Electron correlation methods beryllium atom

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. 

We see that, for atoms or molecules more complex than beryllium, the use of correlated basis sets of Hylleraas type rapidly becomes infeasible and the Cl method and its variants become more attractive. For a correlated basis, the number of terms required to reach a particular metric order can become hopelessly large. In a 10-electron problem like neon, 1596 terms are needed to construct a wave function complete through u = 2. If instead the wave function is limited to a single rfj factor per term, this number is reduced to 561 terms, still a sizeable number for such a low metric order. It must also be kept in mind that antisymmetrizing the wave function means that each term... 

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