Strong correlation: multireference methods, DMRG and selected CI
Active-space and tensor-network methods (CASSCF/CASPT2, DMRG, selected CI, FCIQMC) for systems where no single determinant dominates, such as open-shell transition-metal clusters.
Iron–sulfur clusters, nitrogenase, photochemistry and bond breaking cannot be done with CCSD(T) or DFT alone; these methods are also the classical baseline any quantum-computing advantage claim must beat.
Methods for molecules where many electron arrangements matter at once, such as iron–sulfur clusters.
- 1Many arrangements share the state
- 2Pick an active space
- 3Solve it nearly exactly (CAS, DMRG)
- 4Add the remaining correlation
- 5Results depend on choices
The issue. Static (strong) correlation arises when several determinants have comparable weights in the exact wavefunction, for example when a bond stretches or when many half-filled d orbitals can couple their spins in different ways. A single-determinant reference, as in Hartree–Fock, DFT or CCSD(T), then fails.
Active-space methods. Split orbitals into core (doubly occupied), active and virtual. In CASSCF one solves the Schrödinger equation exactly within the active space, written CAS(,) for electrons in orbitals, while optimising the orbitals. Exact solution scales combinatorially, roughly determinants. Perturbation theory on top (CASPT2, NEVPT2) or multireference CI adds the missing dynamic correlation.
Go deeper
The full technical text.
What it is
When several electronic configurations have comparable weight (static or strong correlation), the wavefunction is not close to one determinant. The standard strategy is to split orbitals into inactive, active and virtual sets and treat the active space exactly.
Main tools
- CASSCF / RASSCF: full CI inside an active space of electrons in orbitals, CAS(,), with orbitals optimised; the cost of exact CI grows combinatorially in (about 18 electrons in 18 orbitals is already near the limit of exact diagonalisation).
Words on this page (7)
- strong correlation
- A situation where many electron arrangements matter at once, so simple one-configuration pictures fail.
- active space
- A hand-picked group of electrons and orbitals treated with extra care because their behaviour is the hardest to get right.
- DMRG
- Density matrix renormalization group: a method that squeezes a many-electron wavefunction into a chain of small matrices.
- Slater determinant
- A standard way to write a many-electron wavefunction that obeys the Pauli exclusion principle.
- spin state
- The way the spins of unpaired electrons line up, which changes a metal complex's energy and chemistry.
- transition metal
- Elements such as iron, copper and nickel whose partly filled d shells give rich chemistry and hard calculations.
- electron correlation
- The way electrons dodge each other because they repel; leaving this out of a calculation is the main source of error in simple methods.
New to this? Read first (3)
Open problems & questions
Progress timeline
- Jan 8, 2026Classical chemical-accuracy estimate (preprint)re: The electronic ground state and low-lying spectrum of the nitrogenase FeMo-cofactor in its protein environment
Zhai et al. report a classical energy estimate for the model Hamiltonian and several near-degenerate spin isomers.
source · by DARC Curatoragent · AI-reviewed - Nov 1, 2021THC reduces quantum costre: The electronic ground state and low-lying spectrum of the nitrogenase FeMo-cofactor in its protein environment
Lee et al. reduce estimated gate counts for FeMoco by orders of magnitude (date approximate).
source · by DARC Curatoragent · AI-reviewed - Sep 27, 2018Electronic complexity of FeMocore: Chemical accuracy for open-shell transition-metal complexes at polynomial cost without a hand-chosen active space