5

No. It is because the lowest three MOs are lower in energy than the corresponding original AOs. In other words, the electrons would rather be there than belong to the separate atoms, as if they wanted the atoms to be together rather than apart. Actually, there is no "as if". These electrons are the force that brings the atoms together. That's ...


3

Your problem seems to stem from confusing the number of linear independent basis functions(which is the same number as the size of the atomic orbital basis with which we started) and the number of all possible functions that can be built using this basis. Just as in a two dimensional vector space, where you have a maximum of two independent basis functions, ...


3

Using the normalisation condition $$c^2_A + c_B^2 + 2c_A c_B S = 1$$ while $c_A = 0$ $$0 + c^2_B + 2 \cdot 0 \cdot c_B S = 1$$ $$ c^2_B = 1 $$ $$ c_B = \sqrt{1} = \pm 1$$


3

As $$\gamma = \dfrac{c_A}{c_B}$$ when $c_A=0$, $\gamma$ must also be zero. This follows as $c_B$ can not be also be zero as the wavefunction is normalised to unity. Thus under such conditions it is invalid to divide through by $\gamma$. Instead simply use the normalisation condition and the fact that $c_A$ is zero to show that $|c_B|=1$ .


3

The short answer is that $\sum |c|^2$ is basically equal to "the number of electrons in the orbital". You might think that this should be 2, not 1. But note that each molecular orbital actually comprises two different "spin orbitals". Each "spin orbital" contains one electron of a particular spin - so there is a spin-up orbital ...


2

Firstly, note that the labels $\sigma$, $\pi$, and $\delta$ aren't universally applicable to MOs; it depends on the molecular geometry. These labels are mostly useful for linear molecules. Non-linear molecules often have MOs that are labelled differently. Methane is a decent example. Other examples include water and ammonia. Restricting ourselves to linear ...


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