In
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 fermion ...
s for the description of the
wavefunction
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter) ...
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 in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
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 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.
See also
*
CASSCF
*
Multi-configurational self-consistent field
Multi-configurational self-consistent field (MCSCF) is a method in quantum chemistry used to generate qualitatively correct reference states of molecules in cases where Hartree–Fock and density functional theory are not adequate (e.g., for mole ...
(MCSCF)
References
Quantum chemistry
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