IDENTIFICATION OF THE DECIPHERED VIBRATIONAL STRUCTURE OF DIATOMIC MOLECULES

G. V. Kovalenok

(Presented by Prof. V. A. Sokolov)

The spectrum of the arc between electrodes made of metallic calcium consists of six band systems. Four weak systems—in the near ultraviolet, blue, and two in the photographic infrared regions—have been most fully analyzed in works [1]–[5]. The systems represent transitions between singlet electronic states and undoubtedly belong to the CaO molecule. Since the structure of two band systems in the visible region had not been deciphered, it was proposed to regard the emitter as the CaO molecule [6]–[8], Ca₂ [4], [9], or CaC [9]. The opinion was also expressed [10] that these bands belong to the CaOH molecule, but proof of its erroneousness immediately followed [11].

The general shortcoming of these works is that the authors propose taking one or another molecule as the emitter without giving convincing justification for their proposal.

In work [12], one of the intense systems in the visible region—the orange system—was analyzed. The investigated part of the spectrum (5900–6500 Å) contains 71 bands, grouped into seven sequences. The vibrational quantum analysis gave good agreement with the experimental data obtained by us and by other authors [6]. The wave numbers fitted into a quantum scheme while preserving an almost constant difference of wave numbers in neighboring horizontal and vertical rows; this indicates that this system belongs to a diatomic molecule. We assumed that the probable emitter is the CaO molecule. However, further investigation cast doubt on our assumption.

It is necessary to emphasize two features of the green and orange band systems that are very important from our point of view:

1) In an atmosphere of air, oxygen, or hydrogen, the same intense band systems appear;

2) the sequences of the orange region are located so close to one another that the entire band system occupies a region of approximately \(1370\ \mathrm{cm}^{-1}\) on the frequency scale, and several sequences can be considered there (subsequently it turned out that there are 7 of them), whereas in the CaO molecule a single band sequence (in the blue region) occupies a region of approximately \(620\ \mathrm{cm}^{-1}\).

The deciphering of the vibrational structure for the orange system made it possible to find the vibrational constants of the investigated (as yet unknown)

molecules; their values are given in Table 1. For comparison, vibrational constants for the normal state of the CaO molecule, obtained by other authors, are included. No information could be found on the CaC molecule.

Table 1

Vibrational constants of the upper and lower states of the orange bands of the molecule under study

It is noteworthy that, with nearly coincident values of $\omega_e'' x_e''$, the vibrational constants of the CaO molecule and of the molecule under study differ by several times; $\omega_e$ for the molecule under study is almost three times smaller than $\omega_e''$ for the CaO molecule.

Here it is necessary to cite the tabulated data [13] on the relation between $\omega_e'' x_e''$ and $\omega_e''$ for certain molecules, which, in our opinion, shed light on the nature of the molecule under study. The data are presented in Table 2.

Table 2

Vibrational constants of the normal electronic states of certain diatomic molecules

It turned out that, for all molecules without exception that are formed from identical atoms, the vibrational frequencies are small in comparison with the vibrational frequencies of the oxides, while the anharmonicities nearly coincide (as a rule, in the oxides $\omega_e'' x_e''$ is slightly larger). Probably, the CaO and

\(\mathrm{Ca}_2\) must obey this regularity. Thus, the opinion is formed that, in the case under consideration, the emitter is the \(\mathrm{Ca}_2\) molecule. Let us try to prove this.

In the preceding article [14], devoted to the question of the method for deciphering the vibrational structure of bands, an interesting dependence of the vibrational constants \(\omega_e''\) on the masses of the molecules \(M\) was described. In the present work the possibilities of curves constructed in the coordinates \(\omega_e''\) and \(M\) are used.

Figure 1 presents a number of such dependences. Molecules obtained by combining atoms of Group I elements with one another form a curve lying lower than the curve for molecules formed by combining one of the atoms of Group I of the Mendeleev periodic system and Group VII (the halogen group). All the curves have the same profile within the limits of the combination of Group I elements with one another or Groups I and VII. Let us note that molecules composed of identical atoms lie at the bend of the lower curve; as the mass of the molecules increases, the curves shift to the right along the \(M\) axis, and the distance between the curves for subsequent molecules (by groups of the system) decreases.

Fig. 1. Vibrational constants of molecules as functions of their molecular weight

By analogy, we construct a curve for molecules formed by a Ca atom with the halogen group (Fig. 2) (for Group II elements the profile of the curves is their own), shift the curve downward, and see that the point with coordinates \(\omega_e'' = 227\ \mathrm{cm}^{-1}\) (the vibrational frequency of the molecule under investigation) and \(M = 80\) (the weight of the \(\mathrm{Ca}_2\) molecule) lies at the bend of the curve.

Thus, the emitter of the bands in the orange region is the \(\mathrm{Ca}_2\) molecule; the bands are the result of an electronic-vibrational transition to the normal state, probably a \(\Sigma - \Sigma\) transition. The \(\mathrm{CaO}\) molecule as the emitter is excluded; as for the \(\mathrm{CaC}\) molecule, its mass is almost half the mass of the \(\mathrm{Ca}_2\) molecule, and consequently its vibrational frequency cannot be equal to \(\omega_e'' = 227\ \mathrm{cm}^{-1}\).

It is not excluded that the \(\mathrm{CaO}\) molecule has its own coarse structure in the visible region; confirmation of this is the extreme saturation of the region \(5900\text{—}6500\ \text{Å}\) with very weak diffuse bands, which it is therefore practically impossible to take into account and decipher. R. Pearse and A. Gaydon [6] cite in their work bands having another, red shading, whereas the \(\mathrm{Ca}_2\) bands have violet shading. We were unable to examine the bands with red shading.

In conclusion, let us note that the experimentally obtained curves (Fig. 1) open up a number of possibilities for studying the spectra of diatomic molecules, although they immediately raise a number of questions, such as the question of the cause of: 1) the convergence of the curves, 2) the sharp decrease in the vibrational constant for molecules consisting of identical atoms, etc.

Fig. 2. Dependence of the vibrational frequency \(\omega_e''\) on the molecular weight \(M\) for molecules with a Ca atom

The system of green bands occupies a spectral region almost two times smaller than the system of orange bands; several overlapping band sequences similar to the sequences in the orange region can be considered. It is possible that this system also belongs to the molecule \(\mathrm{Ca}_2\); to prove this it is necessary to decipher its structure.

LITERATURE

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14. G. V. Kovalenok. Article “On the Method for Deciphering the Vibrational Structure of Electronic Transitions of Diatomic Molecules” (in this collection).