CRYSTALLOGRAPHY

R. P. OZEROV, L. E. FYKIN, N. V. RANNEV, G. S. ZHDANOV

NEUTRON-DIFFRACTION LOCALIZATION OF HYDROGEN ATOMS IN THE STRUCTURE OF LITHIUM SULFATE MONOHYDRATE $\mathrm{Li_2SO_4 \cdot H_2O}$

(Presented by Academician N. V. Belov on 11 VIII 1962)

The motif of the crystal structure of $\mathrm{Li_2SO_4 \cdot H_2O}$* was determined by x-ray diffraction by Ziegler ($^1$). A later refinement of the structure with respect to the positions of the heavy atoms was carried out by x-ray diffraction by Larson and Helm-

Fig. 1. Projection $\sigma(xz)$ of the nuclear density of the structure of lithium sulfate monohydrate

goltz ($^2$); the orientation and magnitude of the interproton vector were studied by the method of nuclear magnetic resonance (NMR) by many authors ($^{3-6}$).

We undertook a neutron-diffraction study of a single crystal of $\mathrm{Li_2SO_4 \cdot H_2O}$ for the purpose of directly localizing the hydrogen atoms in the structure**. Single crystals of irregular shape were used

* Monoclinic unit cell $a = 5.43\,\text{\AA}$, $b = 4.83\,\text{\AA}$, $c = 8.14\,\text{\AA}$, $\beta = 107^\circ 35'$; space group $C_2^2 - P2_1$, number of “molecules” 2.

** The single crystals were provided to us by I. V. Gavrilova, to whom the authors express their gratitude.

with linear dimensions of \(\sim 7\) mm. The crystals had small natural faces, which made it possible to orient them optically directly on the diffractometer \((^7)\). A total of 180 nonzero-intensity reflections of the type \(\pm h0l\) and 90 reflections of the type \(0kl\) were measured \((\lambda = 1.05\ \text{Å})\). In measuring the intensities of reflections of the type \(0kl\) (the center of symmetry is absent in the projection)

Fig. 2. Projection \(\sigma(yz)\) of the nuclear density of the structure of lithium sulfate monohydrate

we encountered the possible influence of anomalous neutron dispersion in scattering by \(\mathrm{Li}^6\) nuclei \((^8)\); however, it was established that for a crystal with the natural mixture of lithium isotopes this effect is small. At this stage no extinction correction was introduced either. The usual absorption correction was introduced (for a cylindrical specimen), the value of \(\mu\) being obtained by calculation from the known cross sections of lithium and hydrogen and experimentally (from the absorption of a very thin neutron beam by the central part of the specimen); in both cases values \(\mu = 2.2\ \text{cm}^{-1}\) were obtained. After this the relative values of the structure amplitudes \(F\) were determined in the usual way.

In the first approximation the projections of the nuclear density \(\sigma(xz)\) and \(\sigma(yz)\) were calculated* from the experimental values of \(F\), the signs of which were determined taking into account the positions only of the heavy atoms (S, O, Li) according to the coordinates of Ziegler \((^1)\). The parameters of the heavy atoms determined from these projections did not change in any appreciable way; they correspond better to the values of Ziegler \((^1)\) than to those of Larson \((^2)\). In both projections, minima corresponding to hydrogen atoms were clearly revealed. The results obtained were used in calculating the projections in the following approximations (Figs. 1 and 2) and in refining the coordinates by the method of differential synthesis. The parameters determining the positions of the hydrogen atoms in the structure are given in Table 1.

* All calculations were carried out on the “Kristall” machines of the L. Ya. Karpov Physicochemical Institute and the “Strela” machine of the Computing Center of Moscow State University named after M. V. Lomonosov.

From the projections, the configuration of the H₂O “molecule” and the system of hydrogen bonds in the structure have been determined. The atoms H₁ and H₂ are located near the atom O₅ (the oxygen atom of the H₂O “molecule”) in such a way that the hydrogen bonds O₅—H₂···O₅′ and O₅—H₁···O₂ are formed (O₂ is an oxygen atom of the SO₄ tetrahedron). The orientation of the interproton vectors is $\alpha = 96^\circ 54'$, $\beta = 43^\circ 12'$ and $\gamma = 47^\circ 36'$ ($\alpha$, $\beta$, $\gamma$ are the angles between the direction of the interproton vector and the positive direction of the axes)

Fig. 3. Projection of the nuclear density of the structure of α-resorcinol $\sigma(xy)$.
$G_1$, $G_3$, $J_2$ and $J_4$ are oxygen atoms, $H$ are hydrogen atoms, $A$, $B$, $C$, $D$, $E$, $F$ are carbon atoms.

is in good agreement with the results obtained by the NMR method (⁶).

Table 1

Position of hydrogen atoms
$(xyz \ \text{and} \ x,\ y+\tfrac{1}{2},\ \bar z)$

The result obtained by us is of interest from two points of view: the interatomic distances in the H₂O “molecule” (O₅—H₁ and O₅—H₂), and especially the angle H₁—O₅—H₂, are substantially greater than those in a free water molecule, in true crystal hydrates, and in the structure of ice (the O—H distances are 1.1 Å and the H—O—H angle is 145°; the most frequently encountered values are 0.99–1.00 Å and 109°). Attention is also drawn to the shortened distance Li₁—O₅ (1.98 Å). These atoms, together with the hydrogen atoms, form a characteristic chain

$$ \cdots \mathrm{Li}_1-\mathrm{O}_5 \begin{matrix} /\mathrm{H}_1\\ \backslash \mathrm{H}_2 \end{matrix} \cdots \mathrm{Li}_1- $$

(Fig. 1), extending through the whole crystal in the direction of the $x$ axis.

The indicated features of the crystal structure of $\mathrm{Li_2SO_4\cdot H_2O}$ may be explained on the basis of ideas about the nature of the Li—O bond,

being developed at present by D. N. Shigorin et al. \(^{(9,10)}\). According to these ideas, the unshared pair of \(p\)-electrons of the oxygen atom occupies certain vacant orbitals of the valence shell of the lithium atom. As a result, the electrostatic equilibrium in the \(\mathrm{H_2O}\) “molecule” is disturbed and the protons diverge through a larger angle. The \(\mathrm{Li—O}\) bond becomes stronger, and in character covalent, which leads to a decrease in the corresponding interatomic distance.

The system of hydrogen bonds in the structure is characterized by the presence of a zigzag infinite chain \(\mathrm{O_5—H_2\cdots O_5'—H_2'\cdots}\), with an angle of \(109^\circ\) at the \(\mathrm{O_5}\) atom, extending along the \(y\) axis (Fig. 2). To this chain, also by means of hydrogen bonds, \(\mathrm{SO_4}\) tetrahedra are attached. Such a system is characterized by a step (period \(b\)) of \(4.83\ \text{Å}\). The presence of an infinite chain of bonds, similar in character but helical, \(\mathrm{O—H\cdots O—H\cdots}\), was established by Bacon \(^{(11)}\) in the structure of \(\alpha\)-resorcinol (Fig. 3). In this case the pitch of the helix (period \(c\)) is \(5.66\ \text{Å}\).

The authors express their gratitude to D. N. Shigorin and I. B. Golovanov for their interest in the work, and also to S. V. Kiselev and V. G. Bryzhev for their assistance in the experiment and calculations.

Physicochemical Institute
named after L. Ya. Karpov

Received
11 VIII 1962

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