Kinetic balance: A partial solution to the problem of variational safety in Dirac calculations

Recent publications have suggested that the satisfaction of a principle we call kinetic balance can provide variational safety in Dirac calculations. The theoretical foundation for this proposal is examined, first in simple one-electron problems, and then (less rigorously) in SCF calculations. The conclusion is that finite basis calculations using kinetic balance are safe from catastrophic variational collapse, but that the ‘‘bounds’’ provided by these calculations can be in error by an amount of order 1/c4. The bounds are applicable to total SCF energies, but not to SCF orbital energies. The theory is illustrated by a series of one-electron calculations.