STRUCTURE OF THE METHANE MOLECULE¹

Victor Henri, Zurich.

Over the past 10 years, a whole series of methods for studying the structure of molecules has been developed, and an almost entirely new branch of molecular physics has emerged. The results obtained are of very general significance, and the application of the theories and principles that has been made on the basis of these studies marks a new period in the development of chemistry.

The structure of the methane molecule is of especially great significance for all of organic chemistry, since it is connected with the fundamental conceptions concerning the carbon atom; and the application of new methods of investigation to the study of the methane molecule has led to very promising results.

Methane is a colorless, odorless gas; it shows a slight deviation from the simple gas laws and liquefies at −164° C. It is the most important component of natural gas: in some places natural gas contains up to 99.3% methane. Since the time of the work of Pasteur, van ’t Hoff, and Le Bel, for more than 50 years the idea of the tetrahedral structure of the methane molecule has been generally accepted; it was assumed that the carbon atom is located at the center of a tetrahedron, and the four hydrogen atoms at the vertices of the tetrahedron (Fig. 1).

¹ Chemical Reviews, 4, 189, 1927.

STRUCTURE OF THE METHANE MOLECULE

From the point of view of modern ideas about the structure of the atom, two of the six planetary electrons of carbon are located close to the nucleus, while the remaining four revolve in the outer orbits. The hydrogen atom has one planetary electron, and the electronic structure of the methane molecule may schematically be represented by Fig. 2, where the dots represent electrons, with the inner electrons enclosed inside the circle.

Fig. 1.

The evidence by which the conception of the tetrahedral structure of the methane molecule is supported is based, first of all, on the fact that methane has no isomeric derivatives. For example, there exists only one dichloromethane, whereas if the structure were not tetrahedral, there would have to exist two isomeric dichloromethanes. The three most general propositions on which all of organic chemistry is built are as follows:

1. The equivalence of the four valences of carbon.
2. The tetrahedral structure of methane.
3. The rigidity of the structure of the molecule.

Fig. 2.

With the development of molecular physics during the last ten years, physicists have introduced new methods for investigating the structure of molecules, and have also achieved

very important successes in the theoretical interpretation of results. These new methods were first tested on certain simple molecules, such as: nitrogen, hydrogen, chlorine, hydrogen chloride, carbon monoxide; then more complex molecules were investigated, and at the present time more than seventy molecules have been studied, of which about fifty have been investigated in my laboratory.

Fig. 3.

The results of the study of the methane molecule may be briefly summarized as follows:

1. The methane molecule is not a tetrahedron, but has the structure of a pyramid. The distance between two neighboring hydrogen atoms is equal to \(1 \text{ Å}\), or \(10^{-8}\ \text{cm}\), and the height of the pyramid is \(0.37 \text{ Å}\). The relative positions of the hydrogen atoms and methane are shown in Fig. 3.

2. When the four hydrogen atoms in methane are replaced by four chlorines, the structure changes and becomes tetrahedral, so that the molecule of carbon tetrachloride is a tetrahedron. The dichloro derivatives of methane have a tetrahedral structure, whereas some tetra-derivatives of methane have the structure of a pyramid. For example, pentaerythritol, where each hydrogen atom is replaced by a \((\mathrm{CH}_2\mathrm{OH})\) group, has a pyramidal structure, as does the molecule of tetraphenylmethane.

Fig. 4.

1. The four valences of the atom are not equivalent. Two of them are of one type, and the other two of another (Fig. 4). Our experimental data lead us to suppose that the six electrons of the carbon atom are distributed in three layers. Two inner electrons occupy the \(1_1\) orbits, while of the four outer elec-

STRUCTURE OF THE METHANE MOLECULE

two occupy the \(2_1\) orbitals, and the other two—the \(2_2\) orbitals (Fig. 5).

These three conclusions are in decisive contradiction with the classical theories on which organic chemistry was built. In the light of the new experimental data, a complete revision of the chemistry of carbon compounds must be carried out.

The experimental methods by means of which these important results were obtained may be divided into five groups:

1. Scattering of light.
2. Absorption spectra.
3. The structure of crystals, studied by means of X-rays.
4. Calculation of the potential energy of molecules.
5. Emission spectra of atoms and molecules.

In what follows, all these methods will be briefly considered and the results obtained with them summarized.

Fig. 5.

1. Scattering of Light.

The best-known example of light scattering is the blue color of the sky, as the result of the scattering of sunlight by the molecules of the atmosphere. Tyndall (1) was the first to study light scattering in detail, and therefore the phenomenon itself was called the “Tyndall effect.” Strutt (Lord Rayleigh—the elder) (2) developed a theory in which it is shown that when a beam of light with intensity \(I_0\) falls on a gas enclosed in a tube, part of the beam is scattered by the gas molecules, and the intensity of this scattered light \(I_1\) (Fig. 6) in a given direction depends on the properties of the molecules, on their volume, and on the number of molecules in \(1\ \mathrm{cm}^3\). The fraction of scattered light is very small and ranges from two to five millionths of the intensity of the incident rays. If the molecules are isotropic, then the scattered light is completely polarized, and the plane

polarization is determined by the directions of both beams \(I_0\) and \(I_1\).

During the last seven years a number of experimental studies have been carried out on the scattering of light by various gases. R. Strutt (Lord Rayleigh, the younger) (3), Cabannes (4), Gans (5), and Raman (6) showed that for rare gases—helium, argon, and neon, which are monatomic—complete polarization of the scattered light is observed. All these molecules are isotropic. In the case, however, of diatomic and triatomic gas molecules—nitrogen, hydrogen, oxygen, carbon monoxide, hydrogen chloride, carbon dioxide, etc.—only partial polarization is observed in the scattered

Fig. 6.

light. This partial polarization is due to the anisotropic character of the molecules indicated. The complete theory, developed by Gans (5), makes it possible to calculate the degree of anisotropy of the molecules, knowing the fraction of the scattered light that is unpolarized. In this way it can be shown that the structure of these various diatomic and triatomic gases can be represented by an ellipsoid. A special study of the methane molecule and other hydrocarbons was carried out by Cabannes (7).

The measurement of the fraction of scattered light that is polarized is in fact associated with great technical difficulties. The pure gas was dried and filtered so that it contained no dust, and was then introduced into a tube having the form of a cross (Fig. 7). An intense beam of monochromatic light was passed through the gas in one direction, and the light scattered perpendicular to this direction was photographed.

…phenomenon. The amount of polarized light was determined with the aid of a system of nicols. The results obtained with methane showed that in this case the fraction of unpolarized light is large, whence it follows that the methane molecule is anisotropic. This is the result of a tetrahedral structure, since it turned out that the molecule has two different moments of inertia. In the case of carbon tetrachloride Kabann found isotropic molecules.

2. Absorption spectra.

When a beam of light containing all wavelengths from the ultraviolet to the infrared passes through a gas, or vapor, enclosed in a tube with quartz windows, then analysis of the light beam \(I_1\) (Fig. 8) after its passage through the gas shows that certain wavelengths are absent; they have been absorbed by the gas. If the beam \(I_1\) falls on the slit of a spectrometer or spectrograph, then one can investigate the absorption spectrum of the gas or vapor. Every substance has an entirely characteristic absorption spectrum, consisting of a large number of lines and bands. Although the number of these absorption bands is measured in thousands, they can be arranged into groups and series in which the distribution can be formulated mathematically; at the present time we can also understand the physical meaning of these mathematical formulations.

Fig. 7.

Fig. 8.

According to Bohr’s theory, absorption of light occurs whenever the internal energy of a molecule increases

jumpwise. In the case of molecules we must consider three kinds of motion: 1) orbital motion of electrons; 2) vibrations of atoms or groups of atoms; 3) rotation of the molecule. From this point of view, the internal energy of molecules in the normal state \(W^0\) can be represented as the sum of three quantities:

\[ W^0 = E_e^0 + E_v^0 + E_r^0, \]

where \(E_e^0\), \(E_v^0\), \(E_r^0\) are respectively the electronic energy, the vibrational energy, and the rotational energy; when a molecule, under the action of light, passes into an excited state, the energy of such an excited molecule will be:

\[ W' = E_e' + E_v' + E_r'. \]

According to the second postulate of Bohr’s theory, the frequency of the absorbed light will be

\[ \nu = \frac{W' - W^0}{h}, \]

where \(h\) is Planck’s constant, equal to \(6.55 \times 10^{-27}\) erg sec.

If only the rotational energy of the molecule is considered, then it can be shown that it depends on two factors: the rotational quantum number and the moments of inertia of the molecule. If the molecule is isotropic, then its energy depends only on one moment of inertia \(I\). Successive states of rotation of the molecule correspond to successive values of the internal energy \(E_r^0\), \(E_r'\), \(E_r'' \ldots E_r^m\); the general formula for a molecule with one moment of inertia has the form:

\[ E_r^m = \frac{h^2 m(m+1)}{8\pi^2 I}. \]

In the transition from the state \(m\) to the next one \(m+1\) or to the preceding one \(m-1\), light of a definite frequency is absorbed. The general distribution of absorption lines is given by the formula:

\[ \nu = \nu_0 + \frac{E_r^{m+1} - E_r^m}{h} \]

or

\[ \nu=\nu_0+\frac{E_r^{m}-E_r^{m-1}}{h}. \]

This distribution depends only on one quantity that is characteristic for the given molecule—namely, on its moment of inertia. This means that in all parts of the absorption spectrum the fine structure, which is determined by the rotation of the molecule, must be one and the same. The rotational spectrum of a molecule with one moment of inertia exhibits a series of equally spaced lines, in which the distance between two successive lines is equal to:

\[ \Delta \frac{1}{\lambda}=\frac{h}{4\pi^2 I}=\frac{5.55\times 10^{-40}}{I}\ \mathrm{cm}^{-1}. \]

Thus, if the distance between two successive lines has been measured, the moment of inertia can easily be calculated. This conclusion has been confirmed by a large number of measurements for various molecules with one moment of inertia—nitrogen, hydrogen, sulfur, hydrogen chloride, carbon monoxide, etc.

In the case of the methane molecule, measurements made by Cooley (8) in the infrared region showed that there exist two different types of fine structure. In the band \(\lambda=3.3\,\mu\) there are many lines for which \(\Delta \frac{1}{\lambda}=5.51\ \mathrm{cm}^{-1}\), but in the band \(\lambda=7.7\,\mu\) the lines are more widely distributed and \(\Delta \frac{1}{\lambda}=9.77\ \mathrm{cm}^{-1}\).

An absorption spectrum possessing such a structure cannot belong to a molecule with one moment of inertia. During the past year these results have been discussed in detail by Dennison (9) and, in particular, by Guillemin (10) from Sommerfeld’s laboratory in Munich.

The absorption spectrum of formaldehyde was studied in my laboratory by me together with Dr. Shu (11). We found a double rotational spectrum with two types of fine structure. This result is especially important because, if a molecule has two moments of inertia \(I\) and \(K\), then it is possible to calculate

their magnitudes from the distribution of fine lines in the absorption spectrum.

If a molecule has two moments of inertia \(I\) and \(K\), then this rotational energy depends on two quantum numbers \(m\) and \(q\). The rotational energy is expressed as

\[ E_r^{mq}=\frac{h^2}{8\pi^2}\left[\frac{m(m+1)}{K}+q^2\left(\frac{1}{I}-\frac{1}{K}\right)\right]. \]

In this formula \(q\) is constant in the transition from the state \(m\) to \(m\pm1\), and \(m\) is constant in the transition from \(q\) to \(q\pm1\). Thus two systems of absorption lines are obtained. With the aid of this formula one can calculate the magnitudes of both moments of inertia. For the methane molecule \(I=3.64\times10^{-40}\) and \(K=5.65\times10^{-40}\); for the formaldehyde molecule \(I=1.41\times10^{-40}\) and \(K=25\times10^{-40}\).

These results show that the methane molecule cannot be a tetrahedron, and the simplest structure that is in agreement with these values is a pyramidal structure. From the magnitudes of the two moments of inertia corresponding to rotation about two axes, one can calculate the distances between the various atoms. The calculations of Hülmen (10) show that the distance between the carbon and hydrogen atoms in methane is \(1.05\times10^{-8}\ \mathrm{cm}\), the distance between carbon and the hydrogen atoms is \(1.15\times10^{-8}\ \mathrm{cm}\), and the height of the pyramid is \(0.375\times10^{-8}\ \mathrm{cm}\). For formaldehyde we found the distance between the carbon and oxygen atoms to be \(1.02\times10^{-8}\ \mathrm{cm}\), and between the two hydrogen atoms—\(1.34\times10^{-8}\ \mathrm{cm}\).

3. The structure of crystals found by means of X-ray analysis.

There is no possibility of investigating the structure of solid methane, but various derivatives of methane have been studied. The crystal structure of pentaerythritol—\(\mathrm{C(CH_2OH)_4}\)—was studied by Mark (12), and his results were confirmed by Hugginson and Hendricks (13). The results show that this compound cannot have cubic symmetry and that the most likely ...

the probable structure of the molecule, which agrees with the experimental data, is the structure of a pyramid. Similar results were obtained with tetraphenylmethane. Proceeding from these results, Weissenberg (14) and Reis (15) developed an entirely new stereochemistry based on the conception of the pyramidal structure of the methane molecule.

4. Potential Energy of the Methane Molecule.

A theoretical study of the stability of various configurations of a molecule formed by one negative ion and one or a greater number of hydrogen ions was carried out by Heisenberg (16), Born (17), Korfeld (18), Hund (19), and—for the methane molecule in particular—by Guilleménot (10). This theoretical investigation is based on the following considerations: 1) between the carbon atom, or, more precisely, the carbon ion, and each of the hydrogen ions there is, first of all, an attractive force proportional to $\frac{1}{r^2}$, and then a repulsive force proportional to $\frac{1}{r^n}$, where $n = 5$ or $7$, or $9$; 2) between the different hydrogen atoms the forces are proportional to $\frac{1}{s^2}$ and $\frac{1}{s^n}$ (Fig. 9); 3) since the hydrogen ion is polarized or deformed by the intramolecular electric field, the resulting dipole exerts an additional action on the hydrogen ions, and this action depends on the deformability coefficient $a$ of the hydrogen ion ($a = 1.34 \times 10^{-24}$). The potential energy of the configuration shown in Fig. 9 can be represented as a sum of terms depending on $\frac{1}{r}$, $\frac{1}{s}$, and $a$:

$$ P = F\left(\frac{1}{r}\right) + G\left(\frac{1}{s}\right) + H\left(a\frac{1}{r}\right). $$

This potential energy has a minimum for a certain definite configuration, and the conditions for this minimum

can be calculated. The form corresponding to the minimum of the potential energy depends on the magnitude of the deformability coefficients \(a\). The results of these calculations show that the potential energy of the tetrahedral configuration is greater than that for the pyramidal form, for for the tetrahedron one obtains \(P = 136 \cdot 10^{-12}\) erg, whereas for the pyramid \(P = 175 \cdot 10^{-12}\) erg.

These calculations thus indicate that the stable form of the methane molecule is a pyramid, and not a tetrahedron. The same method, when applied to the water molecule, gives for it a triangular form (Fig. 10) with an angle of \(66^\circ\), and for the ammonia molecule—a pyramidal form (Fig. 11).

Fig. 9.

Another important result of the mathematical investigation of the potential energy was obtained when this method was applied to the molecule of carbon tetrachloride. In this case the structure corresponding to the minimum of the potential energy is a tetrahedron, and not a pyramid. These conclusions are especially important because they show that not only is the structure of the methane molecule pyramidal, but that its form—

cannot be regarded as rigid and unchanging. It is wrong to think that, since some molecule has a definite form, this form must be preserved in all its derivatives. On the contrary, a molecule is a mobile system of atoms—a system in which the stability of the structure is determined by the minimum of potential energy. In place of the assumption of molecular rigidity—the assumption on which the whole of organic chemistry was formerly built—one should put the recognition of the lability of every molecule. This lability of structure determines chemical reactivity, and if the values of the potential energy for various molecular structures were known, it would be possible to predict chemical reactions.

Fig. 10.

Fig. 11.

5. Emission spectra of carbon atoms.

The carbon atom possesses two inner \(K\)-electrons, which move in circular orbits corresponding to the quantum designations \(1_1\), and four outer, or valence, electrons. Until 1922 it was assumed that these outer electrons were all of the same type and moved in circular orbits \(2_2\). However, in 1924 Fowler (20), in studying the emission spectra of ionized carbon \((C_+)\), found that this spectrum has exactly the same structure as the spectrum of boron. Analysis of the spectrum of boron had already shown earlier that the boron atom contains two outer electrons.

with orbits \(2_2\) and one electron with orbit \(2_1\). From this it followed that ionized carbon (C) must have the very same two types of outer electrons. The structure of the spectrum of carbon for the normal carbon atom and successive ions \(\mathrm{C}_+\), \(\mathrm{C}_{++}\), \(\mathrm{C}_{+++}\), \(\mathrm{C}_{++++}\) was recently investigated by Millikan and Bowen (21), and the general result of their work shows that two types of valence electrons must exist in the carbon atom. Two electrons must have circular orbits \(2_2\), and the other two—elliptical orbits \(2_1\). It follows, therefore, that the four valences of carbon are not equivalent and that two types of valences must be distinguished. Further analysis of the emission spectrum of carbon gives a method for determining the magnitude of the energy required for the successive ionization of the carbon atom. The results obtained were as follows:

\[ \begin{aligned} \mathrm{C} &\to \mathrm{C}_+ &&+ e - &&184\,000 \\ \mathrm{C}_+ &\to \mathrm{C}_{++} &&+ e - &&560\,000 \\ \mathrm{C}_{++} &\to \mathrm{C}_{+++} &&+ e - &&1\,060\,000 \\ \mathrm{C}_{+++} &\to \mathrm{C}_{++++} &&+ e - &&2\,300\,000. \end{aligned} \]

Conclusion.

By applying the modern methods of molecular physics to the study of the structure of the methane molecule, the following conclusions were established, substantiated by five completely independent methods:

1. The four valences of carbon are not equivalent, but are divided into two types.

2. The methane molecule has a pyramidal, and not a tetrahedral, form, as was assumed earlier.

3. The methane molecule is a labile system of atoms—a system capable of assuming various forms in methane derivatives.

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