摘要:

1515Manganese 3d and 4s Electron-density Distribution in Phthalocyaninato-manganese( 11)By Brian N. Figgis, Edward S. Kucharski, and Geoffrey A. Williams,' School of Chemistry, University ofWestern Australia, Nedlands, Western Australia 6009A new analysis of the 11 6 K single-crystal X-ray diffraction data set of good accuracy on P-phthalocyaninato-manganese(l1) has iielded individual 3d and 4s orbital populations on the manganese atom of significant accuracyand qualitative estimates of bonding electron density in the macrocycle ring. The manganese orbital populations(x and y along Mn-N vectors, z perpendicular to the square plane of co-ordinated nitrogen atoms) have beendetermined by a least-squares refinement procedure as dzy1.5(2), duo.6(2), dv~*7(2), dz20-9(2), dza-vao*1(2), and 4s2.0(3).Difference-Fourier syntheses indicate the aspherical nature of the valence charge density on the manganeseatom, and the presence of bonding charge density in the ligand.In the later stages of the structural andorbital population analyses, allowance was made in the scattering model for overlap charge density by placing smallspherical charges of variable population and radial extent between C-C and C-N atom pairs and in the Mn-Nvectors. The present treatment of the data differs from the previous analysis in that refinement of atomic positionaland thermal parameters has been based upon intensities (/), and all 2 265 observations with (sinO)/A \< 0.662 kl,rather than on structure factor amplitudes ( ( F I ) and only the 1 608 reflections with / > 30(/).Full-matrix least-squares refinement on the basis of a spherical atom model yielded R 0.045, and bond lengths and angles of im-proved accuracy are reported. The atomic positional and thermal parameters thus obtained have been used togenerate a set of ' difference structure factors,' Fdr containing, principally, information about the valence chargedensity on the manganese atom. These Fd values have been analysed by least-squares refinement in terms ofaspherical density arising f r m 3d and 4s orbital populations on the manganese atom. The present analysis hasestablished that worthwhile information on chemical bonding in a molecule as large as a transition-metal macro-cycle can be obtained from a low-temperature X-ray data set of good quality, and acts as a guide for a program toinvolve the collection of low-temperature data sets of excellent quality for this purpose.THE geometrical structures of the metallophthalo-cyanines have been studied extensively, in particular bysingle-crystal X-ray diffraction techniques (ref. 1 andrefs.therein), largely on account of their generic relationto the naturally occurring porphyrins, chlorins, andcorrins. We have initiated a program to study thechemical bonding in the metallophthalocyanines, usingthe techniques of X-ray and neutron diffraction over thetemperature range 4.2 to 295 K l3 and polarised neutrondiffraction at 4.2 K.4 The former studies have beendesigned to determine accurately the molecular struc-tures for use in conjunction with the polarised neutronprogram.We have used this information to deducespin-density distributions in paramagnetic phthalo-cyaninato-manganese(n), [Mn(pc)], and -cobalt(II), [Co-(pc)] (pc = phthalocyaninate).I t is an attractive proposition to complement thesestudies with the determination of valence-electrondensities using accurate single-crystal diffraction data.Such electron-density studies have recently been madeon several transition-metal compound^.^ The experi-mental difficulties inherent in every valence-electrondensity study using either extensive and accurate X-raydiffraction data alone, or combined with a neutrondiffraction definition of nuclear positional and vibrationalparameters, are compounded in the case of compoundscontaining a heavy atom such as a transition metal.This is because the valence-electron densities are verysmall in relation to the high electron density of thetransition-metal core.That the asphericity of the chargeabout an open-shell transition metal, due to the d elec-trons, is quite small is evident from the very manysuccessful molecular-structure determinations of transi-tion-metal compounds using single-crystal X-ray dif-fraction data. In these determinations, whicii con-sistently yield low R factors for the agreement betweenobserved and calculated structure factors, a sphericallysymmetrical metal-atom scatterer is used.In preference to embarking on a full-scale valence-electron density study of [Mn(pc)] and [Co(pc)], in whicha very considerable effort would be required to obtainthe most accurate diffraction data possible, we haveundertaken the present study using data for [Mn(pc)],already at hand, which is of good accuracy.The overallaim of this present study is to guide thorough investig-ations of the valence-electron density in metallo-organicand other compounds of this type, and to assess the valuethey are likely to have in understanding the chemicalbonding. If such a study is likely to be successful, it isimportant to be able to optimise experimental conditionssuch as the choice of compound and crystal, the accuracyand extent of the X-ray diffraction data required, andthe temperature. It is also of value to know whetheran accurate X-ray diffraction data set alone can providesufficient information without the need for support fromneutron diffraction data.Finally, the present study wasintended to investigate a novel method of analysingaccurate X-ray data in a chemically meaningful way.In a molecule such as a metallophthalocyanine,interest often focuses on the electronic structure oi themetal atom, and we have concentrated upon thisaspect. In [Mn(pc)], we have treated the ligandvalence-electron distribution only as far as necessary tofacilitate the determination of the manganese atom 3dand 4s electron distribution, including the extent of thedelocalisation onto the ligandJ.C.S. Dalton 1516EXPERIMENTALThe 116 K X-ray diffraction intensity data of a previousstructural analysis of the P-polymorphic form of [Mn(pc)] 1were used in the present work.Crystal Data.1---C3,Hl,MnN,, M = 567.49, Monoclinic,space group P~,/G, a = 14.590(3), b = 4.741(1), G =D, = 1.643 g ~ m - ~ , Mo-K, radiation (graphite-crystalmonochromator), A = 0.710 69 A, p = 6.530 0111-1,' crystaldimensions 0.04 x 0.10 x 0.53 mm, T = 116 f 2 K, 2 265unique observations with (sine)/A 6 0.662 A-1.Structure Refinement.-All 2 265 unique intensitiesmeasured [a complete sphere of data t o (sinO)/A 6 0.595 A-1,with the weakest reflections skipped for 0.595 < (sinO)/A 60.662 A-1] were corrected for absorption and included in thef ull-matrix least-squares refinement of atomic co-ordinatesand thermal parameters. The program CRYLSQ * wasused for least-squares refinement, the function minimisedbeing Clw(A1) 2 where AI = I , - I , and w = l / ~ ( 1 ) ~ is theweight assigned to the To values.The refinement was basedon I, so that all measured data (including those observationswith I , < 0) could be included in the least-squares process,thereby eliminating the bias introduced into data by using ao ( I ) rejection criterion or by setting all negative intensitiesto zero.gA total of 219 variables was refined in the least-squaresrefinement including all positional, anisotropic (C, N, Mn),and isotropic (H) thermal parameters. Refinement con-verged with R( = = Z ~ A I ~ / X ~ I , ] ) 0.044, R' (= [Xw(AI)2/CwIo2]lf)0.070, and x(=[Cw(AI)2/(2 265 - 219)Jt) 1.484. The maxi-mum shift-to-error ratio at convergence was 0.001 : 1.Anexamination of the final observed and calculated intensitiesrevealed no evidence of any multiple scattering or secondaryextinction effects and, in fact, in a trial least-squares cyclethe extinction coefficient did not vary significantly fromzero. On a final difference synthesis, the largest peakswere 0.81 at (000) and -0.68 e A-s at a position close to theMn atom. Some difference-Fourier sections calculated19.301(5) A, (3 = 120.79(1)", U = 1 146.9(4) A3, 2 = 2,through various planes a t this stage (Level I) of the scatter-ing model are shown in Figure 1.Final atomic positional co-ordinates and thermal psra-meters, with estimated standard deviations in parentheses,are listed in Tables 1 and 2.Atomic scattering-factorcurves for neutral Mn, C, and N were from ref. 10, and weremodified for the real and imaginary anomalous dispersioncorrections.ll The scattering-factor curve for H was takenfrom ref. 12. Observed and calculated structure factors arelisted in Supplementary Publication No. SUP 22755The aspherical deformation density around the Mn atom,obvious in the difference sections (Figure l ) , provided thebasic data for the following novel method for extractingvalence orbital populations on transition metals in centro-symmetric cells. A ' difference structure factor ', Fd =F, - F,, was calculated for each observation where F, wasobtained from the scattering model of the Level I stage ofrefinement, with the exception that for Mn the scatteringcurve for only the Ar core 13 was included in the calculationof F,.That is, the spherical approximations to the C, H,and N atoms with their Level I positional and thermalparameters, together with the spherical Ar core of Mn2+, weresubtracted from the F,, leaving a component, Fd, withcontributions from the valence electrons of Mn togetherwith aspherical valence density effects about the other atomsand experimental errors. A section of a Fourier synthesisusing Fd as input is shown in Figure 2, and indicates thehigh degree t o which a spherically symmetrical approxi-mation to the Mn scatterer is valid. The method used toobtain phased, anomalous-dispersion-free F, values foruse in the calculation of Fd is presented in the Appendix.The Fd values were then used in a least-squares refinementof a non-spherically symmetrical valence-electron model forMn.For this purpose, the program ASRED written bytwo of us (G. A. W. and B. N. F.), was used. In ASRED a* For details see Notices to Authors No. 7, J.C.S. Dalton, 197!),Index issue.(27 PP.).*00UJ N000 Lo0 I'u000 m0000 m0 I-0*2500 0*2500 -0.3000 0 3001980 15170?0000 m0 I0.300000 o m0000 m0 I-0,3000 0.3000set of quantization axes is assigned to each atom, and theelectronic valence populations of s, p , and d orbitals on eachatom can be refined by a least-squares process, using theformalism of Weiss and Freeman. l4 Single-electron scatter-ing curves ( j u ) y , p , ( l , (j2)7,,,1, and ( j4)d for each atom type andeach orbital type from a tabulated ~ o u r c e , ~ ~ * l ~ or calculatedfrom an atomic wave function,I6 are used in conjunctionwith the equations for the scattering by p l7 and d e1e~trons.l~Because such theoretical single-electron scattering curvesapply to the free atom or ion, for atoms in a chemicalenvironment i t is necessary to allow some refinement of thescattering-curve shape.This is accomplished in ASREDby a least-squares refinement of an ‘ orbital-expansion ’parameter I where f(s) [ = f,,(vs)] is the single-electronscattering factor a t (sinO)/i, = s and fo(m) is the free-atom000 m0000 m0 I0,3000 -0.3000FIGURE 1 Sections of the deformation density in [Mn(pc)] afterthe Level I stage of refinement.Contours are drawn atintervals of 0.1 e A-3; dashed contours represent negativedeformation density. The dimensions of each section areindicated in nm. ( a ) Section through the MnN, co-ordinationplane, centred on the Mn atom. (b) Section, containing theMn-N(4) vector, perpendicular to the MnN, co-ordinationplane. N(3”), the ligand atom of a neighbouring moleculewith which, in the proposed path for ferromagnetic exchange,the Mn atom interacts, is 0.256 A from the plane; its projectiononto the plane is indicated. (c) Section, containing the Mn-N( 2) vector, perpendicular t o the MnN, co-ordination plane.The projection of the N(3”) atom, which is 0.040 A from theplane, onto the section is indicated.( d ) and ( e ) Sectionscontaining the pyrrole and benzene residues. The bondsbetween hydrogen-substituted carbons have densities generallyless than the other C-C and C-N bonds, an effect attributedto shifts in the carbon atoms from the true nuclear positionswhich cause the near elimination of the C-C bond peaksscattering factor at (sinO)/h = IS. The refinement of Y isassociated with variation of the radial exponents of theatomic wave function.Only limited success was obtained in the refinement of anaspherical valence model for Mn using the Fd valuesdescribed above. However, in the space group P2,/c, aspherically symmetrical scatterer a t (000) does not contri-bute to the class of reflections hkl with k + I = 2n + 1.Hence the Mn contribution to these reflections is extremelysmall, arising only from the aspherical components of boththe valence electrons and the anisotropic thermal motion.Since most of this class of reflections has lFdl values ofsimilar magnitude to the remaining reflections, to whichMn contributes strongly, i t was apparent that asphericalvalence density effects about the C and N atoms were th1518 J.C.S. Daltonmajor contributors to this k + I = 2n + 1 data.Thevalence-electron model for Mn was then refined using only1 151 observations with k + I = 2n and (sine)/h G0.595 A-l.The results are presented in Table 3. In the refinement, thefunction C W ( A F , ~ ) ~ was minimized where w = l/0(1)~ asbefore, and AFd = I F d - F,I where F , is the Mn valence-TABLE 1Final atomic positional co-ordinates for [Mn(pc)] a t 116 K *X l a0.252 8(1)0.253 4( 1)0.073 l(1)0.073 4(1)-0.072 O(2)-0.072 l(1)-0.132 3(2)-0.132 7(1)0.180 2(2)0.179 8(2)0.200 7(2)0.200 7(2)0.291 6(2)0.292 4(2)0.283 l(2)0.283 7(2)0.188 0(2)0.187 9(2)0.097 9(2)0.097 O(2)0.105 8(2)0.105 7(2)0.027 7(2)0.027 8(2)-0.145 8(2)-0.145 6(2)-0.256 3(2)-0.256 l(2)- 0.309 7(2)-0.418 9(2)-0.471 9(2)-0.472 7(2)-0.418 8(2)-0.419 3(2)-0.309 5(2)-0.309 6(2)-0.231 3(2)-0.231 O(2)-0.309 5(2)-0.419 l(2)0.354(2)0.360(2)0.350(2)0.350( 1)0.186(2)0.186( 1)0.02 9 ( 2)0.027(2)- 0.276(2)-0.274(2)- 0.46 1 ( 2)-0.462(2)-0.550(2)- 0.552(2)- 0.456( 2)- 0.457 (2)Y lb0.029 7(5)0.029 7(5)0.225 2(5)0.225 2(4)0.530 4(5)0.531 3(5)0.199 6(5)0.199 8(4)0.201 7(6)0.202 2(5)0.402 2(5)0.401 9(5)0.458 8(7)0.456 7(6)0.662 3(6)0.662 3(6)0.806 2(7)0.807 6(6)0.754 0(6)0.755 2(5)0.547 8(6)0.547 7(5)0.437 l(5)0.436 9(5)0.416 O(5)0.416 3(5)0.503 6(7)0.503 3(6)0.702 5(6)0.704 7(5)0.731 3(7)0.733 l(6)0.568 O(6)0.568 4(5)0.369 7(6)0.368 4(5)0.338 8(6)0.338 4(5)0.150 O(6)0.150 3(5)0.352 (5)0.348( 5)0.7 1 O( 5)0.7 1 1 ( 5)0.953(6)0.96 1 ( 5)0.843 ( 5)0.846(4)0.8 16( 5)0.825(5)0.873 (6)0.880(5)0.590(5)0.59 1 (4)0.2 63 (6)0.259( 5)2160.161 2(l)0.161 5(1)0.097 2(1)0.097 4( 1)0.077 5( 1)0.077 7(1)-0.033 5(1)-0.033 7(1)0.158 8(1)0.158 7(1)0.222 O(1)0.222 O(1)0.296 8(2)0.296 9(1)0.344 l(2)0.344 7(1)0.319 2(2)0.319 6( 1)0.245 2(2)0.245 O( 1)0.197 l(1)0.197 O( 1)0.119 l(1)0.119 l(1)0.008 4(1)0.008 5(1)-0.033 l(1)-0.033 0(1)-0.014 3(2)-0.013 7(1)-0.067 3(2)-0.136 G(2)-0.137 l(1)-0.155 7(2)-0.156 2(1)- 0.102 6( 1)- 0.102 7( 1)-0.103 0(1)-0.102 8(1)-0.067 2(1)0.312(1)0.314( 1)0.399( 1)0.401( 1)0.352( 1)0.354 (1)0.225( 1)0.226( 1)0.030( 1)0.034( 1)- 0.058( 2)- 0.057( 1)-0.175( 1)-0.175( 1)- 0.204( 1)-0.204(1)* Upper and lower values quoted are for Levels I and I1electron contribution to the calculated structure factor.During the refinement, orbital populations were constrainedto lie between 0.0 and 2.0 e.From this valence-electron model, it was apparent thatthe contribution to all the data from aspherical valencedensity effects on the C and N atoms was significant.Theeffects of the aspherical valence density on C and N werestructure refinements respectively. Mn is a t ( O , O , O ) .then included in the scattering model. A crude but effectiveway of doing this, using the crystallographic programs a tour disposal (' X-Ray '76 '),* was to include in the scatteringmodel 26 spherical ' blobs ' of charge at the mid-points ofthe C-C and C-N bonds and on the Mn-N bonds a t positionsone-third of the bond distance from N. This was done,TABLE 2 tFinal atomic thermal parameters for [Mn(pc)] a t 116 K.Upper and lower values quoted are for Levels I and I1structure refinements respectively, u tensors in A2.Anisotropic and isotropic thermal parameters aredefined by T = exp[-22~2(h~a*~U~~ + k2b*2U,2 +12c*2U33 + 2hka*b* U,, + 2hZa*c* U,, + 2klb*c* U,,)]and T = exp[-8n2U(sin20)/A2]Atom 103U11 103U2, lWU,, 103U12 103U,, 103U,,Mn 15.0(3) 19.4(3) 17.2(3) 1.6(3) 8.1(2) -2.5(3)t The complete Table 2 has been deposited in Supplementaryusing the H form factor modified by individual isotropicGaussian functions, initially chosen with U = 0.038 A2,as the scattering curves for the spherical overlap charges,and using individual populations initially fixed a t 0.2 e.The presence of such bonding charge between the aromaticC-C bonds in benzene rings has been discussed previously,l*and its neglect leads t o incorrect atomic positions as12.5(3) 17.0(3) 14.9(3) 1.8(3) 6.7(2) - 2 4 3 )Publication No.SUP 22755.00 In N000 ln N0 I-0.2500 0.2500FIGURE 2 Section through the MnN, co-ordination plane, show-ing the valence-electron density in [Mn(pc)] ; a differencesynthesis using only the Ar core contribution to the Mnscattering. Contour levels as in Figure 1 ; however, contoursare only drawn to ca. 3.5 e and hence the large positivedensity near the Mn nucleus is not contoureddetermined by X-ray diffraction a n a l y ~ i s . ~ ~ l8 The scatter-ing model was refined by least squares, minimisingC W ( A I ) ~ , in two blocks using an iterative procedure. Inthe first cycles, the overall scale, positional, and thermalparameters of C, H, N, and Mn, and the atom population ofMn (220 variables) were refined in one block while the bond-ing charges were held invariant.During these cycles, th1519benzene C atoms moved further out from the centroids of R = 0.045, R’ = 0.060, and x = 1.301 (272 variables).the benzene rings and close to the true nuclear position^.^ The maximum shift-to-error ratio a t convergence wasThe isotropic Gaussian functions and populations of the 0.06 : 1. Final atomic positional co-ordinates and thermalindividual bonding charges, together with the overall scale parameters from this stage of refinement (Level 11) areVariables rused inrefinementSdX,,3dxz3d,z3d za3dxz-la4sYSd I7y4*X hTABLE 3Orbital populations for the Mn atom in [Mn(pc)] aLevel I ‘ difference ’structure factors containingcontributions from Mnvalence electrons plusresidual bonding densitiesLevel I1 ‘ difference ’ structure factors containingonly Mn valence-electron contributionsA A 7\ r-1151 2 023 1151 2 023 1356 2 265 1886reflections b reflections c reflections b reflections c reflections d reflections reflections2.0(5) 1.8(4) 2.0(2) 1.6(2) 1.8(2) 1.5(2) 1.5(2)0.4( 4) 0.0(3) 0.8(2) 0.6(2) 0.9(2) 0.6(2) 0.6(2)0.7(4) 0.2(3) 1.0(2) 0.7(2) 1.0(2) 0.7(2) 0.7(2)0.5(5) 1.2(4) 0.7(3) 1.1(2) 0.5(3) 0.9(2) 0.9(2)2.0(2) 2.0(2) 1.8(2) 1.9(2) 2.0(3) 2.0(3) 2.0(3)0.72(4) 0.7 1 (4) 0.97(4) 0.96 (4) 0.92 (4) 0.91(4) 0.90( 5)0.84(6) 0.83 ( 6) 0.92 ( 7) 0.90(7) 0.85( 6) 0.83 ( 5 ) 0.83( 6)1.680 1.620 1.319 1.295 1.331 1.288 1.3660.0(6) 0.0(4) 0.0(3) 0.2(2) 0.0(3) 0.1(2) 0.1(2)a The least-squares derived estimated standard deviations are given in parentheses for each variable.The x-y-z quantisationaxes on Mn are defined with x along the Mn-N(2) bond, z perpendicular to the MnN, co-ordination plane and y orthogonal to x andz. d (K + I ) = 2n data; (sinO)/h < 0.662A-l. 17 Y is the parameter, discussed in thetext, associated with variation of the radial exponents of the atomic wave function. h The goodness-of-fit index x = [ C W ( A F ~ ) ~ /(N - V)]f, where AFd( = IFd - FYI) is the difference between observed and calculated ‘ difference ’ structure factors and N and Vare the numbers of observations and variables respectively.b ( K + I) = 2n data; (sinO)/h 6 0.595 A-1.“All data within (sine)/h < 0.595 A-1.All data within (sine)/A < 0.662 A-1. f All data with lFol > 5.0 (absolute units).factor, were then refined (53 variables) while all otherparameters were held invariant. The two refinements wererepeated successively until the model converged withTABLE 4Final populations (e) and isotropic Gaussian parameters,U (812), for the bonding charges. The scatteringcurves for the bonding charges were the H scatteringcurve l 2 modified by the function T = exp[-8x2ZJ-(si n28) / A2]Bondingcharge * Population 102uMn-N( 2) 0.40(8) 9(5)Mn-N(4) 0.45(8) 10(4)0.29(4) - 3(2)N( 2 1 -C ( 1 ) 0.06(3) - 7(3)N(2)-C(8) 0.08(3) - 8(2)N(3)-C(8) 0.20( 3) - 5(2)0.19(3) - 5 ( 2 )O.lO(3) -6(3)N(3)-C(9)N(4)-C(9)N(4)-C(16) 0.03( 2) - 9(6)C( l)-C(2) 0.14(3) - 6(2)C( 2)-C( 3) 0.23( 3) - 5(1)CP)-C( 7) 0.17(3) - 5(2) c (3)-C(4) 0.26 (4) - 2(2)C( 4)-C(5) 0.26(4) - 3(2)C( 5)-C( 6) 0.23(3) - 4(2)C(6)-C( 7 ) 0.24( 3) -5(1)C( 7)-C(8) 0.15(3) - 6(2) c (9)-C( 10) 0.14(3) - 8 ( 2 )C( 10)-C( 11) 0.25 (4) -W)C(lO)-C(15) 0.22(4) - 4(2)C(l1)-C(12) 0.15(3) - 7(1)C( 12)-C( 13) 0.29(5) 1(3)C( 13)-C( 14) 0.22(4) --3(2)C(14)-C(15) 0.19(3) -6(1)C(15)-C(16) 0.15(3) - 6(2):; ;;I:; ; i., 0.21(4) - 3(2)* The spherical bonding charge density was placed in themid-point of the Level I C-C and C-N bonds, and in theMn-N bond at a distance one-third of the bond length fromthe N atom.listed in Tables 1 and 2 and the bonding charge parametersin Table 4.Some difference-Fourier sections (Figure 3),calculated a t this stage of the refinement, indicate the extentto which the spherical overlap charges have been able tomodel the aspherical valence-electron density observableabout the C and N atoms in Figure 1. In this Level I1refinement the atom population of Mn was allowed to vary,and refined to the value 0.991(2). The refinement of thispopulation, together with the overall scale factor, accountsfor variations in the ratios of the C and N charges to the Mncharge on including the overlap charges without changingthe populations of the centrosymmetrical components of theC and N atoms from unity. This Mn atom population wasused for the difference-Fourier syntheses of Figure 3.However, in the calculations of structure factors belowinvolving only the Ar core of Mn, an atom population ofunity was used for Mn.Observed and calculated structurefactors are listed in SUP 22755.A new set of ‘ difference structure factors ’, Fd, wascalculated as before, using F, from the Level I1 stage ofrefinement. In this case, the valence electrons of Mntogether with experimental errors in the observed data werethe major contributors to Fd, and a least-squares refinementof a valence-electron model for Mn, using the programASRED as before, was reasonably successful. The finalorbital populations for Mn from refinements using dif-ferent portions of the data are presented in Table 3. The(sinO)/A cut-off of 0.595 A-1 was employed in certain refine-ments as the data were complete to this limit.In thedetermination of the ‘ difference structure factors ’, there isa possibility, discussed in the Appendix, that F d will beincorrectly calculated for cases with IFc[ < lFdl because ofthe uncertainty in the phase of F, in these cases. A refine-ment of the valence-electron model for Mn was also per-formed on all the data excepting those reflections withlFol < 5.0 (absolute units), and the results are presented i1520 J.C.S. DaltonTable 3 . The values of lFdl calculated from the valence-electron scattering model were considerably less than 5 . 0for most of the data. Thus this latter refinement excludeddata for which there was a possibility that F d was in-correctly calculated, as well as excluding those reflectionsTABLE 5Parameters for the Mn atom in [Mn(pc)] froin the siniul-taneous least-squares refinement of tfieriiial and orbitalparameters a with estimated standard deviations inparenthesesVariables Final valueu,, 0.011 2(5)u33 0.012 9(4) u, 2 0.001 5(4)u22 0.016 O(4)u13 0.005 4(2)3dxe 1.8(2)3 4 , 0.5(2)u,3 -0.003 9(4)3 4 , 1.2(2)3dx2-p 0.9(2)3d,r 1.0(?)4s 0.8(3)YSd 1.1 8( 6)Y l s 1.2(3)a The goodness-of-fit index ,y, as defined in Table 3, was 1.286for 2 265 observations and 14 variables. U tensors, in A2,are as defined in Table 2.C The x-y-z quantisation axes onMn are as defined in Table 3. Y is the parameter, discussedin the text, associated with variation of the radial exponents ofthe atomic wave function.in which there were relatively large experimental errors inIFo] and hence F d .The final stage in the refinement of the valence-electronmodel for Mn included the simultaneous refinement of theanisotropic thermal factor for Mn, with the 3d and 4sorbital populations.For this purpose, t o the Level I1 Fdvalues were added the structure factor contributions of theAr core of Mn2+. The resulting phased structure factorscontained the total contribution of the Mn atom to the0 0v) N00 0v) N0 1-0,2500 n. zsoo000 m0000 m0 I000?00TI0.3000-0 -3000 0.3000FIGURE 3 Sections of the deformation density in [Mn(pc)], afterthe Level I1 stage of refinement in which the bonding densitywas included as spherical charges in the scattering model.Contours as in Figure 1 ; dimensions of each section in nm.(a) Section through the MnN, co-ordination plane, centred onthe Mn atom.( b ) and (c) Sections through the pyrrole andbenzene residuesscattering, with only a very small contribution from anybonding charge density on the macrocyclic ligand notaccounted for by the scattering model. The results of thisleast-squares refinement, using the program ASRED asbefore, are presented in Table 5.In the refinements of the valence-electron models for Mn,the ( j o ) , ( j z ) , and ( j 4 ) scattering curves for the 3d electronsof Mn2+ were used,13 while the 4s scattering curve wa1980 1521calculated l9 from a wave function for Mn+ with r = 1 .8 . l SAll the computations were performed on a CDC CYBER 73computer a t the Western Australian Regional ComputingCentre.RESULTS OF STRUCTURE REFINEMENTSThe molecular geometry and atom numbering of thecentrosymmetric [Mn(pc)] molecule are shown in Figure 4.The manganese atom has essentially Dah symmetry, withangles N(2)-Mn-N(4) and N(2)-Mn-N(4') of 90.96(8) and89.04(S)O respectively (Level I1 refinement values). Inter-atomic distances (Table 6) and angles (tabulated in SUPH(31 H(2 1~ " I G U R E 4 An ORTEP drawing of [Mn(pc)] (116 K parameters)The showing the molecular geometry and atom numbering.thermal ellipsoids are drawn at the 80% probability level22755) are given for both Levels I and I1 of refinement.The bond lengths and angles from the present refinementshave consistently lower estimated standard deviations thanthose from the previous refinement,l which are also presentedin the Tables.This increased accuracy is a result ofincluding all the data (including negative intensities), asdistinct from the 3 4 1 ) rejection criterion used previously.For Level I the maximum non-hydrogen-atom bond lengthand angle changes are respectively 1.0 pm and 0 . 5 O , withaverages of 0.4 pm and 0.2'. The bond lengths from theLevel I1 refinement differ from those obtained from theconventional refinements in which bonding charge densityon the ligand is ignored. In particular, the weighted meanvalues of the 12 individual benzene ring C-C bond distancesfrom the Level I and I1 refinements are 139.0(2) and 139.7(1)pm, respectively. As discussed el~ewhere,~.the neglectof aspherical valence-charge density in an X-ray diffractionanalysis of molecular structure, using data of limited resolu-tion re.,?. (sinO)/h < 0.7 A-lJ, can cause the apparentshortening of bond distances. Because some attempt hasbeen made a t the Level I1 stage of refinement t o include theeffects of overlap charge density in the C-C, C-N, and Mn-Nbonds, the bond distances obtained in this refinement areexpected to approach more closely the true internucleardistances obtained from neutron diffraction methods, and acomparison with the results of a 4.2 K neutron diffractonstudy of [Co(pc)]3 reveal this t o be the case.Because of the improvements in accuracy and nuclearpositions in the Levels I and I1 atomic parameters, somedisplacements from and angles between mean planes occurand are deposited in Tables (available in SUP 22755).Foreach of Levels I and 11, relative t o the previous refinement,no change in displacement values greater than 0.4 pm, norin mean plane angle greater than 0.1", occurs.DISCUSSIONGeneral Assessment of the Analysis.-Chemicallysignificant 3d and 4s orbital populations have beenobtained (Tabie 3) for the manganese atom in [Mn(pc)],from our analysis of the 116 K single-crystal X-ray dif-fraction data of moderate extent [(sinO)/A < 0.662 A-1].The results of the orbital population refinements usingvarious sections of data (Table 3) show that the overalltrend amongst these populations is not strongly depen-dent on the portion of the data set used in the refinement.The inclusion of more extensive data in the refinements ineach case yielded lower standard deviations in the orbitalpopulations.Our analysis suffers from some obviouslimitations introduced by the shortcomings of the dataset and the crudity of some features of the scatteringmodel. The fact that it is a model-dependent orbitalpopulation analysis is a limitation from some points ofview, although we defend it for the discussion of featuresof chemical interest on the grounds that there are am-biguities in the translation of more rigorous approaches,such as the method of multipole analysis, into chemicalterms.It was apparent during the population analyses that ifsome account was made in the scattering model for theaspherical valence-electron density about the ligandatoms, the least-squares refinement of the 4s and 3dorbital populations was well behaved, and the resultantpopulations had smaller standard deviations than thosefrom refinements in which no account of the ligandvalence-electron density was made.In the Level I1stage of the present analysis, the ligand valence-electrondensity was modelled by spherical charges of variablepopulations and scattering factors, placed at the mid-points of the C-C and C-N bonds. No attempt wasmade to represent the out-of-plane ' nature of the xbonding in the ligand. While the physical limitations ofthis empirical model are obvious, it is a useful ploy toobtain a better scattering model with a lower goodness offit than the conventional spherical atom approach, onwhich to base a refinement of the valence orbital popula-tions on the manganese atom.Also the bond distancesobtained from this model, in the benzene rings in par-ticular (Table 6), are closer to those obtained fromneutron diffractio: than are those values obtained fromthe conventional refinement neglecting bonding chargedensity (Level I values, Table 6). For X-ray diffractiondata sets of high accuracy and extending to high (sine)/hvalues, collected specifically for the purpose of accurat1522 J.C.S. Daltonelectron density studies on transition-metal atoms, amore sophisticated level of treatment of ligand valence-electron density may prove advantageous.Rather thanspheres, the bonding charge could be represented byellipsoids to take account of the more extended densityperpendicular to the plane of a benzene ring.18 Alter-natively, a multipole refinement of the ligand electrondensity,20 or the aspherical atom refinement proposed byTABLE 6Interatomic distances (A) in [Mn(pc)] at 116 KPrevious 341)refinementular distances *1.93 9 (3)1.942( 3)1.325(5)1.3 16( 4)1.3 96 (3)1.380(5)1.326 (4)1.32 1 (4)1.3 79( 5 )1.392 (3)1.450(5)1.399 (4)1.393 (5)1.384( 6)1.393 (5)1.385(4)1.396(6)1.444(4)1.45 1 (4)1.3 95 (6)1.39 1 (4)1.3 86 (4)1.391 (5)1.388 (6)1.39 7 (4)1.453 (5)0.95 (4)1.02(3)0.96(5)0.92(4)0.93(3)0.97(5)0.9 8 (4)0.93(4)3.400( 2)3.356 ( 3)2.765(3)2.724(4)Level Irefinement1.936( 2)1.940( 2)1.3 19( 4)1.314( 4)1.402( 3)1.383 (4)1.327 (3)1.328( 3)1.38 1 (4)1.3 99 (3)1.45 1 (4)1.398( 3)1.394 (4)1.3 77 (5)1.393 (4)1.381 (3)1.3 93 (4)1.443(3)1.446(3)1.3 85 (5)1.395(3)1.390(4)1.38 7( 4)1.382 (5)1.394(3)1.453( 4)0.95(3)1.03(2)0.96 (3)0.9 7 ( 2)0.92 (2)0.98( 3)0.94( 2)3.399 ( 2)3.3 58 ( 3)2.’761(2)2.721 (3)l.OO(2)Level I1refinement1.940( 2)1.944(2)1.329( 3)1.3 19( 3)1.394( 2)1.38 1 (3)1.33 1 (3)1.329( 2)1.381 (3)1.391 (2)1.449( 3)I .403( 3)1.396( 3)1.391 (4)1.403( 4)1.3 92 (3)1.401 (4)1.441 (3)1.445( 3)1.3 9 7( 4)1.398( 3)1.396( 3)1.400( 4)1.3 93 (4)1.3 99 (3)1.453 (4)1.04(2)0.99 (3)0.99(2)0.9 7 (2)1.02(3)0.95(2)3.407 ( 2)3.364( 2)2.769( 2)2.72 3 (3)l.OO(2)l.OO(2)(b) Selected intermolecular contacts perpendicular to molecularplaneMn - * - N(3”) 3.150( 3) 3.148(3) 3.148 (2)Mn - - - C(8”) 3.41 O( 3) 3.4 09 (3) 3.409( 2)Mn - * - C(9”) 3.546( 4) 3.545( 3) 3.543 (2)* Primed and double-primed atoms are related to the un-primed atom by the operations ( - x , --y, -2) and ( x , - 1 $- y,z) respectively.Hellner,21 are possible means of including the ligandvalence-electron density in the scattering model.In the present analysis, perhaps the most significanterror arises from the correlation between the anisotropicthermal motion of the manganese atom and its asphericalvalence charge density.In order to obtain the orbitalpopulations in Table 3, anisotropic root-mean-squaredisplacements for the manganese atom were obtainedfrom the least-squares refinement of the structuralparameters. The thermal vibration parameters obtainedin this way are not correlated with the valence chargeasphericity to the same extent as they are for the first-rowelements, due to the dominance of the transition-metalcore. However, the parameters describing the aniso-tropy in the electron density about the manganese atomdue to thermal motion will also model to some extentthe anisotropy of the aspherical valence charge density.The information available for analysis in terms of themanganese atom valence-electron density is, then, theway in which the observed electron density differs fromthat which can be described by a spherically symmetricalmanganese atom subject to anisotropic vibrations.Thepresent experiment succeeds partly because the lowtemperature involved (1 16 K) considerably reduces thethermal motion contribution to the asphericity of thecharge density on the manganese atom. Probably, italso succeeds partly because the lower site symmetry ofthe metal atom environment (square planar) leads tohigher anisotropy of the valence-electron distribution.It is generally accepted that analysis in terms of valence-electron distributions requires that the thermal motionbe accurately accounted for and in principle, the thermaleffects should be determined independently or refinedsimultaneously with the orbital population parameters.However, our attempts at such a simultaneous refinementwere unsatisfactory. From the results of this refinement(Table 5), which was very slow to converge, the highdegree of correlation between the anisotropic thermalmotion and the asphericity due to valence chargedensity is apparent.The orbital populations are some-what different from those presented in Table 3 , and inparticular the 3dx3-y3 orbital has gained significantpopulation at the expense of the 3dxz and 4s orbitals, andthe scattering curves for the 3d and 4s electrons havechanged significantly from the free-atom values, as seenin the ‘ orbital-expansion ’ parameters r, which differsignificantly from unity. The results from this simul-taneous refinement of thermal motion and valence chargedensity are not as chemically reasonable as the resultspresented in Table 3 (in particular, the 3dX2+2 orbital isgenerally considered to have zero population in square-planar compounds such as [Mn(p~)]).~~ It is consideredthat in the present case such a simultaneous refinementis of little value as the correlation between thermal andvalence charge density asphericity causes a significantcontribution of the thermal effects into the orbitalpopulations and vice zleysa, and it is not possible todisentangle the two effects. However, such correlationcould be minimised significantly by including in theobserved data set the reflections to very high (sine)/hvalues, to which the contributions of the valence elec-trons on the metal atom are relatively very small.Alternatively, the thermal motion of the metal atomcould be determined independently from a high-angledata refinement, or from neutron diffraction dataobtained at the same temperature as the X-ray data.Inthe latter procedure, the neutron diffraction analysisgives nuclear positions, and the amplitudes of vibration,of the atomic nuclei directly and of the electron densitwithin the context of the Born-Oppenheimer approxi-mation.Chemical Implications.--I t is of considerable interest tocompare the 4s and 3d orbital populations of the man-ganese ion deduced in this work with bonding to, and thephysical properties of, the ion.However, the level atwhich this may be done is not high, firstly because oursimple modelling of the system begs important questionswhich arise in the quantum mechanical treatment ofbonding and secondly, because the theory for a moleculeas large as [Mn(pc)] is necessarily crude. Our analysis ofwithin the framework of crystal-field theory or of th?angular overlap model, does not yield an ordering of thed orbitals likely to lead to an S = 1 rather than highspin (S = 2 ) or low spin (S = 0) ground term for anyreasonable values of the parameters. We have in-vestigated the application of the ligand-field model to[Mn(pc)]. We find that while, as has been demon-~trated,~~-28 it is possible to obtain the S = $ groundterm from certain combinations of the ligand-fieldparameters Dq, Ds, and Dt, or their equivalents, whenanalysed in terms of, say, angular overlap model para-FIGURE 5 &Orbital and tcrm energy ordering sequences for first transition series ions in square-planar stereochemistry such as aphthalocyanine. ( a ) &Orbital sequence arising from four pyridine molecules, based on the angular overlap model with e , l = 0.58,.(b) &Orbital sequence calculated for [Co(porphyrin)].24 (d) Term energy sequenceand orbital configurations arising from ds occupancy of part (c) under interelectronic repulsion perturbation.( e ) Probableterm energy sequence and orbital configurations arising from d5 occupancy of part (c) under interelectronic repulsion perturbation(schematic only)(c) &Orbital sequence calculated for [ F e ( p ~ ) ] .~ ~orbital populations gives the charge on the manganeseatom as close to Mn+, but this figure does not includeany contribution from the bonding charges in the Mn-Nbonds, near the nitrogen atoms, which must containsome small overlap population contribution from thosebonds. A molecularebital calculation on LMn(pc)]itself is not available in the literature to our knowledge,and the most pertinent results are an INDO calculation 23for crude models of [Fe(pc)] and [Co(pc)] and an ab initiocalculation 24 of [Co(porphyrin)]. The limitations of theINDO level of calculation, and the limited basis setpossible for the ab initio calculation of such a largemolecule, restrict the conclusions which may be drawnfrom them to a very qualitative level. For example, inspite of the inclusion of some configurational interaction,the ab initio calculation for [Co(porphyrin)] €ails toreduce the energy of any doublet term below the lowestquartet, so that the observed low-spin ground term isnot reproduced.The INDO calculation on [Fe(pc)] is probably themore pertinent and relevant for our purposes.Like[Mn(pc)], [Fe(pc)] is an intermediate spin case. It ispointed out 23 that a ligand-field type treatment, whethermeters e,, e,,ll, and eml, these are not reasonable in thelight of their values known for other nitrogen-atomdonor systems. If, for example, the angular overlapmodel parameters for four pyridine molecules are usedto calculate a d-orbital ordering, such as that illustratedin Figure 5(a), no quartet term is very near the groundterm.The INDO calculation on [Fe(pc)] and [Co(pc)]suggests that the e, (d,,, dyz) orbitals lie lowest [seeFigure 5(c)] followed by the b2, (dZy) orbital, and that thea,, (dZs) orbital is lowered in energy towards thembecause it is mixed with the ligand orbitals and with the4s orbital more than are the other d orbitals (‘dif-ferential covalency ’ in the parlance of ref. 23). Thisview is supported by observations of the spectra andmagnetic properties of various iron, cobalt, and coppersquare-planar cornple~es.~~The ab initio calculation on [Co(porphyrin)] gives theordering of the d orbitals (a,, < e, < b2, < b,,) [Figure5(b)] and shows a much lower relative energy for the a,,orbital than crystal-field predictions, but this orbitaldoes not seem to include much contribution from mixingwith the 4s metal orbital.This calculation assigns acharge of ca. +1.8 e to the cobalt atom from the effectivJ.C.S. Daltonionisation of most of the two 4s electrons, and ca. -0.57 eto each ligand nitrogen atom.The magnetic susceptibility and anisotropy 3O9 31 of[Mn(pc)] show that the ground term corresponds to theintermediate spin case S = 3, with no orbital degeneracyand that the ground term is 4A2, or 4B2, rather than 4Es.It can be argued that this requires a d-orbital sequencea,, < e, < b, Q b,, [Figure 5(b)] or b, < e, < al, <b,, [Figure 5 ( a ) ] .However, this is not necessarily so.As discussed in ref. 23 in connection with [Fe(pc)], d6,and implicit in other calculations 25-2t3 an order of thetype e, < b, < al, Q b,, can give rise to the configur-ation e,2*b,,2,*a1,2 with the 3A, term lowest, rather thanthe most obvious e,4*b,l*a1,l configuration [see Figure5 ( d ) ] . From all the evidence and calculations (exceptthose on a purely ligand-field basis), the e,-b2,-al, orbitalset seems to be closely spaced in energy for the square-planar phthalocyanine-type compounds of metals frommanganese to copper. The point is, that being so, theground term is not determined primarily by the orderwithin the orbital set, but rather by the effects of inter-electronic repulsions.Accordingly, a 4A 2g ground term,say, for [Mn(pc)] may arise from the configurationeg2*b2g2*a1:.The INDO calculation on [Fe(pc)] states that the e,,b2,, and al, wave functions have d-orbital coefficients of0.98, 0.97, and 0.82 respectively. There is no statementabout the involvement of the 4s metal orbital in thebonding nor of effective charge on the iron atom. Theab initio calculation on [Co(porphyrin)] gives informationabout the composition of the lowest terms which arise,and it is stated that there is very little mixing of ligandorbitals with the half-filled metal d-orbital, which is al,(d,2) for the ZA,, term case. In this calculation the 4selectrons are largely lost to the ligand, giving a charge ofC O ~ - ~ + .Our results do not fit in well with all facets ofthese calculations: we find that the charge on themanganese atom is ca. 1 + , achieved by the delocalisationof a 3d electron (Table 3) rather than the loss of two 4selectrons. We must then propose that there is ratherextensive mixing of at least some of the d orbitals withligand orbitals; to the extent of ca. 24% in fact, fromthe valence model refinement (Table 3) using all 2 265observations. Concomitantly, we expect that thereshould be substantial spin density located on the ligand,and we have observed just that phenomenon in aseparate experiment using the technique of polarisedneutron diffraction. While that experiment has not yetbeen fully analysed, we have suggested that ca.20% ofthe spin of the complex is located away from the man-ganese atom.4 The result is in keeping with the ' dif-ferential covalence ' explanation for the relative loweringof the energy of the a,, orbital outlined in the INDOcalculation, but is much larger in magnitude than thatcalculation would lead one to expect.The extensive delocalisation of the d orbitals wouldseverely affect arguments about the ordering of the dorbitals based upon the magnetic susceptibility or e.s.r.data, since they depend upon the amount of orbitalangular momentum associated with each orbital type,and this is likely to be quite sensitive to the admixtureof ligand orbitals. The delocalisation could affect thetotal spin of the system consequent upon changes of thed-orbital energies and reduction of interelectronicrepulsion parameters and may in part be responsible forthe fact that the ground state of [Mn(pc)] is a spinquartet, S = 3.Given the delocalisation of 24% of the d-electronpopulation, the remaining 3.8 d electrons located on themanganese atom are distributed amongst the valencemolecular orbitals much as expected.If the orbitalordering is accepted to be the same as indicated above[Figure 5 ( c ) ] , for the similar square-planar compounds ofiron and cobalt, and that the interelectronic repulsionslead to the configuration eg2*b2y2*a1g1, the d-orbitalpopulatioiis expected if each is equally delocalised arelisted in Table 7. I t is seen that they compare veryfavourably with our experimental results.TABLE 7Molecular-orbital and d-orbital populations predicted forthe configuration eg2*b2g2*a,g1 with 24% d-electron de-localisation, compared with deductions from thepresent work&Orbital occupancyh r \ DeducedValence Predicted from themolecular Total assuming 24% present workorbital occupancy delocalisation (Table 3)bl, 0 0.0 0.1a,, 1 0.8 0.9b2, 2 1.5 1.5ev 2 1.5 1.3Our results indicate that the radial extents of the 3dand 4s manganese orbitals are contracted from thetheoretical free-atom values. Our procedure employedas starting premises the form factors of Mn2+ for the 3dorbitals and of Mn+ for the 4s orbital.The parametersY~ and Y~~ of Table 3 are the inverses of linear scalingsof the form factors and, being less than unity, indicatethat more contracted orbitals are required to account forthe data.APPENDIXThe Derivation of ' Difference Structure Factors ' containingthe Transition-metal Valence-electron Contribution to theScattering in the Centrosymmetric Case.-The anomalous-dispersion-free ' difference structure factor ', F d , containingthe transition-metal valence-electron contribution to thescattering, is obtained from F d = F, - Fc, where F,, andF, are phased, dispersion-free observed and calculatedstructure factors, with only the spherically symmetrical coreof the transition metal, together with all other scatteringcentres, included in the calculation of F,.The real andimaginary anomalous dispersion contributions, dA , and dBc,are used to obtain a dispersion-free F,, 32 in the centro-F O = (dFo2 - dBc2)' - dA,symmetric case, wherefactor containing a dispersion contribution.is the usual observed structureThe proble1525of which argument of (dFo2 - dBc2)* is appropriate is, ingeneral, solved by assuming t h a t F, and F, have the samephase. However, when thevalence-electron contribution t o the scattering is dominant(IFdl > lF,I), the phase of F, and hence the sign of theappropriate argument of (dFo2 - dBc2)’, is the same as thephase of Fd.After a n initial refinement of the valence-electron model using all F d values derived assumingIFc/ > IFd\, the calculated values of the ‘ difference structurefactors ’ from the preliminary model were examined inrelation with the Fd, F,, and Fo values, and 13 reflectionswere found for which the assumption t h a t F, and F, havethe same phase was obviously incorrect.The F d values forthese cases were correctly determined, using the argument of(dFo2 - dBc2)’ of opposite sign t o the phase of F,, andincluded in subsequent refinements.If - dBC2)fl < ldAcl, the sign of the argument I (dFo2 - dBc2) ‘1 is indeterminate, but any errors arising fromthe assignment of the phase of F, t o the argument wouldprobably be insignificant in the least-squares refinementmethod, especially considering t h a t this case only arises forthe weakest reflections where there are large experimentaluncertainties in ldFol. No examples of this type werepresent, except for a few cases where, due t o experimentalerror, (dFo2 - d B c 2 ) < 0; the best approximation here is t oset dFo2 - dBC2 = 0.The refinement (Table 3) excludingall examples of this type, as well as all observations withIFo] < 5.0 (absolute units), yielded identical orbitalpopulations t o the refinement including all data.This is so for lFcl > I F d l .G. A. W. thanks the Australian Institute of NuclearScience and Engineering for a Research Fellowship.E. S. K. acknowledges receipt of a Commonwealth Post-graduate Research Award. We are grateful t o Drs. E. N.Maslen and P. A. Reynolds for stimulating discussions.[9/1228 Received, 3rd August, 1979REFERENCESR. Mason, G. A. Williams, and P. E. Fielding, J.C.S. Dalton,2 B.N. Figgis, R. Mason, and G. A. Williams, Acta Cryst.,G. A. Williams, B. N. Figgis, R. Mason, S. A. Mason, andB. N. Figgis, R. Mason, A. R. P. Smith, and G. A. Williams,1979, 676.1978, A34, S158.P. E. Fielding, J.C.S. Dalton, 1980, 1688.J . Amer. Chern. Soc., 1979, 101, 3673.M. Iwataand Y . Saito, Acta Cryst., 1973, B29,822; Y . Wangand P. Coppens, Inorg. Chem., 1976, 15, 1122; B. Rees and A.Mitschler, J. Amer. Chem. SOC., 1976, 98, 7918; M. Iwata, ActaCryst., 1977, Ba, 59; A. Mitschler. B. Rees, and M. S. Lehmann,J. Amer. Chem. SOC., 1978, 100, 3390; K. Toriumi, M. Ozinia, M.Akaogi, and Y . Saito, Acta Cryst., 1978, BS4, 1093; K. Toriumiand Y. Saito, ibid., p. 3149; S . Ohba, K. Toriumi, S. Sato, and Y .Saito, ibid., p. 3535; J. N. Varghese and E. N. Maslen, personalcommunication; R. Goddard and C. Kriiger, personal com-munication.6 P. Coppens, in ‘Neutron Diffraction,’ ed. H. Dachs,Springer-Verlag, Berlin, 1978, p. 71.‘ lnternational Tables for X-Ray Crystallography,’ KynochPress, Birmingham, 1962, vol. 3, p. 162.J. M. Stewart, ‘ The X-Ray System,’ Version of March 1976,Technical Report TR-446, the Computer Science Centre, Uni-versity of Maryland.0 F. L. Hirshfeld and D. Rabinovich, Acta Cryst., 1973, A%,510.D. T. Cromerand J. B. Mann, ActaCryst., 1968, A24, 321.l1 D. T. Cromer and D. Liberman, J . Chem. Phys., 1970, 53,12 R. F. Stewart, E. R. Davidson, and W. T. Simpson, J . Chem.‘ International Tables for X-Ray Crystallography,’ Kynochl4 R. J. Weiss and A. J. Freeman, J. Phys. Chem. Solids, 1959,l6 R. E. Watson and A. J. Freeman, Acta Cryst., 1961, 14, 27.E. Clementi and C. Roetti, Atomic Data and Nuclear Datal7 R. McWeeney, Acta Cryst., 1951, 4, 513; B. Dawson, ibid.,A. M. O’Connell, A. I. M. Rae, and E. N. Maslen, Acta Cryst.,J. Avery and K. J. Watson, Acta Cryst., 1977, ASS, 679.2o N. K. Hansen and P. Coppens, Acta Cryst., 1978, A34, 909.21 E. Hellner, Acta Cryst., 1977, BSS, 3813; D. Mullen and E.S. F. A. Kettle, ‘ Co-ordination Compounds,’ Nelson, London,23 D. W. ClackandM. Monshi. Inorg. Chim. Acta, 1977,22, 261.24 H. Kashiwagi, T. Takada, S. Obara, E. Miyoshi, and K.25 E. Konig and R. Schnakig, Inorg. Chim. Acta, 1973, 7, 383.26 E. Konig and R. Schnakig, Theor. Chim. Acta, 1973, 30, 205.27 G. M. Harris, Theor. Chim. Acta, 1968, 10, 119.28 E. Konig and S. Kremer, Ligand Field Energy Diagrams,’Plenum Press, New York, 1977.R. J. Ford and M. A. Hitchman, Inorg. Chim. Acta, 1979, 83,L167, and refs. therein.30 C. G. Barraclough, R. L. Martin, S. Mitra, and R. C. Sher-wood, J . Chem. Phys., 1970, 53, 1638.31 C. G. Barraclough, A. K. Gregson, and S. Mitra, J . Chem.Phys., 1974, 60, 962.32 E. J. Gabe, in ‘ Crystallographic Computing Techniques,’ed. F. R. Ahmed, Munksgaard, Copenhagen, 1975, p. 473.1891.Phys., 1965, 42, 3175.Press, Birmingham, 1974. vol. 4, pp. 103-146.10, 147.Tables, 1974, 14, 177.1964, 17, 990, 997.1966, 21, 208.Hellner, ibid., 1978, BS4, 2789.1969.Ohno, Internat. J . Quantum Chem., 1978, 14, 13

ISSN:1477-9226    

DOI:10.1039/DT9800001515

出版商:RSC    

年代:1980

数据来源: RSC