EPR lineshape function for Ni2+

JOURNAL OF MAGNETIC RESONANCE 70,299-302

(1986)

EPR Lineshape Function for Ni*+ J. C.

SARTORELLI,

J. A.

OCHI,

AND

W.

SANO

Institute de Fisica, Universidade de Srio Paulo, C.P. 20516, 01498, Srio Paula, SP, Brazil Received April 4, 1986; revised June 1 I, 1986

Recently we have studied EPR of several hexahydrated nickel compounds (Z-3): nickel perchlorate (NPC), Ni(ClO& .6H20 and nickel fluoroborate (NFB), Ni(BF&.6HzO. A difficulty found in these studies was to resolve superposedlines to olbtain the center and the width of the component lines as observed in NPC. The resolution of these types of lines requires the knowledge of the individual lineshape function. Functions widely usedto fit experimentalspectraare Gaussianand Lorentzian whose conformational ratios (4) are 2.24 and 4.0, respectively. For NPC and NFB the experimental conformational ratio has intermediate values in the range above. In the present work we propose a new lineshape function which has fitted nicely our Ni2+ EPR spectra and has resolved superposedlines. The Taylor seriesof the inverse Gaussian F = F’eM2, where x = H - Ho (His the alppliedmagnetic field and Ho the center of the line), is . Considering all the terms in the above seriesand taking the inverse would result in a Gaussian. If only the first two terms are retained and the inverse taken, we would have a Lorentzian. Considering more than two terms gives a function intermediate to the Gaussian and Lorentzian. So, we assumeda function of the following type: z=

10 1 + a(H - Ho)2 + fl(H - Ho)4

where Ho, IO, cq and /3 are adjustable parameters.The values of CYand /3 are taken as independent to obtain more flexibility in the adjustment. Compared with Gaussian and Lorentzian fits, just one more parameter has been introduced. The conformational ratio of this function depends on the particular value of the linewidth. Figure 1 shows the conformational ratio R as a function of 6 = fi/a2. The 15= 0.67 givesR = 2.24 which is the same value for a Gaussian.This behavior indicates that calculation of only the R without a careful analysis of the lineshape can lead to ;an erroneous conclusion. O ther properties of the function include the linewidth at Ihalf-maximum intensity

299

0022-2364186 $3.00 CopyFight0 1986 by Academic Press,Inc. All fights of reproduction in any form nscrved.

300

NOTES

1

I 0.2

0

I

I

I

0.4

0.6

0.8

1.

6 FOG. 1. Conformational ratio R as function of 6 = @/cy*.(A) corresponds to the parallel NPC (B) to the perpendicular NFB, and (C) to the perpendicular NPC.

spectrum,

and the maximum slope hs=

E f CY where y+ is the positive root of 1OS’y’+ 9&i.?- (66 - 3)~ - 1. Then the ratio AH& AH,, depends on 6 and (Y,while for Gaussian and Lorentzian shapes the ratios are constant. The EPR spectra were adjusted by computer least-squares fit using the NFB perpendicular spectrum and the NPC parallel and perpendicular spectra, that is, spectra obtained with magnetic field applied perpendicular and parallel, respectively, to the optical axis. Frequently an experimental spectrum has superimposed lines, so we must sum component functions to obtain the total fit. In the case of the NFR perpendicular spectrum, just one function is sufficient because there is only a single line, as can be seen by inspection. The full experimental spectrum was represented by 251 points TABLE 1 Comparative Table of the Parameters of the Perpendicular Spectrum of NFB Obtained with our Function, a Gaussian, and a Lorentzian

Experimental values Our function Gaussian Lorentzian

Ho W) center of line

FO intensity

a (kc-*)

4.76 2 0.05 4.77 4.78 4.77

3.5kO.2 3.44 2.93 2.66

1.77 1.64 1.70

Affl,Z

B W-‘) 0.048 -

AL 1.52-cO.06 1.54 1.17 1.73

b sum of quadratic errors 0.933 9.08 1.41

301

NOTES

I 2

I 4

I 6

I 8

IO

H (KG)

l%. 2. Perpendicular spectrum of NFB (experimental points are shown with dots) and our theoretical fimction (continuous line).

separatedby 40 G. For the sake of comparison, adjustmentsof Gaussianand Lorentzian fitting were done too. The parameters obtained from these adjustments are listed in Table 1. This table indicates that the proposed function is the one that gives the best result in comparison with values from the experimental spectrum and the sums of square errors. The quality of the adjustment can be better appreciated in Fig. 2. The small deviation is due to a slight asymmetry in the experimental spectrum. The parallel spectrum of NPC has two broad lines as a result of the transitions 11) * IO) and I-1) + IO), so two functions must be summed to fit the spectrum. Figure 3 shows the experimental absorption curve with two dashedcurves representing the two components and the solid line showing their sum. The integrated form was preferred becauseit shows clearly the superposition of the lines. This figure shows that the agreementwith the experimental data is excellent. The NPC perpendicular spectrum showed an unusual asymmetric form indicating superposition of lines. The adjustment of this spectrum, which was represented by 20 1 points separatedby 100 G, was done with two functions, one due to the transition /0) + 11) and the other centered exactly at zero field. Figure 4 shows, in the integrated

15 -

d 10 1 I 53

-:M: 0 0

5

'

\ ',

:

,J'

' I' a '\

_ *' 10

:

--__ 15

20

H (KG) FIG.

3. Integrated

padel

SpeCtNm

Of~(eXperimenti

points

are shown

function (continuous line). The resolved lines are shown by dotted lines.

with dots) and theoretical

302

H (KG)

FIG. 4. Integrated perpendicular spectrum of NPC (experimental points are shown with dots) and theoretical function (continuous line). The resolved lines are one broad line centered at the zero field and the other due to the transition IO) -, 11).

form, the two functions and their sum which reproduces nicely the experimental data. The line centered at zero field became identified only after application of the present method and the identification of its position and width will permit us future investigation of its origin. As can be observed from the above results, the introduction of one more adjustable parameter in the Lorentzian, a fourth-degree term in the magnetic field, leads to an improved fit of the experimental absorption curve. The main purpose of this term is to adjust the wings of the line, while the central part remains dominated by the quadratic term, not far from a Lorentzian one. This feature allows us to obtain better values of the center and the width of the component lines when a complex experimental curve is nearly resolved as occurs with the NPC perpendicular spectrum. A small discrepancy between experimental and fitted curves observed for NF’B arises from a small asymmetry of the former. In this case introduction of a new term with an odd exponent term in magnetic field would give a better result, but the additional complication does not justify this procedure. The new function which we have proposed can describe adequately the Ni2+ EPR spectra which have an intermediate shape between Gaussian and Lorentzian, as observed in most solids. Four adjustable parameters are required, one more than for Gaussian and Lorentzian functions. We have presented three different types of EPR spectra of Ni*+ showing the validity of the function. The main utility of this function is to resolve superimposed lines as we have shown in two different cases. ACKNOWLEDGMENTS This work was supported by CNPq and FINEP. REFERENCES 1. 2. 3. 4.

J.C.SARTORELLI, S. IsoTANI,J.A.OCHI,W.SANO,ANDA. P~cc~~~,Chem.Phyx Lett. 57,608(1978). W.SANO,S.ISOTANI,J. A. OCHI, AND J.C. SARTORELLI,J. Phys. Sot Jpn.46,26 (1979). J. B. DOMICIANO, W. SANO, K. R. JURAITIS,AND S. ISOTANI, J. Phys. Sot. Jpn. 48, 1449 (1980). R. S. ALGER, “Electron Paramagnetic Resonance-Technique and Applications,” Interscience, New York, 1968.