The theoretical basis for predicting the chemical reactivity and selectivity of a given molecule using quantum chemical calculations lies in quantum mechanics and molecular orbital theory. Quantum mechanics is a fundamental theory in physics that describes the behavior of matter and energy at atomic and subatomic scales. In the context of chemistry, quantum mechanics is used to describe the behavior of electrons in atoms and molecules.Molecular orbital theory is an approach to understanding the electronic structure of molecules by considering the wave-like nature of electrons. In this theory, electrons are described by wave functions, which are mathematical functions that describe the probability of finding an electron in a particular region of space. These wave functions are called molecular orbitals, and they are formed by the combination of atomic orbitals from the constituent atoms of the molecule.Quantum chemical calculations use mathematical methods and computational algorithms to solve the Schrödinger equation, which is the fundamental equation of quantum mechanics. The Schrödinger equation describes the behavior of the wave function of a system, and its solutions provide information about the energy levels and spatial distribution of electrons in a molecule.By solving the Schrödinger equation for a given molecule, quantum chemical calculations can provide information about the molecule's electronic structure, including the energies and shapes of its molecular orbitals. This information can be used to predict the chemical reactivity and selectivity of the molecule based on several factors:1. The energy of the highest occupied molecular orbital HOMO and the lowest unoccupied molecular orbital LUMO : The energy gap between the HOMO and LUMO is related to the molecule's chemical reactivity. A smaller HOMO-LUMO gap indicates a more reactive molecule, as it requires less energy to promote an electron from the HOMO to the LUMO, leading to chemical reactions.2. The spatial distribution of molecular orbitals: The shape and location of molecular orbitals can influence the reactivity of a molecule. For example, if a molecular orbital is concentrated in a particular region of the molecule, that region may be more susceptible to attack by a reactive species.3. The relative energies of different reaction pathways: Quantum chemical calculations can be used to compare the energies of different reaction pathways, allowing chemists to predict the most likely pathway and the selectivity of a reaction.4. The identification of reactive sites: By analyzing the electron density and molecular orbitals of a molecule, quantum chemical calculations can help identify reactive sites where chemical reactions are more likely to occur.In summary, the theoretical basis for predicting the chemical reactivity and selectivity of a given molecule using quantum chemical calculations lies in the application of quantum mechanics and molecular orbital theory to describe the electronic structure of the molecule. By solving the Schrödinger equation and analyzing the resulting molecular orbitals, chemists can gain insights into the reactivity and selectivity of a molecule.