Ab initio quantum chemistry methods

Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry. The term ab initio was first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a semiempirical study on the excited states of benzene. The background is described by Parr. In its modern meaning ('from first principles of quantum mechanics') the term was used by Chen (when quoting an unpublished 1955 MIT report by Allen and Nesbet), by Roothaan and, in the title of an article, by Allen and Karo, who also clearly define it.

Almost always the basis set (which is usually built from the LCAO ansatz) used to solve the Schrödinger equation is not complete, and does not span the Hilbert space associated with ionization and scattering processes (see continuous spectrum for more details). In the Hartree–Fock method and the configuration interaction method, this approximation allows one to treat the Schrödinger equation as a "simple" eigenvalue equation of the electronic molecular Hamiltonian, with a discrete set of solutions.

Ab initio electronic structure methods have the advantage that they can be made to converge to the exact solution, when all approximations are sufficiently small in magnitude and when the finite set of basis functions tends toward the limit of a complete set. In this case, configuration interaction, where all possible configurations are included (called "Full CI"), tends to the exact non-relativistic solution of the electronic Schrödinger equation (in the Born–Oppenheimer approximation). The convergence, however, is usually not monotonic, and sometimes the smallest calculation gives the best result for some properties.

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