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Crystal structure and colour of SrNiP2O7 and SrNi3(P2O7)2

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Page 1: Crystal structure and colour of SrNiP2O7 and SrNi3(P2O7)2

Solid State Sciences 3 (2001) 669–676www.elsevier.com/locate/ssscie

Crystal structure and colour of SrNiP2O7 and SrNi3(P2O7)2

Brahim El-Balia, Ali Boukharib, Jilali Aridec, Kai Maaßd, Dieter Waldd, Robert Glaume,∗,Francis Abrahamf

a Laboratoire des Matériaux et Protection de l’Environnement, Départment de Chimie, Faculté des Sciences “Dhar Mehraz”, B.P. 1796 Atlas 30003,Fès, Morocco

b Laboratoire de Chimie du Solide Appliquée, Faculté des Sciences, Av. Ibn Batouta, Rabat, Moroccoc Laboratoire de Physicochimie des Matériaux, ENS Takaddoum, B.P. 5118, Rabat, Morocco

d Institut für Anorganische und Analytische Chemie II, Heinrich-Buff-Ring 58, D-35392 Gießen, Germanye Institut für Anorganische Chemie, Gerhard-Domagk-Straße 1, D-53121 Bonn, Germany

f Laboratoire de Cristallochimie et Physicochimie du Solide, ENSCL, Universite de Lille, B.P. 108, 59652 Villeneuve d’Ascq cedex, France

Received 15 February 2001; accepted 20 March 2001

Abstract

The crystal structures of SrNiP2O7 (I) and SrNi3(P2O7)2 (II) have been refined from single crystal data [(I): P21/n, Z = 4,a = 5.2630(16), b = 8.2605(10), c = 12.6018(15) Å, β = 90.224(19)◦, 101 parameters, 1143 independent reflections,R/wR2 =0.029/0.070; (II): P21/c, Z = 2, a = 7.4092(9), b = 7.6594(8), c = 9.4474(10) Å, β = 112.216(9)◦ , 104 parameters, 1484independent reflections,R/wR2 = 0.027/0.063]. SrNiP2O7 belongs to theα-Ca2P2O7 structure family with Ni2+ ions occupyingisolated square-pyramidal sites,d(Ni–O) = 2.032 Å. SrNi3(P2O7)2 is isostructural to AM3(P2O7)2 (A = Ca, Pb and M= Fe, Co,Ni). Two crystallographically independent, slightly distorted [NiO6] octahedra (d(Ni–O) = 2.083 Å) share edges, thus forming chainsalong theb-axis (d(Ni–Ni) = 3.143 and 3.226 Å). The colours of SrNiP2O7 (orange-red) and SrNi3(P2O7)2 (greenish-yellow) aresignificantly different. Reflectance spectra in the UV/VIS/NIR region are reported for SrNiP2O7, SrNi3(P2O7)2, and the isotypicdiphosphates CaNi3(P2O7)2 and BaNi3(P2O7)2. Angular overlap parameters for the Ni–O interaction are derived. The shift ind-electron energies of Ni2+ caused by the change in coordination from [NiO5] (C4v) to [NiO6] (Oh) is reproduced nicely by themodel calculations. 2001 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.

Keywords:Crystal structure; Nickel phosphates; Electronic spectra; Angular overlap model

1. Introduction

Systematic preparative and structural studies on di-phosphates M2P2O7 or (A, M)2P2O7 with A and/or M analcaline earth or divalent 3d-metal ion, have been under-taken during the last two decades. For the pseudo-binarysystem A2P2O7–M2P2O7 solid solutions adopting thethortveitite structure type are known (e.g., (Mg, Cr)2P2O7[1], (Mg, Cu)2P2O7 [2]). Compounds without detectablehomogenenity range are found for the compositions

* Correspondence and reprints.E-mail address:[email protected] (R. Glaum).

AMP2O7 (e.g., BaCuP2O7 [3], SrCrP2O7 [4]) andAM3(P2O7)2 (e.g., CaM3(P2O7)2, M = Co, Ni [5] andPbM3(P2O7)2, M = Fe, Co [6], Ni [7]). Apart from themagnetic properties of some mixed pyrophosphates like(Mg, Cu)2P2O7 [8] or AMnP2O7, A = Ca and Ba [9], noother physical properties have been investigated.

Nickel (II) oxo-compounds show a surprising variabi-lity in colour, which is found to range from orange-redto yellow and even green [10,11]. For octahedrally co-ordinated Ni2+ in Perovskite-like structures the pheno-menon has been explained by Reinen [10] as a resultof differentπ -bonding behaviour towards oxygen ofd0-andd10-ions in the neighbourhood of Ni2+. The inves-

1293-2558/01/$ – see front matter 2001 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.PII: S1293-2558(01)01176-1

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670 B. El-Bali et al. / Solid State Sciences 3 (2001) 669–676

tigation of single crystal and powder reflectance spec-tra of several other nickel (II) oxo-compounds by Ross-man et al. [11] gives more and detailed experimetal evi-dence for the broad range of colours originating fromd–delectron transitions on Ni2+ in oxo-compounds. How-ever, no attempt for a detailed correlation of absorp-tion spectra and coordination geometry of the [NiOx ]chromophor has been made so far. For such a studySrNiP2O7 and SrNi3(P2O7)2 and related nickel phos-phates appear to be particularly interesting, due to thegenerally observed low symmetrical Ni2+ coordinationand its wide range of geometries. For modelling ofd–d transitions of the [NiO5] (SrNiP2O7) and [NiO6](SrNi3(P2O7)2) chromophors within the framework ofthe angular overlap model (AOM) [12–14], the accuratecrystal structures have been determined. Here we reporton synthesis, crystal structure refinement and colour ofSrNiP2O7 and SrNi3(P2O7)2. Spectra of CaNi3(P2O7)2and BaNi3(P2O7)2 are reported for comparison.

2. Experimental

Powder samplesof SrNiP2O7 and ANi3(P2O7)2(A = Ca, Sr, Ba), 2 g each, were synthesized from sto-ichiometric amounts of nickel, alcaline earth carbonateand (NH4)2HPO4. After dissolution of the starting mate-rials in nitric acid the homogenous solutions have beenevaporated to dryness on a heating stirrer. The residueswere ground and heated in air at increasing temperatures(600, 800, 1000 and finally to 1100◦C), each period last-ing one day. The purity of thus obtained powder sam-ples has been controlled by Guinier photographs. Thecolours of the powdery materials vary from red-orange(SrNiP2O7) over pale orange-yellow (BaNi3(P2O7)2),yellow (SrNi3(P2O7)2) to pale yellow (CaNi3(P2O7)2).

Single crystalsof SrNiP2O7 and SrNi3(P2O7)2 havebeen obtained by a different procedure. A mixture ofSrCO3 (4.4288 g, 3 mmol), NiO (2.2410 g, 3 mmol) and(NH4)2HPO4 (7.9233 g, 6 mmol) was ground thoroughlyin a mortar and transferred to a ceramic crucible. Thesample was then heated to 1173 K in a tube furnace,to effect decomposition of the carbonate, followed bymelting (1473 K) in a platinium crucible. After controlledcooling (rate 10◦ h−1) to 773 K the sample was quenchedto room temperature. The product was found to containred-orange crystals of SrNiP2O7 and a few yellowish-green ones, which turned out to be SrNi3(P2O7)2.

Single crystal study.Data sets were measured usinga conventional 4-circle diffractometer (SrNi3(P2O7)2)

Table 1Crystallographic data for SrNiP2O7 and SrNi3(P2O7)2

SrNiP2O7 (I) SrNi3(P2O7)2 (II)

Formula weight 320.27 611.63

Crystal size (mm) 0.16× 0.12× 0.04 0.20× 0.20× 0.15

Color orange-red greenish-yellow

Crystal system monoclinic monoclinic

Space group P21/n P21/c

Unit cell parameters:

a (Å) 5.2691(5) 7.4092(9)

b (Å) 8.2674(8) 7.6594(8)

c (Å) 12.6140(13) 9.4474(10)

β (◦) 90.246(9) 112.216(9)

V (Å3) 549.48(9) 496.34(10)

Z 4 2

ρcalc. (g cm−3) 3.871 4.093

Temperature (K) 293(2) 293(2)

Diffractometer IPDS (Stoe & Cie) Four-circle

diffractometerω-scan

Radiation (λ, Å) Mo-Kα (0.71073)

µ (cm−1) 13.698 11.688

2θ range 2.95–28.00 2.97–31.84

Reciprocal space −6≤ h ≤ 6 −1≤ h ≤ 10

−10≤ k ≤ 10 −11≤ k ≤ 1

−15≤ l ≤ 16 −14≤ l ≤ 13

Collected reflections 4748 2288

I > 2σ(I ) 1184 1484

Number of parameters 101 104

refined

Residual electron density 1.07,−1.52 0.98,−1.10

(min, max) (e Å−3)

R(F)/wR2(F2) 0.027/0.068 0.027/0.063

and an imaging plate diffraction system (SrNiP2O7;IPDS, Fa. Stoe & Cie.), respectively. The structurerefinements (programSHELX-97 [15]) of SrNiP2O7 andSrNi3(P2O7)2 proceeded straight forward with the atomicpositions of SrCrP2O7 [4] and CaNi3(P2O7)2 [5] used asstarting parameters. Table 1 reports crystallographic dataand experimental details on data collection and structurerefinement of SrNiP2O7 and SrNi3(P2O7)2. (See alsoTables 2 and 3.)

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Fig. 1. Reflectance spectra of SrNiP2O7 (a), BaNi3(P2O7)2 (b),SrNi3(P2O7)2 (c), CaNi3(P2O7)2 (d) in the NIR/VIS/UV region. Ticksat the bottom of the spectra indicate electronic transitions calculatedwithin the framework of the AOM (see text for details). Term symbolsin the spectrum of SrNiP2O7 (a) refer to the [NiO5] chromophor withapproximateC4v symmetry.

Powder reflectance measurementswere carried out atroom temperature in the range from 4000 to 32 000 cm−1

using a spectrometer PMQ-II with reflectance adapterRA2 (Fa. Zeiss). The spectra are given in Fig. 1. Theshift in colour from red (SrNiP2O7) to yellow-green(CaNi3(P2O7)2) is reflected by the shift of the minimumin the absorption spectra in the visible region around17 000 cm−1.

3. Results and discussion

Thecrystal structure of SrNiP2O7 is built from slightlydistorted square-pyramidal [NiO5] units and [P2O7]groups (Fig. 2). Corner-sharing of the two building units

Fig. 2. Projection of the SrNiP2O7 structure along[010] (top) and[100] (bottom). Dark grey: [NiO5], light grey: [P2O7], black circles:Sr2+.

results in a three-dimensional structure with tunnels run-ning along[1 0 0] and[0 1 0]. At the interception pointsof the two tunnel types Sr2+ ions are located (Fig. 2).SrNiP2O7 is isotypical with ACuP2O7 (A = Ca [16],Sr [17]) and SrMP2O7 (M = Cr [4], Co [18]), which inturn are all isopointal toα-Ca2P2O7 [19]. The structuretype has been described and discussed on several occa-sions [4,16–18] by now, so no further comments are ne-cessary here. The mean distanced(Ni–O) = 2.033 Å inSrNiP2O7 can be compared to 2.007 Å found for [NiO5]in α-Ni2P2O7 [20] and in general to the value of 2.01 Åreported for Ni2+ in five-fold oxygen coordination [21].

The structure of SrNi3(P2O7)2 can be described interms of chains of edge-sharing [NiO6] octahedra, held

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672 B. El-Bali et al. / Solid State Sciences 3 (2001) 669–676

Fig. 3. Projection of the SrNi3(P2O7)2 structure along[010] (top) and[001] (bottom). Dark grey: [NiO6], light grey: [P2O7], black circles:Sr2+. Vertices of the unit cell are indicated by ‘*’.

together by [P2O7] groups. This ‘covalent’ networkcomprises tunnels parallel to[0 1 0], which contain theSr2+ ions (Fig. 3). Ni–Ni distances within the chainsare 3.14 and 3.23 Å, respectively. Ni2+ cations occupytwo crystallographic sites in the SrNi3(P2O7)2 structure,both showing a slightly distorted octahedral coordinationby oxygen. Ni(1) is surrounded by five [P2O7] groups,one acting as bidendate ligand. Ni(2) is coordinated bysix monodendate [P2O7] groups as illustrated in Fig. 4.The mean distancesd(Ni–O) are 2.091 and 2.074 Åin [Ni(1)O6] and [Ni(2)O6], respectively. These valuesare close to those observed for [NiO6] in α-Ni2P2O7:2.077 Å [20], σ -Ni2P2O7: 2.098 Å [22], Ni3(PO4)2:2.078, 2.091 Å [23], Ni2P4O12: 2.045, 2.067 Å [24], and2.040 Å in NiP4O11 [25].

Bridging angles (P–O–P) for the diphosphate groupswere determined to 128.5◦ and 134.0◦ for SrNiP2O7 andSrNi3(P2O7)2, respectively. Both values are in the typicalrange found for diphosphate groups not restricted bysymmetry.

The colours of SrNiP2O7 (red) and SrNi3(P2O7)2

(greenish-yellow) are two more, remarkable examplesvisualizing the surprising variability of thed-electronenergy levels on Ni2+ created by a particular ligand fieldin a chromophor [NiOx ]. This behaviour has already beenobserved 20 years ago in a comprehensive spectroscopicstudy [11] on a wide range of nickel (II) oxo-compounds.Despite the high quality of their spectroscopic results atthat time, the authors did not present clear cut conclusionson the crystal-chemical origin of the spectral properties ofNi2+.

To our understanding two aspects have to be taken intoaccount for the interpretation of the colour of nickel (II)oxo-compounds [1]. The first and most obvious is the‘real’ (mostly low-symmetrical) coordination geometryof the chromophor, which can be taken from the crys-tal structure refinement. The second, less obvious, how-ever, equally important effect depends on the coordina-tion number of oxygen ligating to a Ni2+ center. Thispoint has recently been introduced to literature as ‘sec-ond sphere ligand-field effects on oxygen ligator atoms’and discussed in considerable detail by Reinen et al. [26].Basically, in their modelπ -bonding between oxygen andthe Ni2+ d-orbitals depends on the coordination num-ber of oxygen. Allowing for this effect in calculations[1] within the framework of theangular overlap model(AOM) [14,27,28] reproduces nicely the significant vari-ations observed in the spectra of [NiOx ] chromophorswhich are otherwise more or less identical with respectto their first coordination sphere. A paper reporting de-

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B. El-Bali et al. / Solid State Sciences 3 (2001) 669–676 673

Table 2Atomic coordinates and isotropic displacement parametersUeq

a for SrNiP2O7 (I) and SrNi3(P2O7)2 (II)b

Atom x y z Ueq (Å2)

SrNiP2O7 (I)

Sr 0.28354(6) 0.34289(4) 0.28098(3) 0.00791(17)

Ni 0.81377(9) 0.14740(5) 0.11300(4) 0.00627(18)

P1 0.75113(15) 0.53742(10) 0.16305(7) 0.0052(2)

P2 0.31224(15) 0.19688(10) 0.98233(7) 0.0057(2)

O1 0.6782(5) 0.3617(3) 0.1511(2) 0.0082(5)

O2 0.6723(5) 0.4026(3) 0.3988(2) 0.0099(5)

O3 0.9457(5) 0.1212(3) 0.2668(2) 0.0078(5)

O4 0.7661(5) 0.1171(4) 0.4518(2) 0.0088(5)

O5 0.4849(5) 0.0641(3) 0.2939(2) 0.00119(5)

O6 0.0963(5) 0.3346(3) 0.4789(2) 0.0083(5)

O7 0.1952(5) 0.1808(3) 0.0911(2) 0.0086(5)

SrNi3(P2O7)2 (II)

Sr1 0.50000 0.00000 0.00000 0.00703(10)

Ni1 0.18413(5) 0.62595(5) 0.02554(4) 0.00489(10)

Ni2 0.00000 0.00000 0.00000 0.00435(11)

P1 0.88817(9) 0.70383(9) 0.19365(7) 0.00378(13)

P2 0.60269(10) 0.44108(9) 0.20091(7) 0.00396(13)

O1 0.39778(29) 0.47868(27) 0.19225(23) 0.00716(36)

O2 0.00170(28) 0.21055(25) 0.13388(20) 0.00620(34)

O3 0.97392(29) 0.57495(26) 0.11296(21) 0.00592(35)

O4 0.68039(28) 0.62949(26) 0.17764(22) 0.00685(34)

O5 0.62448(29) 0.31853(27) 0.08303(21) 0.00684(35)

O6 0.26842(28) 0.88222(26) 0.13524(21) 0.00573(34)

O7 0.84474(28) 0.87661(27) 0.11105(21) 0.00656(35)

aUeq= (1/3)∑

i

∑j Uij a

∗ia∗jaiaj .

b Supplementary material has been sent to the Fachinformationszentrum (FIZ) Karlsruhe, Abt. PROKA, D-76344 Eggenstein-Leopoldshafen,Germany, and can be obtained by contacting FIZ (reference numbers: CSD-411740 for SrNiP2O7 and CSD-411741 for SrNi3(P2O7)2).

tailed information on this topic is in preparation [29]. Inour AOM calculations on SrNiP2O7 and SrNi3(P2O7)2

we have taken into account the modified bonding proper-ties of oxygen in a slightly simplified, yet more easy-to-use way than described by Reinen et al. As can be seenfrom Fig. 4, in the two diphosphates coordination num-bers 3 and 4 are found for oxygen ligating to Ni2+. Foroxygen atoms with C.N.= 3 we have set in our calcu-lationsπ -bonding within the plane (Ni, O, P), which isroughly identical to the best-fit plane through oxygen and

the three adjacent cations, to zero. Perpendicular to thisplane undisturbedπ -bonding interaction(eπ = (1/4)eσ )between oxygen and Ni2+ has been assumed. For oxy-gen atoms with C.N.= 4 noπ -bonding at all has beenallowed. The energieseσ (Ni–O) (Table 4) describing theσ -interactions between Ni2+ and the various O2− havebeen set proportional tod(Ni–O)−5, a correlation thathas been established by experimental results [30] andtheory [31,32] as well. In addition to this considera-tions aboutσ - andπ -bonding we have used in our pa-

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674 B. El-Bali et al. / Solid State Sciences 3 (2001) 669–676

Table 3SrNiP2O7 (I) and SrNi3(P2O7)2 (II). Interatomic distances (Å) and angles (◦) within the coordination polyhedra [NiO5] (I) and [NiO6] (II). Estimatedstandard deviations ford(Ni–O) are less than 0.003 Å, and ford(O–O) less than 0.008 Å. Estimated standard deviations for (O–Ni–O) are less than0.12◦

[NiO5] in (I)

Ni O(3) O(4) O(6) O(1) O(2)

O(3) 1.971 158.01 86.20 105.59 89.22

O(4) 3.9236 2.031 91.84 95.08 87.27

O(6) 2.7412 2.9251 2.044 115.16 165.49

O(1) 3.1972 3.0067 3.4519 2.048 79.34

O(2) 2.8347 2.8269 4.0774 2.6252 2.070

[Ni(1)O6] in (II)

Ni(1) O(3) O(4) O(4) O(6) O(7) O(5)

O(3) 2.041 90.62 85.82 84.63 173.84 78.00

O(4) 2.9136 2.058 77.27 174.55 93.88 95.94

O(4) 2.8001 2.5793 2.072 99.67 99.27 162.44

O(6) 2.7764 4.1370 3.1760 2.084 91.07 85.69

O(7) 4.1260 3.0316 3.1727 2.9799 2.091 97.32

O(5) 2.6695 3.1616 4.2191 2.9119 3.2204 2.197

[Ni(2)O6] in (II)

Ni(2) O(3) O(3) O(2) O(2) O(5) O(5)

O(3) 2.047 180 94.54 85.46 79.75 100.25

O(3) 4.0941 2.047 85.46 94.54 100.25 79.75

O(2) 2.7846 3.0142 2.057 180 94.32 85.68

O(2) 3.0142 2.7846 4.1131 2.057 85.68 94.32

O(5) 2.6695 3.1959 2.8375 3.0605 2.117 180

O(5) 3.1959 2.6695 3.0605 2.8375 4.2329 2.117

rameterization scheme the Racah parameters (B = 886cm−1, C = 3985 cm−1, C/B = 4.5, β = 0.82 [33]) andthe spin–orbit coupling constantζ = 517 cm−1 [33]. Itshould be pointed out that the whole parameterizationleaves in the end just two independent parameters for fit-ting of an observed spectrum. One iseσ (Ni–O)max for theshortest Ni–O distance, the second is the interelectronicrepulsion parameterB. This situation is completely com-parable to the classical interpretation ofd-electron spec-tra using∆ andB [33]. Despite this similarity, the mod-elling within the AOM allows for the individual bond-ing behaviour of each ligand. The additional informationis introduced into the calculations on a purely geomet-ric basis (bondlength, coordination number of oxygen)

well known from the structure refinement. For modelingof the transition energies of Ni2+ the computer programCAMMAG [34,35] has been employed. In Fig. 1 the re-sults of our calculations are compared to the observedspectra. Calculated transition energies are given as barsat the bottom of the corresponding spectra. The lengthof a bar indicates the amount of triplet character obtainedfor this states from our calculations, which allow for com-plete configurational interaction. Thus, the short bars rep-resent states of mainly singlet character. Electronic tran-sitions from the triplet ground state to pure singlet statesare spin-forbidden. However, due to the mixing of tripletand singlet states significant intensities might be gainedfor such transitions [10,14]. In this respect the length of

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B. El-Bali et al. / Solid State Sciences 3 (2001) 669–676 675

Fig. 4. ORTEPplots of the coordination polyhedra [NiO5] in SrNiP2O7and [Ni(1)O6] and [Ni(2)O6] in SrNi3(P2O7)2. Ellipsoids are given atthe 99% probability level.

Table 4Best fit AOM parameters for modeling of thed-electron spectra of Ni2+in SrNiP2O7 (I) and SrNi3(P2O7)2 (II). Global parameters [33]:B =886 cm−1, C = 3986 cm−1 (C/B = 4.5), β = 0,82, ζ = 517 cm−1,k = 0,82

eσ [cm−1]a eπ,x [cm−1]b eπ,y [cm−1]b

[NiO5] in (I)

O(3) 4100 0 1025

O(4) 3529 0 882

O(6) 3418 0 855

O(1) 3385 0 849

O(2) 3209 0 0

[Ni(1)O6] in (II)

O(3) 3450 0 863

O(4) 3309 0 828

O(4) 3195 0 797

O(6) 3105 0 776

O(7) 3050 0 763

O(5) 2384 0 0

[Ni(2)O6] in (II)

O(3) 3400 0 850

O(3) 3400 0 850

O(2) 3322 0 830

O(2) 3322 0 830

O(5) 2876 0 0

O(5) 2876 0 0

aTheeσ are related to each other byeσ ∼ d(Ni–O)−5.b Generallyeπ = (1/4)eσ has been applied. Depending on the coor-

dination number of oxygenπ -bonding might be completely suppressed(see text for details).

a bar relates in a very first approximation to the intensityof an absorption band.

Obviously, our model accounts nicely for the red-shiftof the spectrum of SrNiP2O7 that is due to the chro-mophor [NiO5] in contrast to the spectra of ANi3(P2O7)2(A = Ca, Sr, Ba) that originate from slightly distortedoctahedral [NiO6] groups. It should be stressed that thebonding parameters (eσ , eπ,x , eπ,y ) for the [NiO5] and[NiO6] chromophors are very similar (Table 4) and arerelated byeσ ∼ d(Ni–O)−5. The smaller number of lig-ands (bonds) in [NiO5] is only in parts compensated bystronger interactions between nickel and oxygen due toshorter distances Ni–O, therefore leading to the observed

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676 B. El-Bali et al. / Solid State Sciences 3 (2001) 669–676

red shift. Furthermore, our modeling reproduces nicelythe splitting of the electronic terms of the [NiO5] chro-mophor.

For the structure of the broad absorption band observedin the spectrum of SrNiP2O7 between 17 000 and 27 000cm−1 two effects are responsible. In one part it resultsfrom the splitting of the3T1g(P ) parent state (lablefor Oh) due to the lower symmetry of the [NiO5]chromophor. The shoulder around 17 000 cm−1, however,must be attributed to spin-forbidden transitions from thetriplet ground state3B1 to 1A1, 1A2 and possibly also1E (the latter two originating from the1T1g state inOh

symmetry).We believe that understanding of electronic spectra

of nickel(II) oxo-compounds with chemically reasonablebonding parameters in the AOM framework can only beachieved on the basis of the ‘real’ coordination geometryallowing for second sphere ligand field effects of oxygenas ligator atoms.

Acknowledgements

B. El Bali wishes to thank Dr. C. Day and Dr. A. Lach-gar, from Wake Forest University, North Carolina, USA,and the staff of CERPHOS Laboratories and Documen-tation Center (Casablanca) for their unconditional sup-port. He also thanks Drs M. Taibi and O. Sassi from ENSTakaddoum (Rabat).

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