In theoretical chemistry, an energy profile is a theoretical representation of a chemical reaction or process as a single energetic pathway as the reactants are transformed into products. This pathway runs along the reaction coordinate, which is a parametric curve that follows the pathway of the reaction and indicates its progress; thus, energy profiles are also called reaction coordinate diagrams. They are derived from the corresponding potential energy surface (PES), which is used in computational chemistry to model chemical reactions by relating the energy of a molecule(s) to its structure (within the Born–Oppenheimer approximation). Qualitatively, the reaction coordinate diagrams (one-dimensional energy surfaces) have numerous applications. Chemists use reaction coordinate diagrams as both an analytical and pedagogical aid for rationalizing and illustrating kinetic and thermodynamic events. The purpose of energy profiles and surfaces is to provide a qualitative representation of how potential energy varies with molecular motion for a given reaction or process. Potential energy surfaces In simplest terms, a potential energy surface or PES is a mathematical or graphical representation of the relation between energy of a molecule and its geometry. The methods for describing the potential energy are broken down into a classical mechanics interpretation (molecular mechanics) and a quantum mechanical interpretation. In the quantum mechanical interpretation an exact expression for energy can be obtained for any molecule derived from quantum principles (although an infinite basis set may be required) but ab initio calculations/methods will often use approximations to reduce computational cost. Molecular mechanics is empirically based and potential energy is described as a function of component terms that correspond to individual potential functions such as torsion, stretches, bends, Van der Waals energies, electrostatics and cross terms. Each component potential function is fit to experimental data or properties predicted by ab initio calculations. Molecular mechanics is useful in predicting equilibrium geometries and transition states as well as relative conformational stability. As a reaction occurs the atoms of the molecules involved will generally undergo some change in spatial orientation through internal motion as well as its electronic environment. Distortions in the geometric parameters result in a deviation from the equilibrium geometry (local energy minima). These changes in geometry of a molecule or interactions between molecules are dynamic processes which call for understanding all the forces operating within the system. Since these forces can be mathematically derived as first derivative of potential energy with respect to a displacement, it makes sense