Electron Localization Function at the Correlated Level: A Natural Orbital Formulation

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In this work we present a 2-fold approximation for the calculation of the electron localization function (ELF) which avoids the use of the two-particle density (2-PD). The first approximation is used for the calculation of the ELF itself and the second one is used to approximate pair populations integrated in the ELF basins. Both approximations only need the natural orbitals and their occupancies, which are available for most methods used in electronic structure calculations. In this way, methods such as CCSD and MP2 can be used for the calculation of the ELF despite the lack of a pertinent definition of the 2-PD. By avoiding the calculation of the 2-PD, the present formulation provides the means for routine calculations of the ELF in medium-size molecules with correlated methods. The performance of this approximation is shown in a number of examples ​
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