Hydrogen is also the focus of many high-pressure studies using wall potentials (Section 2.2), and often analytical solutions for energies and other observables are available. As soon as the system size increases, however, approximations have to be used. In quantum chemistry, wave function based methods are often applied, ranging from the mean-field Hartree-Fock (HF) theory to more systematically accurate ab initio correlation methods like MP2 or CCSD(T). The latter method is often referred to as the "gold standard of quantum chemistry". Unfortunately, these high-level methods, especially CCSD(T), can only be used for small molecules with less than 50 atoms. We note, however, that there is ongoing research to accelerate the speed of these calculations to be able to simulate systems containing several hundreds of atoms by introducing additional approximations. Nevertheless, for most quantum chemical calculations, DFT is used to describe the electronic structure of the system of interest, since system sizes up to a few hundred to a thousand or so atoms can be modeled. Depending on the choice of the exchange correlation (XC) functional, observables of different classes of materials can be calculated with good agreement to experimental observations. As shown in Section 3, DFT is used for most studies in computational high-pressure research, too. In these studies, molecules are simulated either in an isolated way (Section 2.3.1) or, alternatively, in confined environments like in (implicit) solution (Section 2. 3.2). If more than one molecule shall be considered or the interaction with the environment needs to be taken into account, explicit solvation models can be applied (Section 2.3.3). However, for treating long-range interactions accurately, calculations are usually performed using periodic boundary conditions (Section 2.4). This methodology allows for simulations of well ordered crystalline structures and phase transitions, e.g., between the liquid and the solid phase.