Question

Write down the Hamiltonian of He+ ion.
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Answer 1

Explanation:

Currently, I am going through Quantum Simulation of Helium Hydride Cation in a Solid-State Spin Register. I am not a chemist but rather a computer scientist hence having trouble following the paper.

I am using this easy to access note on Hartree-Fock approximation.

So, I am not sure how the authors created the molecular Hamiltonian in Eq. 2 of the supplementary material.

H=⎛⎝⎜−2.854040.1306710.00.130671−0.760916−0.3235680.0−0.323568−1.91238⎞⎠⎟

From the note, I understand that the Born-Oppenheimer approximation (Eq. 3) is the starting point.

H=−∑i=1N12∇2i−∑i=1N∑A=1MZAriA+∑i=1N∑j>1N1rij

What should be my following steps to reach at the molecular Hamiltonian.

I am extremely sorry if I am asking for a really long answer.

UPDATE 1: The molecular Hamiltonian is:

H^=−ℏ22MHe∇2He−ℏ22MHNuclear kinetic energy−ℏ22me∇21−

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