PCh9 Lec 4
(4/17/20, bes)
Greetings,
- Only 2.5 weeks left...8 class periods and 2 labs.
- In lab yesterday we continued to use WebMO/Gaussian to carry out some computational activities. As a reminder, this "project" is/was due this morning at 10 am...unless you requested additional time. We are getting close to finishing Ch 9, the hydrogen atom...today and Monday. After that we will move into chapter 10 and 15...and do a lot more WebMO/Gaussian computational projects.
- With the new option you have to drop, change to p/f, or a letter grade on the last day of classes, i am expecting that many of you, on the last day of class, will ask...what is my grade? I will do my best to answer this question, but please keep in mind that...yes...the 3rd exam will be given during finals week...and since there is no final, your three exam scores will now count a greater percent. In addition, is lab really a 4-hour lab? When i ask you to email me stuff, does this count as a homework? I will provide the details associated with grading asap. If you did not know, I hate "grades"...you should all be here to learn..not to earn...a grade. <--this is my new motto!
Sec 9.3 wavefunctions - continued
So, last lecture i asked you to write in your notes, 3 of the hydrogen atom wavefunctions:
- ψ2,1,-1 (r, θ, Φ)
- ψ2,1,0 (r, θ, Φ)
- ψ2,1,+1 (r, θ, Φ)
All of the hydrogen atom wavefunctions are shown on pages 168-169 in the "highlighted" section. It is noted that these wavefunctions are referred to the hydrogen atom eigenfunctions as well as the hydrogen atom orbitals. "Wavefunction-->eigenfunctions-->orbitals" are different ways of saying the same thing. Please note that the subscripts on the eigenfunctions are n, l, and ml --> ψn,l,ml (r, θ, Φ) <-- note that i cannot subscript a subscript, ml...i need to work on my coding!
Your text at this point also want to remind you of how the quantum number l is also related to the s, p, d, f orbital notation:
- l = 0 --> s-orbital,
- l = 1 --> p-orbital,
- l = 2 --> d-orbital,
- l = 3 --> f-orbital.
This collection of wavefunctions/eigenfunction/orbitals is quite an impressive set of mathematical functions that highlight all that is "good" with QM...
- there is a normalization constant in these functions (not easily separated).
- the s-orbitals are the only functions that are "real", all others have "i" and are complex functions reminding us to "square" or take the complex conjugate when determining expected values.
- a trained eye can see the radial part, R(r) and the angular part, Θ(θ) Φ(φ).
...but if you go to Mathematica and try and plot these you will not get the "orbitala pictures" that you have been shown throughout all of your chemistry training. How do the pretty picture arise? ...flip the page...at the bottom of 170 are the "functions" that will generate the pretty orbital pictures...these are a linear combinations of wavefunctions, ψn,l,ml (r, θ, Φ) shown previously. As you may recall, this was also the case with plotting the 3D rotational wavefunctions back in chapter 7. If you are able, consider plotting a few of these in Mathematica.
For the rest of this lecture, i suggest that you continue reading/studying...page 171 --> Sec 9.4 stopping at Sec 9.5 (this is monday's lecture).
To end...one of the fun aspect of pchem-QM is the following: Please visit/watch the following...specfically at 1:34 min...WHAT!!!...is that the correct Schrodinger Equation?
END of Lecture 4.