Total energy with 40 Hylleraas function

If a trial function 9 leads to a kinetic energy 1 and a potential energy Vx which do not fulfill the virial theorem (Eq. 11.15), the total energy (7 +Ei) is usually far from the correct result. Fortunately, there exists a very simple scaling procedure by means of which one can construct a new trial function which not only satisfies the virial theorem but also leads to a considerably better total energy. The scaling idea goes back to a classical paper by Hylleraas (1929), but the connection with the virial theorem was first pointed out by Fock.5 It is remarkable how many times this idea has been rediscovered and published in the modern literature. 

Calculations of total energies and widths of doubly excited states using the Breit-Pauli Hamiltonian and comparison with results from the use of Hylleraas-type basis functions [55]... 

Table 6 Total energy (TE) and correlation energy (CE) estimated as the difference between the wave function expanded in 40 Hylleraas terms (H-WF) and the HF wave function obtained with optimized exponents, for the lowest triplet state of the confined helium atom. All quantities are in hartrees...

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