- #1
eoghan
- 207
- 7
Hi there!
I'm studying the hydrogen molecule. According to the MO technique I start from one-electron molecular orbitals to construct the wave function of the entire molecule.
Afa hydrogen is concerned, I can construct two [tex]^1\Sigma_g[/tex] orbitals:
[tex]\Phi_A=\Phi_g(1)\Phi_g(2)\chi_{0,0}[/tex]
[tex]\Phi_B=\Phi_u(1)\Phi_u(2)\chi_{0,0}[/tex]
Where [tex]\Phi_g(i)[/tex] means that the i-th electron is in the gerale orbital obtained from the one-electron molecule.
Computing the energies for [tex]\Phi_A[/tex] and [tex]\Phi_B[/tex] it is found that only [tex]\Phi_A[/tex] is a bonding orbital, so that the wave function of the hydrogen molecule is [tex]\Phi_A[/tex] where the two electrons are both in the gerale orbital with antiparallel spins.
To improve the accuracy of the model, a linear combination of [tex]\Phi_A[/tex] and [tex]\Phi_B[/tex] can be considered:
[tex]\Phi_T=\Phi_A+ \lambda \Phi_B[/tex]
using this wave function as the trial function for a variational method, [tex]\lambda[/tex] can be found.
Now, this wavefunction can be rewritten as a sum of a covalent bonding wavefuntion and a ionic bonding wavefunction:
[tex]\Phi_T=(1- \lambda )\Phi_A^{COV}+(1+ \lambda )\Phi_A^{ION}[/tex]
and it is found that the coefficient for the ionic bonding is 20% of the coefficient of the covalent bonding.
So.. can I say that the hydrogen molecule is covalent, but with a little part of ionic bonding?
I'm studying the hydrogen molecule. According to the MO technique I start from one-electron molecular orbitals to construct the wave function of the entire molecule.
Afa hydrogen is concerned, I can construct two [tex]^1\Sigma_g[/tex] orbitals:
[tex]\Phi_A=\Phi_g(1)\Phi_g(2)\chi_{0,0}[/tex]
[tex]\Phi_B=\Phi_u(1)\Phi_u(2)\chi_{0,0}[/tex]
Where [tex]\Phi_g(i)[/tex] means that the i-th electron is in the gerale orbital obtained from the one-electron molecule.
Computing the energies for [tex]\Phi_A[/tex] and [tex]\Phi_B[/tex] it is found that only [tex]\Phi_A[/tex] is a bonding orbital, so that the wave function of the hydrogen molecule is [tex]\Phi_A[/tex] where the two electrons are both in the gerale orbital with antiparallel spins.
To improve the accuracy of the model, a linear combination of [tex]\Phi_A[/tex] and [tex]\Phi_B[/tex] can be considered:
[tex]\Phi_T=\Phi_A+ \lambda \Phi_B[/tex]
using this wave function as the trial function for a variational method, [tex]\lambda[/tex] can be found.
Now, this wavefunction can be rewritten as a sum of a covalent bonding wavefuntion and a ionic bonding wavefunction:
[tex]\Phi_T=(1- \lambda )\Phi_A^{COV}+(1+ \lambda )\Phi_A^{ION}[/tex]
and it is found that the coefficient for the ionic bonding is 20% of the coefficient of the covalent bonding.
So.. can I say that the hydrogen molecule is covalent, but with a little part of ionic bonding?