1.1. General

Even today, there are simple chemical compounds for which the crystal structures are not known. The reasons for this deficiency in knowledge include synthetic difficulties, complex phase behaviour, instability in a vacuum and under an inert atmosphere, lack of single crystals, unusual or ambiguous space groups, and disorder. All these difficulties can be found in sodium alkoxides (sodium alcoholates) NaOR and their solvates NaOR·xROH, with R being a lower alkyl group. In principle, these compounds can be easily prepared by the reaction of sodium with the corresponding alcohol. However, in practice, the synthesis of the pure phases presents some obstacles. For example, when sodium is reacted with ethanol and the ethanol excess is removed in vacuo, a white powder remains. This powder turns into a liquid within a few minutes under argon. Further evaporation under vacuum results in a powder, which again liquefies under argon. Finally, a white residue is obtained, which consists of a mixture of two to four different phases, including sodium ethoxide (NaOEt) and its ethanol disolvate NaOEt·2EtOH (Beske et al., 2020). Phase-pure NaOEt is only obtained after a few hours of evaporation under vacuum at 50 °C. The initially formed solvate NaOEt·2EtOH decomposes under vacuum, and even under dry argon, and is stable only in the presence of ethanol vapour. Similar difficulties are observed for other sodium alkoxides (see below). Additionally, all the compounds are very sensitive to moisture.

In industry, as well as in the laboratory, sodium alkoxides are widely used as bases and as reagents in organic synthesis. This is not only true for NaOEt, but also for other alkoxides. For example, sodium tert-amylate (sodium 2-methyl-2-bu­tox­ide, NaO^tAm) is used industrially on a multi-ton scale in the synthesis of diketo­pyrrolo­pyrrole pigments, which today are the most commonly used pigments for red car coatings (Hunger & Schmidt, 2018).

1.2. Historical notes on NaOEt

Sodium ethoxide was synthesized as early as 1837 by Liebig (Liebig, 1837; Beske et al., 2020). Since ethanol was considered the hydrate of ethyl ether (2EtOH ≙ Et₂O·H₂O), sodium ethoxide was regarded as an adduct of di­ethyl ether and sodium oxide, which actually corresponds to the correct stoichiometry: Et₂O·Na₂O ≙ 2NaOEt. Correspondingly, the name `Aethernatron' (Geuther, 1868a,b) was used besides the names `Natriumalkoholat' (Geuther, 1859) and `Natriumäthylat' (Wanklyn, 1869).

Many years later, the crystal structure of sodium methoxide (NaOMe) was determined from powder X-ray diffraction (PXRD) data (Weiss, 1964). Surprisingly, the crystal structure of NaOEt was not determined, although it is isostructural with NaOMe. It would have been an easy task to index the powder pattern of NaOEt manually, because NaOEt crystallizes in the tetragonal crystal system, and the lattice parameters a and b of NaOEt are almost identical to those in NaOMe.

In 1976, the PXRD patterns of NaOEt and NaOEt·2EtOH were published in an article devoted to the thermal stability of alkali ethoxides (Blanchard et al., 1976). Again, no attempt was made to index the powder data.

As much as 30 years later, the powder data of NaOEt and sodium n-propoxide (NaOⁿPr) were indexed, but the crystal structures remained indeterminate (Chandran et al., 2006). Finally, we determined the crystal structure of NaOEt from powder data, and of NaOEt·2EtOH from single-crystal data a few months ago. The crystal structures were recently briefly described in a chemical journal (Beske et al., 2020), without any discussion on the ambiguity of the space group or of the crystal symmetry. Here, we report a full discussion of the ambiguities of the space group of NaOEt, including a Bärnighausen tree of the possible space groups and their subgroups.

1.3. Previous work on other alkoxides

The first determined crystal structure of a sodium alkoxide was that of NaOMe (Weiss, 1964). NaOMe is isotypical to LiOMe (Wheatley, 1961) and crystallizes in a layer structure in the space group P4/nmm, with Z = 2.

Potassium methoxide, KOMe, crystallizes in the same space group type as NaOMe, but the structure is different: whereas the Na⁺ ions in NaOEt are coordinated to four O atoms, the K⁺ ions in KOMe are coordinated to five O atoms in a square-pyramidal geometry (Weiss, 1963; Weiss & Alsdorf, 1970). The O atom is surrounded by five K⁺ ions and the methyl group has a distorted octahedral geometry. A similar structure was found for partially hydrolysed NaOMe with the composition Na(OMe)_1–x(OH)_x, with x ≈ 1/3 (Weiss, 1964).

Sodium tert-butoxide, NaO^tBu, exists in two polymorphic forms. Both structures were determined by single-crystal X-ray diffraction. One of the phases consists of hexamers and crystallizes in the space group P2₁2₁2₁, with Z = 20, with five hexamers per asymmetric unit (Østreng et al., 2014). The other phase contains a 1:1 mixture of hexamers and nonamers in the space group R, with Z = 6, with 90 formula units per unit cell (Greiser & Weiss, 1977; Davies et al., 1982; Nekola et al., 2002). Accordingly, both phases have quite large unit cells.

1.4. Solvates

Sodium alkoxides can form solvates with their corresponding alcohols. Already in 1837 Liebig had prepared an ethanol solvate of NaOEt by the reaction of sodium with ethanol at 50 °C and subsequent cooling of the solution to room temperature, whereupon the mixture turned into a solid (Liebig, 1837). However, Liebig apparently did not recognize this precipitate as a solvate. In 1868, Scheitz determined the composition of this solvate as NaOEt·2EtOH (Geuther, 1868a). This result was confirmed by Marsh (Geuther, 1868b), whereas Wanklyn (1869) determined the composition to be NaOEt·3EtOH. In 1880, Frölich again found a composition of NaOEt·2EtOH using a different method (Geuther & Frölich, 1880). Lescoeur (1895) measured the vapour pressure during slow evaporation of a suspension of NaOEt in EtOH and observed that the vapour pressure did not change between compositions of NaOEt·1.7EtOH and nearly pure NaOEt, and thus concluded that the solvate had the composition NaOEt·2EtOH.

The crystal morphology of NaOEt·2EtOH was described as `völlig durchsichtige farblose nadelförmige Krystalle' (fully transparent, colourless, needle-like crystals) (Geuther, 1868a).

Geuther & Frölich (1880) also described a solvate with a com­position of NaOⁿPr·2ⁿPrOH. A ^tAmOH solvate of NaO^tAm was mentioned by Friedrich et al. (1999), but no composition as given.

The solvates are thermally remarkably stable. NaOEt·2EtOH must be heated at ambient pressure to 200 °C and NaOⁿPr·2ⁿPrOH even to 220 °C before the pure solvent-free alkoxides are obtained (Geuther & Frölich, 1880). Solvent-free NaOEt is also quite stable. According to differential thermal analysis, the decomposition starts at 50 °C, but this decomposition is very slow and occurs over a large temperature range. Finally, at 310 °C the decomposition `adopts an explosive character' (`prendre un charactère explosif'; Blanchard et al., 1976).

Crystals of the solvates of NaOⁿPr, NaOⁱPr and NaO^tAm do form easily when sodium is reacted with the corresponding alcohols and the solution is subsequently carefully evaporated. However, no structure of any sodium alkoxide solvate was determined between 1837 and 2019 (Beske et al., 2020). The reason might be the pronounced sensitivity of the crystals to moisture, air, vacuum and dry inert gas.

1.5. Work in this article

In this article, we describe the synthesis, structure determination, crystal structure and disorder of NaOEt, NaOⁿPr, NaOⁿBu and NaOⁿAm, and of the solvates NaOEt·2EtOH, NaOⁿPr·2ⁿPrOH, NaOⁱPr·5ⁱPrOH and NaO^tAm·^tAmOH. The structures of the solvent-free compounds were determined by PXRD and the structures of the solvates by single-crystal X-ray analyses. In the cases of NaOEt and NaOⁿPr, the space-group symmetry was ambiguous, and the corresponding symmetry relationships were elaborated using a Bärnighausen tree.

2.1. Syntheses

All synthetic procedures were performed under an argon atmosphere using Schlenk techniques. All alcohols, as well as toluene, were dried over sodium and freshly distilled.

2.2. Pre-characterization

The stoichiometry of the solvent-free alkoxides was con­firmed by decomposition experiments with HCl, which verified their stoichiometry. Details are reported in the supporting information. For the solvates, this analysis could not be performed, because the solvates decomposed rapidly when removed from their alcoholic mother liquor.

2.3. Powder X-ray diffraction (PXRD)

For the PXRD studies, the samples were sealed in glass capillaries with a 1.0 mm diameter. The PXRD patterns were measured in transmission mode on a Stoe Stadi-P diffrac­tometer equipped with a Ge(111) monochromator and a linear position-sensitive detector. The capillaries were spun during the measurements. All measurements were performed at room temperature, using Cu Kα₁ radiation (λ = 1.5406 Å), with a 2θ range of 2–100° (2–80° for NaOEt).

2.4. Structure determination from powder data

The crystal structures of the solvent-free alkoxides NaOEt, NaOⁿPr, NaOⁿBu and NaOⁿAm were determined from PXRD data. The powder data were indexed with the program DICVOL (Boultif & Louër, 1991) within the program package DASH (David et al., 2006). The structures were solved by the real-space method with simulated annealing using DASH. Subsequently, Rietveld refinements were performed using TOPAS (Coelho, 2018).

For all four compounds indexing led to a tetragonal unit cell with Z = 2. The systematic extinction indicated P4/n, P4/nmm and P2₁m as possible space groups. The structures were successfully solved in P4/nmm and P2₁m, using two fragments, an Na atom and a rigid alkoxide moiety. The Na atom was placed on the special position, which allowed a distorted tetrahedral coordination [Wyckoff position 2a (, , 0) in P4/nmm origin choice 2; 2a (0, 0, 0) in P2₁m], as explained in §3.1. The alkoxide fragment was placed on a general position, with an occupancy of 0.125 (in P4/nmm) or 0.25 (in P2₁m). In the resulting structures, the C atoms moved close to a site with ..m symmetry, and were subsequently placed on this site, resulting in an occupancy of 0.25 (in P4/nmm) or 0.5 (in P2₁m). In the Rietveld refinements of NaOEt, restraints were only necessary for the H atoms. For NaOⁿPr, NaOⁿBu and NaOⁿAm, additional restraints were applied to the O—C and C—C bond lengths, and to the O—C—C and C—C—C bond angles. All H atoms were refined using restraints on the bond lengths and angles with quite high weights. Further details of the Rietveld refinements are given in the supporting information.

Note that there are two different origin choices for P4/nmm. Origin choice 2 (origin on ) was used for the structure solution, due to the requirements of DASH. In contrast, the origin choice 1 (origin on , as in P2₁m) was used for the Bärnighausen tree.

2.5. Single-crystal X-ray diffraction

A single crystal of NaOEt·2EtOH was placed in a sealed glass capillary and data were collected at −38 (2) °C. Single crystals of NaOⁿPr·2ⁿPrOH and NaOⁱPr·5ⁱPrOH were mounted by freezing them in a drop of oil and their data col­lected under a cold nitro­gen stream at −100 (2) °C using an Oxford Cryosystems cryostream device. Crystals of NaO^tAm·^tAmOH were sealed in a glass capillary under paraffin oil (dried with Na) and their data collected at room temperature.

Single-crystal data were collected on a Bruker SMART APEX three-circle diffractometer equipped with an Incoatec IμS Cu microfocus source with mirror optics and an APEX II CCD detector. The software package APEX3 (Bruker, 2015) was used for data collection and data reduction. The structures were solved by direct methods with SHELXT (Sheldrick, 2015a) and refined with SHELXL (Sheldrick, 2015b). All non-H atoms, except for disordered C atoms, were refined anisotropically. Disordered C atoms were refined isotropically. H atoms bonded to C atoms were treated with the riding model. In the case of NaOEt·2EtOH and NaOⁿPr·2ⁿPrOH, all OH protons could be located by Fourier synthesis. In NaOⁱPr·5ⁱPrOH, it was not possible to detect which of the four ligands coordinating to the Na⁺ ion is the ⁱPrO⁻ anion, and which are the three ⁱPrOH molecules. (The H atom could not be located, all Na—O bonds were of a similar length, all C—O bonds were of similar length, and in addition no decision could be made based on the size of the angles; furthermore, there is a twofold axis through the Na⁺ ion, hence there are always pairs of symmetrically equivalent ligands.) All O atoms of NaOⁱPr·5ⁱPrOH are part of a complex hydrogen-bond network, and obviously the H atoms are disordered within this network. Therefore, for each Na⁺ cation, H atoms with occupancies of 0.75 were placed at all four O atoms connected to the Na⁺ cation. For NaO^tAm·^tAmOH, the electron density indicates that the H atoms of the OH groups are located along hydrogen bonds. However, the limited data quality did not allow an unrestrained refinement of the positions of these H atoms. According to the charge compensation, the H atoms should be disordered, too.

The single crystals of NaOⁱPr·5ⁱPrOH are highly sensitive; they decompose within seconds except when they are kept in their mother liquor under an inert atmosphere. Therefore, only rather poor diffraction data could be obtained. Correspondingly, a large number of restraints had to be used in the refinement. The disordered C atoms were refined isotropically, with restraints on the C—C and C—O bond lengths. The ordered C atoms were refined anisotropically, but their anisotropic displacement parameters were restrained to be similar to those of neighbouring atoms.

3.1. Space group and disorder of sodium ethoxide (NaOEt)

Sodium ethoxide is difficult to obtain as a pure phase. The reaction of sodium with ethanol, with subsequent evaporation at room temperature under vacuum or evaporation at the boiling point at ambient pressure, results in a mixture of two to four phases, including NaOEt and NaOEt·2EtOH. Evaporation under vacuum at 50 °C for several hours leads to phase-pure NaOEt. Nevertheless, most of our recorded powder patterns were contaminated by traces of other phases.

The powder pattern of NaOEt could be indexed with a tetragonal unit cell, with a = b = 6.2, c = 9.1 Å and V = 352 ų. According to Hofmann's volume increments (Hofmann, 2002), the unit-cell volume corresponds to Z = 4. The systematic extinctions pointed to the space group P4/nbm. Further experiments revealed that some of the weak peaks in the powder pattern were actually caused by foreign phases. The pattern of the phase-pure NaOEt could be indexed with a unit cell of half of the initial volume, with a = b = 4.41, c = 9.07 Å, α = β = γ = 90°, V = 176.4 ų and Z = 2.

The systematic extinctions lead to the extinction symbol Pn––, which corresponds to the space group P4/n or P4/nmm (Hahn, 2005). In P4/nmm, the structure could be solved without difficulty by the real-space method with simulated annealing using the program DASH (David et al., 2006). The unit cell contains two formula units. In P4/nmm there are three different Wyckoff positions with a multiplicity of two: positions 2a and 2b with site symmetry m2, and 2c with site symmetry 4mm. A tetrahedral coordination of the Na⁺ ion agrees with a m2 site symmetry. Correspondingly, the Na⁺ ion was set at position 2a. A rigid C₂H₅O fragment was placed on the general position (16k) with an occupancy of 0.125. The best solution was found in about 10 out of 25 runs and had a good profile-χ² value of 7.26. The O atom was found very close to the 4mm site (Wyckoff position 2c), hence it could be set at this site. The ethyl group is disordered around the 4mm site. The two C atoms could be situated on the general position (16k), resulting in eightfold disorder, or on mirror planes parallel to (100) and (010) (Wyckoff position 8i, site symmetry .m.), or on diagonal mirror planes (Wyckoff position 8j, site symmetry ..m), each with fourfold disorder.

The structure was refined by the Rietveld¹ method (Loopstra & Rietveld, 1969) with TOPAS, with the C atoms on the general position (16k). During the refinement, the C atoms moved close to the diagonal mirror planes. Correspondingly, they were set to the sites 8j (..m). The refinements converged with good R values (Table 1) and smooth difference curves (Fig. 1a). The ethyl groups are fourfold disordered around the fourfold axes, see Fig. 2(a). A corresponding structure was also found for lithium methoxide (LiOMe) (Wheatley, 1961) and sodium methoxide (NaOMe) (Weiss, 1964).

Table 1 Rietveld refinement of NaOEt in P4/nmm and P21m under identical conditions, with restrained H-atom positions and a 2θ range of 2–60° The values marked by a ′ are background-subtracted values. N(param) is the number of structural parameters, including the occupancy parameter.   P4/nmm P21m P21m with both orientations of Et Rwp (%) 4.320 4.146 4.149 Rwp′ (%) 16.98 16.30 16.30 Rp (%) 3.205 3.122 3.126 Rp′ (%) 18.21 17.74 17.75 Goodness-of-fit 2.016 1.935 1.936 N(param) 13 13 13 + 1 (occupancy) Occupancy of the ethyl group 0.25 (fixed) 0.5 (fixed) 0.476 (6):0.024 (6)

Figure 1 Rietveld plots of NaOEt performed in different space groups under identical conditions, i.e. (a) P4/nmm and (b) P21m. Experimental data are shown as black dots and simulated data as a red line, with the difference curve in green below. The vertical tick marks denote the reflection positions. The small arrow in (b) denotes the 210 reflection, which is extinct in P4/nmm, but present in P21m.

Figure 2 Structural models of NaOEt in (a) P4/nmm (origin choice 1) and (b) P21m. Colour key: Na violet, O red and C grey (disordered). H atoms have been omitted for clarity. The view direction is [001]. The crystallographic symmetry elements are included.

A symmetry analysis revealed that in the subgroup P2₁m the ethyl groups would have a twofold disorder only. P2₁m is a translationengleiche subgroup of P4/nmm (Wondratschek & Müller, 2004; Aroyo, 2016) [see Fig. 2(b)]. These two space groups are difficult to distinguish from each other using the systematic extinctions in PXRD. P4/nmm requires the reflection condition hk0: h+k = 2n, whereas P2₁m requires only h00: h = 2n and 0k0: k = 2n (Hahn, 2005). However, in the 2θ range up to 60°, the powder pattern contains only one reflection, which is systematically absent in P4/nmm but can be present in P2₁m. This is the 210 reflection, which has an intensity of close to zero (see Fig. 1b). Hence, an examination of the systematic extinctions left the space group ambiguous.

As a test for the space group, Rietveld refinements were performed in P4/nmm and P2₁m under identical conditions (identical treatment of background, profile parameters, anisotropic peak broadening, etc.). It is an interesting peculiarity that the number of structural parameters is identical in both space groups, which is a very rare case for an organic crystal structure in a group–subgroup relationship. Hence, the resulting confidence values of both space groups can be compared directly. The difference in the R values is slightly in favour of P2₁m (see Table 1). The Rietveld plots are very similar, just the 111 reflection at 2θ = 30.28° is significantly better fitted in P2₁m (see Fig. 1).

In both space groups, the structure is very similar, except for the disorder of the ethyl groups. In P4/nmm the ethyl group is disordered around a fourfold axis, which changes to a twofold axis in P2₁m [see Figs. 2(a) and 2(b)].

As a further test for the space group, a Rietveld refinement was performed in the space group P2₁m with two sets of ethyl groups, one in the position x, x + , z (Wyckoff position 8j) according to the P2₁m structure, and the other on the position −x, x + , z, which is occupied in P4/nmm, but not in P2₁m (see Fig. 2). The occupancies of both sets were set at p and  − p. For P2₁m, p would be and for P4/nmm, p is . The parameter p refined to 0.476 (6). This value and the similarity of the R values between this refinement and the refinement in P2₁m clearly indicate that, within the limitations of the powder data, the correct space group is P2₁m instead of P4/nmm.

A complete ordering of the ethyl groups would require further reduction of symmetry, e.g. to P or P2₁. The corresponding Bärnighausen tree (Bärnighausen, 1980; Chapuis, 1992; Müller, 2004, 2006, 2012) is shown in Fig. 3. Such a symmetry reduction would result in a deviation from tetragonal symmetry and/or in a larger unit cell (supercell). Both effects should be clearly visible in the powder pattern. However, the powder pattern of NaOEt gave no indication of either effect. Hence, the space group is likely to be P2₁m.

Figure 3 The Bärnighausen tree of NaOEt. Colour key: Na violet, O red and C grey. H atoms have been omitted for clarity. The view direction is [001]. t2 denotes a translationengleiche subgroup of index two and i2 an isomorphous subgroup of index two. The small tables give the atom types, Wyckoff positions and site symmetries. Occ denotes the occupancy, if different from one. The experimental crystal symmetry is P21m, with Z = 2.

A transition into a translationengleiche subgoup of index 2 is frequently associated with twinning. Correspondingly, the NaOEt crystals may be twinned, i.e. in one domain the orientation of the ethyl groups is that shown in Fig. 2b and in the other domain the groups are rotated by 90°. However, such a twinning cannot be observed by powder diffraction; hence, it remains unclear if the crystals are actually twinned.

The final Rietveld refinements were carried out in P2₁m. No restraints were applied to the Na, C and O atoms. Restraints were only necessary for the H-atom positions. The final Rietveld plot is shown in Fig. 4. Crystallographic data are included in Table 2.

Table 2 Experimental details for NaOMe, NaOEt, NaOnPr, NaOnBu and NaOnAm   NaOMe (Weiss, 1964) NaOEt NaOnPr NaOnBu NaOnAm Crystal data           Chemical formula CH3ONa C2H5ONa C3H7ONa C4H9ONa C5H11ONa CCDC number – 1943793 1998221 1998220 1998219 Mr 54.02 68.05 82.08 96.10 109.12 Crystal system Tetragonal Tetragonal Tetragonal Tetragonal Tetragonal Space group (No.) P4/nmm (129) P21m (113) P4/nmm (129) P4/nmm (129) P4/nmm (129) Z, Z′ 2, 2, 2, 2, 2, Temperature (K) 298 298 298 298 298 a (Å) 4.343 (5) 4.41084 (4) 4. 38439 (5) 4.43232 (9) 4.4084 (2) c (Å) 7.432 (10) 9.06779 (17) 12.1431 (3) 14.0143 (9) 16.9376 (12) V (Å3) 140.2 (2) 176.418 (5) 233.426 (8) 275.318 (19) 329.16 (4) ρcalc (103 kg m−3) 1.28 1.28 1.17 1.16 1.11 Radiation type Cu Kα Cu Kα1 Cu Kα1 Cu Kα1 Cu Kα1 Wavelength (Å) 1.5418 1.5406 1.5406 1.5406 1.5406 μ (mm−1) – 1.845 1.473 1.314 1.154             Data collection           Diffractometer Goniometer with counting tube Stoe Stadi-P Stoe Stadi-P Stoe Stadi-P Stoe Stadi-P Specimen mounting Powder in N2 stream between polymer films 1.0 mm glass capillary 1.0 mm glass capillary 1.0 mm glass capillary 1.0 mm glass capillary Data collection mode Transmission Transmission Transmission Transmission Transmission Detector Counting tube Linear position-sensitive Linear position-sensitive Linear position-sensitive Linear position-sensitive 2θmin (°) 11 2.0 2.0 2.0 2.0 2θmax (°) 103 80.0 100 100 100 2θstep (°) – 0.01 0.01 0.01 0.01             Refinement           Rp 0.159 0.0233 0.0373 0.0347 0.0376 Rwp – 0.0339 0.0479 0.0471 0.0535 Rexp – 0.0214 0.0295 0.0240 0.0273 Rp′(a) – 0.133 0.161 0.175 0.120 Rwp′(a) – 0.134 0.159 0.187 0.158 Rexp′(a) – 0.085 0.0981 0.0951 0.0806 Goodness-of-fit – 1.42 1.62 1.96 1.96 No. of data points 64 observed intensities 7800 9800 9800 9800 No. of parameters 4 40 56 61 72 No. of restraints 0 8 11 21 26 H-atom treatment fH included in C atom Refined with restraints Refined with restraints Refined with restraints Refined with restraints Note: (a) Rp′, Rwp′ and Rexp′ values are background-corrected data according to Coelho (2018).

Figure 4 Final Rietveld plot of NaOEt. Experimental data are shown as black dots and simulated data as a red line, with the difference curve in green below. The vertical tick marks denote the reflection positions.

The crystal structure of NaOEt (Fig. 5b) is similar to the structures of NaOMe and LiOMe (LiOMe type; Fig. 5a). The Na⁺ ions form a quadratic net in the (001) plane. The O atoms are situated in the centre of each mesh 0.734 (3) Å above or below the plane. The ethyl groups point away from the nets on both sides; hence, they form covering nonpolar layers on both sides of the ionic Na–O nets. Subsequent layers are stacked in the [001] direction. This structure can be regarded as an anti-PbO structure. In red PbO (litharge; Boher et al., 1985), the Pb²⁺ and O²⁻ ions form the same net as the O and Na atoms in NaOEt, and the lone pairs of the Pb²⁺ ion in PbO resemble the positions of the ethyl groups in NaOEt (see Figs. 5b and 5c).

Figure 5 The crystal structures of (a) NaOMe, (b) NaOEt and (c) PbO (litharge). Colour key: Na violet, O red, C grey, H white and Pb blue. In part (c), the large light-green balls represent the lone pairs of the Pb2+ ions. The view direction is [100]. For a better comparison, the unit cell of NaOMe was shifted by (0, 0, ) with respect to the original data of Weiss (1964) and the H atoms of NaOMe were added in calculated positions (with a fourfold disorder). Drawings were made with Mercury (Macrae et al., 2020).

LiOMe and NaOMe crystallize in the space group P4/nmm (Z = 2), with the methyl group on the fourfold axis, which causes no problems, because the shape of the methyl group is close to spherical. In contrast, in NaOEt, the crystal symmetry is reduced to P2₁m. Astonishingly, NaOⁿPr and the higher sodium alkoxides again adopt the higher symmetry P4/nmm (Z = 2), with a fourfold disorder of the alkyl groups (see below). This raises the question, why does NaOEt not adopt P4/nmm symmetry? An `intuitive' explanation for the lower symmetry of NaOEt would be that an ethyl group has a `less cylindrical' shape than a methyl or propyl group and, hence, avoids being situated on a fourfold axis. The reduced disorder of the ethyl groups of NaOEt in P2₁m leads to a more efficient packing and a higher density. Actually, the density of NaOEt is 4% higher than the average density of NaOMe and NaOⁿPr, both of which crystallize in P4/nmm.

3.2. Crystal structures, space group and disorder of NaOⁿPr, NaOⁿBu and NaOⁿAm

Sodium n-propoxide (NaOⁿPr), sodium n-butoxide (NaOⁿBu) and sodium n-amylate (sodium n-pentoxide, NaOⁿAm) were synthesized from sodium and the corresponding alcohols. Upon evaporation of the alcoholic solutions, the solvates precipitated initially (as a mixture with the solvent-free phases). Further evaporation led to the solvent-free forms. The compounds are very sensitive to water; hence, any trace of moisture, also from air, had to be avoided during synthesis, evaporation and PXRD measurements.

The powder diagrams could be easily indexed with tetragonal unit cells, with Z = 2. The structures were solved by the real-space method and refined by the Rietveld method.

The crystal structures are similar to that of NaOEt (anti-PbO type). In the case of NaOⁿPr, the space group is ambiguous. A refinement in P2₁m with two sets of alkyl groups, as performed for NaOEt, did not yield clear results. The occupancies refined to values of 0.38 (3) and 0.12 (3), which is exactly midway between 0.25 (for P4/nmm) and 0.5 (for P2₁m) (see Table 3). However, the refinement with one set of alkyl groups gave significantly lower confidence values in P4/nmm than in P2₁m. For NaOⁿBu and NaOⁿAm, refinements in P4/nmm also provided a better fit than in P2₁m (Table 4). Correspondingly, the final refinements of all three compounds were performed in P4/nmm. The final Rietveld plots are shown in Fig. 6. Crystallographic data are included in Table 2. The crystal structures are shown in Fig. 7.

Table 3 Rietveld refinement of NaOnPr in P4/nmm and P21m under identical conditions, with restraints on the C and H atoms The values marked by a ′ are background-subtracted values. The last column denotes a refinement in P21m with two sets of propyl groups, one corresponding to the orientation in P21m and the other rotated by 90°, which is occupied in P4/nmm, but empty in P21m. N(param) is the number of structural parameters, including the occupancy parameter.   P4/nmm P21m P21m with both orientations of nPr Rwp (%) 5.424 5.654 5.386 Rwp′ (%) 17.953 18.714 17.832 Rp (%) 4.198 4.376 4.238 Rp′ (%) 18.139 18.908 18.324 Goodness-of-fit 1.837 1.915 1.824 N(param) 18 18 18 + 1 (occupancy) Occupancy p 0.25 (fix) 0.5 (fix) 0.38 (3):0.12 (3)

Table 4 Rietveld refinement of NaOnBu and NaOnAm in P4/nmm and P21m under identical conditions, with restraints on the C and H atoms N(param) is the number of structural parameters, including the occupancy parameter.   NaOnBu NaOnAm   P4/nmm P21m P4/nmm P21m Rwp (%) 4.620 4.884 5.403 5.762 Rwp′ (%) 18.52 19.30 15.87 17.03 Rp (%) 3.578 3.766 3.875 4.071 Rp′ (%) 18.73 19.11 12.44 13.13 Goodness-of-fit [S] 1.924 2.032 1.974 2.106 N(param) 23 23 28 28

Figure 6 Final Rietveld plots of (a) NaOnPr, (b) NaOnBu and (c) NaOnAm. Experimental data are shown as black dots and simulated data as a red line, with the difference curve in green below. The vertical tick marks denote the reflection positions.

Figure 7 The crystal structures of (a) NaOnPr, (b) NaOnBu and (c) NaOnAm. Colour key: Na violet, O red, C grey and H white. The view direction is [100].

The lattice parameters and the space group of NaOⁿPr agree with the data determined by Chandran et al. (2006).

The n-butyl and n-amyl groups are highly disordered, and the electron density is smeared out, especially for the terminal and the next-to-terminal C atoms. The description of these structures in P4/nmm with fourfold disordered alkyl groups on Wyckoff position 8j is only an approximation of the actual electron density.

We tried to prepare phase-pure powders of solvent-free NaOⁱPr and NaO^tAm, but the crystal structures could not be solved by PXRD yet. The samples probably contained mixtures of different phases.

3.3. Solvates

By crystallization from the corresponding alcohols, we obtained single crystals of four alcohol solvates of sodium alkoxides: NaOEt·2EtOH, NaOⁿPr·2ⁿPrOH, NaOⁱPr·5ⁱPrOH and NaO^tAm·^tAmOH. All of these solvates are sensitive to moisture and air. In a vacuum and under argon (or nitro­gen), they decompose into their solvate-free forms. The decomposition is comparably slow for NaOEt·2EtOH, but fast for NaOⁱPr·5ⁱPrOH. Correspondingly, the solvates must be stored in their mother liquor or in the presence of vapours of the corresponding alcohols or kept at low temperature.

The chemical compositions and crystal structures of these four solvates were determined by single-crystal X-ray diffraction. However, there were three obstacles: (i) the mounting of the crystals on the diffractometer was challenging due to their sensitivity to air, moisture, vacuum and dry inert gas; (ii) the crystal quality was limited, especially for NaOⁱPr·5ⁱPrOH; (iii) the crystal structures of NaOⁿPr·2ⁿPrOH and NaOⁱPr·5ⁱPrOH are highly disordered. In NaOⁿPr·2ⁿPrOH, the disorder affects all of the propyl groups. In NaOⁱPr·5ⁱPrOH, four of the ten ⁱPrOH units are disordered over two widely separated positions each.

The stability of the solvates of the sodium n-alkoxides decreases with increasing chain length. Correspondingly, crystal structures could be determined only for the solvates of NaOEt and NaOⁿPr, whereas the solvates of NaOⁿBu and NaOⁿAm are highly instable, poorly crystalline and decompose rapidly, even under cold dry nitro­gen.

3.3.1. NaOEt·2EtOH and NaOⁿPr·2ⁿPrOH

Sodium ethox­ide and sodium n-propoxide crystallize as needles (see Fig. 8). The single-crystal X-ray analysis (Table 5) revealed the com­pounds to be disolvates with the composition NaOR·2ROH, as determined by Geuther (1868a,b) and Frölich (Geuther & Frölich, 1880). Both solvates are isostructural. The O atom of the alkoxide anion (RO⁻) bridges two Na⁺ ions, leading to helical Na—O—Na—O chains. The chains follow a crystallographic 2₁ screw axis. The Na⁺ ions are additionally coordinated to two alcohol molecules (ROH), resulting in a distorted tetrahedral coordination geometry for the Na⁺ ions. In NaOⁿPr·2ⁿPrOH, all the propyl groups are disordered and most of the C atoms were refined with split positions, with occupancies between 0.40 and 0.60. The OH groups of the alcohol molecules form hydrogen bonds to neighbouring ROH molecules and RO⁻ anions, which additionally stabilize the chains (see Fig. 9). The alkyl groups point outwards. Hence the chains are like tubes, with a polar/ionic inner region and a nonpolar outer region. In the crystal, all the tubes are arranged parallel and form a distorted hexagonal packing (see Fig. 10). However, the space group is different, i.e. P2₁/c for NaOEt·2EtOH and C2/c for NaOⁿPr·2ⁿPrOH.

Table 5 Experimental details for the sodium alkoxide solvates All determinations were carried out with Cu Kα radiation using a Siemens Bruker three-circle diffractometer with an APEXII detector, an Incoatec Iμs microfocus source and mirror optics.   NaOEt·2EtOH NaOnPr·2nPrOH NaOiPr·5iPrOH NaOtAm·tAmOH Crystal data         Chemical formula C2H5ONa·2C2H5OH C3H7ONa·2C3H7OH C3H7ONa·5C3H7OH C5H11ONa·C5H11OH CCDC number 1943794 1998225 1998224 1998227 Mr 160.18 202.26 382.55 198.27 Crystal system Monoclinic Monoclinic Monoclinic Monoclinic Space group (No.) P21/n (14) C2/c (15) C2/c (15) P21/c (14) Z, Z′ 4, 1 8, 1 8, 1 4, 1 Temperature (K) 238 (2) 173 (2) 173 (2) 296 (2) a (Å) 11.622 (6) 23.745 (5) 21.2073 (18) 10.1260 (8) b (Å) 5.1926 (9) 5.0750 (11) 17.1307 (13) 6.0299 (5) c (Å) 17.682 (6) 24.174 (5) 17.825 (2) 20.6944 (18) β (°) 104.08 (3) 111.589 (10) 123.871 (5) 104.16 V (Å3) 1035.0 (7) 2708.7 (10) 5376.9 (10) 1225.18 (18) ρcalc (103 kg m−3) 1.03 0.992 0.945 1.08 Wavelength (Å) 1.54178 1.54178 1.54178 1.54178 μ (mm−1) 1.006 0.849 0.686 0.869 Crystal habit Needle Needle Needle Needle Crystal size (mm) 0.8 × 0.08 × 0.02 0.5 × 0.05 × 0.05 0.4 × 0.02 × 0.02 1 × 0.02 × 0.01           Data collection         θ range (°) 4.14–59.9 3.93–50.9 3.60–40.2 4.41–50.7 Absorption correction Multi-scan (SADABS; Bruker, 2015) Tmin, Tmax 0.2700, 0.7486 0.5182, 0.7500 0.771, 0.875 0.477, 0.991 No. of measured reflections 5735 10 777 9647 13194 No. of unique reflections 1124 1616 1652 1300 Rint 0.317 0.0887 0.0724 0.112           Refinement         No. of parameters 95 114 239 118 No. of restraints 0 0 84 15 wR(F2) 0.2709 0.2984 0.3669 0.1613 R[F2 > 2σ(F2)] 0.2178 0.0954 0.1215 0.0574 S 0.980 1.064 1.196 1.002 Δρmax, Δρmin (e− Å−3) 0.16, −0.20 0.24, −0.20 0.22, −0.17 0.30, −0.26

Figure 8 The crystals of (a) NaOnPr·2nPrOH (image width about 15 mm) and (b) NaOtAm·tAmOH (image width about 2 mm), both in polarized light.

Figure 9 Helical chains in (a) NaOEt·2EtOH and (b) NaOnPr·2nPrOH. Colour key: Na violet, O red, C grey and H white. Hydrogen bonds are drawn as dotted light-blue lines. The H atoms of the alkyl groups have been omitted for clarity. In part (b), the disordered propyl groups are represented by their major-occupied atomic positions only.

Figure 10 The crystal structures of (a) NaOEt·2EtOH (space group P21/c, view direction [010] and displacement ellipsoids at the 50% probability level) and (b) NaOnPr·2nPrOH (space group C2/c, view direction [00]). Selected symmetry elements are shown. In both structures, there is a 21 screw axis in the middle of each chain.

Between the `tubes' there are only van der Waals contacts between the alkyl groups. This structure explains the observed needle-like morphology of both compounds, with the needle axes parallel to the chain direction [010]. The weak interactions between the `tubes' allow them to librate around their long axis, which is manifested in the anisotropic displacement parameters of NaOEt·2EtOH (see Fig. 10a). In the case of NaOⁿPr·2ⁿPrOH, the limited crystal quality and the disorder of the propyl groups prevent an interpretation of the displacement ellipsoids.

The corresponding lithium methoxide solvate, LiOMe·2MeOH, is a disolvate, like NaOEt·2EtOH and NaOⁿPr·2ⁿPrOH, but its structure is different. LiOMe·2MeOH consists of Li₄(OMe)₄(MeOH)₆ tetramers, which are connected through hydrogen bonds via MeOH molecules to form a two-dimensional network. As in NaOEt, the interior layer of this network consists of metal ions and O atoms, whereas the alkyl groups point outwards. These layers are stacked through van der Waals contacts between the methyl groups only.

3.3.2. NaOⁱPr·5ⁱPrOH

Sodium isopropoxide forms a solvate which contains as many as five molecules of iso­propanol per NaOⁱPr unit. Hence, this structure can be regarded as an iso­propanol in which one sixth of the protons of the OH groups are replaced by sodium ions. Correspondingly, the structure of NaOⁱPr·5ⁱPrOH provides an insight into the structure of liquid iso­propanol itself.

The solvate crystallizes in the space group C2/c, with Z = 8. There are two symmetrically independent Na⁺ ions, both on the twofold axis. Each Na⁺ ion coordinates to four O atoms of ⁱPrO⁻ and ⁱPrOH moieties (Fig. 11a). The H atoms of the OH groups could not be located reliably, as they are probably dynamically disordered. Because of the charge compensation, it is expected that in any instance each Na⁺ cation is surrounded by one ⁱPrO⁻ ligand and three ⁱPrOH molecules. These Na(ⁱPrO)(ⁱPrOH)₃ units are connected by further ⁱPrOH molecules to form a chain along the twofold axis parallel to [010] (see Figs. 11a and 11b). All iso­propanol molecules which are not directly coordinated to sodium have an occupancy of 0.5. All iso­propyl groups show disorder.

Figure 11 (a) The crystal structure of NaOiPr·5iPrOH, showing one chain. The view direction is [001], with the b axis horizontal. Displacement ellipsoids are drawn at the 20% probability level. All iPrOH molecules not directly coordinated to Na have an occupancy of 0.5 only. Dotted lines represent the four independent hydrogen-bond networks. The arrows indicate the crystallographic twofold axis. (b) Selected hydrogen-bond networks in NaOiPr·5iPrOH. (c) The crystal structure of LiOiPr·5iPrOH. The disorder of the iPr groups is not shown. In parts (b) and (c), the H atoms are shown as white spheres in calculated positions. The H-atom positions shown here represent only one possibility; actually, the H atoms are disordered and could not be located experimentally. Minus (−) signs denote the anions.

The geometry of the chain is close to 112/m symmetry (rod group No. 11; Kopský & Litvin, 2010).

There are four independent hydrogen-bond networks in each chain, each with an occupancy of 0.5 (see Fig. 11a). Two of these networks are shown in Fig. 11b.

The hydrogen-bond networks are considerably different from those in pure solid iso­propanol. Pure iso­propanol forms different hydrogen-bond networks, depending on the experimental conditions: the high-pressure polymorph exhibits eight-membered rings, whereas the low-temperature polymorph forms helical chains with local 3₁ or 3₂ symmetry (see Fig. 12) (Ridout & Probert, 2014). In contrast, the hydrogen-bond network of NaOⁱPr·5ⁱPrOH contains branching between the alcohol molecules, i.e. alcohol molecules are connected by hydrogen bonds to three other alcohol molecules. There are two different topologies, marked as `Motif A' and `Motif B' in Fig. 11(b). Motif A is also present in LiOⁱPr·5ⁱPrOH (Mehring et al., 2002). Motifs A and B can neither be found in other sodium alkoxide solvates nor in the crystal structures of pure iso­propanol. In liquid iso­propanol, one could expect to find a mixture of all three motifs, namely, rings, chains and branchings.

Figure 12 The hydrogen-bond networks of solid pure iso­propanol. (a) Eight-membered ring in the high-pressure phase. (b) Threefold screw axis in the low-temperature phase. In both structures, some of the iso­propyl groups are disordered.

In NaOⁱPr·5ⁱPrOH, the hydrogen-bonded chains are sur­rounded by the nonpolar iso­propyl groups. Between the chains, there are only van der Waals contacts between the iso­propyl groups (see Fig. 13). Similarly, in both polymorphs of pure ⁱPrOH, the rings and chains have polar surfaces, and are connected to neighbouring rings or chains by van der Waals interactions (see Figs. S1 and S2 in the supporting information).

Figure 13 The crystal structure of NaOiPr·5iPrOH (space group C2/c, view along the chains and view direction [00]). The chains are located on twofold rotation axes, in contrast to the 21 screw axes for NaOnPr·2nPrOH (see Fig. 10b).

The chains of NaOⁱPr·5ⁱPrOH are arranged in a distorted hexagonal packing. The packing seems to be similar to the chain packing in NaOⁿPr·2ⁿPrOH. The space group is also the same (i.e. C2/c). However, the chains in NaOⁱPr·5ⁱPrOH are situated on a twofold rotation axis, whereas the chains of NaOⁿPr·2ⁿPrOH are placed on a 2₁ screw axis (see Figs. 10b and 13).

3.3.3. NaO^tAm·^tAmOH

The X-ray structure analysis revealed that sodium tert-amylate (sodium 2-methyl-2-butano­late, NaO^tAm) forms a monosolvate with tert-amyl alcohol (2-methyl-2-butanol). In this structure, neighbouring Na⁺ ions are bridged by two ligands in the form of a square. The square shares corners with two other squares, leading to chains (see Fig. 14). Each square is centred by a crystallographic inversion centre. The squares are additionally connected by hydrogen bonds. The H atom engaged in this bond is probably disordered, so that in any instance each square contains one ^tAmO⁻ anion and one ^tAmOH ligand, due to electrostatic considerations. The squares form an interplanar angle of 49.8° only, which is apparently caused by the hydrogen bonds. The tert-amyl groups point outwards, as in the other solvates.

Figure 14 A view of the structure of NaOtAm·tAmOH, with displacement ellipsoids drawn at the 50% probability level. The H atoms of the tert-amyl groups have been omitted for clarity. The light-blue lines denote the hydrogen bonds. The H atom is disordered along the hydrogen bond. The black circles represent crystallographic inversion centres. The red symmetry elements represent the approximated local symmetry of the chain (2/b11).

The chain has approximately 2/b11 symmetry, which is a nonstandard setting of 2/c11 (rod group No. 7; Kopský & Litvin, 2010). In the crystal, only the inversion symmetry is maintained in the space-group symmetry P12₁/n1.

The arrangement of the chains (Fig. 15) is similar to that in NaOEt·2EtOH (Fig. 10a). The space group is also the same (P2₁/c, here in the P2₁/n setting). However, in NaOEt·2EtOH, the chains are aligned along the 2₁ axis, whereas in NaO^tAm·^tAmOH, the chains contain inversion centres.

Figure 15 The crystal structure of NaOtAm·tAmOH, viewed along the chains (space group P21/n, view direction [010]), with displacement ellipsoids drawn at the 50% probability level. Selected symmetry elements are shown.