Calculations of atomic and molecular systems with the condition for cancellation of the Coulomb singularities taken into account

A method of variational calculations of atomic-molecular systems is propose d, which takes into account the condition for cancellation of the Coulomb s ingularities that result from the action of the energy operator on the wave function at points where the particles collide. For this purpose, the secu lar equation is supplemented by a term that takes into account the inabilit y of a trial wave function to exactly satisfy this condition. For different values of a weighting factor rho of this additional term, the energy and o ther physical characteristics of the positronium ion e(+)e(-)e(-) and the n egative ion H- of the hydrogen atom are calculated with the use of basis fu nctions chosen in the form of products of exponential and power-law functio ns of interparticle separations. It was found that, for sufficiently large values of the weighting factor (p > 1), the condition for cancellation of t he singularities is virtually exactly satisfied, and, for a given size of t he basis set, the dependence of the results of calculations of the energy a nd expectation values of diverse physical quantities on this factor allows one to find all reliable significant digits in their calculated values.