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An algorithm for determining the element-selective charge density has been developed using the maximum entropy method (MEM), Rietveld analysis and synchrotron X-ray multi-wavelength anomalous powder diffraction data. This article describes in detail both experimental and analytical aspects of the developed method. A structural study of yttrium mono-metallofullerene, Y@C82, 1:1 co-crystallized with toluene using the present technique is reported in order to demonstrate the applicability of the method even when only medium resolution data are available (d > 1.32 Å). Element-selective MEM charge density maps, computed from synchrotron X-ray powder diffraction data collected at three distinct wavelengths around the yttrium K-absorption edge (∼0.727 A), are employed for determining three crystallographic sites of the disordered yttrium.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S002188981300592X/he5595sup1.cif
Contains datablocks global, I, yttrium_mono_metallofullerere_data1, yttrium_mono_metallofullerere_data2, yttrium_mono_metallofullerere_data3

Computing details top

Cell refinement: SP (Nishibori et al., 2007); program(s) used to solve structure: GAIA (Nishibori et al., 2007); program(s) used to refine structure: SP (Nishibori et al., 2007); molecular graphics: pyMOL (DeLano, 2002).

Endohedral metallofullerene top
Crystal data top
YC82·C7H8Z = 1
Mr = 4663.79F(000) = 2324
Orthorhombic, Cmc21Dx = 1.063 Mg m3
Hall symbol: C 2c -2Synchrotron radiation, λ = 0.73330 Å
a = 11.22205 (6) ŵ = 0.33 mm1
b = 34.8174 (2) ÅT = 300 K
c = 11.22569 (7) Åblack
V = 4386.13 (7) Å3cylinder, 3 × 0.4 mm
Data collection top
Large Debye-Scherrer camera
diffractometer
Data collection mode: transmission
Radiation source: synchrotron, SPring-8 BL02B2Scan method: step
Si(111) monochromator2θmin = 3.00°, 2θmax = 32.50°, 2θstep = 0.010°
Specimen mounting: capillary
Refinement top
Refinement on InetProfile function: pseudo-Voigt
Least-squares matrix: full272 parameters
Rp = 0.044348 restraints
Rwp = 0.0150 constraints
Rexp = ?H atoms treated by a mixture of independent and constrained refinement
χ2 = ?Weighting scheme based on measured s.u.'s
7508 data points
Excluded region(s): noneBackground function: split Pearson VII
Crystal data top
YC82·C7H8V = 4386.13 (7) Å3
Mr = 4663.79Z = 1
Orthorhombic, Cmc21Synchrotron radiation, λ = 0.73330 Å
a = 11.22205 (6) ŵ = 0.33 mm1
b = 34.8174 (2) ÅT = 300 K
c = 11.22569 (7) Åcylinder, 3 × 0.4 mm
Data collection top
Large Debye-Scherrer camera
diffractometer
Scan method: step
Specimen mounting: capillary2θmin = 3.00°, 2θmax = 32.50°, 2θstep = 0.010°
Data collection mode: transmission
Refinement top
Rp = 0.0447508 data points
Rwp = 0.015272 parameters
Rexp = ?348 restraints
χ2 = ?H atoms treated by a mixture of independent and constrained refinement
Special details top

Refinement. Rigid-body refinement. The carbon atoms on fullerene molecules and encapsulated Y have rotational displacement,they are approximated by mixuture of a spherical shell model and atoms for reduction of parameters·A center of spherical shell are listed as YSP, CSP. The maximum deviations of carbon bond distances and bond angles from theoretically predicted hollow C82 are less than 0.03 A and 0.2 degree in the restraint Rietveld refinement.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
CSP0.000000.13787 (3)0.2545 (12)0.0189*
YSP0.000000.1118 (8)0.43053 (3)0.0669*0.82092
Y10.115590.104 (4)0.3698 (7)0.31340.04477
Y20.115590.1316 (8)0.4088 (7)0.31340.04477
C10.2211 (3)0.16117 (8)0.0436 (2)0.23770.50000
C20.2182 (3)0.19620 (8)0.0059 (2)0.23640.50000
C30.2171 (2)0.04280 (6)0.2450 (2)0.22630.50000
C40.2155 (3)0.20464 (6)0.4739 (3)0.23000.50000
C50.2124 (1)0.04996 (6)0.3675 (2)0.22350.50000
C60.2132 (3)0.17079 (8)0.5373 (3)0.22740.50000
C70.2822 (2)0.08112 (8)0.4112 (2)0.22660.50000
C80.2825 (2)0.14064 (13)0.4936 (2)0.22910.50000
C90.2225 (3)0.09648 (9)0.0195 (3)0.23530.50000
C100.2180 (2)0.23356 (8)0.1731 (2)0.23600.50000
C110.2214 (3)0.06558 (6)0.0547 (3)0.23330.50000
C120.2173 (2)0.23644 (8)0.2907 (2)0.23590.50000
C130.2806 (2)0.06710 (7)0.1665 (2)0.22690.50000
C140.2797 (2)0.20790 (7)0.3637 (2)0.23000.50000
C150.3358 (2)0.10248 (11)0.2081 (3)0.21680.50000
C160.3339 (2)0.17619 (12)0.3117 (3)0.21920.50000
C170.3424 (2)0.10709 (11)0.3294 (3)0.22280.50000
C180.3417 (2)0.14372 (14)0.3811 (3)0.22420.50000
C190.2444 (1)0.10157 (7)0.5102 (2)0.22990.50000
C200.2823 (2)0.13090 (11)0.0158 (3)0.23020.50000
C210.2799 (2)0.20274 (10)0.1177 (2)0.23050.50000
C220.3322 (2)0.13531 (12)0.1330 (3)0.21480.50000
C230.3310 (2)0.17248 (12)0.1847 (4)0.21560.50000
C240.1108 (3)0.02784 (6)0.1819 (2)0.23530.50000
C250.00000.02131 (5)0.24493 (7)0.23130.25000
C260.00000.02592 (4)0.37120 (8)0.23580.25000
C270.1034 (1)0.03971 (6)0.4313 (1)0.23630.50000
C280.1311 (1)0.09271 (5)0.5686 (2)0.23600.50000
C290.0650 (1)0.06056 (2)0.5285 (1)0.23850.50000
C300.0654 (1)0.12277 (2)0.6181 (1)0.24000.50000
C310.1074 (3)0.22903 (7)0.4669 (2)0.17170.50000
C320.00000.21867 (12)0.5224 (2)0.16930.25000
C330.00000.18512 (6)0.5968 (13)0.17220.25000
C340.1106 (3)0.04255 (7)0.0681 (2)0.17050.50000
C350.1070 (2)0.24795 (8)0.3527 (2)0.17230.50000
C360.00000.05260 (4)0.0086 (1)0.16690.25000
C370.00000.25428 (13)0.2902 (2)0.16770.25000
C380.1048 (1)0.16142 (7)0.6050 (3)0.17250.50000
C390.1129 (3)0.10678 (7)0.0880 (2)0.17370.50000
C400.1075 (2)0.24190 (8)0.1044 (2)0.17210.50000
C410.00000.08540 (3)0.0711 (1)0.16810.25000
C420.00000.25148 (5)0.1621 (1)0.16760.25000
C430.1127 (3)0.14593 (7)0.1036 (2)0.17560.50000
C440.1079 (2)0.21831 (12)0.0030 (2)0.17130.50000
C450.00000.16767 (2)0.1034 (3)0.16950.25000
C460.00000.2068 (3)0.0513 (6)0.16790.25000
C520.500000.071 (5)0.862 (9)0.1512*0.60000
C530.500000.033 (4)0.868 (9)0.1512*0.60000
C540.500000.0106 (4)0.762 (10)0.1512*
C550.500000.028 (4)0.653 (10)0.1512*0.60000
C560.500000.066 (5)0.647 (9)0.1512*0.60000
C570.500000.0885 (5)0.754 (15)0.1512*
C580.500000.1281 (4)0.747 (6)0.1512*
H90.500000.088 (5)0.945 (9)0.1512*0.60000
H100.500000.019 (4)0.957 (9)0.1512*0.60000
H110.500000.0214 (4)0.768 (10)0.1512*
H120.500000.011 (4)0.570 (10)0.1512*0.60000
H130.500000.081 (5)0.558 (9)0.1512*0.60000
H140.42 (1)0.1394 (4)0.791 (6)0.1512*0.30000
H150.500000.1369 (4)0.654 (6)0.1512*0.60000
H160.58 (1)0.1394 (4)0.791 (6)0.1512*0.30000
C670.392 (4)0.0685 (12)0.76 (2)0.1512*0.40000
C680.392 (4)0.0306 (12)0.758 (14)0.1512*0.40000
H240.306 (4)0.0845 (12)0.75 (2)0.1512*0.40000
H250.306 (4)0.0146 (12)0.761 (14)0.1512*0.40000
H290.45 (1)0.1371 (4)0.666 (6)0.1512*0.20000
H300.59 (1)0.1385 (4)0.745 (6)0.1512*0.20000
H310.45 (1)0.1400 (4)0.825 (6)0.1512*0.20000
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Y10.30830.32330.30860.07350.08120.0734
Y20.30830.38740.24460.01370.10870.0183
C10.23410.32200.15710.03200.13130.0428
C20.23450.26680.20790.07820.10850.0883
C30.22120.14260.31520.12760.00390.0053
C40.22680.23700.22610.08880.09440.0891
C50.22050.16300.28700.11580.04670.0597
C60.22540.29700.15990.04280.11990.0561
C70.15660.25420.26920.09910.08620.0536
C80.16170.31930.20630.00550.13370.0046
C90.23100.29560.17920.05700.12090.0705
C100.23520.15620.31670.12830.03530.0479
C110.22840.22590.24550.09860.08840.0895
C120.23520.14540.32720.13200.01550.0216
C130.15920.22080.30070.12240.04930.0384
C140.16400.22870.29730.12020.06080.0466
C150.07620.27740.29670.07290.03120.0101
C160.08170.27750.29830.07770.03750.0131
C170.07620.29210.30020.06490.04820.0134
C180.07910.31140.28210.01340.08380.0048
C190.20220.29640.19110.05360.12390.0561
C200.16210.32040.20820.01140.13410.0096
C210.16470.24290.28370.11100.07700.0545
C220.07800.29790.26840.00440.08070.0016
C230.08060.27710.28910.06950.04720.0150
C240.30150.08900.31540.07620.01610.0501
C250.32000.05400.31980.00000.00000.0072
C260.32680.08140.29930.00000.00000.0822
C270.30620.13810.26460.06350.03660.1092
C280.29250.28840.12700.03650.08310.0879
C290.32250.21430.17860.03090.03540.1331
C300.32410.32860.06720.00630.04860.0343
C310.21660.12580.17270.04080.03050.0796
C320.22860.14580.13350.00000.00000.0888
C330.23300.20500.07870.00000.00000.0657
C340.21450.11310.18400.04330.02720.0738
C350.21770.07900.22020.04870.01410.0445
C360.22500.13100.14470.00000.00000.0869
C370.22620.05250.22450.00000.00000.0176
C380.21870.22660.07210.00990.04860.0330
C390.21850.22250.08000.01450.05080.0443
C400.21750.09580.20300.04580.02130.0639
C410.22670.19130.08620.00000.00000.0706
C420.22610.06210.21470.00000.00000.0432
C430.22140.23720.06810.00360.05310.0115
C440.21630.14970.14800.03550.03580.0828
C450.22890.21800.06170.00000.00000.0429
C460.22650.17030.10690.00000.00000.0820
Geometric parameters (Å, º) top
C1—C201.4237C29—C29i1.4589
C1—C431.4883C30—C30i1.4678
C1—C21.3407C30—C381.4241
C2—C441.4580C31—C321.4039
C2—C211.4513C31—C351.4413
C3—C241.4819C32—C331.4360
C3—C131.4143C33—C381.4396
C3—C51.3986C33—C38i1.4396
C4—C311.4829C34—C361.4523
C4—C61.3770C35—C371.4081
C4—C141.4361C36—C411.4507
C5—C71.4252C37—C421.4413
C5—C271.4617C39—C411.4817
C6—C381.4710C39—C431.3743
C6—C81.3955C40—C441.4037
C7—C191.3864C40—C421.4093
C7—C171.4551C43—C451.4739
C8—C181.4310C44—C461.4136
C8—C191.4381C45—C461.4826
C9—C391.4942C52—C531.3248
C9—C201.4295C52—C571.3569
C9—C111.3607C53—C541.4227
C10—C211.4215C54—C551.3654
C10—C121.3240C54—C681.3985
C10—C401.4889C54—C68ii1.3985
C11—C131.4210C55—C561.3248
C11—C341.4872C56—C571.4340
C12—C141.4661C57—C581.3810
C12—C351.4755C57—C671.3994
C13—C151.4558C57—C67ii1.3994
C14—C161.3891C67—C681.3198
C15—C221.4209C52—H91.1000
C15—C171.3731C53—H101.1100
C16—C181.3757C54—H111.1200
C16—C231.4319C55—H121.1100
C17—C181.4012C56—H131.1300
C19—C281.4634C58—H151.0900
C20—C221.4381C58—H141.1000
C21—C231.4158C58—H161.1000
C22—C231.4184C58—H291.1100
C24—C341.3763C58—H301.0700
C24—C251.4486C58—H311.1200
C25—C261.4265C58—H29ii1.1100
C26—C271.4255C58—H30ii1.0700
C26—C27i1.4255C58—H31ii1.1200
C27—C291.3796C67—H241.1200
C28—C291.4163C68—H251.1100
C28—C301.3956
C2—C1—C20119.41C19—C28—C30118.64
C2—C1—C43119.48C29—C28—C30116.27
C20—C1—C43110.02C27—C29—C28120.24
C1—C2—C21119.31C27—C29—C29i108.20
C1—C2—C44119.45C28—C29—C29i121.58
C21—C2—C44109.97C28—C30—C38120.23
C5—C3—C13121.67C28—C30—C30i121.89
C5—C3—C24120.15C30i—C30—C38108.09
C13—C3—C24108.54C4—C31—C35108.14
C6—C4—C14121.48C11—C34—C24107.05
C6—C4—C31120.14C12—C35—C31107.03
C14—C4—C31108.63C6—C38—C30121.31
C3—C5—C7116.96C9—C39—C43107.76
C3—C5—C27118.02C10—C40—C44107.65
C7—C5—C27118.50C1—C43—C39107.13
C4—C6—C8116.85C2—C44—C40107.07
C4—C6—C38118.19C53—C52—C57119.60
C8—C6—C38118.40C52—C53—C54120.33
C5—C7—C17120.73C53—C54—C55120.42
C5—C7—C19119.91C68—C54—C68ii120.14
C17—C7—C19109.20C54—C55—C56119.25
C6—C8—C18120.84C55—C56—C57120.20
C6—C8—C19120.02C52—C57—C56120.20
C18—C8—C19108.86C52—C57—C58119.94
C11—C9—C20119.83C56—C57—C58119.85
C11—C9—C39119.82C58—C57—C67119.97
C20—C9—C39109.14C58—C57—C67ii119.97
C12—C10—C21119.75C67—C57—C67ii120.01
C12—C10—C40119.79C57—C67—C68119.78
C21—C10—C40109.12C54—C68—C67119.82
C9—C11—C13120.46C53—C52—H9120.00
C9—C11—C34119.72C57—C52—H9121.00
C13—C11—C34108.76C52—C53—H10119.00
C10—C12—C14120.21C54—C53—H10121.00
C10—C12—C35119.73C53—C54—H11120.00
C14—C12—C35108.73C55—C54—H11120.00
C3—C13—C11107.01C68—C54—H11120.00
C3—C13—C15121.38C68ii—C54—H11120.00
C11—C13—C15120.92C54—C55—H12121.00
C4—C14—C12107.18C56—C55—H12120.00
C4—C14—C16121.25C55—C56—H13121.00
C12—C14—C16120.86C57—C56—H13119.00
C13—C15—C17116.10C57—C58—H15110.00
C13—C15—C22118.57C57—C58—H14109.00
C17—C15—C22119.73C57—C58—H16109.00
C14—C16—C18116.30C57—C58—H29109.00
C14—C16—C23118.69C57—C58—H30110.00
C18—C16—C23119.42C57—C58—H31109.00
C7—C17—C15121.88C57—C58—H29ii109.00
C7—C17—C18107.55C57—C58—H30ii110.00
C15—C17—C18121.12C57—C58—H31ii109.00
C8—C18—C16122.13H14—C58—H16110.00
C8—C18—C17107.45H29—C58—H30111.00
C16—C18—C17120.91H29—C58—H31106.00
C7—C19—C8106.92H29—C58—H29ii61.00
C7—C19—C28121.11H29—C58—H30ii54.00
C8—C19—C28121.05H29—C58—H31ii142.00
C1—C20—C9105.32H30—C58—H31111.00
C1—C20—C22122.50H29ii—C58—H3054.00
C9—C20—C22121.73H30—C58—H30ii140.00
C2—C21—C10105.28H30—C58—H31ii55.00
C2—C21—C23122.40H29ii—C58—H31142.00
C10—C21—C23121.82H30ii—C58—H3155.00
C15—C22—C20117.90H31—C58—H31ii60.00
C15—C22—C23119.44H29ii—C58—H30ii111.00
C20—C22—C23117.91H29ii—C58—H31ii106.00
C16—C23—C21118.10H30ii—C58—H31ii111.00
C16—C23—C22119.31C57—C67—H24120.00
C21—C23—C22117.74C68—C67—H24120.00
C3—C24—C34108.31C54—C68—H25120.00
C5—C27—C29121.36C67—C68—H25120.00
C19—C28—C29118.64
Symmetry codes: (i) x, y, z; (ii) x+1, y, z.

Experimental details

Crystal data
Chemical formulaYC82·C7H8
Mr4663.79
Crystal system, space groupOrthorhombic, Cmc21
Temperature (K)300
a, b, c (Å)11.22205 (6), 34.8174 (2), 11.22569 (7)
V3)4386.13 (7)
Z1
Radiation typeSynchrotron, λ = 0.73330 Å
µ (mm1)0.33
Specimen shape, size (mm)Cylinder, 3 × 0.4
Data collection
DiffractometerLarge Debye-Scherrer camera
diffractometer
Specimen mountingCapillary
Data collection modeTransmission
Scan methodStep
2θ values (°)2θmin = 3.00 2θmax = 32.50 2θstep = 0.010
Refinement
R factors and goodness of fitRp = 0.044, Rwp = 0.015, Rexp = ?, χ2 = ?
No. of data points7508
No. of parameters272
No. of restraints348
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement

Computer programs: SP (Nishibori et al., 2007), GAIA (Nishibori et al., 2007), pyMOL (DeLano, 2002).

 

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