Understanding the Concept of Hybrid Bonds: A Basic Explanation

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Hybrid bonds are formed when atomic orbitals combine to create new hybrid orbitals, which can exhibit varying energy levels. This process alters the potential energy experienced by electrons, leading to new bonding and anti-bonding states. The new eigenstates resulting from this combination reflect the changed Hamiltonian when atoms come together. Hybrid bonds play a crucial role in understanding molecular structure and behavior. Overall, the interpretation of hybrid bonds emphasizes the significance of electron interactions in determining molecular properties.
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I probably should ask this in the atomic physics section, but there seem little, if not no activity there...

I am wondering what Hybrid bond is. I took two semester of lower division Chem. and that's it! Now, after getting my physics B.S., I realize that I don't really understand what it is! Here is my current interpretation:
Say you have two atoms, their valence electrons are happily occupying their orbits, i.e. solution to the schodinger's eqn with respect to the potential (p-e,e-e, everything). And the so call electron orbits are basically eigenstates of the Hamiltonian (as complex as it maybe). Now you put the two atoms together, such that the electron in each atom feels the potential of the other guy. So to these electrons, the Hamiltonian changed, and so the old orbits are no longer eigenstates states of the new Hamiltonian, but rather just linear superposition of them. The new eigenstates for the new Hamiltonian are the so call hybrid bonds. Some of these states has lower energy (bonding) and some higher (anti-bonding). One can generalize this to many atom with complicated Hamiltonian...am I right?
 
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Yes, your interpretation is correct. Hybrid bonds are a type of bond that forms as a result of the combination of two or more atomic orbitals to form new hybrid orbitals. These hybrid orbitals can have different energy levels and, depending on their energy, can form either a bonding or an anti-bonding orbital. The electrons in the hybrid orbitals experience a different potential energy than they did in the individual orbitals and the new arrangement of these electrons is what gives the hybrid bonds their unique properties.
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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