Molecular crystals occur in a variety of chemically relevant problems, including pharmaceuticals and organic semi-conductor materials. There has been much interest in developing computational models which can predict crystal structures and properties accurately and with reasonable computational expense. One such model, hybrid many-body interaction (HMBI), fragments a chemical system into monomer, dimer, and many-body interactions, each of which may be handled using a different level of theory. HMBI has been used to predict crystal structures, lattice energies, and relative polymorph stability, particularly in cases where other methods such as periodic density functional theory (DFT) have struggled.
This dissertation extends the HMBI model in two important ways. First, the computational cost of these calculations is significantly reduced by the development and implementation of an algorithm to exploit space group symmetry. This algorithm reduces the number of monomer and dimers calculations that need to be performed by eliminating symmetrically equivalent ones. Exploitation of space group symmetry provides additional computational savings during a crystal geometry optimization by reducing the number of degrees of freedom that need to be optimized, which tends to decrease the number of optimization steps required to reach convergence.
Second, the ability to predict molecular crystal structures and properties at finite temperature is developed by coupling the HMBI model with the quasi-harmonic approximation. Traditional approaches either neglect temperature or approximate it with a harmonic vibrational model. However, molecular crystals expand appreciably with temperature and this expansion has significant impacts on crystal properties. Typically, as crystals expand, the lattice energy weakens and the phonon modes soften. Neglecting this expansion causes thermochemical properties such as enthalpy and entropy to be overestimated near room temperature. The quasi-harmonic HMBI model is demonstrated to predict temperature-dependent molar volumes, thermochemistry, and mechanical properties in excellent agreement with experiment for several small-molecule crystals---carbon dioxide, ice, acetic acid, and imidazole. These developments also pave the way toward computational prediction of molecular crystal phase diagrams as a function of temperature and pressure. Preliminary results examining the high-pressure phase diagram of carbon dioxide are presented.