The Z-1 expansions of the total non-relativistic energies for three- and four-electron systems

Analytical formulas are derived for the Z(-1) (Q(-1)) expansions of the total energies in the two-, three- and four-electron atomic systems. The coefficients in these formulas are determined from the results of accurate and highly accurate computations with correlated wave functions. The accuracy of our formulas is sufficient to evaluate the total ground state energy of an arbitrary non-relativistic ion with two, three and four electrons.