Undergrad Ionic bonding from a quantum mechanics point of view

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The discussion centers on the quantum mechanics of ionic bonding, contrasting it with covalent bonding, which involves electron sharing. It highlights that ionic bonding is characterized by the energetic favorability of electron transfer and the likelihood of electron localization near one atom in a two-atom system. The conversation notes that while ionic bonds arise from electrostatic attraction, a deeper understanding requires examining the stability of ions versus neutral atoms, particularly through concepts like electron affinity and ionization energy. Koopmans theorem is mentioned as a useful tool for approximating these energies based on atomic orbitals. Overall, the quantum nature of ionic bonds can be explored through molecular orbital theory and related quantum concepts.
Ron19932017
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Hi all,

I have a question about the quantum nature of ionic bonds.

I know some ideas about molecular bonding which can combine two ground state of H atom
to get a bonding state and an anti-bonding state which in the case of H2 molecules it correspond to the covalent bonding (sharing of electrons).

However I did not know the quantum mechanics nature of ionic bond.
I know that from energetics, the "transfer" of electron is energetic favourable thus this is a bonding.
I also understand that the ionic bond is not absolute, it only means that the electron is likely to be found close to 1 atom in the case of simple 2-atom molecule.

Can someone kindly explain to me the quantum nature of ionic molecules ?
To be more specify, can molecular orbit theory (or any quantum theory) explain ionic bond?
 
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Ionic bonding depends on one hand on the electrostatic attraction of the ions, which does not require quantum mechanical concepts and on the other hand an understanding of the stability of the ions as compared to the atoms, i.e. the calculation of the electron affinity and ionisation energy. These two quantities can be calculated to a good approximation using Koopmans theorem which states that the latter quantities are approximately equal to the energies of the highest unoccupied and occupied atomic orbitals, respectively.
 
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Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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