Internal Rotation and Infrared Spectra of Formic Acid Monomer and Normal Coordinate Treatment of Out-of-Plane Vibrations of Monomer, Dimer, and Polymer

Abstract

The infrared spectra of the four isotopic species of formic acid were measured in the vapor phase as well as in the solid nitrogen matrix in the region 400–800 cm^—1. Absorption bands in the vapor phase were analyzed by considerations of band contours and comparisons with the frequencies distinctly observed in the matrix, and the previous assignment was revised. The torsional vibrations of the terminal OH groups of short chain polymers of HCOOH were observed in the matrix at 685 and 694 cm^—1. The OH torsional frequencies of the trans isomer were located in the vapor phase at 582 (HCOOH), 576 (DCOOH), 450 (HCOOD), and 448 cm^—1 (DCOOD). The energy difference between the two isomers was determined to be 2.0±0.3 kcal/mole. The potential hindering internal rotation was calculated to be $2\mathrm{V}\mathrm{\hspace{0.17em}(}\mathrm{kcal}/\mathrm{mole}{\text{)=2}}_{\text{·1}}\text{(1−}\cos {\text{θ)+9}}_{\text{·9}}\text{(1−}\cos {\text{2θ)−0}}_{\text{·1}}\text{(1−}\cos \text{3θ)}$ from the energy difference and the fundamental torsional frequencies. The entropy of mixing of the two isomers was found to be 0.3±0.1 cal deg^—1 mole^—1 at 25°C. A normal coordinate treatment was made of the cis and trans isomers of monomer and of the dimer and polymer. The double bond characters calculated from the torsional potential constant agree with those calculated from bond lengths.