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Zero-field splitting in hemin
CHEhlICAL PHYSICS LETTERS
Volume 19, number 1
1
illarch 1973
_-
ZERO-FIELD
SBLITTLNC IN HEMIN
V.R. MARATHE and S. AlITRA Tara Institure of Fundamental Research, Co:aba, Bombay-S, India
Received 18 December 1972
A apin-hamiltonian formalism which includes magetic-field-induced mixing and fourth-order crystal-field terms, is successfuUy employed to explain the Iow-temperature manetic-su.cceptibUity behaviour of hemin.
In hemin (protoporphyrin IX chloride iron (III)) the iron atom is bonded to four pyrrole nitrogen atoms of the planar porphyrin macro-ring, a chloride anion occupying the fifth.apical position to form an approximate square-pyramidal geometry around the iron atom [ 11, The ferric ion in this molecule is high
spin (S = S/2) with the electronic ground state %5/z. The degeneracy of the sextet is party removed by combined effect of spin-orbit coupling and axial crystalline electric field to give three Kramers doublets. A simple spin hamiltonian of the form ti =@ yields that the energy separation between the Kramers doublets M, = +I /2 and i1fs = +3/2 is W and that between fifs = k3/2 and M, = +5/2 40, where D is usually termed as zero-field-splitting parameter. There is considerable interest in the accurate determination of the ground-state splitting in hemin as it is very similar to that in heme proteins. Mossbauer studies on hemin [2,3] suggest that D = 6 cm-l and h;s = 2112 lies lowest. The ESR spectrum of polcrystalline hemin at 4.2’K is characteristic of an &I5 = +-l/2 ground state (g,, = 2, gL = 6) and, though an estimate of D could not be made, it suggests that the next Garners doublet must lie perhaps at least 5 cm-l away from the ground state 141%Recently Richards et al. [5] have directly determined the separations between the ground-state Kramers doublets in hemin by tar-infrared spectroscopy. At 4.2’K only one infrared transition was observed at 13.9 cm-I which was assigned to an MS = ?1/2 + M, = 2312 transition. As the temperature is raised to 20%, the A13= +3/2 level is also’populated and an additional broad absorp-
140‘
‘.
tion band due to an MS = -+3/2 +I%< = +5/2 transition was observed at 27.2 cm-t. The observed transition energies apparently agree well with energy separations, respectively, of W and 40 expected from the simple hamiltonian described above, and so D = 7 cm-l was deduced. This value of D is however very much at variance with that deduced more recently from the low-temperature magnetic-susceptibility measurements on hemin by Maricondi et al. 161. Maricondi et al. have measured the average magnetic susceptibiIity ofhemin between 2.2” and 200°K at a magnetic field of 18 kG. Using the spin hamiltonian ff = DS; + Z&VH,
(1)
an anal!l!rticalexpression for the effective magnetic moments (+,ff> was deduced [7] as a function of D/kT (= x) &
= {.7( 19 + 9e-& +(I&-lle-a
+ 25e-6’)
- 5e-“)]/x(
1 t e-a
+ e-47).
(2)
Eq. (2) gave the best fit to their experimental data over the whole temperature range only when D = I2 cm -l, w,hich is evidently much to large compared to ihe vlauc ob!ained from Mijssbauer and more directly from far-infrared spectroscopy. UsingD = 6 or 7 cm- ;, striking disagreements were observed particularly below 40°K between, the experimentally observed peff values and those calculated by eq. (2).
Volume 19, number 1
CHEMICALPHYSICSLETTERS
Thele are four possible factors which may be responsible for the above discrepancy: (a) neglect of the contribution to the ground state from higher electronic states 4T,(tie) and ‘Tz(ts); (b) neglect of any departure from axial symmetry in the spin hamiltonian; (c) neglect of magnetic-field-induced mixing of the Kramers levels; (d) neglect of fourth-order terms in eq. (1). (a) has been considered by Harris [8] and its effect is fcund to be negligibly small. Experimentally, no departure from axial symmetry is observed. In fact Mijssbauer 12, 3] ad ESR studies [4] on hemin indicate that rhombic distortion, if any, is again negligibly small. Magnetic fields above 10 kG can cause significant mixing of the Kramers levels within the sextet ground state [9]. Eq. (2) is derived using magnetic-field energies as perturbation over zero-field split levels, and using van Vleck’s formula for magnetic susceptibi: lity. Basic assumptions implicit in this calculation are: WQL)
and
/3H< kT.
(3)
Both these assumptions are not, however, valid at high magnetic fields and very low temperatures as of course is the situation that obtains in rationalizing the thermo-magnetic data on hemin. The correct procedure is to calculate the magnetic susceptibility using the basic thermodynamic expression
where the Ei are the energies of the six spin levels of the ground state after simuI1aneous consideration of zero-field and Zeeman-field splittings. Values of i3EJaHcan be calculated by using numerical-differentiation techniques. Fig; 1 shows results of our calculations using the above procedure for D = 7 cm-l and various values of the magnetic field in the temperature range 0 to 20°K. The magnetic moment is found to be both field and temperature dependent. in fig. 2 values of peg calcuIated by this procedure are compared (broken curve) with the experimental data for D = 7 cm-l. H is taken as the experimental value
I hfarch 1973
35-
10 TEMPERATURE
15
J 5
.K
Fig. 1. Theoretical plots showing the characteristic non-linear magnetic behnviour when magnetic-field-induced mixing is included. These c~rvcs are computed for D = 7 cm-’ , and for(n)H=8kG,(b)H= lSkG,(c)H=28kG,(d)H=38kG.
H= 18 kG. It is apparent from fig. 2 that the agreement with D = 7 cm-l (the far-IR value) is rather poor and in fact no reasonably good fit is obtained even if D is varied. It appears that consideration of magnetic-field-induced mixing alone may not be able to explain the magnetic-susceptibility data of hemin over the entire temperature range. We now consider in addition to the magnetic-fleIdinduced mixing, the effect of fourth-order crystal-
Fig. 2. Temperature variation of the effective magnetic moment of hemin, Circlesare the experimentdvdues taken from ref. [6]. Brokencurve is the plot forD= 7 cm-t whenonlymagnetic-field-induced mixing is considered. The solid curve includes in addition to magnetic-field-induced inixing, the ef-’ fe&s of fourthorder mstal-field terms (see text). 141.
field terms in the calculation of zero-field splitting. Such terms are generally important in explaining ESR and zero-field splittings in iron (III) complexes [8, IO]. We again adopt here the spin-hamiltonian formalism I, and consider the hamiltonian in the form:
0; = 3s,2-s(s+
I),
04”= 35S,4- 3OS(S+ I)$+ -6S(S+l)t3S”(St 0,” = 3(e
1 March 1973
CHEMICAL PHYSICS LETTERS
: Volume 19, number 1
25s; 1>*.
+ e_,.
(6)
Here Bg becomesD as defined in eq. (1) when the fourth-order terms are neglecied. For H= 0, the energies of the three Kramers doublets are given as [9], E(cos 8 j-+5/2)+ sin 01F3/2))
z[&+
iJ
7
i i/Z = 2~.2~~-i_
2B,): + 5@a,-1
(9)
The magnetic susceptibility was calculated as described above using eq. (4), and emp!oying the constraints impo;ed by eqs. (8) and (9), a unique set of Bi, B‘I)and Bz was obtained, which gave a very good fit (using the experimental value H= 18 kG) with the experimental Peff values over the entire temperature range (the solid curve in fig. 2 . The best fit is obtained for Bi = 4.84cm-‘, L$d = -2.71 cm-l and S,4 = -5.78 cm-l. We have demonstrated above that the spin-harniltonian formalism with the inclusion of magnetic-fieldinduced mixicg and fourth-order crystal-field terms provides n satisfactory explanation of the low-temperature magnetic susceptibility and the far-infrared data on hcmin. It must be emphasised that use of oversimplified theory as eq. (2) could lead to quite erroneous results in explaining the type of !ow-temperature magnetic data as in hemin.
References
=~B;-B~t[(2B;t~~)2t5(B~)2]1i2, E(cosBIT3/2>-sin81+5/2)} =~B20-B~-[(2920t2B~2tj(B~~2]A/2 E(+)= -@t
7B@ - 4’
(7)
where tan 28 =.5 lJ28,4f(28,0 + 2~:). Considering the two infrared transitions observed at 13.9 and 27.2 cm-‘, we get,
[ 11 G.F. Koenig, Acta Cryst. 18 (1365) 663. [2] C.E. Johnson, Phys. Letters 21 (1966) 491. [3] G. Lang, T. Asakura and T. Yonetani, Phys. Rev. Letters 24 (1970) 961. (41 G. Schoffa, Nature 203 (1964) 640. [5] P.L. Richards, W.S. Caughey, H. Eberspaecher, G. Feher and hi. MaUey, J. Chem. Phys. 47 (1967) 1187. (61 C. Maricondi,W. Swist and D.K. Straub, J. Am, Chem. Sot. 91 (1969) 5205. j7] M. Kotoni, Progr. Theoret. Phys. Suppl. 17 (1961) 4. [S] G. Harris, J. Chem. Phys. 48 11968) 2191. [9] G. Loew, J. Msg. Rcson. 6 (1972) 408. 1101 A. Abragam and B. Bleaney, Electron poramagnetic resonance of transition ions (Clarendon Press, Osford, 1970) p, 142.
Volume 19, number 1
1
illarch 1973
_-
ZERO-FIELD
SBLITTLNC IN HEMIN
V.R. MARATHE and S. AlITRA Tara Institure of Fundamental Research, Co:aba, Bombay-S, India
Received 18 December 1972
A apin-hamiltonian formalism which includes magetic-field-induced mixing and fourth-order crystal-field terms, is successfuUy employed to explain the Iow-temperature manetic-su.cceptibUity behaviour of hemin.
In hemin (protoporphyrin IX chloride iron (III)) the iron atom is bonded to four pyrrole nitrogen atoms of the planar porphyrin macro-ring, a chloride anion occupying the fifth.apical position to form an approximate square-pyramidal geometry around the iron atom [ 11, The ferric ion in this molecule is high
spin (S = S/2) with the electronic ground state %5/z. The degeneracy of the sextet is party removed by combined effect of spin-orbit coupling and axial crystalline electric field to give three Kramers doublets. A simple spin hamiltonian of the form ti =@ yields that the energy separation between the Kramers doublets M, = +I /2 and i1fs = +3/2 is W and that between fifs = k3/2 and M, = +5/2 40, where D is usually termed as zero-field-splitting parameter. There is considerable interest in the accurate determination of the ground-state splitting in hemin as it is very similar to that in heme proteins. Mossbauer studies on hemin [2,3] suggest that D = 6 cm-l and h;s = 2112 lies lowest. The ESR spectrum of polcrystalline hemin at 4.2’K is characteristic of an &I5 = +-l/2 ground state (g,, = 2, gL = 6) and, though an estimate of D could not be made, it suggests that the next Garners doublet must lie perhaps at least 5 cm-l away from the ground state 141%Recently Richards et al. [5] have directly determined the separations between the ground-state Kramers doublets in hemin by tar-infrared spectroscopy. At 4.2’K only one infrared transition was observed at 13.9 cm-I which was assigned to an MS = ?1/2 + M, = 2312 transition. As the temperature is raised to 20%, the A13= +3/2 level is also’populated and an additional broad absorp-
140‘
‘.
tion band due to an MS = -+3/2 +I%< = +5/2 transition was observed at 27.2 cm-t. The observed transition energies apparently agree well with energy separations, respectively, of W and 40 expected from the simple hamiltonian described above, and so D = 7 cm-l was deduced. This value of D is however very much at variance with that deduced more recently from the low-temperature magnetic-susceptibility measurements on hemin by Maricondi et al. 161. Maricondi et al. have measured the average magnetic susceptibiIity ofhemin between 2.2” and 200°K at a magnetic field of 18 kG. Using the spin hamiltonian ff = DS; + Z&VH,
(1)
an anal!l!rticalexpression for the effective magnetic moments (+,ff> was deduced [7] as a function of D/kT (= x) &
= {.7( 19 + 9e-& +(I&-lle-a
+ 25e-6’)
- 5e-“)]/x(
1 t e-a
+ e-47).
(2)
Eq. (2) gave the best fit to their experimental data over the whole temperature range only when D = I2 cm -l, w,hich is evidently much to large compared to ihe vlauc ob!ained from Mijssbauer and more directly from far-infrared spectroscopy. UsingD = 6 or 7 cm- ;, striking disagreements were observed particularly below 40°K between, the experimentally observed peff values and those calculated by eq. (2).
Volume 19, number 1
CHEMICALPHYSICSLETTERS
Thele are four possible factors which may be responsible for the above discrepancy: (a) neglect of the contribution to the ground state from higher electronic states 4T,(tie) and ‘Tz(ts); (b) neglect of any departure from axial symmetry in the spin hamiltonian; (c) neglect of magnetic-field-induced mixing of the Kramers levels; (d) neglect of fourth-order terms in eq. (1). (a) has been considered by Harris [8] and its effect is fcund to be negligibly small. Experimentally, no departure from axial symmetry is observed. In fact Mijssbauer 12, 3] ad ESR studies [4] on hemin indicate that rhombic distortion, if any, is again negligibly small. Magnetic fields above 10 kG can cause significant mixing of the Kramers levels within the sextet ground state [9]. Eq. (2) is derived using magnetic-field energies as perturbation over zero-field split levels, and using van Vleck’s formula for magnetic susceptibi: lity. Basic assumptions implicit in this calculation are: WQL)
and
/3H< kT.
(3)
Both these assumptions are not, however, valid at high magnetic fields and very low temperatures as of course is the situation that obtains in rationalizing the thermo-magnetic data on hemin. The correct procedure is to calculate the magnetic susceptibility using the basic thermodynamic expression
where the Ei are the energies of the six spin levels of the ground state after simuI1aneous consideration of zero-field and Zeeman-field splittings. Values of i3EJaHcan be calculated by using numerical-differentiation techniques. Fig; 1 shows results of our calculations using the above procedure for D = 7 cm-l and various values of the magnetic field in the temperature range 0 to 20°K. The magnetic moment is found to be both field and temperature dependent. in fig. 2 values of peg calcuIated by this procedure are compared (broken curve) with the experimental data for D = 7 cm-l. H is taken as the experimental value
I hfarch 1973
35-
10 TEMPERATURE
15
J 5
.K
Fig. 1. Theoretical plots showing the characteristic non-linear magnetic behnviour when magnetic-field-induced mixing is included. These c~rvcs are computed for D = 7 cm-’ , and for(n)H=8kG,(b)H= lSkG,(c)H=28kG,(d)H=38kG.
H= 18 kG. It is apparent from fig. 2 that the agreement with D = 7 cm-l (the far-IR value) is rather poor and in fact no reasonably good fit is obtained even if D is varied. It appears that consideration of magnetic-field-induced mixing alone may not be able to explain the magnetic-susceptibility data of hemin over the entire temperature range. We now consider in addition to the magnetic-fleIdinduced mixing, the effect of fourth-order crystal-
Fig. 2. Temperature variation of the effective magnetic moment of hemin, Circlesare the experimentdvdues taken from ref. [6]. Brokencurve is the plot forD= 7 cm-t whenonlymagnetic-field-induced mixing is considered. The solid curve includes in addition to magnetic-field-induced inixing, the ef-’ fe&s of fourthorder mstal-field terms (see text). 141.
field terms in the calculation of zero-field splitting. Such terms are generally important in explaining ESR and zero-field splittings in iron (III) complexes [8, IO]. We again adopt here the spin-hamiltonian formalism I, and consider the hamiltonian in the form:
0; = 3s,2-s(s+
I),
04”= 35S,4- 3OS(S+ I)$+ -6S(S+l)t3S”(St 0,” = 3(e
1 March 1973
CHEMICAL PHYSICS LETTERS
: Volume 19, number 1
25s; 1>*.
+ e_,.
(6)
Here Bg becomesD as defined in eq. (1) when the fourth-order terms are neglecied. For H= 0, the energies of the three Kramers doublets are given as [9], E(cos 8 j-+5/2)+ sin 01F3/2))
z[&+
iJ
7
i i/Z = 2~.2~~-i_
2B,): + 5@a,-1
(9)
The magnetic susceptibility was calculated as described above using eq. (4), and emp!oying the constraints impo;ed by eqs. (8) and (9), a unique set of Bi, B‘I)and Bz was obtained, which gave a very good fit (using the experimental value H= 18 kG) with the experimental Peff values over the entire temperature range (the solid curve in fig. 2 . The best fit is obtained for Bi = 4.84cm-‘, L$d = -2.71 cm-l and S,4 = -5.78 cm-l. We have demonstrated above that the spin-harniltonian formalism with the inclusion of magnetic-fieldinduced mixicg and fourth-order crystal-field terms provides n satisfactory explanation of the low-temperature magnetic susceptibility and the far-infrared data on hcmin. It must be emphasised that use of oversimplified theory as eq. (2) could lead to quite erroneous results in explaining the type of !ow-temperature magnetic data as in hemin.
References
=~B;-B~t[(2B;t~~)2t5(B~)2]1i2, E(cosBIT3/2>-sin81+5/2)} =~B20-B~-[(2920t2B~2tj(B~~2]A/2 E(+)= -@t
7B@ - 4’
(7)
where tan 28 =.5 lJ28,4f(28,0 + 2~:). Considering the two infrared transitions observed at 13.9 and 27.2 cm-‘, we get,
[ 11 G.F. Koenig, Acta Cryst. 18 (1365) 663. [2] C.E. Johnson, Phys. Letters 21 (1966) 491. [3] G. Lang, T. Asakura and T. Yonetani, Phys. Rev. Letters 24 (1970) 961. (41 G. Schoffa, Nature 203 (1964) 640. [5] P.L. Richards, W.S. Caughey, H. Eberspaecher, G. Feher and hi. MaUey, J. Chem. Phys. 47 (1967) 1187. (61 C. Maricondi,W. Swist and D.K. Straub, J. Am, Chem. Sot. 91 (1969) 5205. j7] M. Kotoni, Progr. Theoret. Phys. Suppl. 17 (1961) 4. [S] G. Harris, J. Chem. Phys. 48 11968) 2191. [9] G. Loew, J. Msg. Rcson. 6 (1972) 408. 1101 A. Abragam and B. Bleaney, Electron poramagnetic resonance of transition ions (Clarendon Press, Osford, 1970) p, 142.