The molecular geometry of methane CH4 is tetrahedral. This can be determined using quantum mechanics principles, specifically through the application of molecular orbital theory and valence shell electron pair repulsion VSEPR theory.Molecular orbital theory involves solving the Schrödinger equation for the molecule, which provides information about the energies and shapes of molecular orbitals. In the case of methane, the central carbon atom has four valence electrons, and each hydrogen atom has one valence electron. The carbon atom forms four sigma bonds with the hydrogen atoms, utilizing its 2s and three 2p orbitals to create four sp3 hybrid orbitals. These hybrid orbitals are directed towards the vertices of a tetrahedron, with bond angles of approximately 109.5.Valence shell electron pair repulsion VSEPR theory is another approach to predict the molecular geometry. According to VSEPR theory, electron pairs around a central atom repel each other and arrange themselves to minimize this repulsion. In methane, the central carbon atom is surrounded by four bonding electron pairs one for each hydrogen atom . These electron pairs arrange themselves in a tetrahedral geometry to minimize repulsion, resulting in a bond angle of approximately 109.5.Both molecular orbital theory and VSEPR theory predict a tetrahedral geometry for methane, which is consistent with experimental observations.