Can anyone suggest some free software that can visualize the charge density and/or electron localization function (ELF)? More importantly, can we determine/know those values (charge density and/or ELF) to any arbitrary position of the structure - i.e. not just the color map?
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Yes, for example the Python package chemtools gives several examples of calculating the ELF from a Gaussian cube or similar wavefunction file.
At the moment, it will generate a Gaussian-compatible cube, but you can interpolate to whatever point you want. (I haven't gone through the Python code in detail, but I suspect you could get the ELF or other metric at points without generating the cube.)
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$\begingroup$ Thanks @Geoff. Does it calculate the charge densities as well (in addition to ELF)? $\endgroup$– SakCommented Dec 7, 2022 at 20:52
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$\begingroup$ I'm not 100% sure what you mean by "charge density" - do you want the electron density (yes) or the electrostatic potential (yes). See the examples for the range of analysis. $\endgroup$ Commented Dec 8, 2022 at 13:59