# What do 'sigma' and 'pi' in front of ligands in the formula of a coordination compound mean?

The following coordination compound was given in the book Concise Inorganic Chemistry by J.D. Lee (Adapted by Sudarsan Guha) under the topic 'Effective Atomic Number (EAN)':

$$\ce{[Ti(\sigma -C5H5)2 (\pi -C5H5)2]^0}$$

What is meant by the quantifiers $$\sigma$$ and $$\pi$$ in front of the ligand? I have not seen this format with other ligands? If this is to signify $$\sigma$$ and $$\pi$$ bonds, why is it not used in the formulas of metal carbonyls which have synergic bonds (a combination of both $$\sigma$$ and $$\pi$$ bonds)?

In all the 67 occurrences of 'cyclopentadienyl' in the IUPAC Red Book, I was unable to see $$\ce{C5H5-}$$ having a $$\sigma$$ or $$\pi$$ in front of it. Instead I only saw $$\eta$$ being used in the name. I came to know that it is meant to denote 'hapticity'. Is this related to the presence of $$\sigma$$, $$\pi$$?

Tetra(Cyclopentadienyl) compounds such as $$\ce{Ti(C5H5)4}$$ may be made from $$\ce{TiCl4}$$ and $$\ce{Na(C5H5)}$$. The formula may be written as $$\ce{[Ti(\eta_5-C5H5)2(\eta_1-C5H5)2]}$$ where two cyclopentadienyl rings are attached by 5 C-atoms ($$\pi$$ - bonded) and two rings are attached by one C-atom ($$\sigma$$ - bonded).
NMR studies on these tetra(cyclopentadienyl) compounds suggest that in the $$\eta_1$$ rings the C bonded to Ti continually changes, and the $$\eta_1$$ and $$\eta_5$$ rings change their roles.
The first paragraph explains quite well what the author intends by the quantifiers $$\sigma$$ and $$\pi$$. Two rings are bonded by $$\pi$$ donation with a hapticity of 5 and two rings are $$\sigma$$ bonded with a hapticity of 1. This picture should clear things up