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The semi-exponential basis set of radial functions (A.M. Frolov, PhysicsLetters A {\bf 374}, 2361 (2010)) is used for variational computations of boundstates in three-electron atomic systems. It appears that semi-exponential basisset has a substantially greater potential for accurate variational computationsof bound states in three-electron atomic systems than it was originallyanticipated. In particular, the 40-term Larson's wave function improved withthe use of semi-exponential radial basis functions now produces the totalenergy \linebreak -7.47805413551 $a.u.$ for the ground $1^2S-$state in the${}^{\infty}$Li atom (only one spin function $\chi_1 = \alpha \beta \alpha -\beta \alpha \alpha$ was used in these calculations). This variational energyis very close to the exact ground state energy of the ${}^{\infty}$Li atom andit substantially lower than the total energy obtained with the originalLarson's 40-term wave function (-7.477944869 $a.u.$).

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

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