4670
J . Phys. Chem. 1986, 90, 4670-4673
High-pressure Behavior of Solid
F2 at l o w Temperatures
R. D. Etters* and D. Kirint Physics Department, Colorado State University, Fort Collins, Colorado 80523 (Received: January 14, 1986: In Final Form: April 18, 1986)
The equilibrium structures, orientations, and molar volume of solid F, at zero temperature are calculated at pressures 0 I P I100 kbar, by minimizing the Gibbs free energy of a general monoclinic lattice with two molecules per unit cell. This was accomplished with the Fletcher quasi-Newton method, which varies all the independent degrees of freedom until the force on each atom is eliminated. The resulting structures are C2/c, and no evidence of a phase transition is found, which is consistent with recent experimental data. On the basis of these calculated structures, the pressure dependence of the vibron stretch mode frequency is calculated by assuming that the crystal field of the solid acts as a small perturbation on the gas-phase intramolecular potential, and the k = 0 libron- and phonon-mode frequencies are determined with standard lattice dynamics techniques. These predicted frequencies are compared with results from recent Raman scattering measurements.
Introduction
Raman scattering measurements] on solid a-Fzhave recently been made and the optically active vibron and libron modes have been observed at pressures 0 IP I50 kbar for the first time. Consequently, it is the purpose of this work to calculate the properties of the solid under these conditions. The properties determined are the lattice parameters, molecular orientations, molar volume, and the libron-, vibron-, and lattice-phonon-mode frequencies as a function of pressure. The interpretation2 of earlier X-ray diffraction measurements3 at zero pressure shows that the probable structure of a-F2 is monoclinic with space group C2/c, but C2lm has not been entirely ruled out. In a previous calculation4 at zero pressure and temperature, identified as I, we were able to determine the equilibrium properties of a-Fzby constructing an atom-atom representation of the pair potential that gave good agreement with experiment for the second virial coefficient^,^ the molar v o l ~ m e and , ~ the sublimation energy.6 The lattice parameters, molecular orientations, and the libron and phonon frequencies were also predicted with reasonably good accuracy. The equilibrium structures were obtained by optimizing the energy, and invariably either the CLIc or C 2 / m symmetry would result, depending on initial conditions. Because the predicted binding energies of these two structures were very nearly the same, it was not possible to conclude which symmetry is most likely, although the overall agreement of the predicted properties with experiment favored C2/c. Figure 1 shows the monoclinic cell for a-F2,and the C 2 / c space group is distinguished by a tilting of the molecules out of the ac plane away from 2, the normal to the ab plane, as shown. Note that the tilt angle 8 alternates in direction on successive ab planes. It was found that the predicted structure depends critically on the value adopted esu cm2 the for the quadrupole moment 0. For 8 > 0.7 X equilibrium structure is Pa3, like a - N 2 , and for 8 < 0.4 X esu cm2 the structure is the R3m symmetry of 8-O,, which is what the low-temperature a-O2phase would be in the absence of a magnetic interaction.' This sensitivity of the predicted structure to small changes in the potential parameters is consistent with the stability studies performed earlier by English and Venables.* Central to that work4 was the assumption that molecular charge rearrangement in the condensed phase is negligible, unlike solids higher in the halogen ~ e r i e s . In ~ fact, a general examination of the results have led us to conclude that the behavior of a-F2 is much more like solid 0, than it is to the other halogens. Potential and Method
The site-site intermolecular potential adopted is that developed4 in I. Thus, the total potential energy of the system is given by 4
UT = C C A ex~[-aRrj(s)I - B / R , 6 ( s ) + UEQQ+ u i n t r a I
