Understanding Dihydrogen Spin Isomers: An Overview and Explanation

[splitringtail]

I am kinda rusty at my quantum, but I cannot figure out the coupling b/t ortho and para hydrogen forms. My quantum book doesn't discuss it and I really confused with the notation and superficial treatment I see on Wikipedia and other sites.

http://www.york.ac.uk/res/sbd/parahydrogen/outline.html

I understand why ortho is a triplet state b/c they are three orientations of the total spin $$m_{I}={1,0,-1}.$$ Yet, what are these alpha's and beta's on the site? Is the wave functions... both spin up, both spin down, and a linear combination of the two?. Then, for the para form, there's no difference if it is spin up down or down up, so they just take a linear combination and it's a singlet state?

 

[alxm]

"Ortho" and "Para" are just archaic terms for "triplet" and "singlet" electronic states, respectively. I wouldn't use the term 'isomers'. In fact I don't think I've ever seen the term 'spin isomer' before this. It's an excited electronic state of the same molecule. (I explain https://www.physicsforums.com/showpost.php?p=2120686&postcount=2" why triplet/ortho hydrogen is higher in energy, which usually extends to triplet states in general) Alpha and beta spins is just another way of saying 'up' and 'down' spins, or +1/2 and -1/2.

 

[Entropia]

I can understand your confusion with the notation and treatment of dihydrogen spin isomers. First, let's clarify what we mean by spin isomers. Spin isomers refer to the different energy levels that are possible for a molecule due to the spin of its constituent particles. In the case of dihydrogen, the two hydrogen atoms can have either parallel or antiparallel spins, resulting in two possible spin isomers: ortho and para.

Now, in terms of the notation used on the website you provided, the alpha and beta refer to the two possible spin states of a single hydrogen atom. Alpha represents a spin up state, while beta represents a spin down state. In the case of ortho hydrogen, the two hydrogen atoms are in a triplet state, meaning they have three possible orientations of the total spin (m_{I}={1,0,-1}). This is because the two individual spins can be either both up, both down, or a linear combination of the two. The website is simply representing this using the alpha and beta notation.

For para hydrogen, the two hydrogen atoms are in a singlet state, meaning they have only one possible orientation of the total spin (m_{I}=0). This is because, as you correctly pointed out, there is no difference between having both spins up or both spins down. Therefore, a linear combination of the two is sufficient to represent the spin state of para hydrogen.

I understand that this may still be a bit confusing, but it is important to note that this is a simplified explanation and there is much more complexity to the quantum mechanics behind dihydrogen spin isomers. I would recommend consulting with a quantum physicist or delving into more advanced texts for a more thorough understanding. I hope this helps clarify some of your confusion.