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Unformatted text preview: ε π ε ε → =  → = ⇒ → → = ∞ → 3 2 2 1 1 electronic ( =0 all a nucle toms at distances 2 transla ar 0 vibrations ? r t o ion tat q=1 ) ions ? e rans MkT q n V h D → ⇒ = + + . . approximation separation of electronic and nuclear degrees of freedom BornO ppenheimer nuclear motion C M electronic H H H H → && for each nuclear separation R the electronic Schrodinger eq. is solved U(R) ( 29 ( 29 χ χ ε = for each electronic state N n n n nuclear R R n H to specify the position of atoms, we need 3 coordinates N N ⇒ ⇒ total degrees of freedom: 3 coordinates transaltion 3 coord for C.M. 3 orientation 3 coord for rotation 3 relative posi (2 if it's l tion of atom inear) s(vibr N (3N5 if it'slinear) ation) 3 N6 → && for each nuclear separation R the electronic Schrodinger eq. is solved U(R) U(R) is a function of 3N6 coordinates ⇒ How do we describe U(R)? we can use the Harmonic oscillator approximation i we expand U(R) around the minima and neglect all terms with dependece > quadratic... but what about x terms?...
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 Spring '08
 Bowers
 Electron, Normal mode, ic ia, electronic Schrodinger eq.

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