There has been substantial progress in the development of electron correlation methods with some benefits and drawbacks. In this paper, we give a review of electron correlation effects on many body particles system. We focus more on atoms and molecules rather than solid state and take into account single reference case only. We mainly discuss perturbation theory, coupled electron many electron theory and a few versions of coupled electron pair approximations with comparison configuration interaction and some coupled cluster methods in which coupled cluster method is crucially important for the crystalline solids, the electron gas and the heat of the reaction. We also show some results, reported by several authors, to fairly compare and judge the methods’ feasibility mentioned above. <alternatives> [...] </alternatives>
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