The potential energy of the atoms in a molecule can, Ask an Expert

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The potential energy of the atoms in a molecule can sometimes be approximated by the Morse Function

U=A[(e^((R-r)/S) -1)^2-1]

where r is the distance between the two atoms and A,R and S positive constants with S<

I solved for ro, and got ro = R, and then substituted r=ro+x to get

U=A[(e^(-x/S) -1)^2-1] .

I'm not sure how to do the next step to show for small displacements, U has the approximate form U=const+1/2 kx^2.

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