Harald H. Nielsen

The low-frequency vibration rotation bands of the ammonia molecule

Abstract The absorption spectra of ammonia from 1440 cm −1 to 1840 cm −1 and from 510 cm −1 to 1280 cm −1 have been obtained with a vacuum grating spectrometer. The frequencies of the observed lines are given and the energy levels for the ν 4 , ν 2 , and 2 ν 2 vibration-rotation modes computed. A theoretical discussion of the Coriolis interaction between the ν 2 and ν 4 band and the “giant” l-type doubling observed in the ν 4 band is given and the results applied to the observed data.

The infrared absorption spectrum of formaldehyde vapor

Abstract Seven vibration-rotation bands in the spectrum of formaldehyde vapor have been resolved and measured. These have been identified as the six fundamental bands and a combination band ν2 + ν5. One of these, ν3, had not earlier been resolved and in all cases the bands are far better resolved than in earlier works. Vibrational band centers and rotational constants for the molecule are determined in all cases where an analysis could be carried out.

Two Bands in the Infrared Spectrum of Formaldehyde

Two infrared bands of the type arising from oscillations of the electric moment normal to the axis of symmetry have been measured under high dispersion and identified as the two oscillations which are at right angles to each other and which in Sutherland and Dennisons notation are v5 and v6. Their centers are respectively at 1278 cm‐1 and 1165 cm‐1. The anomalous spacing between the principal rotation lines is accounted for on the basis of an interaction between rotation and the two oscillations which are only slightly anisotropic.

Vibrational l-type doubling and l-type resonance in linear polyatomic molecules

Abstract The effect on the vibration-rotation energy of a linear molecule of certain terms in the potential energy function which are nondiagonal in the quantum numbers of vibrational angular momentum, lt and lt′, but diagonal in the quantum number l = lt + lt′ are studied. These terms, which are usually not included in the potential energy functions of linear molecules, depend not only upon the displacement coordinates, but also upon the difference between the polar angles χt and χt′ which the polar displacement vectors rt and rt′ make with an axis normal to the internuclear axis. The effect is to introduce terms in the anharmonic portion of the vibrational energy of the form xtt′ltlt′, but more generally it influences also the effective vibrational and rotational constants of the molecule. The latter effect can only be taken into account by solving a secular determinant. By analogy to the rotational l-type doubling this effect has been referred to as vibrational l-type doubling.

Rotational distortion in linear molecules arising from l-type resonance

Abstract It is pointed out that in linear molecules where rotational distortion of the energy levels arises out of l-type resonance alone that the expansion of the energies in powers of J(J + 1) is frequently invalid except for small values of J. An application of the refined theory is made to the band 2ν2 in the spectrum of DCN and the band ν4 + ν5 in the spectrum of C2H2. It is further pointed out that in molecules where Fermi resonance and l-type resonance occur simultaneously, the expansion of the energies in powers of J(J + 1) is valid for strong Fermi coupling but that for weak Fermi coupling, care must be exercised since here the expansion method may break down. Finally it is indicated that rotational distortion of the variety discussed does not occur in π vibration states.

The Fundamental Absorption Bands in the Infrared Spectrum of Phosphine

The four fundamental bands in the infrared spectrum of PH3 have been analyzed. The bands ν1 and ν3 yield values of B(xx) and [(1—ζ2(z))B(zz)—B (xx)] as well as values for the centers of the bands. The method of Nielsen for arriving at explicit expressions for the rotation term values of ν2 and ν4 has permitted the evaluation also of the quantity (1—ζ4(z))B(zz) and to infer the centers of these bands. The structure of the molecule has been derived from this information and the zeta sums. The PH distance r0 obtained is equal to 1.42A, and the H–P–H angle is equal to 93° 50′.

Infra‐Red Absorption Bands in the Spectrum of Deutero‐Formaldehyde

The spectrum of deutero‐formaldehyde in the infra‐red has been studied from 2.0μ to 13.0μ and seven absorption bands have been found. With these data and the data on the spectrum of the ordinary formaldehyde available it has been possible, making use of the product relations of Redlich, to identify with considerable certainty the fundamental frequencies of the H2CO and D2CO molecules, respectively, as: ν1 = 2780 cm—1, ν2 = 1750 cm—1, ν3 = 2875 cm—1, ν4 = 1503 cm—1, ν5 = 1278 cm—1, ν6 = 1165 cm—1, and ν1′ = 2056.4 cm—1, ν2′ = 1700 cm—1, ν3′ = 2160.3 cm—1, ν4′ = 1106.4 cm—1, ν5′ = 990.2 cm—1 and ν6′ = 938.0 cm—1. With this identification the valence force constants for the formaldehyde molecules have been computed.

Intensities of Rotation Lines in Absorption Bands

An alternate method of computing the influence of vibration‐rotation interaction on the intensities of lines in the band spectra of molecules from that discussed by Herman and Wallis and by Herman and Rubin is presented. The method consists of transforming the Hamiltonian of the molecule by a contact transformation so that the wave functions remain those for a harmonic oscillator‐rotator. The electric moment must then also be transformed by the same contact transformation before the matrix elements of the electric moment are computed. The method is applied to a diatomic molecule and gives the same results as those stated by Herman and Wallis.

Intensities of rotation lines in absorption bands for symmetric molecules of the type AB ⋯ XYZ3

Abstract The interaction of vibration and rotation is considered in the computation of the intensities of rotational lines in the band spectra of the general polyatomic molecule. The calculation utilizes the contact transformation method outlined in an earlier paper by the authors. The general result through first order of approximation is then applied to the case of the axially asymmetric molecule of the type AB ⋯ XYZ 3 . Relations for the intensities of the lines in the types of bands observed are obtained. It is found also, to this order of approximation that the usual selection rules are observed.

Anomalous Centrifugal Distortion Coefficients in Linear Polyatomic Molecules

The theory of the effect of resonance, in particular Fermi resonance and l‐type resonance, on the effective centrifugal distortion coefficient of a molecule for a given vibration state is developed. The theory is applied to certain cases where l‐type resonance occurs and to certain cases where both l‐type resonance and Fermi resonance occur. No instances appear to have been investigated where Fermi resonance occurs without l‐type resonance being present. The agreement between the theory and the experimental results appears to be satisfactory to the approximation of the theory.