quantum chemistry Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions ...

, a complete active space is a type of classification of

molecular orbitals In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding ...

. Spatial orbitals are classified as belonging to three classes: * ''core'', always hold two electrons * ''active'', partially occupied orbitals * ''virtual'', always hold zero electrons This classification allows one to develop a set of

Slater determinant In quantum mechanics, a Slater determinant is an expression that describes the wave function of a multi-fermionic system. It satisfies anti-symmetry requirements, and consequently the Pauli principle, by changing sign upon exchange of two electro ...

s for the description of the

wavefunction A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements mad ...

as a linear combination of these determinants. Based on the freedom left for the occupation in the active orbitals, a certain number of

electrons The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...

are allowed to populate all the active orbitals in appropriate combinations, developing a finite-size space of determinants. The resulting wavefunction is of multireference nature, and is blessed by additional properties if compared to other selection schemes. The active classification can theoretically be extended to all the molecular orbitals, to obtain a

full CI Full configuration interaction (or full CI) is a linear variational approach which provides numerically exact solutions (within the infinitely flexible complete basis set) to the electronic time-independent, non-relativistic Schrödinger equation. ...

treatment. In practice, this choice is limited, due to the high computational cost needed to optimize a large CAS wavefunction on medium and large molecular systems. A Complete Active Space wavefunction is used to obtain a first approximation of the so-called static correlation, which represents the contribution needed to describe bond dissociation processes correctly. This requires a wavefunction that includes a set of electronic configurations with high and very similar importance. Dynamic correlation, representing the contribution to the energy brought by the instantaneous interaction between electrons, is normally small and can be recovered with good accuracy by means of perturbative evaluations, such as CASPT2 and

NEVPT In quantum chemistry, ''n''-electron valence state perturbation theory (NEVPT) is a perturbative treatment applicable to multireference CASCI-type wavefunctions. It can be considered as a generalization of the well-known second-order Møller–P ...

See also