Thermal Contributions to Relative Free Energies of Allotropes and Polymorphs From Density-Functional Theory

Abstract

Relative stabilities of two or more crystalline phases, such as allotropes or polymorphs, can be predicted theoretically using density-functional theory (DFT). Understanding the stability landscape of a given system has far-reaching applications in the pharmaceutical industry and materials modelling. For example, the focus could be to screen for compounds with specific properties, or to complement experiment in determining the isolable crystal structure. Crystal structure prediction (CSP) is a rapidly evolving field of computational chemistry. The over-arching goal of CSP is to predict the crystal structure of a given organic molecule beginning from its 2D chemical diagram. Being able to routinely conduct CSP studies is highly desirable, but is complicated by the complexity of the potential-energy surface that must be explored due to the many possible ways molecules can arrange themselves in the solid-state. DFT is routinely used to compute the relative energies of polymorphs in CSP studies, but temperature effects are frequently neglected. While DFT phonon calculations provide the zero-point and thermal contributions to the relative free energies of polymorphic systems, they are often intractable for the size of systems commonly encountered in CSP studies. The work contained in this thesis aims to study several problems concerning allotropes, polymorphism, and free-energy corrections. We examine two allotropes of carbon, diamond and graphite, and apply DFT to compute the relative free-energy difference. By undertaking this study, we can use high-accuracy theoretical data to determine which allotrope of carbon is more thermodynamically stable. With regards to polymorphism, we examine functionalized [6]helicene systems for organic electronic applications and use DFT to propose several low-energy crystal structures that may be crystallized experimentally. Finally, we conduct a benchmark study of thermal corrections of polymorphic molecular crystals and assess the accuracy of selected low-cost methods in hopes of finding a cheaper alternative to computationally expensive DFT phonon calculations.