Calculation of some integrals for the atomic three-electron problem

Applications of four-body exponentially correlated functions

“…(3) are equal to 0. Hylleraas extended integrals of that kind have been extensively studied in [10][11][12][13][14][15][16][17] using multipole-type expansions and, recently, by the present authors using the analytical recurrence approach [18,19]. Both methods had been successfully applied in high-precision calculations of leading relativistic and QED corrections to the energy of lithium-like systems [3,19,20].…”

Accurate upper and lower bounds to the 2S states of the lithium atom

“…This is the best lower bound that can be calculated with Temple's formula for a given basis set. Positive eigenvalues pi are meaningless because of the condition Ei-) < E , < u in Temple's formula (23)(24)(25).…”

“…Scrinzi [22] also derived the matrix eigenproblem Eqs. (23)(24)(25) Table I1 to determine p . The assignment of the eigenvalues p k to the lower bounds Ej-) is made with Eq.…”

“…Recently, we gave an efficient evaluation of these integrals [8]. The integrals with one factor r;i2 are also given by King [24,25].…”

“…Determine with the method of variance minimization a lower bound EL21 = u < Ep+l, Solve the corresponding matrix eigenproblem Eqs. (23)-(25). Assign the eigenvalues , %k to the lower bounds Ej-), 0 5 i I p with Eq.…”