(IUCr) 22 Space-group changes

Volume 59
Part 1
Pages 43-50
February 2003

Received 5 June 2002
Accepted 9 December 2002

22 Space-group changes

Dore Augusto Clemente ^a and Armando Marzotto ^b ^*

^aDipartimento di Ingegneria dei Materiali e di Chimica Applicata, Università di Trieste, Sede di Pordenone, Via Prasecco 3/A, 33170 Pordenone, Italy, and ^bDipartimento di Chimica Inorganica, Metallorganica ed Analitica, Università di Padova, Via Loredan 4, 35131, Padova, Italy
Correspondence e-mail: clemente@units.it

This paper reports 22 examples of space-group changes from low to higher symmetry. The revisions involve 15 crystal structures that were originally described in space group P2₁, six in P $[\bar 1]$ and one in P1. The relevance of higher-symmetry elements is discussed in connection with the crystallography, the molecular dimensions and, when possible, the spectroscopic properties.

Keywords: space-group changes.

1. Introduction

Recently, many crystal structures have been revised to space groups of higher symmetry (Baur & Tillmanns, 1986; Cenzual et al., 1991; Herbstein & Marsh, 1998; Marsh, 1995, 1999; Marsh & Spek, 2001). The percentage of possible revisions was evaluated (Baur & Tillmanns, 1986) to be about 3% of all the published structures (245000), so that up to 7000 structures may be incorrect. In addition, some crystal structures are reported to have higher symmetry than the true symmetry. This occurs, for example, when all the weak intermediate-layer lines are systematically lost during a peak search, which results in a subcell of the correct unit cell (see e.g. Galdecki et al., 1999; Connick et al., 1996). The detection of the true crystal symmetry is important for several reasons:

(i) the theory of occurrence of three-dimensional space groups;
(ii) the second-order non-linear optics which demand non-centrosymmetric space groups;
(iii) the IR and NMR spectroscopy in the solid state;
(iv) the correct attribution of isomorphism.

2. Data retrieval and methods

Version 5.22 of the CSD (Cambridge Structural Database; Allen & Kennard, 1993) was used (December 2001, 245000 entries). We focused on crystal structures that contain (a) two molecules per asymmetric unit or (b) only one molecule but have a molecular symmetry element such as a mirror plane or twofold axis. We examined over 5000 crystal structures; 340 were shown to be metrically orthorhombic, but orthorhombic symmetry is only really present in 18 of these structures. A centre of symmetry must be added to another four space groups. The space-group changes reported here belong to two categories: (i) an increase in the Laue symmetry (18 examples) and (ii) a change from non-centrosymmetric to centrosymmetric (four examples). For structures in which the Laue class was changed we used firstly our own local (written by DAC) programs CLASS.FOR or CELL.FOR, which classify the crystal structure among the 44 metric classes (Mighell & Rodgers, 1980). If the crystal structure was metrically different from that reported in the literature, the following three tests were applied:

(i) Our program FSCC.FOR read the original cell, space group and coordinates¹ and applied a low isotropic displacement factor (U = 0.02 Å²) to all atoms, to give h, k, l and F_c for at least 10000 reflections distributed over the complete reflection sphere and at high angles. The Miller indices were then transformed according to the matrix found by CLASS.FOR or CELL.FOR to give a reflection data file NAME.HKL, which is adapted for use with SHELXL (Sheldrick, 1997) and retains the structure factors F_c. Then, LAUE.EXE (Farrugia, 1997) or ORDRIFL.EXE (Nardelli, 2001) was used to merge the equivalent reflections using the new Miller indices. If R_int on F_o was lower than 5% the structure was accepted for subsequent analysis.
(ii) The second test was carried out in real space. The atomic shifts² necessary to achieve the higher symmetry (reported in square brackets in Tables 1-22 of the supplementary material³) were compared with the s.u. values averaged over (now) equivalent atoms (reported in parentheses in Tables 1-22 of the supplementary material³). The atomic shift and the s.u. value must be similar.
(iii) A structure-factor calculation was performed using SHELXL (Sheldrick, 1997), which reads the file NAME.HKL, and the coordinates that had been transformed to the new space group and averaged. If the space-group change is correct the R factor must be less than 3%.

We have found that test (i) is the most important and severe. Moreover, the four structures that belong to category (ii) were discovered by consideration of the spread of chemically equivalent distances.

We have also used PARST.FOR (Nardelli, 1983, 1995, 1996). The 22 revised structures after space-group revisions are listed in Table 1,³ together with the CSD Refcode.

Table 1
Structures originally described in space groups that are more properly described in higher symmetries

Included are Refcode, original space group, revised space group, original (Z) and new (Z') number of formula units per cell.

Refcode	Original space group	Revised space group	ZZ'	Formula unit	Atomic shifts^# (×10³ Å) minmax	TMD⁺(Å)	R_int^§ (%)	Transformation vectors	Coordinate transformations^##	Reference
BARJAF	P2₁	C222₁	24	C₁₅H₁₆CoN₄O₈	731	N-O = 1.186 1.272 1.229	4.1	[00 $[\bar 1]$ ] [201] [0 $[\bar 1]$ 0]	x' = (x/2 - z) + 3/4;y' = x/2 - 1/4 ;z' = -y + 0.5059	Minardi et al. (1999)
						Co-N = 2.055 2.11 2.081
CLAECU	P2₁	C222₁	24	C₁₀H₂₀Cl₂CuN₂O₄	25	C-Cl = 1.775 1.785 1.780	2.1	[101] [10 $[\bar 1]$ ] [010]	x' = (x + z)/2 + 3/4; y' = (x - z) /2; z' = y - 0.2243	Ahlgrén et al. (1978)
						Cu-N = 2.037 2.039 2.038
QANXOS	P2₁	C222₁	24	[C₁₆H₃₂Cl₂·CoN₄]⁺ ClO₄^-	214	C-N = 1.468 1.499 1.484	2.0	[101] [10 $[\bar 1]$ ] [010]	x' = (x + z)/2 + 1/4; y' = (-x - z)/2 + 3/4 ;z' = y + 0.0717	House et al. (1999)
						C-C = 1.497 1.512 1.505
SAZPAK	P2₁	C222₁	48	C₂₂H₃₈N₁₂NiO₁₈P₂· C₂H₈N₂·6.5H₂O	756	C-C = 1.333 1.435 1.383	2.8	[ $[\bar 1]$ 0 $[\bar 1]$ ] [10 $[\bar 1]$ ] [0 $[\bar 1]$ 0]	x' = -(x + z)/2 + 1; y' = (x - z)/2 + 1/2; z' = -y + 0.0080	Fiol et al. (1989)
						C-O = 1.385 1.463 1.423
YAKVIP	P2₁	C222₁	48	[C₅H₇N₂O₅Na(H₂O)_2.5]_n· 1.5n(H₂O)₂ (n = 1)	38	C-C = 1.524 1.543 1.533	1.0	[100] [102] [0 $[\bar 1]$ 0]	x' = x - z/2; y'= z /2; z' = -(y + 0.3857)	Davis et al. (1991)
						Na-O = 2.407 2.418 2.411
BOGPIW	P2₁	Cmc2₁	24	[C₇H₅FeO₄S]⁺·[AsF₆]^-	530	C-C = 1.287 1.388 1.336	3.2	[101] [10 $[\bar 1]$ ] [010]	x' = (x + z)/2 + t⁺⁺; y' = (x - z)/2 + 3/4; z' = y - 1	Hartmann et al. (1982)
						C-C = 1.326 1.390 1.357
NOVHUB	P2₁	Cmc2₁	24	[C₆₀H₅₄Cu₂N₃O₃P₄]⁺· [NO₃]^-·CH₃OH	117	C-C = 1.344 1.375 1.359	2.9	[10 $[\bar 1]$ ] [101] [010]	x' = (x - z)/2 + 1/4; y' = (x + z)/2 + 1/4; z' = y	Ruina et al. (1997)
						C-C = 1.377 1.401 1.391
NOHNED	P2₁	P2₁2₁2₁	44	C₂₂H₂₆N₂O₆	112	C-N = 1.309 1.334 1.322	1.9	[100] [010] [001]	x' = x; y' = y - 0.8780; z' = z - 1/4	Casellato, Tamburini et al. (1997)
						C-N = 1.267 1.274 1.270
NOHNED01					217	C-N = 1.282 1.316 1.300	1.7	[100] [010] [001]	x' = x; y' = y-0.8785; z' = z - 1/4	Brianese et al. (1999)
						C-O = 1.394 1.427 1.410
QELPUS	P2₁	P2₁2₁2₁	44	C₂₈H₃₂Cl₂N₂Pd₂·H₂O	279	C-C = 1.310 1.450 1.380	1.8	[100] [010] [001]	x' = x + 3/2; y' = y + 1.0777; z' = z + 3/4	Gül & Nelson (2000)
						C-C = 1.302 1.410 1.352
APLSOL	P2₁	P4₃	44	C₁₅H₁₉BrO₂	677	C-C = 1.286 1.456 1.370	3.7	[001] [100] [010]	x' = z + 1; y' = x + 1; z' = y	McMillan et al. (1976)
						C-C = 1.491 1.604 1.546
DOQZAK	P2₁	P4₃	44	C₁₇H₂₀NO₅V	113	C-N = 1.404 1.431 1.417	1.3	[100] [00 $[\bar 1]$ ] [010]	x' = x - 1/2; y' = -z + 1; z' = y	Rajac et al. (2000)
						C-C = 1.425 1.449 1.438
BAMUBR	P $[\overline 1]$	C2/c	24	2[C₁₆H₃₆N]⁺· [UO₂Br₄]^2-	762	C-C = 1.512 1.581 1.547	2.1	[0 $[\bar 1]$ 1] [0 $[\bar 1\bar 1]$ ] [110]	x' = (x - y + z)/2 + 3/4; y' = (x - y - z)/2 + 1/4; z' = x + 1/2 ^§§	Di Sipio et al. (1977)
						C-C = 1.572 1.634 1.603
FARNER	P $[\overline 1]$	C2/c	24	C₁₀H₂₄Cl₄N₄O₂U	034	C-O = 1.258 1.301 1.278	1.4	[0 $[\overline 2]$ 1] [00 $[\bar 1]$ ] [110]	x' = (x - y)/2 + 1/4 ; y' = (x - y)/2 - z + 1/4; z' = x	Du Preez et al. (1986)
						C-N = 1.323 1.359 1.341
FARNIV	P $[\overline 1]$	C2/c	24	C₁₀H₂₄Br₄N₄O₂U	035	C-O = 1.265 1.310 1.288	1.0	[0 $[\overline 2]$ 1] [00 $[\bar 1]$ ] [110]	x' = (x - y)/2 + 1/4 ; y' = (x - y)/2 - z + 1/4; z' = x	Du Preez et al. (1986)
						U-O = 2.197 2.230 2.213
HIMFUE	P $[\overline 1]$	I2/a	48	C₂₆H₄₃F₃O₃P₂Pd	223	C-C = 1.501 1.567 1.534	1.4	[0 $[\bar 1]$ 1] [ $[\bar 1]$ 00] [1 $[\bar 1]$ $[\bar 1]$ ]	x' = (-y + z)/2 + 1/4; y' = -x - (y + z)/2 + 3/4; z' = -(y + z)/2 + 3/4	Van der Boom et al. (1998)
						C-C = 1.387 1.424 1.405
HORBIZ	P $[\overline 1]$	I2/a	48	C₄₇H₆₃NO₆Si	225	C-C = 1.492 1.517 1.505	2.1	[ $[\bar 1]$ 11] [100] [01 $[\bar 1]$ ]	x' = (y + z)/2; y' = x + (y + z)/2; z' = (y - z)/2	Comins et al. (1999)
						C-C = 1.469 1.494 1.481
PEJVAB	P $[\overline 1]$	I2/m	12	C₈H₁₂S₈Tc₂	16	Tc-S = 2.390 2.392 2.390	1.7	[11 $[\bar 1]$ ] [00 $[\bar 1]$ ] [ $[\bar 1]$ 10]	x' = (x + y)/2; y' = -(x + y)/2 - z + 1; z' = (-x + y)/2	Tisato et al. (1993)
						C-S = 1.836 1.838 1.837
SIXFIO	P1	Ia	24	[C₂₃H₂₅NPPd]⁺·[PF₆]^-	136	Pd-C = 2.194 2.262 2.228	1.3	[0 $[\bar 1]$ 1] [ $[\bar 1]$ 00] [1 $[\bar 1]$ $[\bar 1]$ ]	x' = -(y - z)/2 + 1/2; y' = -x - (y + z)/2 + 1.5295; z' = -(y+z)/2 + 1/2	Crociani et al. (1998)
						Pd-C = 2.060 2.100 2.078
BIHJUX	P2₁	P2₁/m	22	[C₂₃H₃₇CeN₃O₉]³⁺· 3Cl^-·H₂O	51264	C-C = 1.295 1.658 1.469	-	[100] [010] [001]	x' = x; y' = y - 0.0288 ; z' = z	Casellato et al. (1999)
						C-O = 1.313 1.655 1.460
BIHLIN	P2₁	P2₁/m	22	[C₂₃H₃₇DyN₃O₉]³⁺· 3Cl^-·H₂O	59227	C-N = 1.270 1.572 1.417	-	[100] [010] [001]	x' = x; y' = y - 0.0288 ; z' = z	Casellato et al. (1999)
						C-C = 1.250 1.546 1.396
ZEXBUZ-01	P2₁	P2₁/m	22	C₃₃H₅₇ClO₆Zr	991^###	C-C = 1.345 1.450 1.394	-	[100] [010] [001]	x' = x; y' = y - 0.2093 ; z' = z	Casellato, Fregona & Graziani (1997)
						C-C = 1.335 1.417 1.375
PYRHSB	P2₁	P2₁/a	44	[C₅H₆N]⁺·[SbCl₆]^-	20118 ⁺⁺⁺	Sb-Cl = 2.206 2.437 2.321	-	[100] [010] [001]	x' = x + 1/4; y' = y + 0.0277 ; z' = z	Porter & Jacobson (1972)
						Sb-Cl = 2.274 2.440 2.355

^#Only the shifts of the non-H atoms are reported.
⁺The distances in the column labelled TMD are the most disparate pair in the lower-symmetry group and the corresponding value in the higher-symmetry group.
^§R_int is defined as $[\textstyle\sum]$ [F_o(h) - F_o(h')]/ $[\textstyle\sum]$ F_o(h)(mean) (h and h' are the Miller indices of equivalent reflections).
^##When there is more than one residue, the coordinate transformations are strictly valid for the most populated residue.
⁺⁺t = -3/4 for the [C₇H₅FeO₄S]⁺ cation and t = 1/4 for the [AsF₆]^- anion.
^§§Only for the tetra-n-butylammonium cations.
^###tert-Butyl groups are not considered because of their high thermal motion.
⁺⁺⁺Excluding the pyridinium cation because it is disordered.

3. Category (i): increase in Laue symmetry

3.1. From P2₁ (No. 4) to C222₁ (No. 20)

Within this space-group change, the b axis of P2₁ becomes the c axis of C222₁. Since the z coordinate origin is now fixed, an origin shift along c is needed during this change. Moreover, an origin shift along the a and b axes is necessary whenever the original authors have chosen (in P2₁) the origin on the 2₁ axis that meets the other two perpendicular screw axes instead of choosing the origin on the 2₁ axis that meets the two perpendicular twofold axes.

3.1.1. BARJAF

Space group C222₁ can accommodate this chiral Co(II) complex that now lies on a twofold axis along b. The earlier paper noted that `the molecule presents a remarkable non-crystallographic twofold pseudosymmetry around the axis containing Co(II), the midpoint of the C(6)-C(7) bond and C(14) [C15 in the CSD]'. Even so, the dioxolane ring remains distributed over two equally populated conformations related by this twofold crystallographic axis: the endo-C atom connecting the dioxolane O(1) and O(2) is still split into C(13) and C(14), and the methyl C(15) lies on the crystallographic binary axis. We believe that this disorder is not due to refinement in the improper P2₁ space group but is real. In P2₁ the chemically equivalent distances N(4)-O(5) = 1.186 (15) Å and N(3)-O(8) = 1.272 (16) Å are the most disparate, whereas in C222₁ this distance becomes 1.229 Å.

3.1.2. CLAECU

The twofold crystallographic axis along b passes through Cu(1), the midpoint of the ethylenediamine C-C and the two chloroacetato ligands. We note that the original paper stated `the molecules have pseudo C₂ symmetry'.

3.1.3. QANXOS

This Co(III) complex possesses a twofold crystallographic axis parallel to a passing through Cl(1), Co(1) and Cl(2), while the perchlorate anion lies on the crystallographic twofold axis parallel to b. These twofold axes relate atom pairs well within their s.u. values, but the deviations of the perchlorate anion from the averaged values are slightly greater because of its disorder, in which the four O atoms are duplicated by the twofold axis parallel to b.

3.1.4. SAZPAK

In P2₁ there are two independent [Ni(en)(5'GMPH)₂(H₂O)₂](en)·6.5H₂O molecules (5'GMPH is guanosine 5'-monophosphate) in the asymmetric unit. In C222₁ there are two half molecules in the asymmetric unit: one on the twofold axis along a and the other on the twofold axis along b. The original paper states that the complex does not possess a twofold axis, although the authors had verified the presence of a crystallographic twofold axis passing through Ni in the inosine analogue [Ni(en)(5'IMPH)₂(H₂O)₂]·13H₂O (SAZNUC) published in the same work. The two independent ethylenediamine molecules in P2₁ are related by a twofold axis along b, so that the water molecules are related by twofold axes along a or b, with one water molecule on the twofold axis along b.

3.1.5. YAKVIPI

The space-group transformation shows that the two independent organic molecules in P2₁ are related, within the s.u. values, by an additional 2₁ axis along a of space group C222₁. Moreover, two water molecules (O11, O17) are related by a twofold axis along b, and the other two water molecules (O14, O18) lie on two distinct twofold axes along b.

3.2. From P2₁ (No. 4) to Cmc2₁ (No. 36)

This space-group change was discussed by Marsh (1990) for KAFFEC and by Herbstein (1991) for VEXPET. Here, the b axis of P2₁ becomes the c axis of Cmc2₁. Since the origin is arbitrary along both of these axes, no origin shift is needed during this change. However, an origin shift along a and b is needed whenever the original authors have chosen (in P2₁) the origin on the 2₁ axis at the intersection of the n-glide with the b-glide instead of at the intersection of the m-plane with the c-glide.

3.2.1. BOGPIW

Atoms Fe(1), S(1), O(1), O(2) and C(2) of the [C₅H₅Fe(CO)₂SO₂]⁺ cation lie on the mirror plane (m-plane) at x = 0, while As(1), F(1) and F(5) of the octahedral AsF₆^- anion lie on the m-plane at x = 1/2. The deviations from the m-plane are greater than the formal s.u. values for C(2), O(2), F(1) and F(5) because they have large anisotropic displacement parameters (ADPs). However, even if the distances in P2₁ and Cmc2₁ space groups remain almost equal, some distances become more realistic in the latter space group. For example the most disparate C-C (cyclopentadienyl) distances, which range from 1.287 (16) to 1.388 (14) Å, become 1.336 Å. The distances in the Cp ring remain shorter than normal {1.421 (3) Å, e.g. in ( [mu] -CH₂)-[CpMn(CO)₂]₂; Clemente et al., 1982}, probably because of the large libration around the ring-centroid-metal-atom axis. We ascribe the rather high deviations from the m-plane to the high ADPs of these atoms rather than to a real loss of the m-plane. The As-F distances are practically unchanged after the revision and are comparable to those of other AsF₆^- anions (Cameron et al., 2000).

3.2.2. NOVHUB

The orthorhombic cell contains four formula units of [C₆₀H₅₄Cu₂N₃O₃P₄]

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