A The Standard Model's application to competing Covalent Bond theories?

  • Thread starter greswd
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In the quantum mechanics of covalent bonding, there are two competing theories:
https://en.wikipedia.org/wiki/Covalent_bond#Comparison_of_VB_and_MO_theories

Both are complementary, but they don't overlap fully, they still leave some gaps.


What I wanna ask is, can all the literature of the Standard Model distinguish between the theories, and also fill in the gaps left by both?

Or does the problem highlight the gaps of the Standard Model?
 

TeethWhitener

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In the quantum mechanics of covalent bonding, there are two competing theories:
https://en.wikipedia.org/wiki/Covalent_bond#Comparison_of_VB_and_MO_theories

Both are complementary, but they don't overlap fully, they still leave some gaps.


What I wanna ask is, can all the literature of the Standard Model distinguish between the theories, and also fill in the gaps left by both?

Or does the problem highlight the gaps of the Standard Model?
The VB and MO models aren’t really different fundamental theories (so your talk about the Standard Model doesn’t really apply here). They’re more like different approximations to answering the same problem.

VB and MO are both approaches to solving the time-independent Schrodinger equation (##\hat{H}\Psi = E \Psi##) as it applies to molecules. They both assume that the true (extremely complicated) molecular wavefunction ##\Psi## can be approximated as a series of simpler functions ##\phi_i## weighted by coefficients ##c_i##:
$$\Psi = \sum_i {c_i \phi_i}$$
MO theory starts with atomic orbitals for the ##\phi_i##, while VB theory starts with certain bonding/antibonding/non-bonding combinations of atomic orbitals for the ##\phi_i##.
 
639
14
VB and MO are both approaches to solving the time-independent Schrodinger equation (##\hat{H}\Psi = E \Psi##) as it applies to molecules. They both assume that the true (extremely complicated) molecular wavefunction ##\Psi## can be approximated as a series of simpler functions ##\phi_i## weighted by coefficients ##c_i##:
$$\Psi = \sum_i {c_i \phi_i}$$
MO theory starts with atomic orbitals for the ##\phi_i##, while VB theory starts with certain bonding/antibonding/non-bonding combinations of atomic orbitals for the ##\phi_i##.
I see, thanks. Does the wavefunction explain why there is a bonding force?
 
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TeethWhitener

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I see, thanks. Does the wavefunction explain why there is a bonding force?
Ultimately, yes. The easiest way to see this is in the Born-Oppenheimer approximation: Fix the nuclei of a molecule (let's say H2 for a simple example) at their equilibrium bond length and solve the electronic Schrodinger equation to get a ground state energy. Then change the bond length slightly and solve the Schrodinger equation again. Do this several times and you get a potential energy curve that has a minimum at the equilibrium bond length, rather than at infinity. This indicates that a bond exists between the atoms.
 

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