Correlation energy with 40 Hylleraas function

Table 2 Correlation energy (CE) estimated as the difference between the wave function expanded with 40 Hylleraas functions (H-WF) and the HF wave function obtained with optimized exponents, for the lowest singlet state of confined helium atom. All quantities are in hartrees...

For two-electron atoms, many approaches have been applied a review made by Aquino reported the techniques used up to 2009 [20], To date, the expansion of the wave function in terms of Hylleraas-type functions is the technique that gives the lowest energies for several confinement radii [21-23], which can be used as reference when other techniques are proposed for the study of these systems. However, such a technique has not been used for atoms with several electrons, for example, beryllium. In this sense, in this chapter we test the many-body perturbation theory to second order, as a technique to estimate the CE for confined many-electron atoms. In the next section, we discuss the theory behind of the HF method, and the basis set proposed for its implementation for confined atoms. In the same section, the many-body perturbation theory to second order proposed by Moller and Plesset (MP2) [24] also is discussed, and we give some details about the implementation of our code implemented in GPUs [25]. Finally, we contrast our results for helium-like atoms with more sophisticated techniques in order to know the percent of correlation energy recovered by the MP2 method. 

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