The estimates for partial atomic charges start with the very simple Mulliken analysis, which we all study in class, but which is known to be very limited. Beyond this, there is a range of computational methodologies to estimate partial charges; Gaussian for example has multiple options for generating electrostatic "potential-derived" charges. Each method is based on a different theoretical framework with different assumptions, so they are not equivalent.

I'm interested in the simulation of the crystal field (CF) effects (a) in transition metal ions and/or (b) in rare earth (lanthanide) ions via electrostatic models. Any modelling that does not explicitly consider covalent effects is going to be limited to some extent.

My question is: what software and what software and method would be the most adequate to estimate partial atomic charges for the purposes of a electrostatic simulation of the crystal field effects ?

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    $\begingroup$ I don't know that there's a single answer to this question, but I'd consider DDEC6 charges to be a potentially promising approach, as implemented in Chargemol. At least, it'd be worth considering -- certainly over Mulliken. $\endgroup$ – Andrew Rosen Apr 30 at 18:26
  • $\begingroup$ Related! mattermodeling.stackexchange.com/q/1439/5 I hadn't realized this, because your question was from the second day that our site went live, and too much was going on for me to process everything! $\endgroup$ – Nike Dattani Jul 22 at 2:46

There are a few recent atomic partial charge schemes that are useful.

  • You mentioned the electrostatic fitting schemes. These seek to best match the electrostatic potential of the molecule / system, but wouldn't be ideal for your situation. They have problems fitting charges on "buried atoms" such as the metal center of your complex, because they have little effect on the outer electrostatic potential (i.e. all your ligands surround the metal, so it's hard to separate the charge on the metal and the charges on the ligands).
  • Atomic orbital partioning (e.g. Mulliken, NAO, etc.). These methods use atomic orbitals, but are often sensitive to basis set effects.
  • Hirschfeld / Atoms in Molecules (AIM) analysis. These methods seek to partition the electron density to produce charges. Consequently, they'll have little problem with your metal complex. Several schemes exist depending on the program you use, but the open source Horton package can derive most by post-processing.
  • A comment above suggests Thomas Manz's DDEC6 scheme. This has been fairly robust over the last few years although has fewer proponents than Hirshfeld / IBS approaches - possibly because Chargemol is currently the only program with an implementation.

Incidentally, there's an excellent review article "The Atomic Partial Charges Arboretum: Trying to See the Forest for the Trees" that may provide useful context.

In all, no single charge distribution tells the whole story, but a trio of well‐defined ones – i.e., one representative each of the three major classes of Corminboeuf and coworkers – should be able to cover most aspects of it.

The three classes mentioned include electrostatic fitting, atomic orbital partitioning, and electron density partitioning.

For your purpose, I'd highly advocate some type of electron density partitioning - these methods are resistant to basis set effects and won't have issues with buried metal centers in your molecules.

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    $\begingroup$ A great answer! I really like Hirshfeld and CM5 charges (some discussion about this being especially good for redox processes) for transition metal complexes in general. Mostly just empirical observations on my end, but once again, likely better than Mulliken. $\endgroup$ – Andrew Rosen Apr 30 at 20:58
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    $\begingroup$ Considering the careful tuning in CM5, they're probably reliable for many purposes. DDEC6 seems promising, but it's hard to evaluate without more widespread use. $\endgroup$ – Geoff Hutchison Apr 30 at 21:00

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