1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Determinantal wave function of Li using LCAO?

  1. Dec 14, 2015 #1
    1. The problem statement, all variables and given/known data

    The wave function for lithium can be written as:

    | 1sα(1) 1sβ(1) 2sα(1) | ##\frac{1}{\sqrt(3)} ## = ψ(1,2,3)
    | 1sα(2) 1sβ(2) 2sα(2) |
    | 1sα(1) 1sβ(2) 2sα(1) |

    How can each row be a linear combination of atomic orbitals that makes a new orbital in which the electron actually exists if these new functions are made up of the old functions which all have different spin states?

    Like in the first row, |1sα(1) 1sβ(1) 2sα(1)| represents a wave function made up of 3 other wave functions. But two of these wave functions are functions of α (positive spin) and one has β (negative spin) in it. So how can we combine all three orbitals to make a new orbital? You can only have +1/2 or -1/2 spin, nothing in between. So what would the spin state of the new orbital be?

    Could someone clarify this for me? I'm really sorry if I didn't word the question clearly.

    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
  3. Dec 14, 2015 #2

    DrClaude

    User Avatar

    Staff: Mentor

    That last row should be 1sα(3) 1sβ(3) 2sα(3)

    What you get from the Slater determinant is a 3-electron wave function. Using that particular set of atomic orbitals, you get a 3-electron orbital in which 2 electrons are spin-up and one spin-down.

    The total spin of 3 electrons can be 1/2 or 3/2. In the case at hand, the total spin is S = 1/2, and MS = +1/2.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Determinantal wave function of Li using LCAO?
  1. Radial wave function (Replies: 2)

Loading...