539.133 : 535.333-1 ATOMIC POLARIZATION AND SPECTRAL OATA

BY

A. J. DEKKER.

Zur Berechnung von Dipolmomenten ist in manchen Fallen die Kenntnis des Anteils der Ultrarot-Schwingungen an der gesamten Polarisation erforderlich. Die experimentelle Bestimmung von P1 ist meistens sehr schwer, besonders wenn Messun- gen der Dielektrizitatskonstante an Gasen ausgefuhrt werden miissen. Es wird eine Methode angegeben, um diese Ultrarotanteile abzuschatzen. wenn Daten aus Raman- und Ultrarotspektren vorliegen. Die Berechnungen sind im Anschluss an die Theorie von M e c k e fur einige Substanzen durchgefuhrt worden: 3-atomige (gestreckte und gewinkelte) , tetraederformige und einige substituierte Benzenmolekule werden diskutiert.

Introduction. The molecular polarization of a substance may be written:

In 1.

2.

3.

where E stands for the dielectric constant, M for the molecular weight, d for the density, N, for A v o g a d r 0's number and CI for the polarizability.

first approximation P i s composed of: the electron polarization P,, due to the displacement of the electron cloud with respect to the nucleus in the atom, the atomic polarization Pa, caused by the displacement or bending of polar atoms or groups of atoms with respect to each other in the molecule, the orientation polarization Po, due to the directing influence of the electric field on the permanent(dipo1es ,u of the molecules. For this part of the polarization, in the gaseous state, ' the formula of D e b ij e holds:

As to P,, the theory of dispersion leads to P

(2) P, = 2 -- . . . . . . . . . . L i

, vi=-v2

In this formula the yi represent the characteristic frequencies of the electrons, Y the frequency of the applied electric field: the Ci are constants belonging to the yi. The formula holds for the whole spectrum except for the absorption frequencies: when v = vi. P, = 1- co, because the internal friction has not been accbunted for. A formula similar to ( 2 ) may be set up for Pa: in that case the vi represent the characteristic frequencies of the atomic vibrations. The characteristic frequencies of the electrons are about 1015 (ultra-violet) , those of the atomic vibrations about 1014 (infra-red) and the rotation frequencies are of the order of 109 (cm-waves). Thus when measurements of the dielectric constant are carried out with a frequency v of the electric field, only characteristic frequencies higher than v contribute to the value of P. To determine the dipole moment of any substance, the measurements are usually carried out with radio frequencies of about 106, thus the theory of static fields

Atomic polarization and specfral dafa. 123

then holds. T h e polarization in a static field (wave-length = M ) is generally written as P,. T o calculate the dipole moment of a substance, it is necessary in some cases to know the value of P,,,, and P,,=: by subtracting the sum P(( , ! from P,. the value of P,, has been found and ;(, can be calculated. This method can only be applied to substances in the gaseous state, but also for liquids, where the formula of 0 n s a g e r - B o t t c h e r 1 ) gives better results than that of D e b ij e, a knowledge of the refractive index extrapolated to infinite wave-length is required. In many cases P:, is not accounted for in the calculation of ,,(, or the refractive index of the sodium D line is used.

The calculation of P ( , x does not give rise to difficulties: it is sufficient to assume only one characteristic frequency of the electrons to describe the dispersion in the visible range. In principle it would be possible to calculate the value of P,, , , in the same way, but dispersion measurements in the far infra-red are available only for a small number of substances. Another experimental method had been given by E r r e r a 2 ) and E b e r t 3 ) . P , values have been collected by S m y t h 4 ) as well as by F u c h s and W o 1 f 5 ) ) .

Calculation of P:, * ) . 4 1. Only those atomic vibrations contribute to the polarization which are

infra-red-active and consequently give rise to a variation of the dipole moment: molecules consisting of two equal atoms have no atomic polarization and thus are not considered.

T h e characteristic frequency of a diatomic molecule such as HCI is given by the formula

v, = I L/ k / m 2 n

( k is the force constant, m the effective mass = m 1 + "'). Let a displacement

A x of the nuclei with respect to each other cause a variation in the dipole moment of A ((, then the effective charge is defined by A ( ( / A x = e . W h e n the direction of the valency bond and that of the applied electric field E differ by A, the displacement of the nuclei will be given by x = eE cos ??/k. In consequence the induced moment in the direction of E will be ex cos 1') =; e?E cos2 iI/k and the polarizability of this one-dimensional oscillator becomes e? cosz i?/k or, averaged over all possible directions, ez /3 k .

m1m712

4 7 3

As P , == N , . 7, we obtain

By means of this formula, v a n V 1 e c k 6 ) calculated the value of P,, for HCl: k is determined by the characteristic frequency v,,, e2 is a measure of the

C. J. F. H o t t c h e r. Thmis. Leiden 1941 ? ) J. E r r e r a. J. phys. 5, 304 (1924). "1 L. E b c r t . 2. physik. Chem. 113, 124 (1925): 114, 430 (1925). ') C. P. S t n y t h , J. Am. Stiern. SOC. 51, 2351 (1029). 5 , 0. F 11 c h s and K, L. W o I f . Hand- und Jahrb. der Chem. Physik Bd. 6, 11. p. 262.

) In the following m e omit the symbol m . ") J. H. v a n V l e c k , Phys. Rev. 30, 31 (1927).

128 A. I . Dekker, Atomic polarization, etc.

measurements in the liquid state, the agreement is rather good and would be better if values of the effective charges connected with the . (a ) vibrations were available.

The author is much indebted to Prof. Dr. J. C 1 a y for his interest in this work.

Natuurkundig Laboratorium der Universiteit van Amsterdam.

(Received March 1st 1944).