O. Schnepp

Intermolecular Potentials for N2 Molecules and the Lattice Vibrations of Solid α‐N2

The lattice energy, crystal structure, and optical properties in the far infrared and Raman spectrum have been used as a basis to test various forms of an intermolecular potential for N2. The librational mode frequencies observed in the Raman spectrum are exclusively characteristic of the anisotropic part of the intermolecular potential. It was found that the quadrupole–quadrupole interaction term does not give an adequate description of the angle‐dependent part of the intermolecular potential for nitrogen molecules at distances corresponding to the solid. On the other hand, an atom–atom or dumbbell intermolecular potential has been found to give very good agreement between calculated and experimental frequencies of all optical lattice modes. Potentials of the 6–12 type and 6‐exponential types have been used. In order to obtain good quantitative fit to the librational frequencies an effective interatomic distance in the molecule had to be used which is 20% smaller than the actual bond length. Also intensi...

Intermolecular Potential and Lattice Dynamics of the CO2 Crystal

The lattice dynamics of solid CO2 has been treated throughout the Brillouin zone. The molecular librational degrees of freedom have been treated by the use of Eulerian displacement coordinates. The potential model assumes the molecule represented by two centers of interaction (diatomic model) and each molecular pair interaction term is written as a sum of 6–12 terms between interaction centers on different molecules. The three parameters of the potential are obtained by fitting to the five optic modes, from the crystal energy, and by invoking the condition of zero uniform stress. It is found that the interaction between translational and librational degrees of freedom is large inside the Brillouin zone. The low temperature specific heat was calculated and found to agree well with experimental data. In an appendix, the applicability of the classical harmonic oscillator treatment to small molecular solids is discussed, and it is concluded that this approach is justified for solid CO2.

Raman Spectrum of α‐N2

The Raman spectrum of solid α‐N2 has been investigated between 12°–35.5°K. Two lines were observed at 31.5 and at 35.8 cm−1, with intensity ratio 3.6 in favor of the lower‐frequency line. A calculation of the scattering intensities was carried out assuming additivity of molecular polarizabilities. Consideration of relative intensities led to the assignment of the three predicted Raman‐active librational lattice vibrations, assuming a close coincidence of two of these modes. The assignment is supported by an independent frequency calculation.

Quantum Lattice Dynamics of Molecular Solids. II. Application to the Librations of Solid CO2, α‐N2, and o‐H2

The quantum mechanical lattice dynamics formalism developed in the preceding paper for molecular solids is applied to the librational modes at k=0 in solid α‐N2, CO2, and o‐H2, interacting through a quadrupole‐quadrupole potential. Librational wavefunctions are constructed for α‐N2 and CO2, and free rotor wavefunctions were used for librons in solid o‐H2. It is found that the quantum‐mechanical lattice frequencies provide nonnegligible, though not dramatic, corrections to the frequencies calculated in the classical harmonic approximation. For α‐N2 the quadrupole potential provides a satisfactory description of the anisotropic potential, with the quantum‐mechanical frequencies significantly closer to experiment than the classical ones. For CO2 the quadrupole potential provides only part of the anisotropic potential.

The resonance Raman spectrum of azulene

Abstract Excitation profiles have been measured for three Raman lines of azulene in CS 2 solution in the spectral range of the visible absorption system, viz. 665—570 nm. The results are unexpected in as much as the excitation profiles do not exhibit maxima at or near the absorption peaks. The results are interpreted on the basis of contributions to the A -term by other modes than the one studied in the Raman effect. These terms give rise to interferences which lower the excitation profile in some regions while causing maxima at other frequencies.

Resonance raman spectrum of azulene

Abstract Excitation profiles have been measured for three Raman lines (825 cm −1 , 900 cm −1 and 1400 cm −1 ) of azulene in CS 2 solution in the spectral range of the visible absorption system, viz 665–570 nm. The results are unexpected in that the excitation profiles do not exhibit maxirna at or near the corresponding absorption peaks. The results are interpreted on the basis of contributions by other vibrational modes with large Franck—Condon factor relative to the origin in the electronic transition. These Franck—Condon factors were varied to fit the Raman data as well as the absorption spectra. The best fit Franck—Condon factors agree well with those reported for mixed crystal absorption.

Quantum mechanical treatment of librations (and librons) in molecular solids

Abstract A quantum lattice dynamics treatment is presented for the angular degrees of freedom in molecular solids. Variational wavefunctions are chosen to span the whole range from high to low rotational barriers. The theory is applied to quadrupole forces in solid hydrogen, nitrogen and carbon dioxide. It is concluded that quadrupole forces provide a better description of anisotropic forces in nitrogen than in CO2. In the limit, the treatment gives a valid description of the librons in solid ortho-hydrogen.