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What is the electronic structure of methane (CH4) and what are the molecular orbitals involved in its formation, as determined by quantum mechanical calculations?

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Methane  CH4  is a tetrahedral molecule with a carbon atom at the center and four hydrogen atoms surrounding it. The electronic structure of methane can be determined by examining the atomic orbitals of the carbon and hydrogen atoms and how they combine to form molecular orbitals.Carbon has an electron configuration of 1s2s2p. In its ground state, carbon has two unpaired electrons in its 2p orbitals. However, in methane, carbon forms four sigma    bonds with four hydrogen atoms. To achieve this, carbon undergoes hybridization, where one of the 2s electrons is promoted to the empty 2p orbital, resulting in four sp hybrid orbitals.Each hydrogen atom has one electron in its 1s orbital. When the four hydrogen atoms bond with the carbon atom, their 1s orbitals overlap with the carbon's sp hybrid orbitals, forming four  bonds.The molecular orbitals involved in the formation of methane are:1. Four sp hybrid orbitals from the carbon atom, which are formed by the combination of one 2s and three 2p orbitals.2. Four 1s orbitals from the four hydrogen atoms.When these orbitals overlap, they form four  bonds between the carbon and hydrogen atoms, resulting in the tetrahedral structure of methane. Quantum mechanical calculations, such as those performed using the Hartree-Fock method or density functional theory  DFT , can provide more detailed information about the energies and shapes of these molecular orbitals.
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