Studies on the spin Hamiltonian parameters of vitamin B12r

Spectrochimica Acta Part A 71 (2009) 2023–2025

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Studies on the spin Hamiltonian parameters of vitamin B12r Shao-Yi Wu a,b,∗ , Li-Hua Wei a , Zhi-Hong Zhang a , Xue-Feng Wang a a b

Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu 610054, PR China International Centre for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, PR China

a r t i c l e

i n f o

Article history: Received 30 November 2007 Accepted 27 July 2008 Keywords: Electron paramagnetic resonance Crystal-fields and spin Hamiltonians Co2+ Vitamin B12r

a b s t r a c t The spin Hamiltonian parameters g factors gi (i = x, y, z) and the hyperfine structure constants Ai of vitamin B12r have been theoretically studied from the perturbation formulas of these parameters for a Co2+ (3d7 ) ion with low spin (S = 1/2) in rhombically distorted octahedra. The related crystal-field parameters are determined from the point-charge-dipole model and the local structure around Co2+ in vitamin B12r . The theoretical spin Hamiltonian parameters are in good agreement with the experimental data. © 2008 Elsevier B.V. All rights reserved.

1. Introduction Vitamin B12r (cob(II)alamin, or the reduced form of vitamin B12 ) is an important intermediate of B12 during some unique organo-metallic biological reaction of enzymatic process [1,2]. B12r was also found to bind dioxygen reversibly [3,4]. In particular, the paramagnetic Co2+ in B12r can be investigated with the aids of electron paramagnetic resonance (EPR) and electron nuclear double resonance (ENDOR) techniques [5–7], and the spin Hamiltonian parameters g factors gi (i = x, y, z) and the hyperfine structure constants Ai were also measured for the low spin (S = 1/2) Co2+ in B12r . Up to now, however, the above EPR findings have not been theoretically interpreted. As compared with the studies on common high spin (S = 3/2) systems (e.g., the isoelectronic 3d7 Fe+ and Co2+ ions in oxides), investigations on the low spin (S = 1/2) 3d7 ions (e.g., Co2+ in strong crystal-fields) are relatively fewer. Since information about electronic properties and EPR behaviours for Co2+ in vitamin B12r would be helpful to understand structures and functions of this system, studies on the above EPR results for B12r are of significance. In this work, the spin Hamiltonian parameters of B12r are theoretically analyzed from the perturbation formulas of these parameters for a 3d7 ion with low spin (S = 1/2) in rhombic symmetry. In these

∗ Corresponding author at: Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu 610054, PR China. Tel.: +86 28 83202586. E-mail address: [email protected] (S.-Y. Wu). 1386-1425/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.saa.2008.07.041

formulas, the ligand orbital and spin–orbit coupling contributions are taken into account based on the cluster approach. 2. Calculations In vitamin B12 , Co3+ is coordinated to four nearly planar N3− ions and one axial N3− and one axial CN− along the direction perpendicular to the plane [8]. The local structure around Co2+ of the reduced form B12r may be similar to that of Co3+ in B12 during the procedure of reduction. Since the axial Co–N bond length is much longer than that of the planar one, the whole crystal-field acting upon Co2+ can be approximately regarded as an elongated octahedron, with additional rhombic distortion [8]. Co2+ (3d7 ) ions in strong crystal-fields have the orbital doublet 2 E (t 6 e ) with low spin (S = 1/2) as the ground state, which can g 2g g be described as an unpaired electron in eg state [9,10]. As the ligand octahedron is elongated, the ground 2 Eg state would be split into two orbital singlets ε (|x2 − y2 >) and  (|z2 >), with the latter lying lowest [10]. The perturbation formulas of the g factors for a 3d7 ion in tetragonally elongated octahedra have been established by including the contributions from the excited states via the metal spin–orbit coupling coefficient and the cubic crystal-field interactions [10]. However, the contributions from the low symmetrical crystal-fields and the orbital reduction factor due to the covalent reduction of the orbital angular momentum interaction were not taken into account. In addition, the ligand orbital and spin–orbit coupling contributions were neglected as well. In order to investigate the paramagnetic Co2+ center in B12r , the conventional formulas [10] are to be improved by including the above contributions and extended to those under rhombic symmetry. By using the perturbation

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method similar to that in Refs. [9,10], the formulas of the spin Hamiltonian parameters for the rhombically elongated 3d7 cluster can be expressed as follows: 2

2 − 4k(1/E − 1/E ), gz = gs + 2k   /E1z 5z 2z 2 2 + 3k/E − k   (1/E gx = gs + 2k   /E1x x 2x − 1/E5x ), 2 2 + 3k/E − k   (1/E gy = gs + 2k   /E1y y 2y − 1/E5y ), Az = P[− + (4/7)H − (1/14)(gx + gy − 2gs )], Ax = P  [− − (2/7)H + (15/14)(gy − gs )], Ay = P  [− − (2/7)H + (15/14)(gx − gs )]

(1)

increasing the group overlap integrals, and one can approximately adopt the proportional relationship between the admixture coefficients and the related group overlap integrals, i.e., e /Sdpe ≈s /Sds within the same irreducible representation eg . Obviously, when neglecting the ligand orbital and spin–orbit coupling contributions (i.e., taking p0 = 0, Sdp =  = 0 and then  =   = d0 ), the above formulas return to those in the previous work [10]. From the local geometrical relationship, the cubic and rhombic field parameters of the Co2+ center can be determined using the point-charge-dipole model [13–15]:

with 1/Ex = 1/E3x + 1/E4x + 0.38(1/E3x − 1/E4x ), 1/Ey = 1/E3y + 1/E4y + 0.38(1/E3y − 1/E4y ).

(2)

Here gs (=2.0023) is the spin-only value. Ei (i = 1, 3, 4) are the energy separations between the excited 4 T1b , 2 T2a and 2 T2b and the ground 2 Eg states in rhombic symmetry [10,11].  is the core polarization constant. H is the reduction factor characteristic of decline of the anisotropic parts for the hyperfine structure constants due to the metal 3d–4s orbital admixtures [12]. The subscripts ˛ (=x, y and z) denote the various components of the related energy differences due to the rhombic splittings. They can be obtained from the energy matrices of the 3d7 ion in rhombic symmetry: E1z E1x E1y E3x E3y E4x E4y

= 10Dq − 4B − 4C, = 10Dq − 4B − 4C − 3Ds + 5Dt − 3D + 4D , = 10Dq − 4B − 4C − 3Ds + 5Dt + 3D − 4D , = 10Dq + 6B − C − 3Ds + 5Dt − 3D + 4D , = 10Dq + 6B − C − 3Ds + 5Dt + 3D − 4D , = 10Dq + 14B + C − 3Ds + 5Dt − 3D + 4D , = 10Dq + 14B + C − 3Ds + 5Dt + 3D − 4D ,

Nt (1 + 2t /2),

k= P = Nt P0 ,

2 + 2 S 2 − 2 S N 2 = Ne2 [1 + 2e Sdpe e dpe − 2s Sds ]. s ds

eqj (1 + 3 j /eRj ) < r 2 > (3 cos2 j − 1)/Rj3 ,

j=1 6



Dt ≈ (1/21)

eqj (1 + 5 j /eRj ) < r 4 >

j=1

[35 cos4 j − 30 cos2 j + 3 − 7 sin4 j cos 2j ]/Rj5 6 

D ≈ (1/7)

(7)

eqj (1 + 3 j /eRj ) < r 2 > sin2 j cos j /Rj3 , eqj (1 + 5 j /eRj ) < r 4 >

j=1

(3)

(4)

(5)

and the approximate relationship 2 − 2 S N 2 = Nt2 [1 + 2t Sdpt t dpt ],

6 

Ds ≈ (1/14)



where d0 and p0 are the spin–orbit coupling coefficients of the free 3d7 and the ligand ions, respectively. P0 is the dipolar hyperfine structure parameter of the free 3d7 ion. N and  (or s ) are, respectively, the normalization factors and the orbital admixture coefficients. A is the integral Rns|∂/∂y|npy , with the effective (or average) metal-ligand distance R. The molecular orbital coefficients N and  (or s ) can be determined from the normalization conditions Nt (1 − 2t Sdpt + 2t ) = 1, Ne (1 − 2e Sdpe − 2s Sds + 2e + 2s ) = 1,

eqj (1 + 5 j /eRj ) < r 4 > /(36Rj5 ),

j=1

D ≈ (5/42)

  = (Nt Ne )1/2 (d0 − t e p0 /2),

k = (Nt Ne )1/2 [1 − t (e + s A)/2], P  = (Nt Ne )1/2 P0 ,

6 

j=1 6

where B and C are the Racah parameters of the 3d7 ion in crystals. Dq is the cubic field parameter, and Ds, Dt, D and D are the rhombic ones.In the above formulas, the spin–orbit coupling coefficients ,   , the orbital reduction factors k, k and the dipolar hyperfine structure parameters P and P denote the anisotropic (diagonal and off-diagonal) contributions of the spin–orbit coupling, orbital angular momentum and hyperfine interactions for the irreducible representations  (=eg and t2g ) in the 3d7 octahedral clusters. They can be expressed as  = Nt (d0 + 2t p0 /2),

Dq ≈

(6)

Here Sdp (and Sds ) are the group overlap integrals. N is the average covalency factor, characteristic of the covalency effect (or reduction of the Racah parameters B and C) of the central ion in compounds. In general, the admixture coefficients increase with

sin2 j (7 cos2 j − 1) cos j /Rj5 . Here q = −3e (or −e) stands for the effective charge of the ligand N3− (or CN− ), respectively. j /eRj is the effective dipole moment of the jth ligand. According to the structure around Co2+ in B12r [8], the bond lengths and bond angles are: R1 ≈ 1.903 Å, R2 ≈ 1.95 Å, R3 ≈ 1.951 Å, R4 ≈ 1.894 Å, R5 ≈ 2.085 Å, R6 ≈ 1.873 Å,  1 ≈  2 ≈  3 ≈  4 ≈ /2,  5 ≈ 0,  6 ≈ , 1 ≈ 4 ≈ 82.3◦ , 2 ≈ 3 ≈ 94.9◦ (note: the subscripts j = 1–5 stand for the ligands N3− , while j = 6 denotes the ligand CN− ). In view of the covalency effect [15,16], the Racah parameters B and C and the expectation values of the 3d7 radial wave function in compounds can be reasonably expressed in terms of the average covalency factor N by utilizing Zhao’s 3d orbitals for Co2+ [16–18]: B ≈ 1063 N2 cm−1 , < r 2 >≈ 2.357 Na.u.,

C ≈ 3879.4 N2 cm−1 , < r 4 >≈ 19.4538 Na.u.

(8)

From the average Co–N distance R¯ (≈1.9566 Å) and the Slatertype SCF functions [19,20], the group overlap integrals Sdpt ≈ 0.026, Sdpe ≈ 0.067, Sds ≈ 0.054 and A ≈ 1.088 are calculated. The average covalency factor can be estimated from the empirical relationship N2 ≈ 1 − h(N3− ) k(Co2+ ) [21]. Here the parameters h(N3− ) ≈ 2.4 are the characteristic of the ligand, and k (Co2+ ) ≈0.21 [21] are the characteristic of the central metal ion, yielding N ≈ 0.71 for Co2+ in B12r . Thus the molecular orbital coefficients Nt ≈ 0.825, Ne ≈ 0.853, t ≈ 0.487, e ≈ 0.397 and s ≈ 0.322 can be calculated from Eqs. (5) and (6). By using the free-ion values d0 ≈ 535 cm−1 [22] and P0 ≈ 254 × 10−4 cm−1 [23] for Co2+ and p0 ≈ 75 cm−1 [24] for N3− , the parameters  ≈ 449 cm−1 ,   ≈ 443 cm−1 , k ≈ 0.923, k ≈ 0.686, P ≈ 210 × 10−4 cm−1 and P ≈ 213 × 10−4 cm−1 are acquired from Eq. (4). From the EPR studies for Co2+ in tutton salts, the core polarization constant is taken as  ≈ 0.325 [25] and reasonably adopted here. Thus there are two unknown parameters, the effective dipole moment j /eRj (note: a uniform value for both ligands is assumed here for the sake of simplicity and reduction in the number of

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Table 1 The spin Hamiltonian parameters for vitamin B12r

a

Cal . Calb . Expt. [7]

gx

gy

gz

Ax c (×10−4 cm−1 )

Ay c (×10−4 cm−1 )

Az c (×10−4 cm−1 )

2.150 2.234 2.230(5)

2.182 2.289 2.295(5)

2.028 2.031 2.009(5)

−12 −4 −5(1)

−20 10 12(2)

−85 −103 −103(1)

a

Calculations based on neglecting of the ligand orbital and spin–orbit coupling contributions (i.e.,  =   = Nd0 , k = k = N, P = P = P0 N).

b

Calculations based on inclusion of the ligand orbital and spin–orbit coupling contributions. The signs of the observed hyperfine structure constants were not determined. The present studies indicate the negative signs for Ax and Az and positive sign for Ay .

c

adjustable parameters) and the reduction factor H in the formulas of the spin Hamiltonian parameters. Substituting the known values into Eq. (1) and fitting the calculated results to the experimental data, we have

j ≈ 0.006, H ≈ −0.225. (9) eRj The corresponding results (Cal.b ) are shown in Table 1. For comparison, the theoretical values (Cal.a ) based on neglecting of the ligand orbital and spin–orbit coupling contributions (i.e.,  =   = Nd0 , k = k = N, P = P = P0 N) are also listed in Table 1. 3. Discussion From Table 1, one can find that the theoretical spin Hamiltonian parameters (Cal.b ) in this work are in good agreement with the observed values Thus, the EPR experimental results for vitamin B12r are satisfactorily interpreted for the first time. (1) When the ligand orbital and spin–orbit coupling contributions were neglected, the theoretical results (Cal.a ) are not as good as those including the above contributions, i.e., the calculated g anisotropy g [=(gx + gy )/2 − gz ] is much (about 50%) smaller than the experimental result. The studied [CoN5 (CN)] cluster in B12r may exhibit significant covalency, characterized by the small covalency factor N (≈0.71 < 1) and the moderate orbital admixture coefficients (≈0.3–0.5) obtained in this work. Despite the small ligand spin–orbit coupling coefficient (≈75 cm−1 ), neglecting of the anisotropic contributions (i.e., the difference between  and   or k and k ) from the ligands can hardly achieve good agreement between theory and experiment, even by freely adjusting the effective dipole moment. Therefore, the contributions to the spin Hamiltonian parameters from the ligand orbitals should be taken into account for the Co2+ clusters with significantly covalent ligands (e.g., N3− ). (2) The fitted effective dipole moment j /eRj (≈0.006) in this work yields the ratio Dq/B ≈ 2.2, which is near the cross (∼2.2) in the Tanabe–Sugano scheme for 3d7 ions [9,11] and can be regarded as reasonable. It is also in consistence with the low spin (S = 1/2) state of Co2+ under the strong crystal-fields of N3− (and also CN− ) in vitamin B12r , corresponding to the g factors close to 2 [9]. This point is different from the high spin (S = 3/2) Co2+ under weak or intermediate crystal-fields in halides and oxides, corresponding to the g factors close to 4 [9]. On the other hand, the matched reduction factor H (≈ − 0.225) can be attributed to the Co2+ 3d–4s orbital admixtures due to the low symmetrical (axial and non-axial) distortions around Co2+ in B12r , which would depress H from its ideal value of unit in the absence of the above admixtures, as mentioned by the studies on low spin (S = 1/2) Rh2+ (4d7 ) in NaCl [12]. (3) The observed axial anisotropic g (≈0.25) and non-axial ␦g (=gy − gx ≈ 0.07) can be correlated to the local structure around

Co2+ in B12r , i.e., the dominant axial elongation of the octahedron (due to the longer axial Co–N bond R5 ) and the slight perpendicular distortion (due to the deviations of the planar bond angles from the ideal value /2). The above distortions (or local structure) are explicitly included in the formulas of the spin Hamiltonian parameters and those of the axial (Ds and Dt) and non-axial (D and D ) crystal-field parameters. 4. Summary The spin Hamiltonian parameters of vitamin B12r are satisfactorily explained for the first time, using the improved formulas of these parameters for a low spin 3d7 ion in rhombically elongated octahedra. The ligand orbital and spin–orbit coupling contributions are taken into account in view of the significantly covalent ligand N3− . The axial and perpendicular distortions of the crystal-fields around Co2+ account for the corresponding anisotropies of the g factors. Acknowledgement This work was supported by the Support Program for Academic Excellence of UESTC and the Science Foundation of CSTC (no. 2008BB4083). References [1] B. Krautler, D. Arigoni, B.T. Golding, Vitamin B12 and B12 -Proteins, Wiley-VCH, Weinheim, 1998. [2] R. Banerjee, Chemistry and Biochemistry of B12 , J. Wiley & Sons, New York, 1999. [3] E. Jorin, A. Jorin, H.H. Gunthard, J. Am. Chem. Soc. 105 (1983) 4277. [4] E. Hohenester, C. Kratky, B. Krautler, J. Am. Chem. Soc. 113 (1991) 4523. [5] T.D. Smith, J.R. Pilbrow, Coord. Chem. Rev. 39 (1981) 295. [6] G.J. Gerfen, in: R. Banerjee (Ed.), Chemistry and Biochemistry of B12 , J. Wiley & Sons, New York, 1999, p. 165. [7] J.R. Pilbrow, M.E. Winfield, Mol. Phys. 25 (1973) 1073. [8] T. Andruniow, P.M. Kozlowski, M.Z. Zgierski, J. Chem. Phys. 115 (2001) 7522. [9] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Oxford University Press, London, 1970. [10] R. Lacroix, U. Hochli, K.A. Muller, Helv. Phys. Acta 37 (1964) 627. [11] Y. Tanabe, S. Sugano, J. Phys. Soc. Japan 9 (1954) 753, 766. [12] M.T. Barriuso, P.G. Fernandez, J.A. Aramburu, M.J. Moreno, Solid State Commun. 120 (2001) 1. [13] M.G. Zhao, M. Chiu, Phys. Rev. B 49 (1994) 12556. [14] M.G. Zhao, J. Chem. Phys. 109 (1998) 8003. [15] P. Hu, L.H. Xie, P. Huang, Physica B 339 (2003) 74. [16] M.G. Zhao, G.R. Bei, H.C. Jin, J. Phys. C: Solid State Phys. 15 (1982) 5959. [17] M.L. Du, M.G. Zhao, J. Phys. C: Solid State Phys. 21 (1988) 1561. [18] M.G. Zhao, Y.F. Zhang, IEEE Trans. Magn. Mag. 19 (1983) 1972. [19] E. Clementi, D.L. Raimondi, J. Chem. Phys. 38 (1963) 2686. [20] E. Clementi, D.L. Raimondi, W.P. Reinhardt, J. Chem. Phys. 47 (1967) 1300. [21] K.H. Karlsson, T. Perander, Chem. Script. 3 (1973) 201. [22] C.A. Morrison, Crystal Field for Transition Metal Ions in Laser Host Materials, Springer, Berlin, 1992. [23] B.R. McGarvey, J. Phys. Chem. 71 (1967) 51. [24] D.W. Smith, J. Chem. Soc. A (1970) 3108. [25] A. Abragam, M.H.I. Pryce, Proc. Roy. Soc. (Lond.) A 206 (1951) 173.