THE ISOMER SHIFT CALIBRATION CONSTANT IN 57Fe

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THE ISOMER SHIFT CALIBRATION CONSTANT IN 57Fe

E. Mielczarek

To cite this version:

E. Mielczarek. THE ISOMER SHIFT CALIBRATION CONSTANT IN 57Fe. Journal de Physique

Colloques, 1979, 40 (C2), pp.C2-508-C2-510. �10.1051/jphyscol:19792178�. �jpa-00218554�

JOURNAL DE PHYSIQUE Co[[oque C2, supplkment au n ^O 3, Tome 40, mars 1979, page C2-508

T H E ISOMER S H I F T C A L I B R A T I O N CONSTANT I N 57Fe

E.V. Mielczarek

Physics Department, Ceorge Mason Ihziversity, Fairfax, Va. 22030 ^U.S.A. and

Laboratory of Technical Development, National Heart, Lung, and Blood I n s t i t u t e Iiational I n s t i t u t e s of Health, Bethesda, Md. 20014 U.S.A.

Rbsumd.- Le calcul de la constante d'btalonnage de dbplacement isombrique, a, demande que l'on connaisse la densitl de charge au noyau ainsi que la mesure du ddplacement du centre du spectre Mossbauer par ra ort 1 un absorbeur standard. La large gamme de valeurs a, -0,511 1 -0,ll ad ma s-', pour "Fe, le noyau issbauer le plus souvent mesurd, inclut : I) de nombreuses va- leurs a calculdes sur la base dfextrapolation lindaire h partir de deux points seulement, 2) les diffbrences entre calculs de structure atomique, d'orbital mol6culaire et de structure de bande.

Ce rapport prdsente un calcul de la constante d'dtalonnage de d6placement isomdrique fond6 sur une large gamme de mesures et de techniques thdoriques. Ce calcul fournit une valeur a de -0,206 a

: mm s-' 2 8 % . L'utilisation de cette constante pour l'dvaluation des densiti5s de charge dans les

composbs biologiques, est analysde et comparde aux composds inorganiques.

Abstract.- A calculation of the isomer shift calibration constant, a, depends on knowing the elec- tronic charge density at the nucleus and a measurement of the velocity shift of the center of the

~Sssbauer spectrum with respect to some standard absorber. The wide range of a values, -0.511 to -0.11 :a mm s"', for 5 7 ~ e , the most frequently measured Mossbauer nucleus, reflects : 1) many va- lues of a have been calculated from a linear extrapolation of data from only two points, 2) diffe- rences between atomic structure, molecular orbital, and band structure calculations. This paper reports on a calculation of the isomer shift calibration constant based on a wide ran e of measu- rements and theoretical techniques. This calculation yields a value for a of -0.206 a,

f

mn s-' 2 8 % . The use of this constant in evaluating charge densities in biological compounds is surveyed and compared with inorganic compounds.

1. Introduction.- The Mossbauer isomer shift is the shift in the nuclear transition energy reflecting a perturbation of the nuclear energy levels due to electrostatic interaction between the nucleus and its electronic environment. A complete discussion of the effect is given in many review books /I/. For purposes of this paper the effect may be expressed as

Av = aAp(0) (1)

where Av is the difference in nuclear transition energies for two different absorbers expressed in cm s-l, Ap(0) is the difference in electronic charge density at the nucleus for these absorbers and a is the isomer shift calibration constant. Thus a measu- rement of the issbauer isomer shift can yield in- formation about the relative electronic charge densi- ty of the 5 7 ~ e nuclear site. However the calculation of a has often depended on a calculation of the c h a r ge density difference between only two iron charge states, usually Fez+

-

Fe3+. The straight line cons- tructed from this two point difference was then often used to fit data over a wide range of ionic and covalent iron compounds. Because of this linear construct from only two points the calculated values of a which appeared in the literature have ranged from -0.11 to -0.51 at mn s-'/2/. Recently a diffe-

rent approach used measurements on many compounds in conjunction with a range of theoretical techniques 131. This work included measurements on (I) metal alloys coordinated with band structure calculations /3,4,5/, (2) high spin and low spin ferrous and ferric inorganic compounds coordinated with atomic structure and molecular orbital calculations /6,7/, (3) pressure measurements 181 and calculations /9/

on FeFz, (4) and rare gas matrix isolation measure- ments /lo/ on Fe and Fe+ atomic states coordinated with atomic structure calculations. Consequently these measurements and calculations covered the ran- ge of both positive and negative isomer shifts. Addi- tionally by plotting these data versus Fe metal the linear relation was forced through a set point, the origin of the plot. This work is shown in figure I.

The value of a given by this data is -0.206 a: mn s-' 2 8 % .

2. Biological Complexes.- It would be useful to in- clude in this analysis biological complexes, in par- ticular heme proteins and porphyrins. However becau- se of the complexity of these systems extensive charge density calculations for iron containing bio- logical compounds have not been published. The most complete set of calculations for iron containing biological compounds has been published by Zerner

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19792178

et al. 1121 on porphyrin complexes. These molecular orbital calculations considered sixteen Fe porphyrin complexes and successfully predicted that if the iron atom lies in the porphyrin plane only low (S=O) or intermediate (S=l) spin states are possible.

Fig. 1 : Isomer shift (Av with respect to Fe metal at 300 K vs. the charge density with respect to Fe metal from several recent charge-density calcula- tions).

Points : o -Ref. /10/; + points

-

Ref. 121; Apoints- Ref. 161; x points

-

Ref. 191 and 181; points

-

Ref. 171; o points

-

Ref. /3/ and 141.

Figure 2 is a plot of this table. For 5 7 ~ e , positi isomer shift should decrease for increased 4s elec- tron charge density. The ability of Zerner's calcu- lation to predict this general trend is evident from figure 2. Deviations from this trend are probably due to (I) volume corrections, (2) lack of informa- tion about the change in 3s electronic charge, and 3d shielding effects.

Although electronic charge densities at the nuclear Fig. 2 : Isomer shift versus 4s electronic charge site are not calculated in this work, the authors do taken from I'

calculate 4s electronic charge for the sixteen con- However, in a more recent calculation Traut- figurations. Six of these sixteen can represent por- wein and Harris /I31 calculated electron charge phyrins or hemoglobins whose isomer shifts have been densities for four heme proteins, myoglobin (Mb), measured. Table I lists these six complexes chosen hemoglobin (Hb), CO myoglobin (MbCO) and CO hemo- from Zerner et al. 1121, the value for each 4s elec- globin (~bco).

tronic charge calculated by them, and the measured isomer shifts for the ~or~hyrins and hemoglobins.

Table I : 4s electronic population for selected iron complexes and isomer shifts for heme proteins and porphyrins corresponding to these complexes 1121.

I

Iron CompleXa 4s electronic

j

Corresponding

/

Isomer shiftC

:

Reference for

:

populationsb I I heme I I (mm S-I )

:

isomer shift

1 I I 1

111 Fe(II), S=2 I 1 1 I

I 0.354 I Hb I +O. 90 I 1151

(Porph rin with Fe

:

^{1 I I I 1}

0.492

1

out of heme

:

^{I I I I I I I}

plane I ^I 7 1 ^{I I} I

---L---,---,---L---L---L---

1 I 1 I

I

I 0.367 I HbCO I

+o.

18

XI1 Fe(II), S=O I 1151

(Porphyrin with CO)

:

^I 1 ^I I ^I 1

---I---,---L---L---f--- I

IX Fe(II1)

,

^S=1/2

:

^{0.375 I I HiCN I I} +O. 17 ^I I / 151

(Porphyrin with CN)

:

^I I ^I I ^I I

---I-,---L---L---f--- I

I I I I

I 0.339 I Fe (TPP) I +0.42

I1 Fe(I1, S=l I 1161

(Porphxrin with Fe

:

^{I I I I I I}

0.492 A out of h e w

:

^{I I I 1 I 1}

plane) ^I _I ^I _I ^I I ^I I

---L---L---L---L--- 1

X Fe(III), S-512

:

^0.408

:

Protoporphyrin

;

^{+0.22 I I /I71}

(Porphyrin with C1)

: :

^{IX chloro I I 1 I}

----,---L---,---L---L---L---

XI Fe(II1)

,

^{51512 0.356 I I HiOH I I +O. 18 I I 1151}

(Porphyrin with OH)

;

I

I 1

1 1 I

I I 1 I A

a) Reference 1121. The roman numeral identifies the complex in table 4 of reference / 121.

b) Taken from table 6 of reference 1121.

-

c) With respect to Fe metal

-

d) Hi-ferric hemoglobin, xb-ferrous hemoglobin.

c2-5 10 JOURNAL DE PHYSIQUE

Using Hcckel type self consistent field molecular orbital calculations for MbCO and HbCO, and configu- ration interaction calculations for Hb and Mb, Traut- vein and Harris calculated that a should be -0.242

+

^{0.039 ao3} mm s-'. This value is in good agreement with the value of -0.209

+

^{a mm} s-I found from

figure 1. Using this latter value for a and the measured isomer shifts for Hb complexes table I1 lists the charge densities for Hb complexes with respect to Fe metal.

The errors can be calculated for column 3 of this table by taking the sum of the experimental error and the 8% error given for the calculation of a. In addition to this the measurements for the 02, OH, N3. CN, and Hz0 complexes should be corrected by about 0.03 mm s-' to take care of the temperature dependent contribution to the iron shift (second or- der Doppler effect). Thus, although table I1 can be used to estimate charges in charge denslties for Hb and Mb complexes, a realistic use of the table must take into account the large errors.

Table I1 : Charge density of Hb, Mb complexes using the a calculated from figure 1

!charge densitya: Isomer shifta

j

Temperature Reference for Complex ^{I I}

;

^{nan s-' I I} I (K)

:

^{I Column3}

1 I 1 I

I I 1 t

Mb

I I I 1

-4.36

:

^{+0.900 f 0.017}

:

^{300 K I I 1141}

Mb

t I I I

-4.17 :+0.86 f0.03

:

^{3 0 0 K I I /I 4/}

I I I I

-02 -1.06

:

^{+0.222 4 0.017}

:

^{300 K I I} / 14/

I I I

HbCO -0.873

:

^{+0.18 2 0.05}

:

^{195 K t 1} / 15/

I I I I

HbOz -0.970

:

^+0.20

+

^0.05

:

^{195 K I I} / 151

I I I 1

Hb -0.436

:

^+0.90

+

^0.05

:

^{195 K I I} / 151 HiOH

1 I I 1

-0.873

:

^c0.18

+

^0.05

:

^{195 K I 1 /I 51}

I I I 1

HiCN -0.083

:

^+0.17

+

^0.05

:

^{195 K I I /Is/}

1 I I 1

HiHz0

:

^-0.970

:

^+0.20

+

^0.05

:

^{195 K 1 I /Is/}

I I I I

HiN3 -0.073

:

^+0.15

+

^0.05

:

^{195 K I I /15/}

I 1 1 I

I 1 I I

a) with respect to Fe metal

-

^{b) deoxy Mb} single crystal

-

c) deoxy Mb polycrystal- line powder

-

^{d) Hi}

-

ferric hemoglobin, Hb

-

ferrous hemoglobin

References

/I/ Goldanski, V.I., and Herber, R.H., (Academic Press, New York) 1968, Chap. I.

/2/ Duff, K.J., Phys. Rev. B

9

(1974) 66.

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11

(1975) 1026.

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17

(1978) 91.

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ftL

(1967) 2584.

191 Reschke, R., Trautwein, A., and Harris, F.E., Phys. Rev. B

2

(1977) 2708.

/lo/ Micklitz, H., and Litterst, F.J., Phys. Rev. Lett.

2

(1974) 480.

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55

(1971) 141.

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5

(1966) 363.

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2

(1975) 65.

1141 Trautwein, A., Struct. and Bond

2

^{(1974) 101.}

1151 Lang, G. and Marshall, W., Proc. Phys. Soc.

87

^{(1966) 3.}

/16/ Dolphin, D., Sams, J.R., Tsin, T.B., Wang, K.L., J. Am. Chem. Soc.

98

(1976) 6970 and references therein.

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51

(1969) 2624.