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LCAO MO SCFπ-electron calculations on the magnetic circular dichroism of porphin, protoporphyrin, and porphyrin a
LCAO MO SCFn-ELECTRON
IS November 1377
CHEMK’AL PRYSICS LlXTERS
Volume 52. number I
CALCULATIONS
OF PORPHIN, PROTOPORP~iYRIN,
ON THE MAGNETIC CIRCULAR
AND PORPH~IN
DICHROISM
a
A.KAITO,T.NOZAWA,T.YAMAMOTO,M.HATANO Chemical Researdz fnstit~tc of Non-aqueous Stwdai .Japait
SoMions,
Tohoku
UMWS@Y,
and Y. OR11 Department of Biology, Faculty ofScieme, Toyamka, Osaka. &pan
Osaka ihwerslty.
Received 22 July 1977
The transition energies, the oscillator strengths, and the ,4/L) values of porphin, protoporphyrin, and porphyrin a were calculated within the framework of the Wiser-I’arr-Popfc approximation. The calculated values are in reasonable agreement wzth the experimental data obtained from the ab$orption and magnetic circular dichroism spectra of metal porphin, low-spin ferrous protoheme, and low-spin ferrous hemc a. The rna~netic circular dtchroism of the Q and Soret band% in the heme a and the protoheme was analysed in term5 of an “appYent” A term which origmatcs from the magnet:c mixing between the component\ of the nearly degenerate excited state.
CH=CH,
1. Introduction Magnetic circular dichroism (MCD) spectra of porphyrin and its derivatives are of wide interest because they clearly rcfiect the characteristics of electronic structures of porphyrins, namely, the heme redox state, the spin state, the figand state, and the nature of the substituent groups of the porphyrin perimeter. In a previous paper [1], the MCD spectra of cytochrome oxidase and heme a derivatives have been reported_ The MCD spectra of low-spin ferrous heme a derivatives in the visible region were found to be opposite in sign to those of low-spin ferrous protohemes [l ,2]. The unique MCD profiles in low-spin ferrous heme a derivativcs were considered to be attributable to the existence of a formyl side chain at the position 8 Ii ] _ The experimental MCD spectra have been analysed in terms of the three Faraday parameters [3,4] - The Faraday n term ordinates from the Zeeman splitting of the degenerate ground or excited state. The temperature-dependent C term is induced by the poptdation difference of the ground state sublevels whose
Iron
porphin
Protoherne
&4* 4OON
efi,
hi,
CtOiW
Heme a 154
Cl&
Volume
52, nurnbcr 1
15 November 1977
CHE:MICAL PHYSICS Lt3-TERS
degeneracy is removed by the external masetic field. The Faraday f? term arises from the magnetic mixing among electronic states. The Faraday A and C terms are expectcd only when the molecules have an n-fold axis (n > 2), while the B term IS present for all molccules. Attempts have been made to calculate the Faraday parameters on the basis of semi-empirical SCF MO calculations. The Faraday A terms of coronene and triphenylene [5], coronene negative ions 161, porphyrins [7j, nonbenzenoid hydrocarbons [8], and benlcne derivative< [9] have been calculated within the framework of the Parker-Parr-Pople (PPP) approximation [lo]. The calculated values are in good agrecment with the experlrnental data. The PPP method also succeeded in explainin g the expcrimcntal Faraday U terms of various aromatic tqanic compounds [I 1 -131. In the present report, WCcalculate the Faraday parameters of porphin, protoporphyrm, and porphyrin a on the basis of the PPP method, in order to explain the intriguing experimental finding that the sign of the MCD of low-spin ferrous hcmc a is opposite to that of metal porphin and low-spin ferrous protohcmes.
the z-components of the orbital and spin angular momentum operators, respectively. The wavefunctions of the excited states in the presence of the magnetic fidd, Ii,>, are expressed as linear combinations of lil)
and Ij2k
Ii*)=
C,‘li,)
+ C&L
The energy of the perturbed cxcitcd states, E,‘, and the coefficients, Ct and Cz, are obtained by solving the secular equation, Ej, -E
k =O,
1 -k
(3)
q* - E
where
-
-1111
I&
lj$Ii_,
The solution ofeq.
.
cf
= -(hi,
(4
(3) IS summarized
E,? - (EjI + q2 + aq:!
as follows.
,
6)
- Ej2 + d1l2)
X [2d 2 ‘(El,
2. “Apparent” II terms in substituted
(2)
- ZQd’/‘]-II2
,
6)
porphyrim c$ = 21/24d
The substitution on the porphyrin ring splits the degeneracy in the excited states of porphyrins, which make it impossible to analyse the MCD of substituted porphyrins in terms of the Faraday A term. IEowcvcr, the substituted porphyrins exhibit MCD spectra with a dispersion shape quite analogous to the Faraday A term. In this section we relate the MCD spectra of substituted porphyrins to the magnetic properties of the nearly degenerate excited states. We consider the transition from the nondegenerate ground state, la>, to a pair of degenerate or nearly degenerate states, lil) and (j2). The electronic states, la>, ljl), and ljZ> arc expressed in real form. The zerofield energies of the states, la), ljl>, and lj2), are designated as EO, 13, , and Ej-- , rcspcctively. When a constant magnetic field, Hz, IS applied along the z-axis, the perturbing hamlltonian is given by
(1) where pr is the z-component of the magnetic moment operator, fl is the Bohr magneton, and L, and S, are
2 (El,
- q;,,
&q-m,
(7)
where -
L?=(Ej,
+4$.
Ej2)2
The ellipticity 141
(8)
0 per unit path length 1s described as
0 = -(8n2A@c) X {f(v,q-+) ff(v,vi_)
Im(alm,I~+)(~+Imy(u) Im(aIm,li-)(i-fnl,,la)),
(91
where Na is the number of molecules per unit volume in the ground state, Q, mx and m,, arc the X- and Ycomponents of the electric moment operator, respectivcly , and v k is (Eik - Eo)/hc. The band shape function,f(v, u,~‘>,k assumed to be the damped oscillator model, namely,
f(v,ly) where
= v”r/{(+
- v”p
+ A-q,
(10)
r is the 1incv;idth at half height and v is the
1.55
15 November
CHEMICAL YHYSICS LIXTERS
Volume 52, number 1
1977
wavenumber of light. The electric moment matrix element in eq. (9) leads to eq. (1 I) using cqs. (2), (6), and (7) Jm(alm,li’>(i+l~n~la) = + (E/~‘~2)((aIm,!jl)(i21m,,la) -
(11)
The expression for the ellipticity, 0, is obtained substitution of cq. (1 1) into eq. (9) 0 = -&?N,H,/3hc)n
{f(Y,Yj_) -f(U,
by the
yi+)}/O
, (12)
where A = 3 Im(jl I~zIj2~(~olm,Ijl~~j21~nyl~~
l/x
- ~aIm,li2)(illm,la)).
03)
If we convert 0 into the molar ellipticity per unit magnetlc tield, [Olni (deg dl dm-L mole--1 G-l) and express n in square debye X 0, eq. (13) becomes [Q,
lo-’
hn
’ I
Y x IO-’
km-’
1
Y I m-3
(cm-’
,
Fig. 1. Dispersion functions, ff(u, vi-) - f(~, Y~)}~~c/&/~ (upper), and cf(y, vi-1 +f(v. LJJ*)}/~(lower). ‘Ike splittings. VI*-1ui-, are (A) 2 cm-‘. (B) 1000 cm-‘, and (C) 2000 cm . The band center, (“1~ + v,-)/2. and the Iincwidth, I-, arc wt to be 20000 cm-’ and 2000 cm-‘, respectively.
= -21.35 A (f( Y,yj_)--f(u,u,+))Irc/~‘~~,(14)
Eq. (13) can be applied only to molecules oriented along the dIrection of the light propagating vector (z-axis). For an isotropic medium, cq. (13) should be averaged over molecular orientations, resulting in
In this method, the nth moments are computed by numerically integrating the MCD and absorption spectra in accordance with
A = I1~~~j~l~lj~>~~almlj~~X~j~1~~zln~.
(15)
The dispersion curve in eq. (14), cf(v, v._) f(v, “j +) 1 held lj2, is shown in fig. 1, al&g with the dispersion shape function of the absorption spectra,
UMln =
156
dv ,
J’
([O],,/v)~”
dv,
(16)
band
~fb4v,-) +f(Y,~-+)l/2. When Iit) and i-J$ are the components of completely degenerate excited state of porphyrins with a four-fold axis, cq. (1.5) agrees with the “actual” A term defined by Buckingham and Stephens [3 1, and d1j2 corresponds to the Zceman splitting. The present theoretical treatment also holds true for the substituted porphyrins with lower symmetry, in which the magnetic mixing between !hc nearly degencratc excited states gives rise to the MCD with similar dispersion shape to the A term. In this work, the MCD of the nearly degenerate transition of the substituted porphyrin is treated a$ the “apparent” A term which is given by eq. (15). The method of moments is a powerful technique for extracting the “actual” and “apparent” A terms.
_I-(E/V) v”
band
where E is the molar extinction coefficient in P cm-1 mole-l. From eqs. (14) and (16), the following relation hetwecn the first moment (O,), and A is obtained (f?,),
= - 21.35A(5_
- “i+> rrhc/2d112 = 33.53A . 07)
If we include the B terms due to the magnetic mixing among electronic states other than that between the states ljl> and lj2), the zeroth and the first moments are summarized as follows [4] :(J = -33.53B, WMll
= -33.53(/I
F=(E)I/(EJ-J.
- Bv'),
CIW
Volume 52, number
CHF~MICAI. I’IIYSICS 1-CITERS
1
3.tilculations The transition energies. oscillator strengths, and the “actual” and “apparent” Faraday A terms were calculated on the basis of the PPP CI approximation. The orbitals of the central metal and the axial ligands were neglected. One-center core integrals, ivG, and oneCenter electron repulsion integrals, rplr, are evduated from the valence state ionization potentials and electron affinities determined by 1Iinze and Jaffti [ 141. The formal charge of the porphyrin moiety is assumed to be zero. That is, the core charge of the central mtrogen atom is taken to bc 1.5, and TNN and It’/, are determined as follows. TNN = {l&(trtrtr’n - AN (trtrtr27G + I&(trtrtrn rVN = -
-b trtrtr2n)
+ trtrtr)
{Ih(trtrtr2n
+ IL (trtrtd
+ trtrtf”) (1%
- IA (trtrtd
+ Litrtrn)}/2,
-* trtltrl)
-’ trtrtrfl)]/:!
+ kaco),
- o-5 TNN ,
apv = 2e2/h,,
(20)
+ YJ
, (2 1)
where R,, is the intcratomlc distance and the corrclation parameter, k,is set lo be 2.0 [ 161. Bond length and bond angle of the porphyrin ring were taken from the experimental data of tetraphenylporphin [ 171. Configuration iritcraction among sin@y cxcltcd conlig‘I-able 1
One-center parameters _-- -- ---____--
_
C 0 N -_----------_-_-c_l_-
Wg(“v) - --_-------_-11.16 17.70 20.315
urations below 6 eV was taken Into account _ Then, the I.CAO MO coefficients, obtained by the PPP method, were dcorthogonalizcd by the mversc Lowdm transformation [IS], and the oscillator strength and the “actual” and “apparent” /i tcI111swere calculatcd using Slater orbitals [19], The elcctrlc trnnsltion moments were evaluated by the chpole length, f, illld by the dipole vcloclty, V, operalors. nalnely,
-- e(Ulrlj),
The bailed computations of the atomic integrals of the electric and magnetic moment operators are described 111rcfs. [20,2 I]The calculations were carncd out usmg an ACOS 700 computer in the computer center of I’ohoku UnlVcrslty.
4. Results and diwuwion
where Zk, Z&, and AN are the first ioniiration potential, the second ionization potential, ancl the electron affinity, respectively. One-center parameters used in the present calculations arc summarized in table I. Twocenter core integrals wcic calculated using the Wolfsberg--Helmholtz equation [ 1 S] - Two-center electron repulsion integr& were evaluated by the modified Nishimoto-Mataga equation [ 161, namely, Y,, = eZI(R,
15 Novcrnbcr 1977
-----. 7FP (CVI II.13 IS.23 14.55
The low-spm ferrous. porphyrins show two a* + 7~ transltions in the region of 1SOOO---25000 cm-'. The lower energy OIIC IL cdlcd Q band iIrld higher cneqy one Soret band. Gccordmg to the generally accepted theory of the electronic structure of porphyrins (four orbital model), thcsc two n* + n transitions arise from the one-electron eXCltiltlOn from the nearly degcncratc highest occupied molecular orbit&, 9;1,II and Qa,u, to the doubly degenerate lowest unoccupied molcc~l,lr orbital, &,_ That is, the two excited states arc written as linear combinations of the electronic configurations, + Qc ). ‘I’(&iT L,-+ Qc ) anti ‘IJ(&ll,, The calculztcd transition eneriy and A/D value of porpldn can be reasonably compared with the capenmental values of metal octaetliylporpflyriris (OE.P), rcported by Gale et al. [23_], and the results arc shown in table 2. The expcrlmcntal transition cnergles of the Q and Soret bands arc clearly reproduced by the PPI’ metl~cl usmg the modified Nishimoto-Mataga CC~IJZItlon [I 61 for the two-center electron repulsion Intcgals. The experimental A/D ViIIucS arc slightly affected by the nature of the central metal. The calculated A/D values are in good agrcemcnt with the cxperimental data in sign and in magnltlldc. The calcijlated transition encrgics, oscillator 1.57
Volume 52, numbW
CIIEMICAL
I
‘rabIe 2 ~.~~eriRl~~~~~ data of rnctJ1 OctJ~t~~ylpGrp~~yrlR(OEP) -__-_--__
_.-....__-I.--------
PHYSICS LETTERS
Q u+-o ---..
_-
___
__-
IO””
_-___
(cm-’
m _-_-_-
__
-
_
Soret __. --
-
v x 10-j
A/D
(cm-‘) __-_
Cctn -I>
(P) _____P_I-----_--
-_c_-_----
_-
-__-
u x 1o-3
nlu
)
ClI(OW)
17.78
17’
18.89
0.59
Zn(OEP)
17.54 17.91
1.77 1.06
18.71
0.9
24.46
0.93
19.05 19.23
0.36
tR.08
0.33
25.4
M0L.Y) CO(OE~)
1977
and Wctifated data of porphin ---...._--_--__-wI__---
00-o ---._ “X
I5 Novambcr
_
AID -
-
(P)
24.92 24.84
-
--
0.19 0.15 0.29 -0.2
calcu!ated __
porphin _ _ ___
2.L5
16.9
--_-_-
--___
I--
-
-
“-
-.-
-
24.7
__------..“__---
-._
-
USCof the method of moments [4f (eq. (18)). The experimental A‘[D values arc somewhat influenced by the axial ligartds. Although the dipole length method produces larger theoretical oscillator strengths than the dipole velocity method, the c~~cu~~t~d A’/D values reasonably agree with the experimental values both in sign and in order of magnitudu. The calculnted res:llts for porphyrin a :mc,l the experimental data of low-spin ferrous hcrne a me summarimd in table 4. The MCD spectra of hcmc a have been previously reported [l ] . The formyl group in hernc a causes the red-shift in the transition encrgics, relative to metal porphin and protohemc. The calculated splittings of the Q and Soret bands in porphyrin
strengths, and /I’/0 values of pr~~toporphyrin are corn-pared with the experimental dnta of low-spin ferrous hemoglobins in table 3, where the “apparent”~ term is designated as A’. A detailed anrtlysis of the MSL) spectra of low-spit ferrous ~lcmo~lobins will DC reported in the near future. The calculated and observed transition energies are slightly smaller than tl_Jse of metal porphins. The splittings of the Q and Sorct bnnds are calcuEatcd to be 17 cm-l and 73 aW1. respectmly, and are much smailer than the experjm~nt~l linewidths. For the Q band, two overlapping vibronic bands, Q+,-, and Q,+o, were resolved by the gaussisn curve fitting procedure, and then the experimcr~ti~l OS-
ciilator st~e~~~t~~s and A’/D vaIues were obtained by
Experimental dat:i of low-sptnFe(U) hcrnoglobm (Hb) con~pk%cs and cJlcul&cd data of protoporptlyrln _--____
---
w--s
-_
-
-
-
Q 0+-O
- -_-
_ .-
-_
--
-L_
I?-”
(cm --___I-_
__
__-_
--__-
---
Q w-0
---up
vx
--
f
A’lD
)
(0) __,___-_
IJX
Soret --
1V3
---
----
f
(cm-‘) ___--__
I
-
vx10-3
A’lD
_--_A--
A’fD
f
ccm- ’ ) _-----z__
W) --
---
WI
~~p~rxrn~~r~i
a-Hbf-‘s(ll) CO
17.5
0.016
1.0
a-IlbFc(II)
17.5 17.4
2.0 1.3 2.3 3.0
38.5 18.6 18.5 18.5 18.6 18.6
0.095 0.121 0.084
0.37 0.57 0.10
24.2 24.3 24.3
1.20 1.40 1.29
0.097 0.112 0.094
OS9
24.1
1.22
0.20
0.33
24.3 24.3
1.24 1.18
0.08 0.16
0.27 0.13 0.23
CO
17.5
@-HbFe(II)NO
17.5
0.020 0.019 0.023 0.0?3
~-~~b~e~iI) 07_ calculated
17.3
0.020
2.3
16.7
G.018 0.00s
2.19
23.9
5.53
0.04
2.19
23.9 --
L-82
0.04
NO
a-HbFe(11) 02 p-iltKk(I1)
protoporphyrm pa) _-
vb) I_
-
-
16.7 -_
-
.--
___-__
31 Calculated by tbc dipole kngtb mathod.
158
0.088 --_
0.16
_-_-
h) Caicukztcd by the dipole velocity method.
_
_
Volume
52, number
1
CHEMICAL
Table 4 Eupcrin1cntal data of low-spin ------_-
Fe(H)
heme B and calculated --
Q _______-
--
experimental low-spin Fe(H) hemc a calcul.lted porphyrin 21 r”) Vb) -_- - -_- -_ by the dipole
LLTTFRS
15 November
data of porphyrin rl --.----.-_-
- -.-Sorct -__
__--_-----
Y x 1o--3 f (cm-’ ) __________-_-_-_-c__.-------_---_-_---__-
________
a) Calculated
PllYSICS
A’lll
Y x lo-’
Co)
(cm-’
23 0
16.6
0.13
-0.79
16.6 16.6 _ -_- ---
0.039 0.015 ___
- 1.40 23.7 -0.55 23.7 - __---_____----_--_---------
length
mathod.
_--- --
b) Catculntccl
-.----_
by the dipole
and 309 CITI~-~,respectively. The formy1 group in heme a sphts the degeneracy of the cxcited states of porphyrin more largely than the vmyl group in protoherne. The cslculatcd oscillator strcngtbs of Q hand and the magnitude of the A’/D value of the Soret band are smaller than the experimental values. The PPP method, however, explains the experimental result that the sign of the MC:D of low-spin ferrous heme a is opposite to that of metal porphin and lowspin ferrous protoheme. One of the most important critique on the present calculation is the neglect of the orbltals of the central metal and axial ligand. Tables 2 and 3 show that the A/D and A’/0 values are affected to some extent by the nature of the central metal and the axial @and. The formation of the o-type coordination bond between the central metal ion and the nitrogen atom of a are 73 cm-’
the porphyrin ring is considered to have some influence on the MCD and absorption spectra. The present assumption of neutral porphyrin is, however, supported by the results of the extended IItickcl calculation [23] that the formal charge on the metal ion is considerably neutralircd. In conclusion, the PPP method successfully explains the signs of the “actual” and “apparent” A terms of metal porphin, protohemc, and herno a, although a theoretical refinement, in particular, the inclusion of the orbitals of the metal and the axial l&and, is required for more quantitative agreement between theory and experiment.
-
velocity
-
- -__-
______
- -__ _ _ .- _____-___
f
)
1977
-
/I’lD (P)
0.74
-0 46
5.1s 1.68
-0.05 -0.05
method
Referencec
111Y.
Orit, T. Nolawa and hl. Ilnt.lno, Blochcmlrtry, submittcd for publication 121 L. Vickcry, T. No;lnwa and K. Sauer, J. Am. Chcm. Sot. 98 (1976) 343; G.T. Babcock, L .t. Vrckery and G. Palmer, J. IIrol. Chem. 251 (1976) 7907. 131 A.D. Iluckmph.lm and P.J. Stcptwn\, Ann. I&w. Phy5 Chem. 17 (1966) 399. [41 P.N. Schatc. dnd A.J. hlcC.tffcry, Quart. Rev C’hcm. Sot. 23 (I 969) 552. (51 P.J. Stcphcns, P.N. Sclratr, A.lI Ritchic and A.J. hlcCaffcry, J. Chcm. 1’11~s.48 (1968) 132. 161 P.J. %and\tra, D.J. Scholtens and RX. Eoning, J. c’hcm. Phys. 57 (1972) 3831. and C. WLX,\ Jr., Thcorct. 171 A.J. bicIIt~git. hl Gouterman Chim. Acta 24 (1972) 346. 181 A. Tajlri. H. Uchlmura and hl. tk1tano. Cheru 1’11~s. Letters 21 (1973) 568. ISI A. Kaito, A. TaJ1ri and hl. flatano, J. Am. Cbcm. Sot. 97 (1975) 5059 [lOI R. PAriser and R.G. Parr, J. Chem. Phys 21 (1953) 466, 767: J.A. Poplc, Trans. Faraday Sot. 49 (1953) 1375. ItI1 J. hlichl, Chcm. Phy5. Letters 39 (1976) 386.43 (1976) 457, and refcrenccs therein. I17-1 A. Knito, A. Tajiri and hl flatano, J. Am. Chcm. Sot. 98 (197(i) 384. iI31 R.J. van dcr Wal and P.J. Zandstr.l, J. Chcm. Phys. G4 (1976) 2261; P.R. Boudcwrjn, W.C. Nleuwpoort and P.J. Zdndstra. Chen1. Phys. Letters 37 (1976) 123. 1141 J. Hinze and 1I.H. Jaffti, J. Am. Chem. Sot. 84 (1962) 540. J. Chcrn. Pbys. 20 (1952) iI51 M. Wolfsberg and L. Helmholtr. 837.
159
Volume
51. number
1
CZICMICAL
1161 I;. ‘Tomono and K. Ni~f~~lnoto, IWI. C~ICIIL Sot. Japan 49 (1976) 1179. [ 171 J.1.. Hoard. hf.J. Hamor and T.A. Hamor, J. Am. Chem. sot. 85 (1963) 2334. 11 S] P.-O. Loadm, J. Chcm. Pbfs f8 (1950) 365. 1191 J.C Slatcr, l’hys. Rev. 36 (1930) 57. [ZO] A. Irnamur~, ‘I-. Iltr,lno, C. Nagau and r. Tsurtw, Bl;li. Chem. SOC. JapitIl 45 (1972) 396.
PHYSICS
LETTERS 121 ] hf. SIX&~,
15 November
1977
Y. Nihei and 11. Kamada, BulI. Chem. Sot. Japan 42 (1969) 323. 1221 R. Gale, A.J. hfcC,lffery and M.D. Rowe, J. Chern. Sot. Dalton Trans. (1972) 596. 123 1 M. Zerner and h-i. ~outer~~n, Theorct. Cbim. Acta 4 (1966) 44.
IS November 1377
CHEMK’AL PRYSICS LlXTERS
Volume 52. number I
CALCULATIONS
OF PORPHIN, PROTOPORP~iYRIN,
ON THE MAGNETIC CIRCULAR
AND PORPH~IN
DICHROISM
a
A.KAITO,T.NOZAWA,T.YAMAMOTO,M.HATANO Chemical Researdz fnstit~tc of Non-aqueous Stwdai .Japait
SoMions,
Tohoku
UMWS@Y,
and Y. OR11 Department of Biology, Faculty ofScieme, Toyamka, Osaka. &pan
Osaka ihwerslty.
Received 22 July 1977
The transition energies, the oscillator strengths, and the ,4/L) values of porphin, protoporphyrin, and porphyrin a were calculated within the framework of the Wiser-I’arr-Popfc approximation. The calculated values are in reasonable agreement wzth the experimental data obtained from the ab$orption and magnetic circular dichroism spectra of metal porphin, low-spin ferrous protoheme, and low-spin ferrous hemc a. The rna~netic circular dtchroism of the Q and Soret band% in the heme a and the protoheme was analysed in term5 of an “appYent” A term which origmatcs from the magnet:c mixing between the component\ of the nearly degenerate excited state.
CH=CH,
1. Introduction Magnetic circular dichroism (MCD) spectra of porphyrin and its derivatives are of wide interest because they clearly rcfiect the characteristics of electronic structures of porphyrins, namely, the heme redox state, the spin state, the figand state, and the nature of the substituent groups of the porphyrin perimeter. In a previous paper [1], the MCD spectra of cytochrome oxidase and heme a derivatives have been reported_ The MCD spectra of low-spin ferrous heme a derivatives in the visible region were found to be opposite in sign to those of low-spin ferrous protohemes [l ,2]. The unique MCD profiles in low-spin ferrous heme a derivativcs were considered to be attributable to the existence of a formyl side chain at the position 8 Ii ] _ The experimental MCD spectra have been analysed in terms of the three Faraday parameters [3,4] - The Faraday n term ordinates from the Zeeman splitting of the degenerate ground or excited state. The temperature-dependent C term is induced by the poptdation difference of the ground state sublevels whose
Iron
porphin
Protoherne
&4* 4OON
efi,
hi,
CtOiW
Heme a 154
Cl&
Volume
52, nurnbcr 1
15 November 1977
CHE:MICAL PHYSICS Lt3-TERS
degeneracy is removed by the external masetic field. The Faraday f? term arises from the magnetic mixing among electronic states. The Faraday A and C terms are expectcd only when the molecules have an n-fold axis (n > 2), while the B term IS present for all molccules. Attempts have been made to calculate the Faraday parameters on the basis of semi-empirical SCF MO calculations. The Faraday A terms of coronene and triphenylene [5], coronene negative ions 161, porphyrins [7j, nonbenzenoid hydrocarbons [8], and benlcne derivative< [9] have been calculated within the framework of the Parker-Parr-Pople (PPP) approximation [lo]. The calculated values are in good agrecment with the experlrnental data. The PPP method also succeeded in explainin g the expcrimcntal Faraday U terms of various aromatic tqanic compounds [I 1 -131. In the present report, WCcalculate the Faraday parameters of porphin, protoporphyrm, and porphyrin a on the basis of the PPP method, in order to explain the intriguing experimental finding that the sign of the MCD of low-spin ferrous hcmc a is opposite to that of metal porphin and low-spin ferrous protohcmes.
the z-components of the orbital and spin angular momentum operators, respectively. The wavefunctions of the excited states in the presence of the magnetic fidd, Ii,>, are expressed as linear combinations of lil)
and Ij2k
Ii*)=
C,‘li,)
+ C&L
The energy of the perturbed cxcitcd states, E,‘, and the coefficients, Ct and Cz, are obtained by solving the secular equation, Ej, -E
k =O,
1 -k
(3)
q* - E
where
-
-1111
I&
lj$Ii_,
The solution ofeq.
.
cf
= -(hi,
(4
(3) IS summarized
E,? - (EjI + q2 + aq:!
as follows.
,
6)
- Ej2 + d1l2)
X [2d 2 ‘(El,
2. “Apparent” II terms in substituted
(2)
- ZQd’/‘]-II2
,
6)
porphyrim c$ = 21/24d
The substitution on the porphyrin ring splits the degeneracy in the excited states of porphyrins, which make it impossible to analyse the MCD of substituted porphyrins in terms of the Faraday A term. IEowcvcr, the substituted porphyrins exhibit MCD spectra with a dispersion shape quite analogous to the Faraday A term. In this section we relate the MCD spectra of substituted porphyrins to the magnetic properties of the nearly degenerate excited states. We consider the transition from the nondegenerate ground state, la>, to a pair of degenerate or nearly degenerate states, lil) and (j2). The electronic states, la>, ljl), and ljZ> arc expressed in real form. The zerofield energies of the states, la), ljl>, and lj2), are designated as EO, 13, , and Ej-- , rcspcctively. When a constant magnetic field, Hz, IS applied along the z-axis, the perturbing hamlltonian is given by
(1) where pr is the z-component of the magnetic moment operator, fl is the Bohr magneton, and L, and S, are
2 (El,
- q;,,
&q-m,
(7)
where -
L?=(Ej,
+4$.
Ej2)2
The ellipticity 141
(8)
0 per unit path length 1s described as
0 = -(8n2A@c) X {f(v,q-+) ff(v,vi_)
Im(alm,I~+)(~+Imy(u) Im(aIm,li-)(i-fnl,,la)),
(91
where Na is the number of molecules per unit volume in the ground state, Q, mx and m,, arc the X- and Ycomponents of the electric moment operator, respectivcly , and v k is (Eik - Eo)/hc. The band shape function,f(v, u,~‘>,k assumed to be the damped oscillator model, namely,
f(v,ly) where
= v”r/{(+
- v”p
+ A-q,
(10)
r is the 1incv;idth at half height and v is the
1.55
15 November
CHEMICAL YHYSICS LIXTERS
Volume 52, number 1
1977
wavenumber of light. The electric moment matrix element in eq. (9) leads to eq. (1 I) using cqs. (2), (6), and (7) Jm(alm,li’>(i+l~n~la) = + (E/~‘~2)((aIm,!jl)(i21m,,la) -
(11)
The expression for the ellipticity, 0, is obtained substitution of cq. (1 1) into eq. (9) 0 = -&?N,H,/3hc)n
{f(Y,Yj_) -f(U,
by the
yi+)}/O
, (12)
where A = 3 Im(jl I~zIj2~(~olm,Ijl~~j21~nyl~~
l/x
- ~aIm,li2)(illm,la)).
03)
If we convert 0 into the molar ellipticity per unit magnetlc tield, [Olni (deg dl dm-L mole--1 G-l) and express n in square debye X 0, eq. (13) becomes [Q,
lo-’
hn
’ I
Y x IO-’
km-’
1
Y I m-3
(cm-’
,
Fig. 1. Dispersion functions, ff(u, vi-) - f(~, Y~)}~~c/&/~ (upper), and cf(y, vi-1 +f(v. LJJ*)}/~(lower). ‘Ike splittings. VI*-1ui-, are (A) 2 cm-‘. (B) 1000 cm-‘, and (C) 2000 cm . The band center, (“1~ + v,-)/2. and the Iincwidth, I-, arc wt to be 20000 cm-’ and 2000 cm-‘, respectively.
= -21.35 A (f( Y,yj_)--f(u,u,+))Irc/~‘~~,(14)
Eq. (13) can be applied only to molecules oriented along the dIrection of the light propagating vector (z-axis). For an isotropic medium, cq. (13) should be averaged over molecular orientations, resulting in
In this method, the nth moments are computed by numerically integrating the MCD and absorption spectra in accordance with
A = I1~~~j~l~lj~>~~almlj~~X~j~1~~zln~.
(15)
The dispersion curve in eq. (14), cf(v, v._) f(v, “j +) 1 held lj2, is shown in fig. 1, al&g with the dispersion shape function of the absorption spectra,
UMln =
156
dv ,
J’
([O],,/v)~”
dv,
(16)
band
~fb4v,-) +f(Y,~-+)l/2. When Iit) and i-J$ are the components of completely degenerate excited state of porphyrins with a four-fold axis, cq. (1.5) agrees with the “actual” A term defined by Buckingham and Stephens [3 1, and d1j2 corresponds to the Zceman splitting. The present theoretical treatment also holds true for the substituted porphyrins with lower symmetry, in which the magnetic mixing between !hc nearly degencratc excited states gives rise to the MCD with similar dispersion shape to the A term. In this work, the MCD of the nearly degenerate transition of the substituted porphyrin is treated a$ the “apparent” A term which is given by eq. (15). The method of moments is a powerful technique for extracting the “actual” and “apparent” A terms.
_I-(E/V) v”
band
where E is the molar extinction coefficient in P cm-1 mole-l. From eqs. (14) and (16), the following relation hetwecn the first moment (O,), and A is obtained (f?,),
= - 21.35A(5_
- “i+> rrhc/2d112 = 33.53A . 07)
If we include the B terms due to the magnetic mixing among electronic states other than that between the states ljl> and lj2), the zeroth and the first moments are summarized as follows [4] :
= -33.53(/I
F=(E)I/(EJ-J.
- Bv'),
CIW
Volume 52, number
CHF~MICAI. I’IIYSICS 1-CITERS
1
3.tilculations The transition energies. oscillator strengths, and the “actual” and “apparent” Faraday A terms were calculated on the basis of the PPP CI approximation. The orbitals of the central metal and the axial ligands were neglected. One-center core integrals, ivG, and oneCenter electron repulsion integrals, rplr, are evduated from the valence state ionization potentials and electron affinities determined by 1Iinze and Jaffti [ 141. The formal charge of the porphyrin moiety is assumed to be zero. That is, the core charge of the central mtrogen atom is taken to bc 1.5, and TNN and It’/, are determined as follows. TNN = {l&(trtrtr’n - AN (trtrtr27G + I&(trtrtrn rVN = -
-b trtrtr2n)
+ trtrtr)
{Ih(trtrtr2n
+ IL (trtrtd
+ trtrtf”) (1%
- IA (trtrtd
+ Litrtrn)}/2,
-* trtltrl)
-’ trtrtrfl)]/:!
+ kaco),
- o-5 TNN ,
apv = 2e2/h,,
(20)
+ YJ
, (2 1)
where R,, is the intcratomlc distance and the corrclation parameter, k,is set lo be 2.0 [ 161. Bond length and bond angle of the porphyrin ring were taken from the experimental data of tetraphenylporphin [ 171. Configuration iritcraction among sin@y cxcltcd conlig‘I-able 1
One-center parameters _-- -- ---____--
_
C 0 N -_----------_-_-c_l_-
Wg(“v) - --_-------_-11.16 17.70 20.315
urations below 6 eV was taken Into account _ Then, the I.CAO MO coefficients, obtained by the PPP method, were dcorthogonalizcd by the mversc Lowdm transformation [IS], and the oscillator strength and the “actual” and “apparent” /i tcI111swere calculatcd using Slater orbitals [19], The elcctrlc trnnsltion moments were evaluated by the chpole length, f, illld by the dipole vcloclty, V, operalors. nalnely,
-- e(Ulrlj),
The bailed computations of the atomic integrals of the electric and magnetic moment operators are described 111rcfs. [20,2 I]The calculations were carncd out usmg an ACOS 700 computer in the computer center of I’ohoku UnlVcrslty.
4. Results and diwuwion
where Zk, Z&, and AN are the first ioniiration potential, the second ionization potential, ancl the electron affinity, respectively. One-center parameters used in the present calculations arc summarized in table I. Twocenter core integrals wcic calculated using the Wolfsberg--Helmholtz equation [ 1 S] - Two-center electron repulsion integr& were evaluated by the modified Nishimoto-Mataga equation [ 161, namely, Y,, = eZI(R,
15 Novcrnbcr 1977
-----. 7FP (CVI II.13 IS.23 14.55
The low-spm ferrous. porphyrins show two a* + 7~ transltions in the region of 1SOOO---25000 cm-'. The lower energy OIIC IL cdlcd Q band iIrld higher cneqy one Soret band. Gccordmg to the generally accepted theory of the electronic structure of porphyrins (four orbital model), thcsc two n* + n transitions arise from the one-electron eXCltiltlOn from the nearly degcncratc highest occupied molecular orbit&, 9;1,II and Qa,u, to the doubly degenerate lowest unoccupied molcc~l,lr orbital, &,_ That is, the two excited states arc written as linear combinations of the electronic configurations, + Qc ). ‘I’(&iT L,-+ Qc ) anti ‘IJ(&ll,, The calculztcd transition eneriy and A/D value of porpldn can be reasonably compared with the capenmental values of metal octaetliylporpflyriris (OE.P), rcported by Gale et al. [23_], and the results arc shown in table 2. The expcrlmcntal transition cnergles of the Q and Soret bands arc clearly reproduced by the PPI’ metl~cl usmg the modified Nishimoto-Mataga CC~IJZItlon [I 61 for the two-center electron repulsion Intcgals. The experimental A/D ViIIucS arc slightly affected by the nature of the central metal. The calculated A/D values are in good agrcemcnt with the cxperimental data in sign and in magnltlldc. The calcijlated transition encrgics, oscillator 1.57
Volume 52, numbW
CIIEMICAL
I
‘rabIe 2 ~.~~eriRl~~~~~ data of rnctJ1 OctJ~t~~ylpGrp~~yrlR(OEP) -__-_--__
_.-....__-I.--------
PHYSICS LETTERS
Q u+-o ---..
_-
___
__-
IO””
_-___
(cm-’
m _-_-_-
__
-
_
Soret __. --
-
v x 10-j
A/D
(cm-‘) __-_
Cctn -I>
(P) _____P_I-----_--
-_c_-_----
_-
-__-
u x 1o-3
nlu
)
ClI(OW)
17.78
17’
18.89
0.59
Zn(OEP)
17.54 17.91
1.77 1.06
18.71
0.9
24.46
0.93
19.05 19.23
0.36
tR.08
0.33
25.4
M0L.Y) CO(OE~)
1977
and Wctifated data of porphin ---...._--_--__-wI__---
00-o ---._ “X
I5 Novambcr
_
AID -
-
(P)
24.92 24.84
-
--
0.19 0.15 0.29 -0.2
calcu!ated __
porphin _ _ ___
2.L5
16.9
--_-_-
--___
I--
-
-
“-
-.-
-
24.7
__------..“__---
-._
-
USCof the method of moments [4f (eq. (18)). The experimental A‘[D values arc somewhat influenced by the axial ligartds. Although the dipole length method produces larger theoretical oscillator strengths than the dipole velocity method, the c~~cu~~t~d A’/D values reasonably agree with the experimental values both in sign and in order of magnitudu. The calculnted res:llts for porphyrin a :mc,l the experimental data of low-spin ferrous hcrne a me summarimd in table 4. The MCD spectra of hcmc a have been previously reported [l ] . The formyl group in hernc a causes the red-shift in the transition encrgics, relative to metal porphin and protohemc. The calculated splittings of the Q and Soret bands in porphyrin
strengths, and /I’/0 values of pr~~toporphyrin are corn-pared with the experimental dnta of low-spin ferrous hemoglobins in table 3, where the “apparent”~ term is designated as A’. A detailed anrtlysis of the MSL) spectra of low-spit ferrous ~lcmo~lobins will DC reported in the near future. The calculated and observed transition energies are slightly smaller than tl_Jse of metal porphins. The splittings of the Q and Sorct bnnds are calcuEatcd to be 17 cm-l and 73 aW1. respectmly, and are much smailer than the experjm~nt~l linewidths. For the Q band, two overlapping vibronic bands, Q+,-, and Q,+o, were resolved by the gaussisn curve fitting procedure, and then the experimcr~ti~l OS-
ciilator st~e~~~t~~s and A’/D vaIues were obtained by
Experimental dat:i of low-sptnFe(U) hcrnoglobm (Hb) con~pk%cs and cJlcul&cd data of protoporptlyrln _--____
---
w--s
-_
-
-
-
Q 0+-O
- -_-
_ .-
-_
--
-L_
I?-”
(cm --___I-_
__
__-_
--__-
---
Q w-0
---up
vx
--
f
A’lD
)
(0) __,___-_
IJX
Soret --
1V3
---
----
f
(cm-‘) ___--__
I
-
vx10-3
A’lD
_--_A--
A’fD
f
ccm- ’ ) _-----z__
W) --
---
WI
~~p~rxrn~~r~i
a-Hbf-‘s(ll) CO
17.5
0.016
1.0
a-IlbFc(II)
17.5 17.4
2.0 1.3 2.3 3.0
38.5 18.6 18.5 18.5 18.6 18.6
0.095 0.121 0.084
0.37 0.57 0.10
24.2 24.3 24.3
1.20 1.40 1.29
0.097 0.112 0.094
OS9
24.1
1.22
0.20
0.33
24.3 24.3
1.24 1.18
0.08 0.16
0.27 0.13 0.23
CO
17.5
@-HbFe(II)NO
17.5
0.020 0.019 0.023 0.0?3
~-~~b~e~iI) 07_ calculated
17.3
0.020
2.3
16.7
G.018 0.00s
2.19
23.9
5.53
0.04
2.19
23.9 --
L-82
0.04
NO
a-HbFe(11) 02 p-iltKk(I1)
protoporphyrm pa) _-
vb) I_
-
-
16.7 -_
-
.--
___-__
31 Calculated by tbc dipole kngtb mathod.
158
0.088 --_
0.16
_-_-
h) Caicukztcd by the dipole velocity method.
_
_
Volume
52, number
1
CHEMICAL
Table 4 Eupcrin1cntal data of low-spin ------_-
Fe(H)
heme B and calculated --
Q _______-
--
experimental low-spin Fe(H) hemc a calcul.lted porphyrin 21 r”) Vb) -_- - -_- -_ by the dipole
LLTTFRS
15 November
data of porphyrin rl --.----.-_-
- -.-Sorct -__
__--_-----
Y x 1o--3 f (cm-’ ) __________-_-_-_-c__.-------_---_-_---__-
________
a) Calculated
PllYSICS
A’lll
Y x lo-’
Co)
(cm-’
23 0
16.6
0.13
-0.79
16.6 16.6 _ -_- ---
0.039 0.015 ___
- 1.40 23.7 -0.55 23.7 - __---_____----_--_---------
length
mathod.
_--- --
b) Catculntccl
-.----_
by the dipole
and 309 CITI~-~,respectively. The formy1 group in heme a sphts the degeneracy of the cxcited states of porphyrin more largely than the vmyl group in protoherne. The cslculatcd oscillator strcngtbs of Q hand and the magnitude of the A’/D value of the Soret band are smaller than the experimental values. The PPP method, however, explains the experimental result that the sign of the MC:D of low-spin ferrous heme a is opposite to that of metal porphin and lowspin ferrous protoheme. One of the most important critique on the present calculation is the neglect of the orbltals of the central metal and axial ligand. Tables 2 and 3 show that the A/D and A’/0 values are affected to some extent by the nature of the central metal and the axial @and. The formation of the o-type coordination bond between the central metal ion and the nitrogen atom of a are 73 cm-’
the porphyrin ring is considered to have some influence on the MCD and absorption spectra. The present assumption of neutral porphyrin is, however, supported by the results of the extended IItickcl calculation [23] that the formal charge on the metal ion is considerably neutralircd. In conclusion, the PPP method successfully explains the signs of the “actual” and “apparent” A terms of metal porphin, protohemc, and herno a, although a theoretical refinement, in particular, the inclusion of the orbitals of the metal and the axial l&and, is required for more quantitative agreement between theory and experiment.
-
velocity
-
- -__-
______
- -__ _ _ .- _____-___
f
)
1977
-
/I’lD (P)
0.74
-0 46
5.1s 1.68
-0.05 -0.05
method
Referencec
111Y.
Orit, T. Nolawa and hl. Ilnt.lno, Blochcmlrtry, submittcd for publication 121 L. Vickcry, T. No;lnwa and K. Sauer, J. Am. Chcm. Sot. 98 (1976) 343; G.T. Babcock, L .t. Vrckery and G. Palmer, J. IIrol. Chem. 251 (1976) 7907. 131 A.D. Iluckmph.lm and P.J. Stcptwn\, Ann. I&w. Phy5 Chem. 17 (1966) 399. [41 P.N. Schatc. dnd A.J. hlcC.tffcry, Quart. Rev C’hcm. Sot. 23 (I 969) 552. (51 P.J. Stcphcns, P.N. Sclratr, A.lI Ritchic and A.J. hlcCaffcry, J. Chcm. 1’11~s.48 (1968) 132. 161 P.J. %and\tra, D.J. Scholtens and RX. Eoning, J. c’hcm. Phys. 57 (1972) 3831. and C. WLX,\ Jr., Thcorct. 171 A.J. bicIIt~git. hl Gouterman Chim. Acta 24 (1972) 346. 181 A. Tajlri. H. Uchlmura and hl. tk1tano. Cheru 1’11~s. Letters 21 (1973) 568. ISI A. Kaito, A. TaJ1ri and hl. flatano, J. Am. Cbcm. Sot. 97 (1975) 5059 [lOI R. PAriser and R.G. Parr, J. Chem. Phys 21 (1953) 466, 767: J.A. Poplc, Trans. Faraday Sot. 49 (1953) 1375. ItI1 J. hlichl, Chcm. Phy5. Letters 39 (1976) 386.43 (1976) 457, and refcrenccs therein. I17-1 A. Knito, A. Tajiri and hl flatano, J. Am. Chcm. Sot. 98 (197(i) 384. iI31 R.J. van dcr Wal and P.J. Zandstr.l, J. Chcm. Phys. G4 (1976) 2261; P.R. Boudcwrjn, W.C. Nleuwpoort and P.J. Zdndstra. Chen1. Phys. Letters 37 (1976) 123. 1141 J. Hinze and 1I.H. Jaffti, J. Am. Chem. Sot. 84 (1962) 540. J. Chcrn. Pbys. 20 (1952) iI51 M. Wolfsberg and L. Helmholtr. 837.
159
Volume
51. number
1
CZICMICAL
1161 I;. ‘Tomono and K. Ni~f~~lnoto, IWI. C~ICIIL Sot. Japan 49 (1976) 1179. [ 171 J.1.. Hoard. hf.J. Hamor and T.A. Hamor, J. Am. Chem. sot. 85 (1963) 2334. 11 S] P.-O. Loadm, J. Chcm. Pbfs f8 (1950) 365. 1191 J.C Slatcr, l’hys. Rev. 36 (1930) 57. [ZO] A. Irnamur~, ‘I-. Iltr,lno, C. Nagau and r. Tsurtw, Bl;li. Chem. SOC. JapitIl 45 (1972) 396.
PHYSICS
LETTERS 121 ] hf. SIX&~,
15 November
1977
Y. Nihei and 11. Kamada, BulI. Chem. Sot. Japan 42 (1969) 323. 1221 R. Gale, A.J. hfcC,lffery and M.D. Rowe, J. Chern. Sot. Dalton Trans. (1972) 596. 123 1 M. Zerner and h-i. ~outer~~n, Theorct. Cbim. Acta 4 (1966) 44.