The electronic Hamiltonian for the H molecular ion under the Born-Oppenheimer approximation is R 2m, 460...

 

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The electronic Hamiltonian for the H molecular ion under the Born-Oppenheimer approximation is R 2m, 460 46 4RA where the parameters, m, h, 4me, and e are as defined for atomic systems and all represent atomic unit quantities, ra represents the distance between the electron and nucleus a, and Ras is the distance separating the two nuclel. In atomic units, this Hamiltonian becomes 111 TA TRAB (a) Noting that the atomic unit for energy is the hartree, defined as Em() that the eigenvalue corresponding to the Wnim (7,0,0),,m) state of the hydrogen atom can be written, 1 E 32m what is the result of the operation ()125) expressed in atomic units? (Note: You may need to define n,, and im for the 3s state.) (b) Suppose one wanted to study a system, Hy", that includes three protons and two electrons. How would the Hamiltonian for this system be written in atomic units? Be prepared to answer questions about what any new terms represent in this new Hamiltonian. Note: Use numbers to label the electrons and uppercase letters for the nuclei (protons). The electronic Hamiltonian for the H molecular ion under the Born-Oppenheimer approximation is R 2m, 460 46 4RA where the parameters, m, h, 4me, and e are as defined for atomic systems and all represent atomic unit quantities, ra represents the distance between the electron and nucleus a, and Ras is the distance separating the two nuclel. In atomic units, this Hamiltonian becomes 111 TA TRAB (a) Noting that the atomic unit for energy is the hartree, defined as Em() that the eigenvalue corresponding to the Wnim (7,0,0),,m) state of the hydrogen atom can be written, 1 E 32m what is the result of the operation ()125) expressed in atomic units? (Note: You may need to define n,, and im for the 3s state.) (b) Suppose one wanted to study a system, Hy", that includes three protons and two electrons. How would the Hamiltonian for this system be written in atomic units? Be prepared to answer questions about what any new terms represent in this new Hamiltonian. Note: Use numbers to label the electrons and uppercase letters for the nuclei (protons).