abinitio

Ab initio, Latin for “from the beginning,” is a term used in chemistry and physics to describe computational methods that aim to determine molecular properties directly from quantum mechanics without empirical parameters. In quantum chemistry, ab initio calculations solve the electronic Schrödinger equation for fixed nuclear positions under the Born-Oppenheimer approximation, yielding energies, geometries, and properties from first principles.

The most basic ab initio method is Hartree-Fock (HF), which models electron interaction in an average way but neglects dynamic correlation. To capture electron correlation, post-Hartree-Fock methods are employed, including Møller–Plesset perturbation theory (MP2, MP3, MP4), configuration interaction (CI), and coupled cluster (CC) theory, with CCSD and CCSD(T) often regarded as highly reliable for small to medium systems. Multi-reference methods such as CASSCF and MRCI are used when near-degeneracy effects are important.

Calculations rely on basis sets—collections of mathematical functions used to describe molecular orbitals. Ranging from minimal to extensive correlation-consistent sets, the choice of basis set influences accuracy and cost, with extrapolation toward the complete basis set limit a common practice.

Ab initio approaches also extend to excited states via methods like EOM-CC and ADC, while preserving the first-principles character. Relativistic effects for heavy elements may be included through scalar-relativistic Hamiltonians or relativistic effective core potentials.

Applications include predicting molecular geometries, reaction energetics, vibrational frequencies, and potential energy surfaces. Limitations include rapidly increasing computational cost with system size and the need for careful treatment of basis set and correlation effects. Ab initio methods contrast with semi-empirical and some density functional approaches, which introduce approximations or parameterizations.