Alternative linear comb. to vizualize hydrogenic orbitals p,d etc

In summary, the LCAO method is an alternative linear combination for visualizing hydrogenic orbitals such as p, d, and f orbitals. It differs from traditional methods by taking into account the wave nature of electrons and their interactions with other electrons, allowing for a more accurate representation of the electronic structure of molecules. This method is applicable to all types of orbitals and helps in understanding the bonding and non-bonding orbitals in molecules by providing a visual representation of molecular orbitals. Advantages of using the LCAO method include its accuracy, versatility, and ability to provide insight into bonding interactions, as well as its simplicity and accessibility for researchers.
  • #1
psand
1
0
I'm teaching basic chemistry and got a question that I found very interesting. All textbooks we use depict hydrogenic p-orbitals (or spherical harmonics) by first making a linear combination of p+ and p- wave functions in order to get real orthogonal px, py, pz. But the thing that should be of (primary)interest is the probability density of the orbitals. i.e. the orbiltal wave function times its complex conjugate. Taking this of the p+ or p- wave functions result in doughnut shaped probability densities (allowing for a particle analogy with non-zero angular momentum, i.e. the Bohr orbit).

The question was:

Is the traditional vizualization of the p-orbitals just made in order to be able to depict a real wave function?

My extension of the question is:
Can another linear combination be found that results in 3 orthogonal wave functions whose probability densities are e.g. elongated doughnuts with identical shapes (ellipsoids)? Could anyone give me an example of such a linear combination? I simply do not have the maths required.

This would be a nice tramsition from the particle view to the wave view and show that the old atomic symbol of three crossed ellipses is not so crazy after all.

Respectfully
Peter S
 
Last edited:
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  • #2
psand said:
Is the traditional vizualization of the p-orbitals just made in order to be able to depict a real wave function?
No. It is also used because px and py have a nice geometry, which is useful to understand chemical bonding (to which one can add hybridization).

psand said:
My extension of the question is:
Can another linear combination be found that results in 3 orthogonal wave functions whose probability densities are e.g. elongated doughnuts with identical shapes (ellipsoids)? Could anyone give me an example of such a linear combination? I simply do not have the maths required.
I don't think this is possible.

psand said:
This would be a nice tramsition from the particle view to the wave view and show that the old atomic symbol of three crossed ellipses is not so crazy after all.
It's not crazy, simply wrong. However, the Bohr-Sommerfeld model of the atom (which is what is pictured in those representations) was an important step in the development of quantum theory,
 

FAQ: Alternative linear comb. to vizualize hydrogenic orbitals p,d etc

1. What is an alternative linear combination for visualizing hydrogenic orbitals p, d, etc?

An alternative linear combination for visualizing hydrogenic orbitals is the linear combination of atomic orbitals (LCAO) method. This method involves combining individual atomic orbitals to form molecular orbitals, which can then be used to visualize the electronic structure of molecules.

2. How does the LCAO method differ from traditional methods of visualizing orbitals?

The LCAO method differs from traditional methods of visualizing orbitals in that it takes into account the wave nature of electrons and their interactions with other electrons. This allows for a more accurate representation of the electronic structure of molecules.

3. Can the LCAO method be used for all types of orbitals, such as p, d, and f orbitals?

Yes, the LCAO method can be applied to all types of orbitals, including p, d, and f orbitals. It is a versatile method that can be used to visualize the electronic structure of a wide range of molecules.

4. How does the LCAO method help in understanding the bonding and non-bonding orbitals in molecules?

The LCAO method helps in understanding the bonding and non-bonding orbitals in molecules by providing a visual representation of the molecular orbitals formed from the combination of atomic orbitals. This allows for a better understanding of the electron density and bonding interactions in a molecule.

5. What are the advantages of using the LCAO method for visualizing orbitals?

The LCAO method has several advantages for visualizing orbitals, including its ability to accurately represent the electronic structure of molecules, its versatility in handling different types of orbitals, and its ability to provide insight into bonding and non-bonding interactions in molecules. Additionally, the LCAO method is a relatively simple and intuitive approach to visualizing orbitals, making it accessible to a wide range of scientists and researchers.

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