Accurate Hylleraas-likefunctions for the He atom with correct cusp conditions

Abstract

In this letter, a set of ground state wavefunctions for the He atom is given. The functions are constructed in terms of exponential and power series as similar as possible to the Hylleraas functions of Chandrasekhar and Herzberg (1955 Phys. Rev. 98 1050). The accuracy of the calculated energies is found to be about 10 −4 au and all the cusp conditions at the Coulomb singularities are satisfied. The nine-parameter functions proposed here are found to have better local energy than those given by the 6 and 14 terms Hylleraas functions of Chandrasekhar. The mean value of various functions evaluated with the different proposals shows their good quality. These properties highly qualify the function to be used as an alternative to the Chandrasekhar functions in collisional problems. The whole set of functions given here can be considered as an alternative to the proposals of Chandrasekhar (1955

Hylleraas- and Kinoshita-type wave functions with correct cusp conditions

“…An alternative and simple method to construct a wave function with a correct Kato's cusp condition is described in [18,19]. Assume that a function ψ(r 1 ,r 2 ,r 12 ) with correct cusp conditions is given.…”

“…We call this procedure the GR method. In the work [18,19] the following standard separable choice was made for ψ(r 1 ,r 2 ,r 12 ):…”

“…The local energy E loc = H ψ/ψ is suitable for measuring the quality of the wave function [18,23,24]. For the exact solution the local energy is a constant.…”

“…In recent papers such a variational calculations are carried out, where interparticle coordinates are used, and the exact fulfillment of the cusp conditions are taken into account from the very beginning [18][19][20]. In this paper we follow this line of research but we use Hylleraas-and Kinoshitatype functions.…”

Atomic Properties of the Two-Electron System using Variational Monte Carlo Technique

“…Recently, Alexander et al [19] have proved that variational Monte Carlo (VMC) techniques can accurately evaluate the lowest-order relativistic corrections and the mass polarization term for the three lowest states of the helium atom with symmetry 1 S, 3 P , and 3 D, using a set of medium-quality, explicitly correlated wave functions. The obtained results are in good agreement with that obtained using a high-quality Hylleraas wave function.…”