The Chemical Bond Energy from Molecular Orbitals

2 The Chemical Bond Energy from Molecular Orbitals 

In Appendix 10 we look in detail at the simplest molecular system, the dihydrogen cation H2+. This is a molecule with only one electron, and so only electron-nuclear and nuclear-nuclear interactions need be considered. Here, we summarize the findings of Appendix 10 and identify the contributions to the total energy of the molecule in terms of the basis functions. 

To estimate the MO energies we turn to the Schrddinger equation applied to the MO SALCs, which is simply written thus  

the subscript i is used to label the MO, (py, for this H2+ example, taking i = 1 would set (pi to Icrg . The MO is a function that, as we have seen, describes how an electron is distributed over space. In Equation (7.17), H is the Hamiltonian, which contains the operators to obtain the energy of the electron averaged over its distribution the result is the orbital energy E, which is a simple number. 

To obtain Eigure 7.8, the Hamiltonian for the electron states was first split into electronic kinetic T and potential V operators  

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