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I fully understand and recognise the manner and which the series works.

I cannot find any references for the change in sigma donor capability moving up the series.

For example, comparing $\ce{Cl-}$ and $\ce{NH3}$. Which of the two would be more a more willing sigma donor ?

Does this have something to do with how diffuse the orbitals are ?

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The spectrochemical series is an ordering of relative ligand interaction strength with metal ions. It can be used to infer relative $\sigma$-donor strength, if $\pi$-interactions are not possible for those particular ligands. Examples of this type ligand with no $\pi$-interactions include $\ce{NH3}$, $\ce{CH3-}$, and $\ce{H-}$.

Most ligands will exhibit $\pi$-interactions, operating as $\pi$-donors or $\pi$-acceptors, and these interactions dominate the ordering of the spectrochemical series. The $\sigma$-donor interactions are obscured and heavily affected by the $\pi$-interactions. Experimentally all of these effects are important, and it is difficult to separate these interactions from one another.

For example, the $\sigma$-donor interaction of a $\pi$-acceptor ligand is drastically increased from some initial level. $\pi$-backbonding reduces electron density at the metal center, leading to increased $\sigma$-donation (which increases $\pi$-backbonding, and so on). This will make a given $\pi$-acceptor ligand act as a better $\sigma$-donor than would be expected. The converse effect is observed with $\pi$-donor ligands reducing $\sigma$-donor strength.

The complexity of these interactions tempers the question of gauging $\sigma$-donor interactions only. The combined bonding effects influence one another.

Theoretically separating out $\sigma$-donor interactions from all $\pi$-interactions could be possible computationally, but I am unaware of any research on this specific topic. From a very general standpoint, improved metal-ligand orbital overlap will increase $\sigma$-donor strength, which may help estimate these characteristics qualitatively.

Most inorganic textbooks should be able to provide further detail on this topic under sections on ligand field theory.

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    $\begingroup$ can relative Bronsted basicity be used gauge sigma donor capabilities? $\endgroup$
    – Dissenter
    Commented Jan 7, 2015 at 20:28
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    $\begingroup$ I would say that Lewis basicity would be a better approach to evaluating sigma-donation as this is more accurate in how ligands coordinate to metals. Gauging Lewis basicity as only sigma-donation generalizes somewhat the complete electronic structure. Nevertheless, this seems like a good way to determine approximate sigma-donation strength. Below is a link to a book that has more information on this, where it appears they have computational and thermodynamic values for complexation enthalpies of various Lewis bases to Lewis acids such as BF3: books.google.com/books?id=KsF44nB9Ex8C $\endgroup$
    – venture
    Commented Jan 7, 2015 at 21:20

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