Question

Atomic orbital coefficient in the homo of a molecule

Answer 1

Answer:

If you imply the Bond Orbital ordering and each atomic orbital contribution to molecular orbital, then you open the output file, after that find the "(Occupancy) Bond orbital/ Coefficients/ Hybrids". you should see the section as follow:

(Occupancy) Bond orbital/ Coefficients/ Hybrids

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1. (0.98892) BD ( 1) C 1 - C 2

( 49.44%) 0.7032* C 1 s( 35.44%)p 1.82( 64.51%)d 0.00( 0.06%)

0.0002 0.5953 -0.0034 0.0009 -0.0210

0.0467 0.0035 0.0001 0.0056 -0.0012

-0.0001 0.0000 0.8014 -0.0119 0.0081

0.0034 -0.0002 0.0018 0.0002 0.0050

0.0233

( 50.56%) 0.7110* C 2 s( 35.86%)p 1.79( 64.10%)d 0.00( 0.04%)

0.0001 0.5984 -0.0241 -0.0011 0.0004

-0.0125 0.0374 0.0035 -0.0020 -0.0023

-0.0007 -0.0001 0.0000 -0.7990 0.0322

-0.0087 -0.0005 -0.0001 -0.0023 0.0002

0.0010 0.0189

Answer 2

Molecular orbital theory involves solving (approximately) the Schrodinger equation for the electrons in a molecule. To review from Chapter 1, this is a differential equation in which the first and second terms on the right represent the kinetic and potential energies

While the Schrodinger equation can be solved analytically for the hydrogen atom, the potential energy function V becomes more complicated - and the equation can then only be solved numerically - when there are many (mutually repulsive) electrons in a molecule. So as a first approximation we will assume that the s, p, d, f, etc. orbitals of the atoms that make up the molecule are good solutions to the Schrodinger equation. We can then allow these wavefunctions to interfere constructively and destructively as we bring the atoms together to make bonds. In this way, we use the atomic orbitals (AO) as our basis for constructing MO's.
We have actually seen linear combinations of atomic orbitals before when we constructed hybrid orbitals in Chapter 1. The basic rules we developed for hybridization also apply here: orbitals are added with scalar coefficients (c) in such a way that the resulting orbitals are orthogonal and normalized. The difference is that in the MO case, the atomic orbitals come from different atoms.
The linear combination of atomic orbitals always gives back the same number of molecular orbitals. So if we start with two atomic orbitals (e.g., an s and a pz orbital as shown we end up with two molecular orbitals. When atomic orbitals add in phase, we get constructive interference and a lower energy orbital. When they add out of phase, we get a node and the resulting orbital has higher energy. The lower energy MOs are bonding and higher energy MOs are bonding and higher energies MOs are anti bonding
Hope it helps!!❤️❤️