The correlation-function potential-harmonic and generalized Laguerre function calculation on the 1S states of the helium atom Original Research Article

We present the correlation-function potential-harmonic and generalized Laguerre function method (CFPHGLF), and apply it to the n 1S (n = 1 − 4) states of the helium atom. We find that the eigenenergies for 2 1S, 3 1S and 4 1S states from the present CFPHGLF method are much better than those from the previous potential-harmonic and generalized Laguerre function method (PHGLF) (Intern. J. Quantum. Chem. 55 (1995) 47), and they only have errors in the fourth decimal place for 2 1S, the fifth decimal place for 3 1S and 4 1S states compared with those from exact variational method and the correlation-function hyperspherical-harmonics and generalized Laguerre function method (CFHHGLF) of the complete set expansion. However, the eigenenergy for the ground state 1 1S is not as good as that from the PHGLF method because of omitting the potential harmonic (PH) bases relevant for electron-electron correlation. The results are also discussed relative to some other hyperspherical harmonic (HH), PH, Hartree-Fock and variational configuration interaction (CI) methods.