Existence of additional solutions to the equations of the
Hartree–Fock method occurring usually in the case when potential energy surfaces of different
electronic states are drawn close together. Within the spin-restricted
Hartree–Fock method (
RHF), singlet and triplet instabilities are distinguished. The former involves the existence
of another solution with lower energy and the electron distribution of lower symmetry.
It may be regarded as an indication that the initially assumed
molecular shape needs correction. The triplet instability involves rejection of the condition of
double occupancy of molecular orbitals and thus transition to the spin-unrestricted
Hartree–Fock method (
UHF). The triplet instability is a necessary, but insufficient, condition for the conclusion
as to the
biradical character of the
ground state of a given system.
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