EINSTEIN VERSUS DEBYE SOLID IN THE MODELLING OF THE Pa3 PHASE OF ACETYLENE. A.T.H. Lenstra, K. Verhulst & C. Van Alsenoy, Department of Chemistry, University of Antwerp (UIA), Belgium
Minimum-energy geometries of acetylene were obtained using standard ab initio methods as well as the electrostatic crystal field (ECF) approach. The calculated difference in C-C bond length between gas phase and solid state is 0.002Å. An experimental verification is therefore practically impossible. Neutron and X-ray studies produced not only a solid-state geometry, but also ADP's. For acetylene in its cubic phase the displacements along and perpendicular to [1,1,1] are given by: <U2>||= T and <U2>^= T + 3Lr2. For the molecular translation (T) and libration (L) we calculated the relevant energy profiles. Via Boltzmann statistics we reconstructed U|| and U^ within the Einsteinian ECF approximation. Since U^ is too small the librational analysis appears to be inadequate. To incorporate intermolecular interactions caused by electron overlap we extended our wavefunctional unit to a supermolecule which contains the reference molecule and its two nearest-neighbour coordinating shells. The potential gouverning the axial length is practically harmonic: E(a-<a>)= f (a-<a>)2 with <a>=6.10Å (observed 6.094Å at 131K) and f=43kJ/molÅ2. This leads to an axial rms of 0.095Å at 131K. The translational displacement of the central molecule is also harmonic with a force constant of 38kJ/molÅ2, giving a rms amplitude of 0.120Å at 131K. To reproduce U|| we need to sum the two individual rms-values, which means that translational disturbance and lattice relaxation operate in phase. Elasticity links these oscillators via an action/reaction mechanism preserving the minimum-energy unit cell. Molecular libration within this supermolecule approach boils down to a rms of 6.5deg. which is smaller than the ECF-value of 8.5deg.. Assuming that the libration provokes an equi-important lattice relaxation, the combined librational oscillator has a rms-angle of 13deg.. This academic construction is factual, because it explains not only the C-C shrinkage (1.212(2)Å gas versus 1.177(6)Å solid) but also the observed U^-values.