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Unformatted text preview: = - = = 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 Born-O 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 = 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 (3N-5 if it'slinear) ation) 3 N-6 && for each nuclear separation R the electronic Schrodinger eq. is solved U(R) U(R) is a function of 3N-6 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