Improved Hylleraas calculations for ground state energies of lithium ISO–electronic sequence

Abstract

The 'S ground state of lithium iso-electronic sequence is calculated by the use of Hylleraas-type wave functions. A 92 term one-spin wave function was used for lithium atom calculations. The energy obtained was -7.478031 a.u. as compared with the previous best value of -7.478025 a.u. calculated by Larsson. In addition, improved energies for 2 = 4 to 8 were calculated by the use of 60 term wave functions. This work thus provides the lowest ab initio ground state energies for lithium sequence to date.

Eigenvalues and expectation values for the 1s22s2S, 1Zhou1, Drake2 1995Phys. Rev. A16191391View full textAdd to dashboardCite

“…in units of 2RM, where RM=(1p/M)R, and p, = mM/(m+M) is the electron reduced mass and M is the [11] Ahlenius and Larsson [12] Sims and Hagstrom [13] Ahlenius and Larsson [14] Muszynska et al [15] Ho [16] Pipin and Woznicki [17] King and Shoup [4] Kleindienst and Beutner [18] King [5] King and Bergsbaken [19] Jitrik and Bunge [20] Chung et al [9] McKenzie and Drake [ …”

Asymptotic-expansion method for the evaluation of correlated three-electron integrals

“…[7 -13].The main technique used by these authors (except Fromm and Hill) is to expand r, in terms of individual coordinates r and r, as well as Legendre polynomials. One way to avoid infinite summations is to place some restrictions on the choice of basis set so that at least one of the three powers in each integral is even [7,8,11,14]. However, such restrictions may seriously affect the rate of convergence of the basis set.…”

Analytic evaluation of three-electron integrals

“…1) can be singular at points where their sum is not singular, as was pointed out in Sec. II C. Numerical evaluation at or near such cancelling singularities requires that the cancellations be performed analytically before the numerical evaluation is carried out; this prevents the excessive round off error which would otherwise occur at step 13 of Sec.…”

“…The result is M(I1, m1, lz, mz, l3, m3, n1', nz, n3, n12, n23, n31', a1,az, a3, a12, a23, (1.2) would be to work out a formula for the derivative needed in (1.4) by repeated differentiation of (2. 1) with the aid of (2.2) -(2.9). However, such formulas f' or derivatives grow in complexity at a rapidly increasing rate; thus this approach is to be avoided.…”

“…An extensive discussion of (1.1) and related ideas for getting the two-particle cusp behavior right has been given recently by Kutzelnigg. Unfortunately, the widespread use of I r;r, I correlation factors has so far been precluded by the lack of analytic formulas for certain of the matrix element integrals which arise. The present paper opens the door to the practical use of trial functions such as ( l. 1) by evaluating the previously intractable three-electron integral J(n t, nz, n3, n1z, nz3, n3, , a1,az, a3, a1z, az3, a31) n& -1 n2 -1 n3 1 Pl» 1 llg3 1 1131 -1 3 3 3 r1 rz r3 112 rz3 r31 exp( -a1r1azrz a3r3atzrlz -az3rz3 -a31r31}d I td rzd r3 (1.2) for all non-negative integers nt, nz, n3, ntz, nz3, n31, where ri:= I r;rl I. Here a:=b means a =b by definition.…”