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

Question

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 $\sigma$, $\pi$?

Answer 1

Concise Inorganic Chemistry¹ has the following to say about this tetra(cyclopentadienyl) titanium complex:

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

References:

1. Lee, J. D. Concise Inorganic Chemistry. 5th ed, Wiley publishers & Blackwell Science, pp. 696, 1996