Electron correlation

Electron correlation concerns the dependence between electronic degrees of freedom that cannot be captured by treating each electron as moving independently. In a quantum-chemical use of the term, correlation usually means effects beyond the best single-Slater determinant Hartree-Fock method; that method already includes exchange associated with fermionic antisymmetry.

The distinction matters when comparing approximations. Dynamic electron correlation describes additional instantaneous avoidance even when one electronic configuration dominates. Static electron correlation becomes important when several configurations have comparable significance, as during some bond-dissociation processes. A correlation energy is therefore defined relative to a stated reference calculation, and the physical need for multiple configurations is different from merely allowing a single orbital to change shape.

The exact ground-state energy minus the minimum Hartree-Fock energy for the same Hamiltonian and variational constraints. It is nonpositive when compared with the unrestricted variational minimum. Correlations beyond a single determinant can substantially change phase boundaries at low density.

A normalized product of two identical bonding orbitals built from separated orthogonal centers has finite weight in configurations with both electrons on one center. Repulsion penalizes that ionic weight even when hopping disappears. Mixing configurations can instead approach one electron per center while preserving the required spin and exchange symmetries.

The correlated instantaneous avoidance of electrons beyond a single Slater determinant. It can remain important even when one configuration dominates, as for an isolated closed-shell helium atom; it is distinct from the near-degeneracy problem of static electron correlation.

Electron correlation caused by the need for multiple important configurations, often when several molecular orbitals are nearly degenerate. Stretching a homonuclear two-electron bond makes a single doubly occupied orbital retain unphysical ionic contributions; a suitable combination of configurations cancels them.

A strongly correlated material whose low-energy electronic quasiparticles have a very large thermodynamic effective mass. An enhanced electronic heat capacity coefficient, spin susceptibility and quantum-oscillation cyclotron effective mass are complementary signatures; they need not all be related by a single isotropic band mass. A Kondo lattice is an important setting for such behaviour. In CeAl3, low-temperature specific heat and quadratic resistivity provided an early quantitative example.^[ref]

For quasiparticles with density of states $g(E_F)$ including both spins, the leading electronic heat capacity is $C=\gamma T$ with $\gamma ={\pi }^2{k}_B^{2}g(E_F)/3$. A narrow heavy band makes this coefficient large. The density of states and heat capacity must use consistent extensive, molar or volumetric normalization.

The 1975 measurements of CeAl3 below $0.2\mathrm{K}$ found an electronic heat capacity coefficient of $1.62\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-2}$ and a quadratic electrical-resistivity coefficient of $35\mu \mathrm{\Omega }\mathrm{cm}{\mathrm{K}}^{-2}$. These are complementary thermal and transport signatures of an unusually dense low-energy electronic spectrum.^[ref] A temperature sweep and a $C/T$ versus $T^2$ fit separate the electronic intercept from a Debye lattice term; the transport comparison tests a Fermi liquid temperature law.

Antiferromagnetic exchange between a localized magnetic moment and conduction electrons produces strong low-energy correlations and screening of the moment. In a dilute magnetic-impurity metal, a resistance minimum and a low-temperature logarithmic increase are characteristic signatures over an appropriate temperature range. The strong-coupling low-temperature regime cannot be obtained by extending the logarithm indefinitely.

A periodic array of local moments coupled to conduction electrons. Competition between screening, coherent hybridization and intersite magnetic interactions can produce a heavy fermion material, magnetic order or a correlated insulating state.

A Kondo lattice develops coherent low-energy quasiparticle bands below a material-dependent coherence scale. This lattice scale need not equal the single-impurity Kondo screening scale. Coherence can produce a heavy Fermi liquid with narrow bands, large electronic heat capacity and low-temperature quadratic resistivity.