# η1 or sigma complex involving cyclopentadienyl anion

When $\ce{\eta^1-C5H5-}$ acts as a ligand, does the donor carbon become $sp^3$ hybridized, and would this be a sigma donor through sigma orbitals? Or, is it $sp^2$ where the lone pair is donated through a pi orbital, making it a sigma donor through a pi orbital?

The second option seems much more likely as the ligand changes the $\ce{C}$ attached to metal randomly with time through rearrangements.

Also, does "sigma complex" and "pi complex" only differentiate the hapticity? as $\ce{\eta^1-C5H5-}$ is a sigma complex and $\eta^3$, $\eta^5$ are pi complex.

Even though depictions of $\eta^1$-coordination might suggest a $\mathrm{sp^3}$-carbon donating, there is little evidence, that it actually is. Taking the example you have presented in your answer from Casey et. al.[1] I have run a geometry optimisation to obtain molecular orbitals at the DF-BP86/def2-SVP level of theory. The following geometry parameters around the coordinating carbon already suggest only little pyramidalisation: \begin{array}{lrr}\hline \text{Parameter} & \text{Experimental [1]} & \text{DF-BP86/def2-SVP}\\\hline \mathbf{d}(\ce{Re-C^1}) & 236.0 & 240.2\\ \mathbf{d}(\ce{Re-H}) & 288.7 & 282.6\\ \mathbf{d}(\ce{Re-C^2}) & 317.8 & 321.3\\ \mathbf{d}(\ce{Re-C^5}) & 315.6 & 315.6\\ \angle(\ce{Re-C^1-H}) & 114.3 & 100.7\\ \angle(\ce{Re-C^1-C^2}) & 110.8 & 109.5\\ \angle(\ce{Re-C^1-C^5}) & 108.5 & 106.4\\ \angle(\triangle[\ce{C^1C^2C^5}]\ce{-H}) & 122.8 & 139.1\\ \text{RMSD} & 0.0 & 0.1\\\hline \end{array}

We know that crystal structures are not really that accurate with protons, hence I'd put a little more trust into the calculation at this point. The paper does not give a value for any protons.
Here is a picture of the calculated structure.

When we look at the canonical MO we will see that all (occupied) π-obitals of the Cp-ligand are still there. Obviously they are distorted, but clearly recognisable.

The second orbital is the HOMO-1, which is the main contribution for the coordination, and the last is the HOMO (click for large). The only s-contribution to the HOMO-1 is from the carbon of the $trans\text{-}\ce{CO}$-ligand (and some hydrogen).
In output numbers, missing from 1 are minor contributions (<0.05):

 Alpha occ 81 OE=-0.276 is C39-p=0.19 C42-p=0.12 C41-p=0.12 C43-p=0.11 C40-p=0.11
Alpha occ 87 OE=-0.185 is C39-p=0.26 C42-p=0.23 C41-p=0.22 Re24-d=0.08 C27-s=0.05
Alpha occ 88 OE=-0.153 is C43-p=0.32 C40-p=0.32 C41-p=0.13 C42-p=0.12


When we localise the orbitals with the Natural Bond Orbital (NBO) analysis, we find a lone-pair at $\ce{c^1}$ (blue/orange) which donates into the anti-bonding $\ce{Re-^{$trans$}CO}$ orbital (yellow/red):

The composition of the lone pair orbital is

     (Occupancy)   Bond orbital / Coefficients / Hybrids
36. (1.27157) LP ( 1) C 39            s(  8.77%)p10.40( 91.23%)d 0.00(  0.00%)


The low occupancy is normal for donor-acceptor-complexes with some covalent character.

TL;DR Most $\eta^1$ complexes are in first approximation π-coordination complexes like the definition suggests[2]. This may change significantly when moieties are altered.

Further thoughts:
Wikipedia makes one important statement (it rarely does, but here it is true)3:

Molecules with polyhapto ligands are often fluxional, also known as stereochemically non-rigid.

You can expect that in $\eta^1$-ligands the metal can easily migrate from one carbon to another, as the MO show. I would expect some kind of pseudo-rotation.

### Ref.

1. Charles P. Casey, Joseph M. O'Connor, William D. Jones, Kenneth J. Haller. Organometallics 1983, 2 (4), 535–538. (link via doi, pdf via researchgate.net) Crystallographic data via CCDC number: 1118829.
2. η (eta or hapto) in inorganic nomenclature
3. Wikipedia: Hapticity and fluxionality

Casey and coworkers in Organometallics 1983, 2, 535:

http://www.ilpi.com/organomet/cp.html

It's $sp^3$

• It is really not that easy. Just because you found a Lewis structure that displays it like an sp3 carbon, does not mean that this is actually true. There is a lot of flexibility in these complexes and I very much doubt that there is much s character in the co-ordination bond. Sorry, but I have to down-vote your answer. – Martin - マーチン Jan 27 '17 at 12:05