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lecture notes6

Vibrational the bond can stretch or compress 1dof

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Unformatted text preview: (H2 and CO) are diatomic. Its basic degrees of freedom are: Translational: The motion of the center of mass (3dof). Electron orbital: The electrons have a spatial wave function. Electron spin: The unpaired electrons carry spin. Vibrational: The bond can stretch or compress (1dof). Rotational: With the center of mass fixed, the direction of the bond can change (2dof). Nuclear spin: In the case of homonuclear molecules, and occasionally with radio transitions, the nuclear spin degree of freedom is often important. The translational degrees of freedom are trivially separated. The others represent internal degrees of freedom of the molecule and are important to the physics that we will use in the next lecture. We will discuss electronic structure first since it is most closely related to the physics of atoms. A. ELECTRONIC STRUCTURE Electrons in molecules occupy molecular orbitals. Just as for atoms, the orbitals can be classified by their symmetry properties. In particular, if we work in cylindrical coordinates with the nuclei lying along the z ­axis, then the orbitals will have a dependence ~eimϕ, where m is the projection of the angular momentum onto the internuclear axis. An orbital is designated as a σ ­orbital if m=0, a π ­orbital if m=±1, and a δ ­orbital if m=±2. The σ orbitals are usually nondegenerate, but the π, δ, etc. orbitals come in pairs of equal energy (±m). A diatomic molecule may have two identical nuclei, in which case it is called homonuclear (otherwise it is heteronuclear). Homonuclear molecules also possess parity symmetry, under which a particular orbital may be even or odd. This is designated with a “g” subscript for even orbitals and a “u” for odd, e.g. σg, σu, etc. With the exception...
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