Beryllium functional, testing

Aronchick JM, Rossman MD, Miller WT. Chronic beryllium disease diagnosis, radiographic findings, and correlation with pulmonary function tests. Radiology 1987 163(3) 677-682. 

In 1968, a group of keynote papers was published by Miller and Ruedenberg [41, 42, 43]. They introduced an optimization procedure for geminals, presented a proof for Arai s theorem, analyzed the advantages and the limitations of the simple APSG wave function, introduced the augmented separated-pair expansion (which develops the wave function in terms of APSG-type terms), and tested the theory on beryllium-like atoms. 

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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