{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture notes6

In this case one must distinguish several types of

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: th having a s g the same sign angular momentum, 1Δ g , or opposite sign, 1 Σ + . g A molecule may have multiple states corresponding to the same term; these are distinguished with letters in front of the term symbol. The ground state always € € receives the letter X: e.g. the ground state of O2 would be written X 3Σ− . The letters g denoting excited states are historical and follow no discernable pattern. B. ROTATION € We now consider the motion of the nuclei in the Born Oppenheimer approximation, i.e. treating the electronic wave function as evolving adiabatically as the nuclei move. The rotation of a closed ­shell molecule involves the motion of the nuclei as well as the electrons. It can be treated to a first approximation like a rigid rotator (we will investigate vibration later). This gives rise to angular momentum quantum numbers J and M and an angular wave function ~YJM(θ,φ), with energy levels 2J(J+1)/2I, where I is the moment of inertia. The parity is (−1)J, in accordance with the parity of the spherical harmonic. Typical moments of inertia are ~few × 104 mea02, leading to energy levels in the microwave (~1011 Hz) for small J. A molecule with nonzero Λ or S exhibits more complicated behavior. In this case, one must distinguish several types of angular momentum: Angular momentum Total Projection on internuclear axis Electron orbital L Λ Electron spin S Σ Total orbital N Λ (No nuclear orbital a.m. || axis) Total orbital + spin J Ω We have already described the quantum numbers Λ and S. We also know that J is conserved. In order to identify the energy levels, however, we must consider two limiting cases: Hund Case (a): The precession of the electron spin around th...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern