A compact boundary-condition- determined wavefunction for two-electron atomic systems

Highly compact wavefunctions with a clear physical meaning for the He atom and He-like isoelectronic ions for Z = 1–10 are written as a symmetrized product of exp[(ar + br2)/(1 + r)] electron–nucleus terms and an electron–electron Jastrow factor to satisfy the correct asymptotic behaviour both at short and long interparticle distances. Some parameters are chosen to satisfy exactly the cusp conditions, while the others are optimized by variational Monte Carlo calculations. The wavefunction energy is within 2 millihartrees from the non-relativistic limit in the entire Z-range, improving previously published work on similar compact wavefunctions. We tested the validity of the 'coalescence wavefunction' approximation. The Z-dependence of the optimized parameters allows us to write a general form of the wavefunction, using Z as an explicit parameter and four parameters independent of Z. We checked the validity of this wavefunction on the case Z = 30.