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Unformatted text preview: 14Feb2011 Chemistry 21b – Spectroscopy Lecture # 18 – Diatomic Bonding/Electronic Structure & the Franck-Condon Approximation As well described in Chapter 11 of McQuarrie, for diatomics heavier than H 2 , we start with the simplest implementation of LCAO-MO description outlined previously, and then fill in the orbitals as a function of energy. The procedure is straightforward for homonuclear diatomic, since the atomic orbital energies all line up and since there is inversion symmetry that can be used to classify the resulting molecular orbitals. For heteronuclear species, such as HF or HCl, the interactions are only significant if the atomic orbital energies are close to each other (think about perturbation theory). Let’s consider the first row diatomic species as cases in point (see Figure 11.5, McQuarrie). Since the electronegativity increases across the periodic table rows to the right, the overall orbital energy decreases as Z increases from Li to F. The 1 s orbitals combine to yield bonding and anti-bonding orbitals and are filled for all species. Recall that it is the component of the orbital angular momentum along the bond that is a “good” quantum number, and for s orbitals the resulting M.O.s are always cylindrically symmetric and so are σ in character. Bonding σ orbitals have g inversion symmetry, anti-bonding u inversion symmetry. For the p orbitals, if the z axis is along the bond axis then the p z atomic orbitals combine to yield a σ M.O., while the p x , p y orbitals yield π M.O.s. For the latter, it is the u combination that is bonding while the g combination is anti-bonding. The σ g 2 p z M.O. is much more sensitive to the nuclear charge than are the π u 2 p x,y orbitals, and starts out at higher energy than the latter for Li 2 , but drops below the π u 2 p x,y M.O.s for O 2 and F 2 . Thus, the orbital energy ordering up to N 2 is given by σ g 1 s σ u 1 s σ g 2 s σ u 2 s ( π u 2 p x 2 p y ) σ g 2 p z ( π g 2 p x 2 p y ) σ g 2 p z , and two electrons can be placed into each M.O. according to the Pauli Principle. For O 2 and F 2 the ( π u 2 p x 2 p y ) /σ g 2 p z ordering is swapped; and for degenerate orbitals (the π orbitals here, for transition metal species the d orbitals need to be considered), if there are only two electrons we place one electron each into the M.O.s with parallel spins. Thus, B 2 and molecular oxygen are predicted to be paramagnetic with ( σ g 1 s ) 2 ( σ u 1 s ) 2 ( σ g 2 s ) 2 ( σ u 2 s ) 2 ( π u 2 p x ) 1 ( π u 2 p y ) 1 and ( σ g 1 s ) 2 ( σ u 1 s ) 2 ( σ g 2 s ) 2 ( σ u 2 s ) 2 ( σ g 2 p z ) 2 ( π u 2 p x ) 2 ( π u 2 p y ) 2 ( π g 2 p x ) 1 ( π g 2 p y ) 1 ground states....
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This note was uploaded on 01/03/2012 for the course CH 21b taught by Professor List during the Fall '10 term at Caltech.
- Fall '10