This book provides a promotional exercise to foster the application of quantum mechanics to petrology. It addresses long-standing discrepancies in high-pressure melting data and provides a full appraisal of anharmonicity , essential for computing heat capacities, Gibbs free energy, and energy landscapes. Unlike empirical models, quantum-mechanical simulations deliver first-principles accuracy for complex systems, from pure oxides to quaternary compositions, using advanced mathematical tools like Delaunay Fragmentation and Convex Hull Analysis.