n d t h e force c o n s t a n t s were a d j u s t e d to give the best fit to the data. T h e experim e n t a l f r e q u e n c i e s w e r e t a k e n f r o m t h e single site fluorescence s p e c t r u m of F B P in a n t h r a c e n e [7]. This s p e c t r u m c o n t a i n s v i b r a t i o n a l m o d e s of symm e t r y type A , a n d B1, since these can c o m b i n e with t h e B3, a n d B2, p o r p h i n excited electronic states to give allowed transitions to t h e A , g r o u n d state. T w e n t y - t h r e e e x p e r i m e n t a l f r e q u e n c i e s w e r e used to adjust t h e force c o n s t a n t s by a w e i g h t e d least s q u a r e s m e t h o d in w h i c h the w e i g h t i n g factor for e a c h f r e q u e n c y was p r o p o r t i o n a l to t h e inverse of t h e frequency. T h e final values of t h e force c o n s t a n t s are listed in T a b l e 2. T h e average e r r o r in calculating t h e 23 e x p e r i m e n t a l f r e q u e n c i e s was 10 cm 1 or a p p r o x i m a t e l y 2 % .
CALCULATION
T h e n o r m a l m o d e calculation was p e r f o r m e d using t h e W i l s o n " G F " m e t h o d [8] a n d a slightly
* Work supported by Public Health Services Grant GM 21897, National Institute of General Medical Sciences. S.A.A.36/5 n
RESULTS AND DISCUSSION
T h e calculated values of t h e n o r m a l m o d e frequencies and the potential energy distribution (P.E.D.) of t h e n o r m a l v i b r a t i o n s are listed in T a b l e 3. T h e P . E . D . gives t h e p e r c e n t a g e c o n t r i b u t i o n of 463
J. BOHANDY and B. F. KIM
464 (a)
F4~
P - - -E2- 1 ~F3
F
C4/
E3 I
-~
~
y
~ C 5
(~
-J
Table 1. Structural parameters used for the calculation of the Cartesian coordinates of free base porphin ~"
~
B6
Distance ®N Distance (i)Cm Distance OH Bond length B2 Bond length D2 Bond length F2 Bond length B3 Bond length D3 N®C m z. ~32 2~ e2 >'2 01 c3
21
[ E1 BI~ C8" ~
~ 4 %
(b) 4
~
i5
/~4 56
4
X3 / t<3
5(~
~31 \ ,5
Fig, 1. Internal coordinates used in the normal mode calculation of free base porphin: (a) stretching and (b) bending. a particular class of internal c o o r d i n a t e force cons t a n t s to t h e v i b r a t i o n a l e n e r g y of t h e n o r m a l m o d e . O n l y c o n t r i b u t i o n s g r e a t e r t h a n 10% are included. A l s o s h o w n in T a b l e 3 are F B P vibrat i o n a l f r e q u e n c i e s o b t a i n e d f r o m single site fluoresc e n c e in this l a b o r a t o r y a n d f r e q u e n c i e s a n d symm e t r y of F B P v i b r a t i o n s o b t a i n e d f r o m Shpolskii s p e c t r a (low t e m p e r a t u r e optical spectra of p o r p h y rins dissolved in a l k a n e solvents such as n - o c t a n e ) at 77 K by GRADYUSHKO et al. [12]. T h e y assigned t h e s y m m e t r y o n t h e basis of fluorescence polarization m e a s u r e m e n t s a n d the a r g u m e n t t h a t a p p r o x i m a t e m i r r o r s y m m e t r y of t h e intensities of a b s o r p tion a n d fluorescence s p e c t r a exists for B ~ vibrations while c o n s i d e r a b l e d e v i a t i o n s exist for the totally s y m m e t r i c Ag vibrations. T h e s y m m e t r y ass i g n m e n t s for t h e e x p e r i m e n t a l f r e q u e n c i e s of F B P in a n t h r a c e n e w e r e m a d e o n t h e basis of the freq u e n c y calculation. A l t h o u g h t h e r e is good agreem e n t b e t w e e n t h e two e x p e r i m e n t a l o b s e r v a t i o n s with r e s p e c t to f r e q u e n c y a n d intensity, t h e 1607, 1490, 1223, 1174, 1137 a n d 1(151 cm 1 v i b r a t i o n s
2.065 A 3.444 1.205 1.380 1.431 1.060 1.376 1.462 45 ° 125.5 ° 107.9 ° 126.3 ° 127.1' 109.8°
disagree in t h e i r s y m m e t r y assignment. R e s o n a n c e R a m a n spectra of F B P h a v e also b e e n r e p o r t e d [5, 6]. T h e values of the vibrational frequencies agree well with fluorescence spectra, as expected, b u t t h e s y m m e t r y of the vibrations was not discussed. O n e sees f r o m T a b l e 3 that, except for the C H a n d N H stretch f r e q u e n c i e s a b o v e 3000 cm ~, t h e r e are n o p u r e modes. This is an i m p o r t a n t fact to c o n s i d e r w h e n m a k i n g a p p r o x i m a t i o n s in vibronic analyses of porphyrins. It has b e e n suggested [13] t h a t a good a p p r o x i m a t i o n to m a k e w h e n dealing with p o r p h y r i n s is t h a t the C H v i b r a t i o n s are not i m p o r t a n t for the v i b r o n i c coupling of w-~r* transitions in t h e optical a b s o r p t i o n a n d emission spectra. I n d e e d , t h e stretch c o o r d i n a t e s b e t w e e n a t o m i c centers w h i c h c o n t r i b u t e w electrons are t h o u g h t to b e t h e i m p o r t a n t c o o r d i n a t e s for vibrationally ind u c e d e n h a n c e m e n t of t h e f o r b i d d e n vibronic Q states. V i b r a t i o n a l m o d e s which contain significant c o n t r i b u t i o n s from h y d r o g e n a t o m s in t h e i r internal c o o r d i n a t e d e c o m p o s i t i o n can b e c o m e e n h a n c e d , nevertheless, by t h e i r C C a n d C N stretch c o n t r i b u tions. F o r example, t h e e x p e r i m e n t a l vibronic lines in t h e 1 1 0 0 - 1 3 0 0 cm 1 region are primarily due to Table 2. Force constants for free base porphin 1. 2. 3. 4. 5. 6. 7, 8. 9. 10. 11. 12. 13. 14. 15, 16. 17.
NH stretch CN stretch CH stretch CeC#stretch %Cy stretch Cc~Cm stretch CeNH bend CCH bend CflCaN bend CmCaN bend C~NCa, bend CaC#C/' bend %CmC,/bend C~fCeCm bend CC,CC;CC,CN; CN,CN stretch stretch CC,CCHstretch bend CC,CCC;CC,CCN; CN,CCN; CN,CNC stretch bend
6.86 6.82 5.12 5.41 6.87 5.62 0.45 043 1.02 1.27 2.00 1.24 1.37 0.98 0.42 0.18 0.21
mdyn/,&
mdyn/A
mdyn/,\ mdyn mdyn
A normal mode analysis of free base porphin Table 3. Calculated and observed frequencies of in-plane vibrations of free base porphin Symmetry
Obs. (a)
Obs (b)
Ag
1607 s 1595 vs 1529 vw
1600 1490
1400 vw 1348 m 1174 s
1358 1219 1129 1057
972 w 950 s
950
719 m 272 w 151 vw
720 309 152
3531 3076 3075 3071 1599 vs 1593 1540 nl 1516 1418 w 1346 m 1188 w 1107 w 1103 968 m 952 748 w 704 w 292 vw 172
Blq
1688 vw 1575 w 1490 m 1383 1314 1223 1137 1051 986
s m
m w m w
722 m 488 w
1616 vs
1387 s 1318 m 1178 nl
974 w 787 ~ 420 vw
118 w B2u
1406 1362 1262 1137 965 970
841 719
B3u
1589
1262 1158 1098 1033 951 809 690
Calc
3073 3071 3069 1714 1575 1481 1469 1388 1325 1193 1133 1041 991 864 722 506 407 124
PED.
835 710 368 344
9913} 99~3) 99(3) 48(7) 58{2) 37(4) 4114) 28~81 77{8) 69(8) 75(8) 3012} 31(2) 45[12) 40112) 48(101 28{61 51113) 99(3) 99(3) 99(3) 47(7) 33(2} 40(6) 34(4) 32~61 37181 56161 74{8) 80{8) 34(2) 37(4) 32112) 1719) 39H0~ 3016~
3531 3075 3072 3069 1602 1570 1521 1474 1385 1260 1151 1104 1032 958 822 708 370 340
9913) 99(3) 99131 36(2) 32(6) 59{2) 3614i 96181 64{8) 7418) 80(8) 30{2) 40(4) 29112) 1719} 39{10) 30(6)
3076 3072 3070 1715 15/5 1559 1479 1412 1314 1257 1144 1106 991 966
%{F C =)
99(1) 9913) 99(3) 99(3) 41(2) + 48(6) + 36(51 + 3312) + 40(5) " 42(5) + 82(81 80(8) * 80(8) + 53(4) + 32(4) + 22(13)'+ 27(11) + 3916~ + 45110) -
13{10) 2914) 31(4) 30(5) 31{6) 30(6)
+ + + +
+ 11(14) + 1014) 11(11) + 11110) 1416) + 1218) 1818) 28(2)
1115) 12(51 1312) 20(2) + 15{11) 20{4) + 1712} + 17{10) 1819) + 1516) + 16(141 13111) 28(141 + 12~2)
37~21 - 12~6) 26(6) 3616) * 2018} 28(2) + 13i8) 26(7) + 22(4) + 1916) 1116) + 10141 1316) 1414) 2816) 18181 + 1616} 14{8) + 11{13) 18!9) 36(14) 23(14) + 16(41 23110) + 11(14)
+ + + * + + + + + + + + +
37(2) + 1316) 2114) * 15(10) * 10{111 21~51 + 1814) + t3(8) 2115) * 2018i + 1412) 24121 + 22(7) + 18151 17(4) * 1617) + 1516) 1916) 12{4) 11151 1816) + 1118) 1812) * 10111) 15110) + 1314) + 13113) 15114) + 13112i + 13111} * 271141 + 151141
99{1}
+ 25{6) + 1614) + 10110) + 2215) + 15(2) + 14{4) { + + + + + + + + + +
23(5) + 2116) + 21(8) 2515) + 23(4) + 20(6) 1516) 1314) 11151 2716} + 13181 1712) 1614) + 15110) + 13113) 17112) + 11{11) + 11161 27114) 15{14)
465
T h e results of experimental studies of i.r. spectra of F B P have b e e n reported [14] and can be c o m pared with this calculation. In D2h symmetry, the o u t - o f - p l a n e B1, and the in-plane B2, and B 3 , vibrations are i.r.-active. A tentative assignment of s o m e of the observed i.r. frequencies [14] to calculated B2, and B3, m o d e s is m a d e in Table 3. It was suggested [14] that: (a) the 1224, 1 1 8 4 and 1 0 4 8 c m 1 vibrations m a y be due to allowed inplane C H deformations; (b) the N H in-plane deformation frequency is 9 7 0 cm-1; and (c) the 6 9 0 and 6 2 0 cm a vibrations are in-plane pyrrole ring deformations. With respect to these suggestions, this calculation s h o w s that: (a) although the primary in-plane i.r.-active C H d e f o r m a t i o n frequencies are in the l l 0 0 - 1 3 0 0 c m I region, assigning 1 2 2 4 , 1 1 8 4 and 1 0 4 8 c m I to them results in a 3 0 50 cm -a error which is much larger than the average; (b) the only calculated in-plane m o d e s which d e p e n d on the N H d e f o r m a t i o n force constant occur at 1 7 1 5 , 1 4 1 2 and 1 3 7 4 c m -~ in B2,, not in the vicinity of 9 7 0 cm-1; and (c) 6 9 0 cm 1 could very well be an in-plane pyrrole ring deformation corresponding to either 7 0 8 or 7 1 0 c m -1 but 6 2 0 cm , doesn't correspond to any calculated inplane vibration. O ~ o s H x et al. [1] reported far i.r. frequencies of 360, 335, 3 1 0 and 2 2 0 c m i for FBP. Table 3 s h o w s that 2 2 0 and 3 1 0 c m -1 are m o s t likely o u t - o f - p l a n e /31, vibrations since these frequencies are less than any of the calculated in-plane i.r. active vibrations. T h e 335 and 3 6 0 cm-1 vibrational frequencies can be assigned to Ba, or B3, m o d e s but there is no w a y to c h o o s e b e t w e e n the two. There are s o m e obvious ambiguities in the assignment of s o m e of the experimentally observed vibrational frequencies to calculated normal modes. Theoretical intensities w o u l d be an obvious aid in solving this problem. T o this end, calculations of the transition strengths of the vibronic transitions in free base porphin and metal porphins have b e e n initiated in this laboratory. REFERENCES
~A~ and Big. Ref. [7], B2u and B3u. Ref. [14]. b Ref. [12]. the C C H bending forces but are still prominent in the vibronic spectrum. In fact, the 1 1 7 4 cm 1 vibration is o n e of the stronger lines in the fluorescence spectrum e v e n though it is mainly a C C H bending vibration. T h e 1 2 2 3 and 1 3 1 4 c m I lines have m e d i u m intensity, while the 1383 cm -~ line which contains 30% contribution from the C C H bending force constant is the s e c o n d strongest fluorescent line. T h e hydrogen atoms should not, therefore, be neglected in the vibronic analysis of porphins. O f course, neglect of the hydrogen atoms also causes errors in the vibrational frequencies and in the n u m b e r of vibrational states.
[1] H. OGOSm, Y. SAITO and J. K. NAKAMOTO, J. Chem. Phys. 5"/, 4194 (1972). [2] M. ABE, T. KrrAGAWA and Y. KYOGOKu, Chem. Lett. Z49, (1976). [3] S. SUNDER and H. BERNSTEIN, J. Raman Spectr. 5, 351 (1976). [4] H. Sus~ and J. S. ARD, Spectrochim. Acta 33A, 561
(1977). [5] A. L. VERMA and H. J. BERNSTEIN, Biochem. Biophys. Res. Comm. 5"/, 255 11974). [6] R. PLUS and M. LUTZ, Spectrosc. Lett. 7, 73 11974). [7] B. F. KIM and J. BOHAYDY, J. Mol. Spectr. "/3, 332 ( 1978). [8] E. B. WItSON, JR., J. C. DECIUS and P. C. CROSS, Molecular Vibrations. McGraw-Hill, New York (1955). [9] N. FUHRER, V. B. KARTHA, K. G. KIDD, P. J. KRUEGER and H. H. MAYrSCH, N.R.C,C. Bulletin
466
J. BOHANDY and B. F. KIM 15, Computer Programs for Infrared Spectrophotometry X X X I X - X L I , Normal Coordinate
No.
Analysis (1976). [10] B. M. L. CHEN and A. TUI.INSKY, J. Am. Chem. Soc. 94, 3-144 (1972). [11] D. W. S c o w l J. Mol. Spectr. 37, 77 (1971).
[12] A. T. GRAI)YUSHKO, K. N. SOLOVEV and A. S. ST,\RUKHIN, ()pt. ~pectr. 40, 267 (19761. [ 13] M. G o u I't-;RMAN. Thc porph_,,rins, Physic~d Chemistry. Part A, Volume lI1. p. 130 (edited by DAVID DOLPHIN). Academic Press, New York (1978). [14] S. F. MASON, d. Chem. Soc. 976 (1958).
0584 8530/80/05(11-046350200/(1
A normal m o d e analysis of free base porphin* J. BOHANDY a n d B. F. K1M Johns Hopkins University, Applied Physics Laboratory, Laurel, MD 20810, U.S.A.
(Received 1 August 1979) A b s l r a ~ - - T h e in-plane vibrational modes of free base porphin have been calculated. The results are compared to high resolution single-site fluorescence spectra and a tentative assignment of some experimental i.r. vibrational frequencies is made. The importance of the peripheral hydrogen atoms in vibronic analyses of porphins is discussed. INTRODUCTION
T h e r e h a v e b e e n several r e c e n t r e p o r t s of n o r m a l coordinate calculations o n m e t a l l o p o r p h y r i n s . OGOSH~, SAITO a n d NAKAMOTO. [1] calculated the e i g h t e e n i n - p l a n e i.r. active E , v i b r a t i o n s of zinc, copper, a n d nickel p o r p h i n in D4h symmetry. ABE, KITAGAWA a n d KYOGOKU [2] r e p o r t e d t h e n o r m a l c o o r d i n a t e s of t h e R a m a n active i n - p l a n e m o d e s of nickel o c t a e t h y l p o r p h i n ( N i O E P ) a n d mesod e u t e r a t e d N i O E P . SUNDER a n d BERNSTEIN [3] p e r f o r m e d n o r m a l c o o r d i n a t e calculations on all of t h e i n - p l a n e A ~ , A2~, Bt~, B2~ a n d E~ v i b r a t i o n s of several c o p p e r p o r p h y r i n s , including C u p o r p h i n (CUP) while S u s l a n d ARD [4] m a d e t h e s a m e calculation for C u P a n d NiP using a different force field. M u c h of this p r e v i o u s w o r k was p r o m p t e d by t h e m a n y r e p o r t s of r e s o n a n c e R a m a n (RR) spectra of h e i n e p r o t e i n s a n d m e t a l l o p o r p h y r i n s . It is m o r e difficult to o b t a i n R R spectra of f l u o r e s c e n t materials such as zinc p o r p h i n a n d free b a s e p o r p h i n (FBP). H o w e v e r , VERMA a n d BERNS~ TEIN [5] o b t a i n e d R R s p e c t r a of F B P using a r o t a t ing cell t e c h n i q u e . T h e lowest f r e q u e n c y m o d e r e p o r t e d was 527 cm t. PLUS a n d L u T z [6] r e p o r t e d excitation spectra of 21 R R b a n d s of F B P in d i m e t h y l f o r m a m i d e b u t s o m e of t h e i r m e a s u r e m e n t s were also b o t h e r e d by fluorescence. In cases such as FBP, w h e r e fluorescence is p r o m i n e n t , t h e optical fluorescence a n d a b s o r p t i o n spectra are p e r h a p s m o r e a p p r o p r i a t e for e x p e r i m e n t a l d e t e r m i n a t i o n s of the r e l e v a n t v i b r a t i o n a l frequencies. Recently, this l a b o r a t o r y p u b l i s h e d the h i g h resolution single site a b s o r p t i o n a n d fluorescence spectra of F B P d o p e d in a n t h r a c e n e ( F B P / A ) [7]. W e r e p o r t ~ere the results of a n o r m a l m o d e calculation of tile i n - p l a n e v i b r a t i o n s of F B P a n d a comp a r i s o n to e x p e r i m e n t a l values of t h e vibrational frequencies.
modified version of c o m p u t e r p r o g r a m s o b t a i n e d f r o m t h e N a t i o n a l R e s e a r c h Council of C a n a d a [9]. F B P has 38 a t o m s a n d t h e classification of t h e p l a n a r m o d e s in D2h s y m m e t r y is 19A~ + 1 8 B ~ + 18B2, + 18B3~. Figure 1 shows t h e 110 i n - p l a n e internal coordinates which were used, including 37 r e d u n d a n t coordinates. A D2h s y m m e t r y matrix was used to facilitate the g r o u p i n g of the frequencies. T a b l e 1 lists t h e F B P structural p a r a m e t e r s of CHEN a n d TULINSKY [10] which were e m p l o y e d in t h e calculation. A valence force field was used a n d the initial values for t h e force c o n s t a n t s were t a k e n to be e q u a l to t h o s e used for c o p p e r p o r p h i n [3], except for the N H s t r e t c h a n d C N H b e n d w h o s e c o n s t a n t s were t a k e n f r o m t h o s e of pyrrole [l 1]. All s t r e t c h s t r e t c h i n t e r a c t i o n c o n s t a n t s not involving a comm o n a t o m , all s t r e t c h - b e n d i n t e r a c t i o n c o n s t a n t s n o t involving a c o m m o n b o n d , a n d all b e n d - b e n d i n t e r a c t i o n s were ignored. T h e C,,,H stretch a n d C ~ H stretch c o n s t a n t s were given the s a m e value. T h e calculated f r e q u e n c i e s were c o m p a r e d to t h e e x p e r i m e n t a l values a n d t h e force c o n s t a n t s were a d j u s t e d to give the best fit to the data. T h e experim e n t a l f r e q u e n c i e s w e r e t a k e n f r o m t h e single site fluorescence s p e c t r u m of F B P in a n t h r a c e n e [7]. This s p e c t r u m c o n t a i n s v i b r a t i o n a l m o d e s of symm e t r y type A , a n d B1, since these can c o m b i n e with t h e B3, a n d B2, p o r p h i n excited electronic states to give allowed transitions to t h e A , g r o u n d state. T w e n t y - t h r e e e x p e r i m e n t a l f r e q u e n c i e s w e r e used to adjust t h e force c o n s t a n t s by a w e i g h t e d least s q u a r e s m e t h o d in w h i c h the w e i g h t i n g factor for e a c h f r e q u e n c y was p r o p o r t i o n a l to t h e inverse of t h e frequency. T h e final values of t h e force c o n s t a n t s are listed in T a b l e 2. T h e average e r r o r in calculating t h e 23 e x p e r i m e n t a l f r e q u e n c i e s was 10 cm 1 or a p p r o x i m a t e l y 2 % .
CALCULATION
T h e n o r m a l m o d e calculation was p e r f o r m e d using t h e W i l s o n " G F " m e t h o d [8] a n d a slightly
* Work supported by Public Health Services Grant GM 21897, National Institute of General Medical Sciences. S.A.A.36/5 n
RESULTS AND DISCUSSION
T h e calculated values of t h e n o r m a l m o d e frequencies and the potential energy distribution (P.E.D.) of t h e n o r m a l v i b r a t i o n s are listed in T a b l e 3. T h e P . E . D . gives t h e p e r c e n t a g e c o n t r i b u t i o n of 463
J. BOHANDY and B. F. KIM
464 (a)
F4~
P - - -E2- 1 ~F3
F
C4/
E3 I
-~
~
y
~ C 5
(~
-J
Table 1. Structural parameters used for the calculation of the Cartesian coordinates of free base porphin ~"
~
B6
Distance ®N Distance (i)Cm Distance OH Bond length B2 Bond length D2 Bond length F2 Bond length B3 Bond length D3 N®C m z. ~32 2~ e2 >'2 01 c3
21
[ E1 BI~ C8" ~
~ 4 %
(b) 4
~
i5
/~4 56
4
X3 / t<3
5(~
~31 \ ,5
Fig, 1. Internal coordinates used in the normal mode calculation of free base porphin: (a) stretching and (b) bending. a particular class of internal c o o r d i n a t e force cons t a n t s to t h e v i b r a t i o n a l e n e r g y of t h e n o r m a l m o d e . O n l y c o n t r i b u t i o n s g r e a t e r t h a n 10% are included. A l s o s h o w n in T a b l e 3 are F B P vibrat i o n a l f r e q u e n c i e s o b t a i n e d f r o m single site fluoresc e n c e in this l a b o r a t o r y a n d f r e q u e n c i e s a n d symm e t r y of F B P v i b r a t i o n s o b t a i n e d f r o m Shpolskii s p e c t r a (low t e m p e r a t u r e optical spectra of p o r p h y rins dissolved in a l k a n e solvents such as n - o c t a n e ) at 77 K by GRADYUSHKO et al. [12]. T h e y assigned t h e s y m m e t r y o n t h e basis of fluorescence polarization m e a s u r e m e n t s a n d the a r g u m e n t t h a t a p p r o x i m a t e m i r r o r s y m m e t r y of t h e intensities of a b s o r p tion a n d fluorescence s p e c t r a exists for B ~ vibrations while c o n s i d e r a b l e d e v i a t i o n s exist for the totally s y m m e t r i c Ag vibrations. T h e s y m m e t r y ass i g n m e n t s for t h e e x p e r i m e n t a l f r e q u e n c i e s of F B P in a n t h r a c e n e w e r e m a d e o n t h e basis of the freq u e n c y calculation. A l t h o u g h t h e r e is good agreem e n t b e t w e e n t h e two e x p e r i m e n t a l o b s e r v a t i o n s with r e s p e c t to f r e q u e n c y a n d intensity, t h e 1607, 1490, 1223, 1174, 1137 a n d 1(151 cm 1 v i b r a t i o n s
2.065 A 3.444 1.205 1.380 1.431 1.060 1.376 1.462 45 ° 125.5 ° 107.9 ° 126.3 ° 127.1' 109.8°
disagree in t h e i r s y m m e t r y assignment. R e s o n a n c e R a m a n spectra of F B P h a v e also b e e n r e p o r t e d [5, 6]. T h e values of the vibrational frequencies agree well with fluorescence spectra, as expected, b u t t h e s y m m e t r y of the vibrations was not discussed. O n e sees f r o m T a b l e 3 that, except for the C H a n d N H stretch f r e q u e n c i e s a b o v e 3000 cm ~, t h e r e are n o p u r e modes. This is an i m p o r t a n t fact to c o n s i d e r w h e n m a k i n g a p p r o x i m a t i o n s in vibronic analyses of porphyrins. It has b e e n suggested [13] t h a t a good a p p r o x i m a t i o n to m a k e w h e n dealing with p o r p h y r i n s is t h a t the C H v i b r a t i o n s are not i m p o r t a n t for the v i b r o n i c coupling of w-~r* transitions in t h e optical a b s o r p t i o n a n d emission spectra. I n d e e d , t h e stretch c o o r d i n a t e s b e t w e e n a t o m i c centers w h i c h c o n t r i b u t e w electrons are t h o u g h t to b e t h e i m p o r t a n t c o o r d i n a t e s for vibrationally ind u c e d e n h a n c e m e n t of t h e f o r b i d d e n vibronic Q states. V i b r a t i o n a l m o d e s which contain significant c o n t r i b u t i o n s from h y d r o g e n a t o m s in t h e i r internal c o o r d i n a t e d e c o m p o s i t i o n can b e c o m e e n h a n c e d , nevertheless, by t h e i r C C a n d C N stretch c o n t r i b u tions. F o r example, t h e e x p e r i m e n t a l vibronic lines in t h e 1 1 0 0 - 1 3 0 0 cm 1 region are primarily due to Table 2. Force constants for free base porphin 1. 2. 3. 4. 5. 6. 7, 8. 9. 10. 11. 12. 13. 14. 15, 16. 17.
NH stretch CN stretch CH stretch CeC#stretch %Cy stretch Cc~Cm stretch CeNH bend CCH bend CflCaN bend CmCaN bend C~NCa, bend CaC#C/' bend %CmC,/bend C~fCeCm bend CC,CC;CC,CN; CN,CN stretch stretch CC,CCHstretch bend CC,CCC;CC,CCN; CN,CCN; CN,CNC stretch bend
6.86 6.82 5.12 5.41 6.87 5.62 0.45 043 1.02 1.27 2.00 1.24 1.37 0.98 0.42 0.18 0.21
mdyn/,&
mdyn/A
mdyn/,\ mdyn mdyn
A normal mode analysis of free base porphin Table 3. Calculated and observed frequencies of in-plane vibrations of free base porphin Symmetry
Obs. (a)
Obs (b)
Ag
1607 s 1595 vs 1529 vw
1600 1490
1400 vw 1348 m 1174 s
1358 1219 1129 1057
972 w 950 s
950
719 m 272 w 151 vw
720 309 152
3531 3076 3075 3071 1599 vs 1593 1540 nl 1516 1418 w 1346 m 1188 w 1107 w 1103 968 m 952 748 w 704 w 292 vw 172
Blq
1688 vw 1575 w 1490 m 1383 1314 1223 1137 1051 986
s m
m w m w
722 m 488 w
1616 vs
1387 s 1318 m 1178 nl
974 w 787 ~ 420 vw
118 w B2u
1406 1362 1262 1137 965 970
841 719
B3u
1589
1262 1158 1098 1033 951 809 690
Calc
3073 3071 3069 1714 1575 1481 1469 1388 1325 1193 1133 1041 991 864 722 506 407 124
PED.
835 710 368 344
9913} 99~3) 99(3) 48(7) 58{2) 37(4) 4114) 28~81 77{8) 69(8) 75(8) 3012} 31(2) 45[12) 40112) 48(101 28{61 51113) 99(3) 99(3) 99(3) 47(7) 33(2} 40(6) 34(4) 32~61 37181 56161 74{8) 80{8) 34(2) 37(4) 32112) 1719) 39H0~ 3016~
3531 3075 3072 3069 1602 1570 1521 1474 1385 1260 1151 1104 1032 958 822 708 370 340
9913) 99(3) 99131 36(2) 32(6) 59{2) 3614i 96181 64{8) 7418) 80(8) 30{2) 40(4) 29112) 1719} 39{10) 30(6)
3076 3072 3070 1715 15/5 1559 1479 1412 1314 1257 1144 1106 991 966
%{F C =)
99(1) 9913) 99(3) 99(3) 41(2) + 48(6) + 36(51 + 3312) + 40(5) " 42(5) + 82(81 80(8) * 80(8) + 53(4) + 32(4) + 22(13)'+ 27(11) + 3916~ + 45110) -
13{10) 2914) 31(4) 30(5) 31{6) 30(6)
+ + + +
+ 11(14) + 1014) 11(11) + 11110) 1416) + 1218) 1818) 28(2)
1115) 12(51 1312) 20(2) + 15{11) 20{4) + 1712} + 17{10) 1819) + 1516) + 16(141 13111) 28(141 + 12~2)
37~21 - 12~6) 26(6) 3616) * 2018} 28(2) + 13i8) 26(7) + 22(4) + 1916) 1116) + 10141 1316) 1414) 2816) 18181 + 1616} 14{8) + 11{13) 18!9) 36(14) 23(14) + 16(41 23110) + 11(14)
+ + + * + + + + + + + + +
37(2) + 1316) 2114) * 15(10) * 10{111 21~51 + 1814) + t3(8) 2115) * 2018i + 1412) 24121 + 22(7) + 18151 17(4) * 1617) + 1516) 1916) 12{4) 11151 1816) + 1118) 1812) * 10111) 15110) + 1314) + 13113) 15114) + 13112i + 13111} * 271141 + 151141
99{1}
+ 25{6) + 1614) + 10110) + 2215) + 15(2) + 14{4) { + + + + + + + + + +
23(5) + 2116) + 21(8) 2515) + 23(4) + 20(6) 1516) 1314) 11151 2716} + 13181 1712) 1614) + 15110) + 13113) 17112) + 11{11) + 11161 27114) 15{14)
465
T h e results of experimental studies of i.r. spectra of F B P have b e e n reported [14] and can be c o m pared with this calculation. In D2h symmetry, the o u t - o f - p l a n e B1, and the in-plane B2, and B 3 , vibrations are i.r.-active. A tentative assignment of s o m e of the observed i.r. frequencies [14] to calculated B2, and B3, m o d e s is m a d e in Table 3. It was suggested [14] that: (a) the 1224, 1 1 8 4 and 1 0 4 8 c m 1 vibrations m a y be due to allowed inplane C H deformations; (b) the N H in-plane deformation frequency is 9 7 0 cm-1; and (c) the 6 9 0 and 6 2 0 cm a vibrations are in-plane pyrrole ring deformations. With respect to these suggestions, this calculation s h o w s that: (a) although the primary in-plane i.r.-active C H d e f o r m a t i o n frequencies are in the l l 0 0 - 1 3 0 0 c m I region, assigning 1 2 2 4 , 1 1 8 4 and 1 0 4 8 c m I to them results in a 3 0 50 cm -a error which is much larger than the average; (b) the only calculated in-plane m o d e s which d e p e n d on the N H d e f o r m a t i o n force constant occur at 1 7 1 5 , 1 4 1 2 and 1 3 7 4 c m -~ in B2,, not in the vicinity of 9 7 0 cm-1; and (c) 6 9 0 cm 1 could very well be an in-plane pyrrole ring deformation corresponding to either 7 0 8 or 7 1 0 c m -1 but 6 2 0 cm , doesn't correspond to any calculated inplane vibration. O ~ o s H x et al. [1] reported far i.r. frequencies of 360, 335, 3 1 0 and 2 2 0 c m i for FBP. Table 3 s h o w s that 2 2 0 and 3 1 0 c m -1 are m o s t likely o u t - o f - p l a n e /31, vibrations since these frequencies are less than any of the calculated in-plane i.r. active vibrations. T h e 335 and 3 6 0 cm-1 vibrational frequencies can be assigned to Ba, or B3, m o d e s but there is no w a y to c h o o s e b e t w e e n the two. There are s o m e obvious ambiguities in the assignment of s o m e of the experimentally observed vibrational frequencies to calculated normal modes. Theoretical intensities w o u l d be an obvious aid in solving this problem. T o this end, calculations of the transition strengths of the vibronic transitions in free base porphin and metal porphins have b e e n initiated in this laboratory. REFERENCES
~A~ and Big. Ref. [7], B2u and B3u. Ref. [14]. b Ref. [12]. the C C H bending forces but are still prominent in the vibronic spectrum. In fact, the 1 1 7 4 cm 1 vibration is o n e of the stronger lines in the fluorescence spectrum e v e n though it is mainly a C C H bending vibration. T h e 1 2 2 3 and 1 3 1 4 c m I lines have m e d i u m intensity, while the 1383 cm -~ line which contains 30% contribution from the C C H bending force constant is the s e c o n d strongest fluorescent line. T h e hydrogen atoms should not, therefore, be neglected in the vibronic analysis of porphins. O f course, neglect of the hydrogen atoms also causes errors in the vibrational frequencies and in the n u m b e r of vibrational states.
[1] H. OGOSm, Y. SAITO and J. K. NAKAMOTO, J. Chem. Phys. 5"/, 4194 (1972). [2] M. ABE, T. KrrAGAWA and Y. KYOGOKu, Chem. Lett. Z49, (1976). [3] S. SUNDER and H. BERNSTEIN, J. Raman Spectr. 5, 351 (1976). [4] H. Sus~ and J. S. ARD, Spectrochim. Acta 33A, 561
(1977). [5] A. L. VERMA and H. J. BERNSTEIN, Biochem. Biophys. Res. Comm. 5"/, 255 11974). [6] R. PLUS and M. LUTZ, Spectrosc. Lett. 7, 73 11974). [7] B. F. KIM and J. BOHAYDY, J. Mol. Spectr. "/3, 332 ( 1978). [8] E. B. WItSON, JR., J. C. DECIUS and P. C. CROSS, Molecular Vibrations. McGraw-Hill, New York (1955). [9] N. FUHRER, V. B. KARTHA, K. G. KIDD, P. J. KRUEGER and H. H. MAYrSCH, N.R.C,C. Bulletin
466
J. BOHANDY and B. F. KIM 15, Computer Programs for Infrared Spectrophotometry X X X I X - X L I , Normal Coordinate
No.
Analysis (1976). [10] B. M. L. CHEN and A. TUI.INSKY, J. Am. Chem. Soc. 94, 3-144 (1972). [11] D. W. S c o w l J. Mol. Spectr. 37, 77 (1971).
[12] A. T. GRAI)YUSHKO, K. N. SOLOVEV and A. S. ST,\RUKHIN, ()pt. ~pectr. 40, 267 (19761. [ 13] M. G o u I't-;RMAN. Thc porph_,,rins, Physic~d Chemistry. Part A, Volume lI1. p. 130 (edited by DAVID DOLPHIN). Academic Press, New York (1978). [14] S. F. MASON, d. Chem. Soc. 976 (1958).