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configuration interaction retaining a reference determinant and its single and double excitations. Conventional matrix-vector iterations have leading $O(o^2{v}^4)$ work for occupied and virtual dimensions $o,v$, hence $O(N^6)$ when both grow with system size. Truncated CI is not generally size extensive.

A correlation between many-electron states classified by total spin and spatial symmetry along a nuclear path. Orbital occupations, spin adaptation and configuration interaction are needed; one-electron energy curves alone are not a state diagram.

Restricted Hartree–Fock incorrectly retains ionic configurations when a homonuclear bond dissociates. As overlap vanishes, its symmetry-preserving occupied orbital approaches $({\varphi }_A+{\varphi }_B)/\sqrt{2}$. The doubly occupied spatial product containsThe first and last terms place both electrons on one separated atom. Their combined probability remains one half, while the correct neutral singlet has one electron on each atom. The resulting spurious Coulomb repulsion raises the restricted dissociation limit. This is missing static electron correlation, not a failure of the Born-Oppenheimer approximation.

A two-configuration expansion using both ${\sigma }_g^2$ and ${\sigma }_u^2$ can cancel the ionic terms and recover the Heitler–London separated-atom singlet. Configuration interaction in the appropriate active space or a multiconfigurational self-consistent treatment supplies this remedy. The Unrestricted Hartree-Fock method can instead localize opposite spins on different atoms and give the correct separated-atom energy, but its single determinant breaks spin symmetry and is not the pure singlet at intermediate separation. The distinction between restricted and symmetry-broken descriptions of stretched hydrogen is treated in the original analysis of Coulson and Fischer.^[ref]

For conventional CISD, the leading matrix-vector contraction scales as $O(o^2{v}^4)$ in occupied and virtual orbital dimensions. If both grow proportionally to a system-size parameter $N$, the familiar estimate is $O(N^6)$ work per iteration; the iteration count and integral-storage strategy add implementation-dependent costs.

Calculated potential energy surfaces can predict equilibrium geometries and harmonic force constants, permitting comparison with diffraction-derived structures, rotational constants and vibrational spectra. Calculating several roots or different charge states can also estimate excitation or ionization energies. Such predictions depend on basis and truncation quality; truncated CI is not generally size extensive and is not automatically reliable for strongly multiconfigurational bond breaking. The quoted polynomial scaling is for CISD, not full configuration interaction, whose determinant space grows combinatorially.