Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into efficient computer programs, to calculate the structures and properties of molecules and solids. Its necessity arises from the fact that — apart from relatively recent results concerning the hydrogen molecular ion (see references therein for more details) — the quantum many-body problem cannot be solved analytically, much less in closed form. While computational results normally complement the information obtained by chemical experiments, it can in some cases predict hitherto unobserved chemical phenomena. It is widely used in the design of new drugs and materials. 15.1: Overview of Quantum Calculations The variational principle says an approximate energy is an upper bound to the exact energy, so the lowest energy that we calculate is the most accurate. This limiting energy is the lowest that can be obtained with a single determinant wavefunction . This limit is called the Hartree-Fock limit, the energy is the Hartree-Fock energy, the molecular orbitals producing this limit are called Hartree-Fock orbitals, and the determinant is the Hartree-Fock wavefunction. 15.2: Gaussian Basis Sets Although any basis set that sufficiently spans the space of electron distribution could be used, the concept of Molecular Orbitals within the LCAO suggests a very natural set of basis functions with atomic-type functions centered on each nuclei. One choice are the exact hydrogen AO's, known as Slater-type orbitals (STO)--describing the radial component of the functions. However, the computation of the integrals is greatly simplified by using Gaussian-type orbitals (GTO) for basis functions, inst 15.3: Extended Basis Sets Today, there are hundreds of basis sets composed of Gaussian Type Orbitals (GTOs). The smallest of these are called minimal basis sets, and they are typically composed of the minimum number of basis functions required to represent all of the electrons on each atom. The largest of these can contain literally dozens to hundreds of basis functions on each atom. 15.4: Orbital Polarization Terms The use of a minimal basis set with fixed zeta parameters severely limits how much the electronic charge can be changed from the atomic charge distribution to describe molecules and chemical bonds. This limitation is removed if STOs with larger n values and different spherical harmonic functions in the definition of STO’s are included. Such functions are called polarization functions because they allow for charge polarization away form the atomic distribution to occur. 15.5: The Ground-State Energy of H₂ 15.6: Quantum Calculations