Hylleraas wave functions revisited

 

Toshikatsu Koga

 

• Department of Applied Chemistry, Muroran Institute of Technology, Muroran, Hokkaido 050, Japan

 

 

ABSTRACT

 

Optimality of the combination of N terms used in the Hylleraas N‐term wave function is examined for several two‐electron atoms. It is pointed out that the N‐term wave function given in the literature is not always the best N‐term function for a fixed N. For example, the known Hylleraas six‐term function Ψ₆=exp(−ζs) (1+c₁u+c₂t²+c₃s+c₄s²+c₅u²) yields the energy of −2.903 329 354 a.u. for the helium atom, whereas a new six‐term function Ψ_6,opt=exp(−ζs) (1+c₁u+c₂t²+c₃u²+c₄s²u+c₅s³u) gives a much lower energy of −2.903 452 763 a.u. It is also shown that the best combination of N terms depends largely on the nuclear charge.

 

https://sci-hub.se/https://doi.org/10.1063/1.462164