Richard M. Badger

A Relation Between Internuclear Distances and Bond Force Constants

It has been found that for diatomic molecules the relation between the bond force constant, k0, and the internuclear distance, re, is quite accurately given by the expression k0(re—dij)^3 = 1.86×10^5, where dij is a constant depending only on the rows in the periodic table in which the two elements comprising the molecule are located. The expression holds not only for the normal state but for all excited states with a few possible exceptions. Some uses of the relation are discussed and an extension to polyatomic molecules is suggested.

The Relation Between the Internuclear Distances and Force Constants of Molecules and Its Application to Polyatomic Molecules

The relation between the internuclear distances and force constants found for diatomic molecules is discussed, and is shown to carry over to polyatomic molecules. It is shown that internuclear distances of polyatomic molecules can be predicted from vibrational data alone, with considerable accuracy.

Spectroscopic Studies of the Hydrogen Bond. II. The Shift of the O–H Vibrational Frequency in the Formation of the Hydrogen Bond

The association spectra of a number of acids and alcohols in the region lambdalambda9000–11,000 have been observed both in solution and in the pure liquids. In each case a broad band with maximum near lambda10,000 was observed while in the alcohols an additional weaker band near lambda9000 appears to be present. Evidence is presented that the lambda10,000 band is to be identified with the O[Single Bond]H group. This evidence includes the behavior of the association band with change in concentration and temperature and its presence in several substances in which absorption other than that due to the O[Single Bond]H group is practically absent in the region studied. New evidence is given that a weak intermolecular hydrogen bond is formed between acetone and methyl alcohol. It is pointed out that the presence of absorption in the narrow O[Single Bond]H bands is not to be taken as evidence of the absence of hydrogen bonds in case the absorption is weak. The character of the O[Single Bond]H absorption in the case of intermolecular hydrogen bonds is discussed and the probable nature of the spectrum in the case of an intramolecular bond is indicated. A relation between the energy of the hydrogen bond and the shift of the O[Single Bond]H vibrational frequency is pointed out and its use is suggested in the interpretation of certain spectra.

Absolute Intensities of the Discrete and Continuous Absorption Bands of Oxygen Gas at 1.26 and 1.065 μ and the Radiative Lifetime of the 1Δg State of Oxygen

Laboratory measurements have been made of the absolute intensities of the discrete-line absorption band at 1.26 µ, and of the continuous bands at 1.26 and 1.065 µ in oxygen gas at pressures up to 4.3 atm. It has been shown that discrete and continuous absorptions are quite independent features, the one being a measure of the intrinsic transition probability in isolated molecules, the other of its enhancement in collision complexes. In the former the lines show significant pressure broadening, but the integral molecular absorption coefficients are constant; in the latter they are proportional to pressure and continuous absorption dominates in the 1.26-µ region at about ½ atm oxygen pressure.The radiative half-life of isolated 1Δg oxygen molecules is estimated to be 45 min, and the effect of gas pressure on the rate of decay has been predicted.

The Band Envelopes of Unsymmetrical Rotator Molecules. I. Calculation of the Theoretical Envelopes

Since the majority of molecules of chemical interest are too heavy to permit resolution of the rotational structure of the infra‐red bands, it is of interest to find what information can be derived from a study of the band envelopes. Considerations of the type which Gerhard and Dennison have made for symmetrical molecules have been extended to the unsymmetrical rotator. By the use of an approximation method the envelopes of the three elementary types of band have been calculated for nine different sets of molecular parameters.

The Infrared Spectrum and the Structure of Gaseous Nitrous Acid

An investigation of the infrared spectrum of nitrous acid has shown that in the gaseous state this substance exists in two tautomeric species which are believed to be trans‐ and cis‐forms. The cis‐form is of higher energy by about 506 calories mole−1. A complete vibrational analysis is given and the OH in plane bending frequencies are found to be 1260 cm−1 and ∼1292 cm−1, and the out of plane frequencies 543 cm−1 and 637 cm−1 for the trans‐ and cis‐molecules, respectively. From the rotational constants the O–N–O angle is estimated to be 118° for the trans‐form and 114° for the cis‐form, from which conclusions are drawn regarding the electronic structure of the molecule. The standard entropy of nitrous acid at 25° is calculated.

The Planarity of the Urea Molecule

Arguments based on infra-red observations were recently presented by W. E. Keller for the planarity of the urea molecule in the crystalline state. Though plausible, we have not found these completely convincing since the statement that in a nonplanar model one of the A_1 hydrogen bending fundamentals should be essentially inactive is based on certain assumptions, and not on a selection rule required by symmetry. The really conclusive evidence is to be found in the 3µ region where the resolving power of the spectrometer employed by Keller seems to have been inadequate. In the planar model four N-H valence frequencies may be active, two of which have the character A_1. In the nonplanar C_(2v) model only three of these fundamentals can be active, and only one of these has the character A_1.

The Infrared Spectra of HOCl and DOCl

We have recently observed the spectra of hydrogen hypochlorite and deuterium hypochlorite in the region 1-15μ as part of a general program of study of simple molecules. Since, so far as we are aware, no spectroscopic data has heretofore been reported on these substances, the preliminary results are of sufficient interest to be presented at this time.

Spectra of Urea and Thiourea in the 3μ Region

Observations are reported on the polarized infrared spectra of single crystals of urea and thiourea in the 3μ region. Complex structures accompanying the N – H fundamentals appear, at least in considerable part, to be attributable to combinations and overtones of fundamentals in the neighborhood of 1650 cm—1.

A Reinvestigation of the Vibration Spectrum of Ozone

Several analyses of the vibration spectrum of ozone have been proposed in recent years, all of which have been open to serious objection. Either they have failed to account for the observed structure of all the infrared bands, or if consistent with this structure have required an acute angled molecular model which is not in accord with the structure determination by electron diffraction. These difficulties appear to have resulted in part from some misconceptions regarding the relative intensities of the ozone bands, but chiefly from the previous failure to recognize the fundamental band of the vibration v_1.