Quantum chemistry methods

A method for calculating electronic states of mainly isolated systems such as molecules is collectively called quantum chemical calculation. Many applications often implement various calculation methods based on the molecular orbital method. The Hartree-Fock approximation is a method of optimizing the molecular orbital wave functions by approximating the many-body wave function with a single Slater matrix. To incorporate the electron correlation effect ignored in the Hartree-Fock approximation, one can use the perturbation method, the Configuration Interaction (CI) method, the coupled cluster (CC) method, etc. The perturbation theory treats electron correlation within perturbation expansion, and is called the Møller-Plesset (MP) method. Depending on the order of the perturbation, it is expressed as MP2, MP3, MP4, etc. In the CI method, in addition to the ground state obtained by the Hartree-Fock method (a state in which electrons are occupied into the orbits below the Fermi energy), we prepare states in which only one electron is moved from its electron configuration (one electron excited state), states in which two electrons have moved (a two-electron excited state), etc., and minimize energy by considering their linear combination. In the CI method, when the number of prepared slater wave functions is increased, the wave function always approaches an exact wave function. However, since the calculation cost increases exponentially, the expansion is usually terminated at a specific order. Depending on how many sets of the Slater wave functions are prepared, we call the methods as Full-CI, CID (two-electron excitation only), CISD (one- and two-electron excitation only), and QCISD (improved CISD). The CC method improves a wave function by taking a partial sum for a specific configuration. Depending on which configuration is considered, we call the methods as CCD (two-electron excitation only), CCSD (one- and two-electron excitation only), and CCSD (T) (three-electron excitation is considered in perturbation theory). In addition to these Hartree-Fock-based methods, electronic state calculations based on the density functional theory are also widely used.