Compact and accurate variational wave functions of three-electron atomic systems constructed from semi-exponential radial basis functions

The semi-exponential basis set of radial functions [A.M. Frolov, Phys. Lett. A 374, 2361 (2010)] is used for variational computations of bound states in three-electron atomic systems. It appears that the semi-exponential basis set has a substantially greater potential for accurate variational computations of bound states in three-electron atomic systems than was originally anticipated. In particular, the 40-term Larson’s wave function improved with the use of semi-exponential radial basis functions now produces the total energy –7.4780581457 a.u. for the ground 1²S-state in the ^￥Li^infty{rm Li} atom (only one spin function c₁chi_1 = abaalphabetaalpha - baabetaalphaalpha was used in these calculations). This variational energy is very close to the exact ground state energy of the ^￥Li^infty{rm Li} atom and is substantially lower than the total energy obtained with the original Larson’s 40-term wave function (–7.477944869 a.u.).