J. C. Raich

The anisotropic interaction between nitrogen molecules from solid state data

The development of an angle‐dependent interaction potential for slightly nonspherical molecules is outlined, concentrating on molecular nitrogen. The suggested N2–N2 pair potential combines the radial dependence of the Barker type potential used for the rare gases with a modification of the treatment of anisotropy by the Berne–Pechukas Gaussian overlap model. This potential includes quadrupolar and long range dispersion contributions as determined from experiment or semiempirical studies. The valence potential parameters are determined by a fit of beam scattering and solid state measurements. This potential provides satisfactory agreement with Raman and neutron scattering measurements only when the anharmonic contributions to the lattice potential energy are included. A comparison of the suggested potential with a number of other presently available potentials, determined from a variety of measurements, as well as recommendations as to the limits of possible use are made. Possible steps which would lead t...

Torsional ground state splitting for tetrahedral molecules

With improved neutron scattering and nuclear magnetic resonance techniques it has been possible to observe the splitting of the torsional ground state—commonly referred to as tunnel splitting—of a number of high symmetry molecules in various crystal fields. The tunnel splitting depends nearly exponentially on the strength of the potential experienced by a molecule as it rotates in the crystal. Tunneling spectroscopy may thus be developed into a sensitive probe for measuring rotational potentials once the relation between the potentials and the tunnel splitting is known. We have used the pocket state formalism to calculate the splitting for tetrahedral molecules in tetrahedral fields. With increasing potentials the wave function becomes smaller in the overlap region making an accurate prediction of the tunnel splittings more difficult. Our calculation provides reliable results for splittings from 200 μeV down to about 1 μeV. Detailed predictions are made for the isotope effect in solid methane and for the ...

α‐γ Transition in Solid Nitrogen and Carbon Monoxide at High Pressure

We have examined the stability of the experimentally observed γ phase of solid nitrogen in order to test the validity of various forms of the intermolecular potential for N2. It was found that a Lennard‐Jones repulsive potential between nonbonded atoms fails to explain the stability of the tetragonal γ phase, whereas a parametric, shape‐dependent, hard‐core potential gives a satisfactory account of this high‐pressure phase of solid N2. The behavior of solid nitrogen‐15 is discussed briefly. On the basis of the hard‐core potential one would predict that a γ phase also exists for carbon monoxide, although at a very much higher pressure.

Self‐consistent calculation of the phonon‐libron spectrum in α‐N2

The temperature dependence of the librational and translational lattice modes in α nitrogen is calculated on the basis of two approximate treatments. The random phase approximation is shown to be unsatisfactory in predicting the temperature dependence of the librational frequencies. The self‐consistent phonon approximation is found to be a definite improvement over the random phase approximation. The first model uses quadrupolar interactions alone, the second an atom‐atom potential. Although the atom‐atom potential is moderately successful in fitting observed properties, the evidence for the necessity of a more complete potential, containing quadrupolar as well as short range and long range anisotropic terms, is discussed.

k=0 Librational Spectrum for Solid α‐N2

An alternative description of the k=0 librational spectrum of solid α‐N2 is given. A variational method where the wavefunctions of the hindered rotator are expanded in terms of spherical harmonics is used. The present calculations are limited to electrostatic quadrupole—quadrupole interactions. The k=0 librational frequencies are compared with the results obtained by classical lattice dynamics and another variational method as well as experiment.

On the phase transition in sym‐triazine‐mean field theory

A Landau mean field description of the nearly second order phase transition in sym‐triazine crystals at ∼200 K is presented. A model Hamiltonian is generated which consists of the appropriate symmetry elastic constant terms, molecular rotational energy, and rotation–translation coupling terms (to second order in both strains and rotations). Due to the symmetry of the crystal in the high (R3c) and low (C2/c) temperature phases, third order terms in the rotational order parameter are nonvanishing; the transition is thereby a first order one (although only weakly so). This Hamiltonian is then converted to a free energy by addition of an entropy term calculated for an orientation distribution (about the z axis) based on pocket state functions. The Landau mean field model is developed by choosing a set of order parameters Ry (molecular rotation about the y axis) and strains e5 and (e1‐e2). The free energy expression is used to calculate relations between order parameters by setting ∂F/∂Ry=∂F/e5=∂F/∂e7=0. Coup...

Equilibrium configuration of an N2 monolayer adsorbed on graphite

Abstract A nitrogen monolayer adsorbed on graphite is found to be unstable with respect to a registered one sublattice structure. A four sublattice structure, which stabilizes the monolayer, is postulated. Phonon dispersion curves for the four sublattice structure are presented.

Self‐consistent phonon calculation of the β phase and the α‐β transition in solid nitrogen

The self‐consistent phonon approximation of anharmonic lattice dynamics is applied to solid β nitrogen. Completely disordered molecular orientations and a Lennard‐Jones 6–12 intermolecular potential are assumed. The quantities calculated are the phonon spectrum and the thermal expansion as a function of temperature at zero pressure. The α‐β fcc‐hcp transition temperature is estimated on the basis of two models for the molecular ordering in the β phase. Although the computations are intended primarily to explore the application of the self‐consistent phonon method to a treatment of structural phase transitions in simple molecular crystals, comparison is made with existing experimental data.

Soft Modes in Molecular Crystals

The self‐consistent phonon approximation is applied to study the temperature dependence of the libron and phonon modes for simple molecular crystals. Several linear chain models are studied to illustrate the soft mode behavior of these excitations near the orientational order—disorder transitions that occur in many molecular crystals. It is shown that both libron and phonon frequencies are strongly temperature dependent in the neighborhood of the transition in qualitative agreement with experimental observations. Both the cases of strong and weak orientational coupling are considered. The effects of the cubic anharmonic terms are also discussed.

The anisotropic interaction between hydrogen molecules

The extent to which it is possible to estimate the anisotropic potential between two hydrogen molecules directly from ab initio calculations of the short range repulsive part of the interaction potential and the available semiempirical van der Waals and quadrupolar potentials is investigated. The anisotropic potential parameters e0(R), e2(R), e4(R), and B (R) due to nonquadrupolar anisotropic interactions are estimated for hydrogen in the range of intermolecular separations from 2.5 to 5 A. At the nearest neighbor distance in solid hydrogen, R0=3.756 A, we recommend the following values e0=−0.002 cm−1, e2=−0.027 cm−1, e4=−0.016 cm−1, and B=−0.310 cm−1. At the next nearest neighbor distance of √2 R0, we suggest e0=−0.0011 cm−1, e2=−0.0017 cm−1, e4=−0.0029 cm−1, and B=−0.131 cm−1.