Neutron diffraction structures of water in crystalline

research papers Neutron diffraction structures of water in crystalline hydrates of metal salts ISSN 2052-5206

Graham S. Chandler,a* Magdalena Wajraka‡ and R. Nazim Khanb

Received 22 January 2015 Accepted 16 March 2015

Edited by S. Parsons, University of Edinburgh, Scotland ‡ Present address: School of Natural Sciences, Edith Cowan University, 270 Joondalup Drive, Joondalup 6027, Australia. Keywords: neutron diffraction; metal salts; hydrates; water structures. Supporting information: this article has supporting information at journals.iucr.org/b

a School of Chemistry and Biochemistry, The University of Western Australia, 35 Stirling Highway, Crawley 6009, Australia, and bSchool of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley 6009, Australia. *Correspondence e-mail: [email protected]

Neutron diffraction structures of water molecules in crystalline hydrates of metal salts have been collected from the literature up to December 2011. Statistical methods were used to investigate the influence on the water structures of the position and nature of hydrogen bond acceptors and cations coordinated to the water oxygen. For statistical modelling the data were pruned so that only structures with oxygen as hydrogen acceptors, single hydrogen bonds, and no more than two metals or hydrogens coordinated to the water oxygen were included. Multiple linear regression models were fitted with the water OH bond length and bond angle as response variables. Other variables describing the position and nature of the acceptors and ions coordinated to the waters were taken as explanatory variables. These variables were sufficient to give good models for the bond lengths and angles. There were sufficient structures involving coordinated Mg2þ or Cu2þ for a separate statistical modelling to be done for these cases.

1. Introduction

# 2015 International Union of Crystallography

Acta Cryst. (2015). B71, 275–284

Considerable variation in the geometry of water was reported by Chiari & Ferraris (1982) in their survey of the structures of crystalline hydrates obtained from neutron diffraction. Chiari & Ferraris (1982) used simple regression models, fitting one explanatory variable at a time, to discern relationships between the water environment and the water structure. Using the hypothesis that the geometry of a water molecule in a hydrate is determined by interactions with near neighbours, we have examined whether statistical methods can identify relationships between the near neighbour positions and the shape of water molecules. In the present paper multiple linear regression models were used to examine these relationships. The study has been restricted to hydrates of metal salts in order to limit the size of the data set, to limit the complexity of the statistical analysis and because we are particularly interested in the influence of the metal. As far as we are aware, the only studies examining the dependence of the geometry of water on its environment in hydrated metal salts are those of Ferraris & Franchini-Angela (1972), Chiari & Ferraris (1982) and that of Ferraris et al. ˚ with W (1986) that studied examples where W O 2.66 A being a water molecule oxygen. Unlike the present study these earlier works included a small number of non-salts. The structures used in the paper of Chiari & Ferraris (1982) excluded any structures showing disorder, symmetry ambiguities, uncertainties about the hydrogen-bonding scheme, gross inaccuracy or other flaws. Using these same criteria we have added to the Chiari & Ferraris (1982) data by including neutron structures from the literature up to December 2011. http://dx.doi.org/10.1107/S2052520615005387

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research papers Table 1 List of the compounds reviewed (reference abbreviations are in the code below).

42

1209 231 925 101 175 1883 19 2290 1699 172 21 5508 928 361 319 290 318 170 310 2737 46 141 349 209 3725 1064 249 165 707 1499 801 2803 1804 51 1895 179 419 383 1721 2179 395 395 1350

Ag4Ge7O166D2O Al(IO3)32HIO36H2O Al(NO3)39D2O Al2(C6COO)616H2O BaBr22H2O Ba(ClO3)2H2O BaCl2D2O BaCl22H2O BaC2O4H2C2O42H2O BaC4O43H2O BaC6(C6H5)2O44H2O Ba(NO2)2H2O Ba(OD)Cl2D2O Ba(OH)23H2O Ba(OH)2H2O Ba(OH)I4H2O Be[C2(COO)2]4H2O Be(IO3)24H2O BeSO44H2O Ca(C3H2O4)2H2O Ca[C6(C2H5)2O4]3H2O CaCl26H2O CaHAsO42H2O CaHAsO4H2O CaHPO42H2O Ca(IO3)2D2O Ca(IO3)26H2O CaSO412H2O CaSO42H2O Ca2KH7(PO4)42H2O Cd(C5H7NO4)2H2O Cd(C6H8N3O2)22H2O Cd(NO3)24D2O Co(IO3)24H2O Co(NH4)2(BeF4)26H2O CoSO46D2O Cr(ND4)2(SO4)26D2O CsAl(SO4)212H2O CsCr(SO4)212H2O CsFeCl32D2O CsFe(SeO4)212H2O CsFe(SO4)212H2O CsGa(SO4)212D2O

75 73 83 98 66 76 75 78 76 70 87 74 74 80 72 77 75 70 84 70 75 72 95 75 75 88 77 96 85 82 74 80 82 02 84 87 85 83 94 86 95 84 64

ZEKGA ACBCA SPCRA JACSA JCPSA ACSAA ZEKGA ACBCA ZEKGA CJPSA ACBCA ACBCA ACBCA ACBCA ACAPC ACBCA INOCA ACBCA ACCCA ACBCA CSCMC CSCMC ACBCA CSCMC CSCMC ACBCA ACBCA JSSCB JCPSA ACBCA FEREL ACBCA ACBCA JPCMA JCPSA ACBCA ACCCA TMPMA ZENBA ACBCA MRBUA ACBCA ACCRA

141 29 28 120 44 30 142 34 144 48 43 30 30 36 26 33 14 26 40 26 4 1 51 4 4 44 33 126 82 38 6 36 38 14 80 43 41 32 49b 42 30 40 17

330 2393 393 8715 2230 735 129 1408 1 1091 517 1421 1421 2869 1358 3155 2653 77 1803 827 709 185 43 713 717 228 3933 184 5636 15 191 1032 2555 4045 423 523 8 187 1334 253 1235 584 863

CuSO45D2O Cu2(CH3CO2)42H2O Cu3(ZrF7)216H2O Fe(ND4)2(SO4)26D2O Fe3(PO4)24H2O HgCl22KClH2O HgCrO412H2O HgSeO4H2O Hg3(OH)2(SO4)2H2O K(B5O10H4)2H2O KCa4(Si8O20)F8H2O -KC6H11O7H2O -KC6H11O7H2O KI3H2O KMnCl32H2O KNa[Pt(CN)4]3H2O KPtCl3(C2H4)H2O K2C2O4H2O K2[CO(NCS)4]2CH3NO2H2O K2CuCl42H2O K2Cu(SeO4)26H2O K2Cu(SO4)26H2O K2[FeCl5(H2O)] K2Ni(SO4)26H2O K2Zn(SO4)26H2O K5[H(ON(SO3)2)2]H2O La2Mg3(NO3)1224H2O LiCd3COO2D2O LiC8H5O4H2O LiClO43H2O LiHCOOH2O LiNO33H2O LiOHH2O LiTlC4H4O6H2O Li2SO4H2O Mg(C4H3O4)26H2O MgCl26H2O MgHPO43H2O Mg(IO3)24H2O MgNH4PO46H2O Mg(NO3)26H2O MgSO36H2O MgSO44H2O

78 75 75 00 71 85 71 87 77 77 82 78 74 82 79 77 80 71 72 78 93 86 92 89 00 78 04 72 95 93 77 88 93 93 86 01 88 85 88 66 96 72 72

ACBCA ACBCA DANKA ACCCA ACBCA ACCCA ACBCA ACCCA ACBCA ACBCA ICHAA ACBCA ZSKSS ACBCA ACBCA DANKA ACBCA JCPSA PHYSA CSCMC ACBCA AJCMA ACBCA ACCCA CRTNA PRVBA INOCA CSCMC JPCMA CMMTA BCSJA ZAACA ZEKGA ACCCA ACCCA JSSCB ZAACA JCPSA ZEKGA ACBCA JSSCB CSCMC INOCA

34 31 224 56 27 41 27 43 33 33 57 34 15 38 35 236 36 54 57 7 49 39 48 45 35 18 43 1 7 5 50 566 208 49 42 157 566 83 183 20 125 1 11

3502 890 580 1289 354 638 2269 1015 1976 558 237 1975 712 401 19 393 1387 3990 215 127 192 1023 166 26 501 2179 8049 367 4725 1631 3167 49 19 944 141 283 49 2426 319 842 261 371 1840

42 18 46 18 42 42 33 1 26 56 152 115 42 52

1350 2711 1337 2711 1350 1350 1293 189 220 4352 161 11304 8524 2121

CsMn(SO4)212D2O CsMo(SO4)212D2O CsRh(SO4)212H2O CsRu(SO4)212D2O CsTi(SO4)212D2O CsV(SO4)212D2O Cs2[Pt(CN)4]H2O Cs2Cu(SO4)26H2O CuCl22H2O CuF22H2O Cu(HC8O4)22H2O Cu(ND4)2(SO4)26D2O Cu(ND4)2(SO4)26D2O CuSiF64D2O

73 82 71 87 67 79 74 84 84 76 78 82 84

JCDTB ACBCA ACBCA JSSCB ACCRA ACBCA AASTO ACCCA ACCCA ACBCA SPCRA ACBCA ACCCA

38 27 66 22 35 108 40 40 32 23 38 40

816 1799 66 242 182 1679 507 1521 1800 987 343 2671 1658

MgSO47H2O MgS2O36H2O MnCl24H2O MnFeF5(H2O)2 NaAl(SO4)212H2O NaBr2H2O NaH2AsO4H2O NaH[C4H2O4]3H2O NaHC2O4H2O NaH2PO42H2O NaNH4SeO42H2O Na[S2CN(CH2)4]2H2O Na2Al2Si3O102H2O

77 78 71 84 88 89 79 92 88 77 79 73 96

ACBCA ACBCA INOCA JACSA AJCMA EJSIC ACBCA ACCCA JSSCB KOKSA SPCRA INUCA JSSCB

33 34 10 106 41 26 35 48 75 3 24 9 125

2997 88 323 5319 1289 419 2317 1192 15 1594 336 629 261

91 82 83 91 91 68 93 78 89 88 88 82 89 90 88 99 92 96 69 78 89 86 71 72 71 98 97 95 00 84 77 76 69 02 75 93 91 66 91 78 90 90 03

JPCSA ZEKGA ACCCA JSSCA ZEKGA JCPSA ZEKGA ACBCA ACCCA JSSCB JSSCB JCPSA ZENBA ACCCA ZEKGA ZEKGA JSSCB ZEKGA ACBCA ACBCA JSSCB ACCCA ACBCA ACBCA JCSIA ACCCA JMSTA JSSCB ZEKGA ACCCA ACBCA ACBCA ACBCA BPASC ACBCA ACBCA ACCCA ACCRA JCDTB PRVBA JCDTB JCDTB INOCA

52 159 39 92 197 48 208 34 45 73 74 76 44b 46 183 214 96 211 25 34 79 42 27 28

03 93 93 93 03 03 77 72 57 72 80 93 03 96

INOCA JCDTB AJCMA JCDTB INOCA INOCA ACBCA CSCMC JCPSA JCPSA ZEKGA JACSA INOCA ACCCA

54 416 117 215 40 33 32 25 50 31 49 47 21 18

Na2B4O5(OH)48H2O Na2CO3H2O Na2Cr2O72H2O Na2Fe(CN)5NO2D2O Na2HAsO47H2O Na2H2SiO44H2O Na2H2SiO45H2O Na2D2SiO47D2O Na2[Pt(CN)4]3H2O Na2[Pt(CN)4Br2]2H2O Na2S9H2O Na2S2O35H2O Na2Zn(SO4)24H2O Na3AsS48D2O Na3SbS49D2O NbN2H6OF5H2O [Ni(C5H9D2N2O)2D]ClD2O Ni(C5H11N2O)2HClH2O Ni(IO3)22D2O Ni(NH4)2(CrO4)26H2O NiSO46H2O Ni(SO4)2(ND4)26D2O Pb(ClO3)2H2O Pt(C5H5N)4Cl23H2O RbD2PO4D2O RbFeCl32D2O RbV(SO4)212H2O Rb2Cu(SO4)26H2O Rb2FeCl5D2O SbOReO42H2O SnCl22D2O SrBr2H2O SrCl2D2O SrCl22D2O SrCl26H2O Sr(DC2O4)12(C2D4)D2O SrI2H2O Sr(NO2)2H2O Sr(OH)2H2O Th(NO3)45H2O Ti(DPO4)2D2O Tl2Cu(SO4)26H2O [UO2(H2O)[CO(NH2)2]4(NO3)]NO3 UO2(NH2O)23H2O UO2(NH2O)24H2O UO2(NO3)22H2O V(H2O)6[H5O2](CF3SO3)4 V(ND4)2(SO4)26D2O VO(HPO4)2H2O Y(C2H5SO4)39H2O Zn(C4H3O4)24H2O ZnC4O44H2O ZnF24H2O Zn(HSeO3)22H2O Zn(NO3)22Hg(CN)27H2O Zr(DPO4)2D2O

Journal codes AASTO ACAPC ACBCA ACCCA ACCRA ACSAA AJCHA BCSJA BPASC CJPSA CMLTA CMMTA CRTNA CSCMC

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Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Nat. Acta Chem. Scand. Acta Cryst. B Acta Cryst. C Acta Cryst. Acta Chem. Scand. A Aust. J. Chem. Bull. Chem. Soc. Jap. Bull. Pol. Acad. Sc. Chem. Can. J. Phys. Chem. Lett. Chem. Mat. Cryst. Res. Technol. Cryst. Struct. Commun.

Graham S. Chandler et al.

DANKA EJSIC FEREL GEOCA ICHAA INOCA INUCA JACSA JCDTB JCPKB JCPSA JCSIA JINCA JMSTA

Crystalline hydrates of metal salts

Dokl. Akad. Nauk SSSR Eur. J. Solid State Inorg. Chem. Ferroelectrics Geochem. (USSR) Inorg. Chim. Acta Inorg. Chem. Inorg. Nucl. Chem. Lett. J. Amer. Chem. Soc. J. Chem. Soc. Dalton J. Chem. Soc. Perk. Trans. 2 J. Chem. Phys. J. Chem. Soc. A J. Inorg. Nucl. Chem. J. Mol. Struct.

JPCMA JCPSA JSSCB KPKSA MRBUA PHYSA PRVBA SPCRA TMPMA ZAACA ZEKGA ZENBA ZSKSS

J. Phys. Condensed Matter J. Phys. Chem. Solids J. Solid State Chem. Koord. Chem. Mater. Res. Bull. Physica (Utrecht) Phys. Rev. B Sov. Phys. Crystallogr. Tschermaks Min. Petr. Mitt. Z. Anorg. Allgem. Chem. Z. Kristallogr. Z. Naturforsch. Zh. Strukt. Khim.

Acta Cryst. (2015). B71, 275–284

research papers Prior to the comprehensive, but carefully pruned survey of Chiari & Ferraris (1982), there had been a number of reviews of X-ray and neutron structures of hydrates (Tovborg-Jensen, 1948a,b; Bernal, 1953; Chidambaram, 1962; Malenkov, 1962; Hamilton, 1962; Clark, 1963; Baur, 1965; Hamilton & Ibers, 1968; Falk & Knop, 1973; Olovsson & Jo¨nsson, 1976; Speakman, 1973, 1974, 1975, 1976, 1977, 1978). Since the Chiari & Ferraris (1982) paper, the only other survey of hydrates dealt with water molecules donating short hydrogen bonds (Ferraris et al., 1986), although Wells (1984) reviews hydrate structural patterns, and in his Introduction to Hydrogen Bonding, Jeffrey (1997) has a small section on water coordination in hydrates. The data for this paper are presented in the next section. x3 presents the statistical modelling of the relation between the geometry of water in these metal salts and variables describing the positions of the near neighbours of the water molecules. Further sections describe the characteristics of the hydrogen bonding to water H atoms, and of the cations or H atoms coordinated to the water oxygen.

completes a right handed coordinate system. The polar coordinates of the cations coordinated to water are located using the coordinate system shown in Fig. 2. The origin is at the water oxygen. The Z-axis is perpendicular to the plane of the water, the X-axis is the external bisector of the HOH angle and the Y-axis completes a right-handed system. Water is in the XY plane which is shown along with the XZ plane. All the data are available in the supporting information.

2. Data In this paper the selection criteria adopted by Chiari & Ferraris (1982) were used. Powder neutron data satisfying the criteria were included. All the compounds surveyed by Chiari & Ferraris (1982) are included here. A total of 169 hydrated metal complexes containing 393 unique water molecules are considered here with more accurate recent data replacing old data. The hydrated metal salts used in the present study are listed in Table 1 using the abbreviation reference scheme proposed by Brown et al. (1976). Only structures uncorrected for thermal motion were examined. The relevant bond lengths and angles were recalculated for each structure with CrystalExplorer (Wolff et al., 2010) or Molview (Cense, 1989). Input files1 to run CrystalExplorer on any of the compounds in Table 1 are available. The near neighbours to a water were taken to be the cations or hydrogen coordinated to the water oxygen and acceptors to the water H atoms. A hydrogen bond was identified as having an acceptor hydrogen distance less than the sum of the van der ˚ ; Baur, 1972) and the Waals radius of hydrogen (1.0 A acceptor. The largest van der Waals radii from either Bondi (1968) or Pauling (1960) were used. We have taken the coordination about water to be that described in the original papers, but if that was absent, cations were considered to be coordinated to water if their distance from oxygen was less than or approximately equal to the sum of the oxygen ionic radius and the cation radius. The angular coordinates and ’ used to describe the positions of proton acceptors as defined in Fig. 1 are relative to a Cartesian coordinate system with its origin at the donor hydrogen. Here the XY plane is the water plane with X along the OH direction and the Y-axis directed so that the other hydrogen of the water has a positive Y coordinate. The Z-axis 1

http://130.95.176.70/tonto/wiki/index.php/Metal_hydrate_CIFs.

Acta Cryst. (2015). B71, 275–284

Figure 1 Coordinate system for the proton acceptors. The axes used by Chiari & Ferraris (1982) are in brackets.

Figure 2 Coordinate system for cations. The axes used by Chiari & Ferraris (1982) are in brackets. Graham S. Chandler et al.


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research papers Table 2 The variables in the data (see Figs. 1 and 2 for details of the geometry). Variable

Description

OH HOH CchargeX

˚ ) (continuous) The O—H bond length (A The H—O—H angle ( ) (continuous) Cation charge (categorical) X = 1: cation charge = 1 X = 2: cation charge = 2 etc. ˚ ) (continuous) Cation—O distance (A ˚ ) (continuous) H—acceptor distance (A See Fig. 1 ( ) (continuous) See Fig. 1 ( ) (continuous) See Fig. 2 ( ) (continuous) See Fig. 2 ( ) (continuous) Location of acceptors (categorical). Takes values: Inside: both acceptors inside H—O—H angle; Outside: both acceptors outside the H—O—H angle; Neither: one on each side The number (1 or 2) of cations in the structure

CO HA ’ " Side

Ncations

3. Statistical analysis The R package (R Development Core Team, 2014) was used for statistical analysis. The data contain a total of 393 water molecules. Oxygen is the only acceptor with sufficient data to allow a good statistical investigation using multiple linear regression models. Accordingly, in order to remove the variability caused by different acceptor atoms, only water molecules with oxygen acceptors were considered. The modelling was further restricted to cases where each hydrogen has only one hydrogen bond and the number of cations coordinated to each water is limited to two or one. This leaves 263 molecules. Since there are two OH bonds per water, this gives a total of 526 data points for the analysis of the OH bond length. Variables used in modelling are described in Table 2. Two linear models (Fox, 1997) were fitted, one with the water oxygen hydrogen bond length (OH) and the other with the water bond angle (HOH) as a response variable. The other variables were taken as explanatory variables. Linear models are essentially multiple regression models which allow categorical variables such as ion type and charge to be included in the analysis. These models are linear in the coefficients, but admit non-linearity in the explanatory variables (Fox, 1997). The advantage of the linear models used in this study compared with fitting several simple regression models (that is, with only one explanatory variable at a time) is that the effect of each variable is estimated while simultaneously accounting for the effect of other variables. In addition, the interaction (or combined effect) between variables can also be investigated. Fitting several simple regression models can also suffer from Simpson’s paradox (Agresti, 2007; Fox, 1997), that is, the effect of a variable can be completely reversed when other variables are included in the model. This is particularly important when categorical variables are involved. Finally, the effect in a simple model may not be due to the variable in the model, but other ‘lurking’ variables not in the model, and this can be minimized if all these variables are included in the model simultaneously.

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We investigated how the response variables [OH bond length (OH) and bond angle (HOH)] depend on the cation charge (CchargeX), cation-to-oxygen distance (CO), H– acceptor distance (HA), , ’, , " (as defined in Figs. 1 and 2), and location of acceptors (that is, Side). When OH is a response variable HOH is an explanatory variable. CchargeX ˚ and and Side are categorical variables. All lengths are in A angles in . Final models were arrived at after removing all data for which the standardized residuals deviated by around three standard uncertainties or more and refitting the model to the data. The number of data points removed in each model are given in Tables 3 and 4, where the models are summarized. Statistical significance was taken at the 5% level. 3.1. Water molecules coordinated to a single cation

The initial models contained data for all water molecules coordinated to a single cation, giving a total of 292 data points. This was then restricted to cations with charge 2 or 3, then further to those with charge 2. Since there are sufficient examples involving coordination of water to Mg2+ or Cu2+ the models were further restricted to data involving either of these two ions, and finally to those with only Mg2+ or Cu2+. The results are shown in Tables 3 (OH bond length) and 4 (HOH angle). Below each table are listed two common goodness-offit measures for linear models – the residual standard error (RSE), the smaller the better, and the coefficient of determination (COD), r2 where 0 r2 1, and 100r2 is the percentage of variation explained, so the larger the better. 3.1.1. Models for OH bond length. Table 3 summarizes the results of fitting the OH bond length using all the variables of Table 2. Coefficients are given only for variables and interaction terms that show significance at the 5% level. Interpreting linear models needs care. As an example, consider the All model for OH bond length. Taking coefficients from Table 3 the model equation is OH ¼ 1:197 0:0001 " 0:11 HA 0:004 þ 0:002 HA: 0:018 CO þ 0:015 Ccharge2 þ 0:018 Ccharge3 þ 0:028 Ccharge6: ð1Þ The intercept has the usual statistical interpretation, that is, this is the OH bond length when all explanatory variables are zero. For the continuous variables, such as , a unit increase in results in a decrease (as indicated by the negative sign) of 0.004 in the mean OH bond length, assuming all the other variables are fixed. The variables HA and have a statistically significant interaction term, denoted by HA: . The term HA: indicates a multiplicative effect, and the product of the values of these variables is put in the equation. In the present case the interaction term indicates that as the product HA increases, the OH bond length also increases. The categorical variable CchargeX with five levels, since there are only cations with charge = +1, +2, +3, +4 and +6, takes the value of 1 if the cation charge is X. The interest here is in determining if there are any differences in the OH bond length at different values of charge. The comparison is with Ccharge1. Ccharge2, Ccharge3 and Ccharge6 appear in the model, indicating that Acta Cryst. (2015). B71, 275–284

research papers Table 3

Table 4

Oxygen–hydrogen bond length models for single cation structures with various levels of specialization.

HOH angle models for single cation structures with various levels of specialization.

Points Intercept " HA ’ HA: CO HOH Ccharge2 Ccharge3 Ccharge6 Outside RSE r2 Outliers Min Max Range Mean SD

All

Charge = 2, 3 Charge = 2 Mg, Cu Mg

Cu

292 1.197 0.0001 0.11 0.004 – 0.002 0.018 – 0.015 0.018 0.028 – 0.0130 0.61 6 0.878 1.019 0.141 0.972 0.021

276 1.365 – 0.131 0.005 – 0.003 0.017 0.001 – – – 0.005 0.0122 0.61 5 0.914 1.019 0.105 0.928 0.019

42 1.138 0.0004 0.099 – – – – – – – – – 0.0071 0.65 3 0.949 1.019 0.070 0.976 0.0117

210 1.401 – 0.119 0.004 – 0.002 0.024 0.002 – – – 0.006 0.0129 0.56 3 0.914 1.019 0.105 0.969 0.0195

92 1.094 0.0004 0.074 – – – – – – – – – 0.0131 0.52 2 0.914 1.019 0.105 0.968 0.0188

50 1.179 – 0.049 – 0.0001 – – – – – – 0.012 0.0139 0.52 2 0.914 0.992 0.078 0.961 0.0185

the mean OH bond length is larger when the cation charge is 2, 3 or 6 compared with when the charge is 1. Ccharge4 is absent since there are too few cations with charge = 4 to be significant in this model. From Table 3 it is clear from r2 and RSE that all models give a good fit to the water bond lengths. By far the most important variable is HA. One must be careful, because the variation in ˚ , whereas in a very few molecules the HA is only around 1 A variation in can be some tens of degrees, so this term can be comparable to the effect of HA. The variation of OH length with the distance to an acceptor is well established experimentally (Steiner, 1998; Chiari & Ferraris, 1982; Ferraris et al., 1986). The bond valence model of Brown (2002) would predict this effect from changes in HA or . In Brown’s model the bond strength of an acceptor decreases as the HA distance increases, thereby releasing bond strength to the hydrogen that is used in strengthening bonding to the oxygen resulting in a decrease of the OH bond length. In a like manner, since hydrogen bonds have their greatest strength when they are linear, if the hydrogen bond is bent then the bonding strength of an acceptor towards the hydrogen would be lowered. In the All model the variables CO and CchargeX are significant. Again the statistical model agrees with the bond valence model that predicts an increase in CO would give a decrease in OH because of the decrease in the cation to oxygen bond strength as the cation oxygen distance increases, leaving more bond strength on the oxygen to be used in the oxygen hydrogen bond thereby decreasing the OH length. The lengthening of the OH bond as the cation charge increases in the All model can also be understood within the bond valence model, since the bond strength of cations increases with charge. Consequently, a larger cation charge would lead to lengthening of the OH bond as observed and the coefficients nicely follow this since the coefficient for Ccharge3 is larger Acta Cryst. (2015). B71, 275–284

Points Intercept " CO Ccharge2 C1TypeMg Inside Outside Outside: ":CType RSE r2 Outliers Min Max Range Mean SD

All

Charge = 2,3

Charge = 2

Mg, Cu

Mg

Cu

146 115.91 0.08 2.87 – 1.48 – 0.75 1.56 – – 1.835 0.51 2 101.4 114.4 13.0 108.2 2.6

138 118.90 0.08 4.39 0.13 – – 0.77 1.76 0.13 – 1.677 0.59 3 101.4 114.4 13.0 108.2 2.6

105 119.27 0.08 4.60 – – – 0.95 2.07 – – 1.587 0.64 1 101.4 114.4 13.0 107.9 2.6

46 111.04 0.09 6.36 0.15 – 3.12 1.44 1.55 – 0.10 1.469 0.59 0 104.1 114.3 10.2 108.1 2.2

25 108.4 – – – – – – – – – – – 0 104.1 112.5 8.4 108.4 2.0

21 110.21 0.10 – – – – – 2.79 – – 0.88 0.88 0 104.9 114.3 9.4 107.8 2.4

than that for Ccharge2 and so on. This effect is not significant in the Charge = 2, 3 model. Previous authors have noted a negative exponential relationship between OH bond distances and hydrogen bond distances to oxygen as an acceptor. Only when the hydrogen ˚ do the observed bond distances become less than 1.6 A curves show non-linear behaviour (Yukhnevich, 2009; Steiner & Saenger, 1994; Alig et al., 1994). The data collected here ˚ with very have a minimum hydrogen bond distance of 1.52 A ˚ few data less than 1.6 A. Consequently, we do not see evidence of non-linear behaviour in plots of predicted OH distances versus observed OH distances, nor does the use of an exponential function of HA in the model give an improved fit. 3.1.2. Models for HOH angle. In modelling the water bond angle it was necessary to exclude any explanatory variables describing the positional parameters of individual acceptor atoms since there is one set per H atom in each water molecule. It was not possible to meaningfully include two different values of HA, or ’ into the analysis for a single water bond angle. Instead the collective disposition of the acceptors is included through the variable Side. The variation of the water bond angle (HOH) in solids is much less studied than the variation in bond length. Simple qualitative explanations of observed variations in the water bond angle such as exist for the changes in bond length have not been made. Further explanation of changes in the HOH angle resulting from the interaction of the environment with a water molecule in a crystal requires a theoretical examination of the interactions. Nevertheless, there are clear relations in the statistical models shown in Table 4. Table 4 shows that all models except for Mg give good fits to the data. The variable with the largest coefficients in Table 4 is CO, the cation oxygen distance, and would appear to be the most important determinant of the bond angle. However, variation in CO is only ˚ . By contrast " has small coefficients, but this angle around 1 A varies from 0 when there is trigonal coordination to around Graham S. Chandler et al.


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research papers 50 when there is tetrahedral coordination and where the contribution to the bond angle from " would be comparable to that from CO. The decrease in the water bond angle associated with an increase in " has been attributed by Hamilton & Ibers (1968) to an increase in p-character of the bonding orbitals on oxygen. A new variable, Side, becomes significant in models for the bond angle in water. It was never important in models for the water bond length. Side is a categorical variable depending on whether a projection of the acceptors to both water H atoms onto the water plane lies outside the water bond angle (Outside), inside the water bond angle (Inside) or has one acceptor lying inside the bond angle and one outside (Neither). It can be seen from Table 4 that all models for the HOH angle are strongly affected by Side. The table shows that compared with acceptors classified as Neither, those classified as Outside promote larger bond angles on average while those classified as Inside have smaller bond angles on average. This response can be understood as the tendency for hydrogen bonds to be linear. If both acceptors lie outside the water bond angle then the angle opens so that the hydrogen bonds can approach linearity. When both acceptors lie inside the water bond angle the angle closes. Because of variations in the data associated with different cation types having different characteristic values for CO and " and different modes of interaction of the cation with a water oxygen, it was expected that as the data sets were simplified to have only one cation type, fitting models to the data would be easier and yield better models. This is true for Cu which gives an excellent model having only two significant parameters even though the number of data points are barely sufficient to support the statistical analysis. Mg does not conform to this thinking. With Mg the analysis does not identify any significant variables and the fit is poor. The random scatter of data for Mg affects the fit of the Mg, Cu model by obviously lowering the agreement factors maintained by the Cu data. The type of data exhibited by the Mg compounds cannot be general because if they were, the satisfactory fits for the other models would not be attained. 3.2. Water molecules coordinated to two cations

Further modelling was carried out where the data were restricted to two cations coordinated to water (234 points). Since there are now two cation charges, their sum (TchargeX) was included in the model, where X is the sum of the charges. With two coordinating cations it no longer makes sense to include the geometrical variables ", and the distance CO, which were significant in the single cation cases, since there is one set of these variables for each cation. However, the angle between the two cations was considered and found to be unimportant. Variable selection leaves simple models that are best expressed as equations, which are OH ¼ 1:140 0:092 HA þ 0:008 Tcharge4 ðRSE ¼ 0:0149; r2 ¼ 0:458; Min ¼ 0:8880; Max ¼ 1:014Þ ð2Þ

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HOH ¼ 104:6 þ 1:68 Outside ðRSE ¼ 1:9670; r2 ¼ 0:2916; Min ¼ 99:9; max ¼ 111:8Þ: ð3Þ The model for the OH bond length after removing four outliers is not as good as those for the single cations, but is still satisfactory even though the variables connected with determining the position of cations are not used. Again the variable HA is the most important with shorter OH bond lengths as HA increases. When the total charge is +4 the OH bond length is longer. The model for the HOH angle is unsatisfactory. Only one variable was significant, and it is not sufficient to describe the behaviour of the bond angle. The inability to find a model for HOH without any variables describing the position of the cations is to be expected when the importance of the variable CO in the single cation models for HOH is considered. 3.3. Water molecules coordinated to one or two cations

The final model combined the data for one and two cations (524 points). We investigated if there were any differences between the single cation and two cation structures using the categorical variable Ncations2. Ncations2 becomes significant if structures having two cations coordinated to water have significantly different response variables compared with cases where only one cation is coordinated. The model equation for the OH bond length is OH ¼ 1:279 0:0008 HOH 0:128 HA 0:003 þ 0:002 HA : þ 0:003 Ncations2 þ 0:011 Tcharge2 þ 0:013 Tcharge3 þ 0:013 Tcharge4 þ 0:017 Tcharge6 ð4Þ ðRSE ¼ 0:0136; r2 ¼ 0:537Þ: The model for the OH bond length is almost as good as those for the single cations even though the variables connected with determining the position of cations are not used because this model includes data from water molecules that are coordinated to two cations, but, as shown by the single cation models, these variables are not important determinants of the OH bond length. The most important variable is still HA. The model for the HOH angles is very poor. It has no statistically significant variables and the RSE is very low, presumably because there are no variables accounting for the position of coordinating cations in the model and they were shown to be the dominating influence in single cation models of the water angle.

4. Graphical and tabular examination of the data 4.1. Classification of water molecules

Another way of examining the data is to use graphical representations to examine matters like the deviation of acceptors from linearity, or to use tabulation to reveal the average geometry of water molecules in a number of artificially devised classes. These methods give insights into the data that extend beyond the restriction on the linear modelActa Cryst. (2015). B71, 275–284

research papers

Figure 3 Distrution of for single acceptors.

ling to only having oxygen as an acceptor and show some further characteristics of the interactions of near neighbours with water molecules. 4.2. Graphical presentation

Most water molecules in the data have each hydrogen as a single hydrogen bond donor. In rare instances only one of the H atoms is a donor. The observations on hydrogen bonds refer to these two cases. The distribution of the angle , measuring the deviation from linearity of the hydrogen bonds, is shown in Fig. 3. In these inorganic crystals the majority of hydrogen bonds are not linear, the greatest frequency of being in the range 5–10 . The acceptors are spread around the OH direction with a large preference for ’ near 0 or 180 (Fig. 4). So the acceptors lie

predominantly near the plane of the water molecule. This is different from the distribution noted by Chiari & Ferraris (1982). This predominance is influenced by 36 of these acceptors being from -alums (Tregenna-Piggott et al., 2003, 2004). The contribution from these 36 acceptors is shaded in Fig. 4. For cations coordinated to the water oxygen there is a strong preference for them to be close to the XZ plane of Fig. 2, which is perpendicular to the water plane. Most cations then are close to being along either the lone pair direction or in the trigonal direction. For the case where there is only one coordinating cation, Fig. 5 is a plot of the frequency with which ions of different charge are found within a range of the angle " (see Fig. 2). The bars in Fig. 5 are shaded to distinguish the " distribution for formally +1, +2, +3, +4 and +6 charged ions. There are only three examples of singly charged ions being the only atom coordinated to water. These occur in LiC8H5O4H2O and K5H(ON(SO3)2)2H2O. Using the definition that " < 30 refers to trigonal bonding indicates these three singly charged ions are coordinated in a trigonal arrangement. The remaining coordinating atoms classed as having a +1 charge in Fig. 5 are actually hydrogen which has a preference for the lone-pair direction. Singly charged metal cations, however, prefer to be involved in structures with two singly charged ions coordinated to a water. Where a doubly charged cation is the only ion coordinated to a water, even though there is a clear maximum for " between 50 and 60 , there are a comparable number with " < 30 , so that there is no preference for these cations to have trigonal or lone pair coordination. However, where they are coordinated along the lone pair direction they much prefer to occupy a position near the ideal regular tetrahedral angle. With ions that are formally triply charged there is a preference, and the great majority are trigonally coordinated. There are very few examples in the data with formal charges greater than +3.

Figure 4

Figure 5

Distribution of ’ for single acceptors. The contribution from -alums is in black.

Distribution of " for cations that are the only cation coordinated to a water.

Acta Cryst. (2015). B71, 275–284



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research papers Table 5 ˚ ) and angles ( ) for water molecules with only single hydrogen bonds arranged into classes Maximum, minimum and average values of bond lengths (A determined by coordination to cations. Data for molecules with one H singly hydrogen bonded and the other hydrogen bonded in some other way are excluded. All acceptor types are included. Explanation of subdvision of classes by letters. C: M1+; K: H; D, J: M2+; M, N: Mn+ (n > 2); A: M+, M+; B: M2+, M2+; E: H, H; G: M+, H; H: M2+, H; H0 : M2+, M+; H00 : Mn+, H. Class 10

Class 1

Class 2

C

D

M

J

K

N

A

B

E

G

H

H0

H00

No. of molecules O—H Min. Av. Max.

3 0.878 0.935 0.970

71 0.858 0.958 1.003

42 0.934 0.983 1.016

57 0.917 0.972 1.019

3 0.922 0.965 0.993

8 0.932 0.976 1.053

73 0.891 0.958 1.020

24 0.940 0.980 1.017

18 0.859 0.958 1.006

38 0.925 0.968 1.014

27 0.910 0.975 1.028

12 0.933 0.975 1.000

2 0.980 0.992 1.012

H---A

Min. Av. Max.

1.826 2.036 2.336

1.553 1.918 2.499

1.556 1.725 2.228

1.614 1.817 2.247

1.826 1.985 2.178

1.608 1.751 1.927

1.566 2.097 3.074

1.600 1.938 2.763

1.740 1.918 2.409

1.628 1.923 2.550

1.604 1.828 2.632

1.679 1.803 2.204

1.661 1.697 1.736

H—O—H

Min. Av. Max.

107.3 109.6 112.6

103.2 109.1 114.4

103.9 109.2 113.8

101.4 106.4 109.3

102.4 103.4 104.4

105.6 107.5 109.7

100.7 105.4 109.8

99.9 104.6 109.1

101.8 105.4 110.1

102.4 105.7 110.5

101.7 106.3 109.5

104.0 106.2 111.8

106.1 106.1 106.1

C—O—C

Min. Av. Max.

– – –

– – –

– – –

– – –

– – –

– – –

79.6 98.8 150.7

86.3 107.6 139.9

82.8 102.5 118.5

72.6 97.7 129.5

99.1 111.1 131.6

96.2 126.3 139.0

94.5 96.3 98.1

A—O—A

Min. Av. Max.

92.3 109.3 126.3

60.9 115.2 170.1

81.5 105.5 131.2

63.8 106.2 130.1

96.2 100.4 104.6

97.3 105.7 113.8

76.5 106.0 142.8

57.0 100.2 125.4

68.8 109.2 141.6

90.5 107.3 144.8

76.0 107.3 136.9

87.7 105.1 122.4

95.2 99.1 103.0

4.3. Tabular presentation

In making a tabular presentation water molecules were classified into classes using the facts that cations coordinated to water vary in charge, number and geometrical arrangement about the oxygen. Previous workers (Chiari & Ferraris, 1982; Ferraris & Franchini-Angela, 1972) assigned water molecules into four classes that were further subdivided into several types. We classified water molecules according to Chiari & Ferraris (1982) with the variation that Class 1 contains water molecules with one coordinated ion trigonally bonded to the metal, defined as having " 30 . The remaining singly coordinated examples are in Class 10 . Class 2 has water molecules coordinated to two cations approximately in the lone pair directions. We do not consider the small number of Class 3 or Class 4 molecules from the Chiari & Ferraris (1982) classification. Each class is subdivided according to whether the coordination is to a metal ion or hydrogen, and further still depending on the charge of the cations. Thus, in Classes 1 and 10 the letter C refers to singly charged cations (M+), K to hydrogen (H), D and J to M2+, and M and N to Mn+ (n > 2). For Class 2, A refers to a pair of singly charged cations (M+, M+), B to a pair of doubly charged cations (M2+, M2+), E to two H atoms (H,H) and in similar notation G refers to (M+, H), H to (M2+, H), H0 to (M2+, M+) and H00 to (Mn+, H). A summary of this subdivision is also given in the footnote to Table 5. The extreme values of the geometric parameters have been extended beyond the previously published compilations, but the average water bond lengths and bond angles are mostly close to those published by Chiari & Ferraris (1982). The

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average OH bond lengths are unusual. There are sufficient short OH bond lengths to make the average OH bond lengths shorter than the gas phase value from electron diffraction ˚ ; Shibata & Bartell, 1965) for seven out of the (0.976 0.003 A 13 sub-classes in Table 5. In fact, 18 O—H bond lengths less ˚ are recorded in the present work. than 0.9 A It is well known that hydrogen bonding to a covalent OH bond leads to lengthening of the OH bond. Where crystallographic studies using neutrons have been confined to temperatures less than 130 K this is observed in a set of organic compounds (Steiner & Saenger, 1994). This strict adherence to giving bond lengths greater than the gas-phase water O—H distance is not observed in the data reviewed by us and, since a similar lengthening would be expected from coordination to a metal, is probably because the data are uncorrected for thermal motion. However, the possibility should be considered that in some instances OH bond shortening could occur in the crystal, as has been observed for the N—B bond in the HCN–BF3 molecule (Burns & Leopold, 1993). Although, since the N—B bond in HCN–BF3 is very much weaker than the OH bond in water, this would seem to be an unlikely explanation for the short OH bonds observed in hydrates of metal salts. Two cations repel each other forcing them to be aligned with the lone pair directions. This is generally observed. Furthermore, the effect of cation charge can be seen in the average values for the angles (C—O—C) subtended by the cations at the water oxygen. Sub-classes 2B, 2H and 2H0 , where a +2 ion is present, have larger average values for the C—O—C angle shown in Table 5 than those containing only singly charged ions, 2A, 2E and 2G. Acta Cryst. (2015). B71, 275–284

research papers Table 6 ˚ ) and angles Maximum, minimum and average values of bond lengths (A ( ) for water molecules with only single hydrogen bonds distinguished by acceptor atoms. Acceptor

N

O

F

S

Cl

Br

No. of hydrogen bonds O—H Min. Av. Max.

21 0.902 0.947 0.977

593 0.826 0.968 1.053

35 0.930 0.967 1.001

34 0.920 0.960 0.991

48 0.917 0.958 1.012

7 0.938 0.951 0.959

H---A

Min. Av. Max.

1.867 2.221 2.698

1.556 1.830 2.409

1.553 1.737 2.032

1.724 2.349 2.573

2.102 2.265 2.645

2.397 2.526 2.826

Min. Av. Max.

9 102.2 104.4 106.0

273 87.2 107.0 114.4

13 105.0 107.4 110.6

14 100.7 105.1 107.7

21 102.4 106.9 113.3

3 102.5 103.9 104.7

Min. Av. Max.

7 76.5 98.5 114.9

265 57.0 108.5 170.1

13 92.9 103.9 116.8

12 81.9 104.8 126.0

21 84.7 109.9 143.2

3 76.9 87.0 103.5

No. of values H—O—H

No. of values A—O—A

The average data values in Table 5 confirm the result from linear modelling that the length of the O—H bond is influenced by the charge of a coordinated cation. As the charge on the cations coordinated to the water increases the average OH length shown in Table 5 increases, i.e. sub-classes 1C, 1D and 1M; 10 J and 10 N; and 2A, 2H0 and 2B. Also there are trends connected with the acceptors that can only be seen from Table 6. The average OH lengths increase as the acceptor atoms move across a period and decrease as the acceptor atoms move down a group. Average HOH angles increase as the acceptor atoms move across a period and decrease as they move down a group. These are changes that would be expected from the change in electronegativity of the acceptor atoms.

5. Conclusions Linear regression models have been applied to water molecules in hydrated metal salts where there is either only a single or two cations coordinated to a water molecule and the hydrogen acceptor atom is oxygen. Provided a small number of outliers are removed from the data it has been shown that the geometry of a water molecule in these circumstances is very well determined by parameters describing the positions of the near neighbours of the water molecule. For the cases where there is only a single cation the most important parameter governing the OH length is the distance between the hydrogen and its acceptor atom (HA). There are a larger number of factors affecting the bond angle. The most important of these is the position of the acceptor atoms with respect to the water angle. There are three possibilities for the projection of the acceptors onto the water plane. If these projections both lie outside the bond angle then the bond angle is larger compared with the situation where one projection lies inside the angle and one lies outside it, and if both lie inside the bond angle then the water angles are Acta Cryst. (2015). B71, 275–284

smaller by comparison. For the bond angle the distance between the water oxygen and coordinating cation is also an important determinant. For the cases involving two cations the only significant factor for the OH bond length is again HA. No satisfactory model for the HOH angle could be found for these two cation cases. A good model for the OH bond length is also obtained when the data for one and two cations were combined. Again the most important parameter is HA. For this combined data no satisfactory model for the bond angle could be obtained.

References Agresti, A. (2007). An Introduction to Categorical Data Analysis. New York: Wiley. Alig, H., Lo¨sel, J. & Tro¨mel, M. (1994). Z. Kristallogr. 209, 18–21. Baur, W. H. (1965). Acta Cryst. 19, 909–916. Baur, W. H. (1972). Acta Cryst. B28, 1456–1465. Bernal, J. D. (1953). J. Chim. Phys. Physiochem. Biol. 50, C1–C12. Bondi, A. A. (1968). Physical Properties of Molecular Crystals Liquids and Glasses. New York: Wiley. Brown, I. D. (2002). The Chemical Bond in Inorganic Chemistry: The Bond Valence Model. IUCr Monographs on Crystallography 12. Oxford University Press. Brown, I. D., Brown, M. C. & Hawthorne, F. C. (1976). BIDICS-1976s. McMaster University, Hamilton, Ontario. Burns, W. A. & Leopold, K. R. (1993). J. Am. Chem. Soc. 115, 11622– 11623. Cense, J.-M. (1989). Tetrahedron Computer Methodology, 2, 65–71. Chiari, G. & Ferraris, G. (1982). Acta Cryst. B38, 2331–2341. Chidambaram, R. (1962). J. Chem. Phys. 36, 2361–2365. Clark, J. R. (1963). Rev. Pure Appl. Chem. 13, 50–90. Falk, M. & Knop, O. (1973). Water a Comprehensive Treatise, Vol. 2, pp. 55–88. New York: Plenum Press. Ferraris, G. & Franchini-Angela, M. (1972). Acta Cryst. B28, 3572– 3583. Ferraris, G., Fuess, H. & Joswig, W. (1986). Acta Cryst. B42, 253– 258. Fox, J. (1997). Applied Regression Analyis, Linear Models, and Related Methods. California: Sage. Hamilton, W. C. (1962). Annu. Rev. Phys. Chem. 13, 19–40. Hamilton, W. C. & Ibers, J. A. (1968). Hydrogen Bonding in Solids. New York: Benjamin. Jeffrey, G. A. (1997). An Introduction to Hydrogen Bonding. Oxford University Press. Malenkov, G. G. (1962). Zh. Strukt. Khim. English. Ed. 3, 206–226. Olovsson, I. & Jo¨nsson, P. G. (1976). The Hydrogen Bond, Vol. 2, pp. 393–456. Amsterdam: North Holland. Pauling, L. (1960). The Nature of the Chemical Bond, 3rd ed. Ithaca: Cornell University Press. R Development Core Team (2014). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, http://cran.r-project.org/. Shibata, S. & Bartell, L. S. (1965). J. Chem. Phys. 42, 1147–1151. Speakman, J. C. (1973). Mol. Struct. Diffr. Methods, 1, 208–217. Speakman, J. C. (1974). Mol. Struct. Diffr. Methods, 2, 45–52. Speakman, J. C. (1975). Mol. Struct. Diffr. Methods, 3, 86–92. Speakman, J. C. (1976). Mol. Struct. Diffr. Methods, 4, 65–77. Speakman, J. C. (1977). Mol. Struct. Diffr. Methods, 5, 99–106. Speakman, J. C. (1978). Mol. Struct. Diffr. Methods, 6, 117–129. Steiner, T. (1998). J. Phys. Chem. A, 102, 7041–7052. Steiner, T. & Saenger, W. (1994). Acta Cryst. B50, 348–357. Tovborg-Jensen, A. (1948a). Acta Chem. Scand. 2, p. 532. Tovborg-Jensen, A. (1948b). PhD thesis, University of Copenhagen. Graham S. Chandler et al.


283

research papers Tregenna-Piggott, P. W. L., Andres, H.-P., McIntyre, G. J., Best, S. P., Wilson, C. C. & Cowan, J. A. (2003). Inorg. Chem. 42, 1350– 1365. Tregenna-Piggott, P. W. L., Spichiger, D., Carver, G., Frey, B., Meier, R., Weihe, H., Cowan, J. A., McIntyre, G. J., Zahn, G. & Barra, A.-L. (2004). Inorg. Chem. 43, 8049–8060.

284



Wells, A. F. (1984). Structural Inorganic Chemistry. Oxford University Press. Wolff, S. K., Grimwood, D. J., McKinnon, J. J., Turner, M. J., Jayatilaka, D. & Spackman, M. A. (2010). CrystalExplorer, Version 3.0. The University of Western Australia. Yukhnevich, G. V. (2009). Crystallogr. Rep. 54, 212–217.

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