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Calculate the binding energy of a hydrogen molecule and a helium atom in their ground state using Quantum chemical calculations of non-covalent interactions. What is the strength of the interaction between these two species?

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To calculate the binding energy of a hydrogen molecule  H2  and a helium atom  He  in their ground state, we can use the quantum chemical method called Symmetry-Adapted Perturbation Theory  SAPT . SAPT is a powerful method for studying non-covalent interactions between molecules, such as van der Waals forces, hydrogen bonding, and electrostatic interactions.The binding energy  E_bind  can be calculated as the difference between the energy of the interacting system  E_int  and the sum of the energies of the isolated species  E_H2 + E_He :E_bind = E_int -  E_H2 + E_He To perform the SAPT calculations, we need to use a quantum chemistry software package like Gaussian, Psi4, or ORCA. These programs require input files with information about the molecular geometry, basis set, and method.For this problem, we can use the following input parameters:1. Molecular geometry: Place the H2 molecule and He atom at a reasonable distance, e.g., 3  apart.2. Basis set: Use a standard basis set like 6-31G* or aug-cc-pVDZ.3. Method: Choose the SAPT method, e.g., SAPT0 or SAPT2+.After running the calculations, the software will provide the energies of the isolated species  E_H2 and E_He  and the interacting system  E_int . Subtract the sum of the energies of the isolated species from the energy of the interacting system to obtain the binding energy.It is important to note that the interaction between a hydrogen molecule and a helium atom is expected to be very weak, as both species are closed-shell systems with no significant electrostatic or covalent interactions. The binding energy will likely be on the order of a few kJ/mol or less, which is much weaker than typical covalent bonds  e.g., H-H bond in H2 has a bond dissociation energy of around 436 kJ/mol .

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