for MO between C-S, is the sigma bond higher in energy than pie bond since it is applied to C.So when we do MO for C-S,do we use that rule in this as well

To compare the energy levels of sigma (σ) and pi (π) bonds in a molecule, we need to consider the molecular orbital (MO) theory. MO theory describes the bonding and antibonding interactions of atomic orbitals to form molecular orbitals.

In a sigma bond, the bonding orbitals overlap end-to-end along the internuclear axis. The electron density is concentrated between the nuclei, resulting in a strong and stable bond. On the other hand, a pi bond forms when two atomic orbitals overlap side by side, with the electron density concentrated above and below the internuclear axis.

In the case of a C-S bond, the carbon atom has two atomic orbitals involved in the bond: the 2p orbital and a hybridized orbital (such as sp, sp2, or sp3 hybridization). The sulfur atom also contributes its atomic orbitals to form the molecular orbitals.

Based on the rules of MO theory, the sigma bond is generally lower in energy than the pi bond. This is because the sigma bonding MO has a greater overlap of atomic orbitals, leading to stronger bonding interactions and lower energy levels. Conversely, the pi bonding MO has less overlap and weaker bonding interactions, resulting in higher energy levels.

When you perform molecular orbital calculations for a C-S bond, you would typically consider both the sigma and pi bonding interactions. You can use the principles of MO theory to determine the relative energies of the sigma and pi molecular orbitals. By comparing the energy levels, you can assess which bonding interaction is higher or lower in energy.

It's important to note that the actual energy difference between the sigma and pi molecular orbitals may vary in different molecules or compounds, depending on factors such as atomic sizes, electronegativities, and the presence of other molecular interactions. MO theory provides a theoretical framework, but experimental and computational approaches are usually required to obtain accurate energy levels for specific molecules.