PHYSICAL CHEMISTRY

G. M. MIKHAILOV, A. G. LUNDIN, S. P. GABUDA, and K. S. ALEKSANDROV

PROTON MAGNETIC RESONANCE IN SELENOUREA

(Presented by Academician V. N. Kondrat’ev on 24 VII 1961)

Selenourea is one of the compounds of the type EC(NH₂)₂, where E denotes the elements O, S, Se. A schematic view of the selenourea molecule is given in Fig. 1. Urea OC(NH₂)₂ (¹, ²) and thiourea SC(NH₂)₂ (³, ⁴) have already been studied by the nuclear magnetic resonance method. In these studies the presence of reorientation (internal rotation) of urea molecules above 300° K and of thiourea molecules above 220° K was found.

We have studied, by the proton magnetic resonance method, a polycrystalline sample of selenourea in the temperature range from 77° K to room temperature. In doing so, we obtained the dependence of the second moment of the proton-resonance absorption line on temperature, presented in Fig. 2.

The value of the second moment at low temperatures, equal to 18.2 oersted, makes it possible to determine the distance between protons in the NH₂ groups. It may be assumed that the N—H distance in such compounds, as follows from numerous determinations (⁵, ⁶), is about 1 Å; therefore the contribution from the interaction of a proton with the nearest nitrogen to the second moment, calculated by the Van Vleck formula (⁷), is 2 oersted. The contribution of the protons of neighboring NH₂ groups is more difficult to calculate, since the crystal structure of selenourea is unknown. It may be supposed, however, that it is close to the structure of thiourea. Under this assumption, the contribution of the protons of neighboring groups to the second moment is 0.15 oersted. The remaining 15.85 oersted are due to the proton–proton interaction within the NH₂ group. According to the Van Vleck formula this corresponds to a distance between the protons in the NH₂ groups equal to 1.75 Å, which is close to the analogous distance in urea (⁸) and thiourea (⁶).

The decrease of the second moment from 18.2 to 6.9 oersted as the temperature changes from 130 to 180° K may be caused either by rotation (reorientation) of the NH₂ groups about the C—N bond, or by rotation of the whole molecule about its Se=C axis. As is known (⁹), upon reorientation of groups of atoms the decrease of the second moment is determined by the factor

\[ k = \frac{1}{4}(3\cos^2\theta - 1)^2, \tag{1} \]

where θ is the angle between the direction of the proton–proton vector and the axis of reorientation. It is easy to see that a decrease of the second moment from 18.2 to 6.9 oersted corresponds to an angle θ = 30°. Such an angle is realized only if the selenourea molecule rotates about the Se=C axis (see Fig. 1), whereas rotation of the NH₂ group about the C—N bond does not satisfy this condition (the angle between the C—N reorientation axis and the p—p vector is 90°). It should be noted that the decrease of the second moment from 18.2 to 6.9 oersted could also be explained by rocking of the NH₂ groups about the C—N bond through an angle of ±40°. However, as Das showed (¹⁰), the probability of such large amplitudes of oscillation is negligibly small, and therefore this possibility should be rejected as unrealistic.

The dependence of the second moment on temperature makes it possible to calculate the height of the potential barrier that hinders the rotation of the molecules \(\mathrm{SeC(NH_2)_2}\). As Gutowsky and Pake showed \((^{11})\), the temperature dependence of the second moment is determined by the expression

\[ S_2(T)=S_2^{\mathrm{l}}+\left(S_2^{\mathrm{h}}-S_2^{\mathrm{l}}\right)\frac{\pi}{2}\operatorname{arc\,tg}\left(\frac{\gamma S_2^{1/2}(T)}{2\pi\nu_k}\right), \tag{2} \]

where \(S_2^{\mathrm{l}}\), \(S_2^{\mathrm{h}}\), and \(S_2(T)\) are the second moments, respectively, at low temperatures, high temperatures, and at temperature \(T\); \(\nu_k\) is the correlation frequency of reorientation, which can be represented in the form \((^{10,11})\)

\[ \nu_k=\nu_0\exp\left(-\frac{V_0}{kT}\right) =\frac{1}{2\pi}\left(\frac{2V_0}{I}\right)^{1/2}\exp\left(-\frac{V_0}{kT}\right); \tag{3} \]

where \(V_0\) is the so-called torsional frequency of rotation of a molecule with moment of inertia \(I\) over a barrier of height \(V_0\); \(k\) is Boltzmann’s constant; \(T\) is the absolute temperature.

The moment of inertia of the selenourea molecule for its rotation about the \(\mathrm{Se=C}\) axis was calculated on the assumption that the \(\mathrm{C—N}\) and \(\mathrm{N—H}\) distances are analogous to the corresponding distances in urea and thiourea, and is \(I=70.5\cdot 10^{-40}\ \mathrm{g\cdot cm^2}\).

Fig. 1. Schematic view of the selenourea molecule

With the aid of formula (2), from experimental data on the temperature dependence of the second moment one can determine the dependence of the correlation frequency \(\nu_k\) on temperature. Comparing it with the dependence calculated by formula (3), one can, for a known moment of inertia, determine the height of the potential barrier \(V_0\). Figure 3 gives the theoretical dependences \(\nu_k(T)\), calculated by formula (3), for different values of \(V_0\), and the experimental values calculated by formula (2). As can be seen from the figure, the experimental values agree well with the theoretical dependence for

\[ V_0=(6.0\pm0.4)\ \text{kcal/mole}. \]

Fig. 2. Temperature dependence of the second moment of the proton-resonance absorption line in a polycrystal of \(\mathrm{SeC(NH_2)_2}\)

Thus, it may be regarded as established that, in selenourea crystals, reorientation (rotation) of the \(\mathrm{SeC(NH_2)_2}\) molecules takes place around the \(\mathrm{Se=C}\) axis at temperatures above \(130^\circ\ \mathrm{K}\). It should be noted, however, that such “rotation” is not continuous. The torsional frequency of rotation of a selenourea molecule having energy greater than \(V_0\), as is seen from formula (3), is of the order \(\nu_0\approx 10^{12}\ \mathrm{Hz}\). The reorientation process itself apparently consists of very rapid turns of the molecules, repeated rather frequently, through an angle of \(180^\circ\), and more rarely through \(360^\circ\) or more. The correlation frequency \(\nu_k\) in fact represents the result of averaging these turns over all the molecules participating in the motion, on the assumption that their rotation occurs uniformly with frequency \(\nu_k\).

The correlation frequency determined from the experimental data for a temperature of \(150^\circ\ \mathrm{K}\) is of the order of \(10^4\ \mathrm{Hz}\), and for room temperature about \(10^{10}\ \mathrm{Hz}\). Thus, even at room temperature the lifetime of a molecule in the state of “rest” is approximately 100 times greater than the time spent by the molecule in rotation, while at a temperature of \(150^\circ\ \mathrm{K}\) the ratio of these times is \(10^8\).

Of great interest is the nature of the potential barrier limiting the rotation of selenourea molecules. Although in the general case the nature of such barriers is unclear, in this particular case one may assume that the barriers limiting the rotation of the molecules \(\mathrm{SeC(NH_2)_2}\) are intermolecular hydrogen bonds \(\mathrm{NH}\cdots\mathrm{Se}\). This, in particular, is confirmed by the fact that the barriers to rotation of thiourea and urea molecules, calculated according to \((^2,{}^3)\), are respectively 9 and 12.7 kcal/mole. At the same time it is known \((^8)\) that the hydrogen bond \(\mathrm{NH}\cdots\mathrm{S}\) in thiourea is weaker than the bond \(\mathrm{NH}\cdots\mathrm{O}\) in urea. From our point of view this is understandable, since strong hydrogen bonds \(\mathrm{NH}\cdots\mathrm{E}\) should correspond to high potential barriers limiting the rotation of \(\mathrm{EC(NH_2)_2}\) molecules. Thus, the value we have obtained for the barrier height for rotation of selenourea molecules, \(V_0 = 6\) kcal/mole, indicates that the hydrogen bonds \(\mathrm{NH}\cdots\mathrm{Se}\) are still weaker than the bonds \(\mathrm{NH}\cdots\mathrm{S}\) and \(\mathrm{NH}\cdots\mathrm{O}\) in thiourea and urea.

Fig. 3. Temperature dependence of the correlation frequency of reorientation of \(\mathrm{SeC(NH_2)_2}\) molecules

The authors express their gratitude to V. F. Dvoryankin for providing the selenourea sample.

Institute of Physics
Siberian Branch of the Academy of Sciences of the USSR

Siberian Technological Institute

Received
18 VII 1961

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