When calculating the non-spin-polarized electron localization function (ELF), within VASP, you get a single readout of the elf corresponding to all explicitly treated valence electrons. When you calculate a spin-polarized ELF, however, the ELF output is split into a spin up elf and a spin down elf. My question is how should we go about plotting, or presenting, these two data sets? Is summing the up and down intensities to get a "total elf" (using the chgsum.pl script for example) a reasonable thing to do?
The spin separated ELF intensities are also generally lower then the non spin separated ELF intensities, and so in this in this same way, would the separation of the spin up and spin down intensities be a partial reason for this difference? In the systems I've been studying for example, this generally seems to be the case (as in the sum of spin up and spin down intensities at each grid point in my simulation cell approximately equals the ELF intensities of a non spin polarized version of the same system). So would plotting a single ELF figure depicting the individual sum of the spin up and spin down ELFs be correct?
The ELF of Becke is defined for a single spin channel using the Fermi-hole curvature. Only for closed-shell systems this can be "unified" in formula for the total density. To circumvent this problem for spin-polarized system I have defined the "spin-polarized" ELF formula (M. Kohout and A. Savin, Int.J. Quantum Chem. 60, 875, 1996) using Savins reformulation of ELF as given by kinetic energy densities. Then, there is just single ELF diagram for the system. However, more consistem analysis is given by the utilization of ELI-D for triplet coupled electrons. ELI-D removes the unpleasant ratio with respect to the homogeneous electron gas. Just check the papers dealing with the electron localizability indicator (ELI-D). An remark to the ELF from VAPS: ifonly the valence electrons are considered for ELF then the result can be wrong due to incorrect core-valence separation. For this check the paper M. Kohout and A. Savin, J. Comp. Chem. 18, 1431, 1997.
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