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.


[![display](https://i.stack.imgur.com/1F8iCl.jpg)](https://i.stack.imgur.com/1F8iC.jpg)


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. 


[![mo81](https://i.stack.imgur.com/Z7Jgub.jpg)](https://i.stack.imgur.com/Z7Jgu.jpg)[![mo87](https://i.stack.imgur.com/EoJofb.jpg)](https://i.stack.imgur.com/EoJof.jpg)[![mo88](https://i.stack.imgur.com/7NU2vb.jpg)](https://i.stack.imgur.com/7NU2v.jpg)


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):
[![interaction of localised orbitals](https://i.stack.imgur.com/zCEALl.jpg)](https://i.stack.imgur.com/zCEAL.jpg)


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](https://i.stack.imgur.com/EoJof.jpg):



> 
> 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](https://dx.doi.org/10.1021/om00076a010), [pdf via researchgate.net](https://www.researchgate.net/publication/231722947_Intermediates_in_the_associative_phosphine_substitution_reaction_of_e5-C5H5ReCO3)) Crystallographic data via [CCDC](https://www.ccdc.cam.ac.uk) number: [1118829](https://www.ccdc.cam.ac.uk/structures-beta/Search?Ccdcid=1118829).
2. [η (eta or hapto) *in inorganic nomenclature*](http://goldbook.iupac.org/H01881.html)
3. [Wikipedia: Hapticity and fluxionality](https://en.wikipedia.org/wiki/Hapticity#Hapticity_and_fluxionality)


 4

Casey and coworkers in Organometallics 1983, 2, 535:


[![enter image description here](https://i.stack.imgur.com/2ixhv.gif)](https://i.stack.imgur.com/2ixhv.gif)


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


It's $sp^3$


 3