Point Charge Model of XY2 Linear Symmetric Molecules

Point Charge Model of XY2 Linear Symmetric Molecules.—It is possible to model the potential energy in a molecule usefully by more primitive models than those just discussed. We consider here some consequences of a point charge model employed by Ray and Parr.69 So that we can be more specific than in the previous section, let us consider briefly the ideas of their approach with reference to linear triatomic molecules of the symmetric type XY2. 

If Rx and R2 are the YX and XY distances in a molecule YXY and 8 is the YXY angle, then the total Born-Oppenheimer energy E=T+ Vhas a potential energy Vgiven by53 

The vibrational problem of a symmetric molecule XY2 is most frequently described in terms of a quadratic valence force field. This is given in terms of a bond stretching force constant K1U the bond-bond interaction constant K12 and the bending force constant Koo  

In the conventional simple valence force field approximation, mixed derivatives of the type (d3E/dR1dd2)n2 and (33 /3/f2902)j x are neglected. In fact they are usually relatively small. Using these approximations, it follows from the above equations that 

Following Simons,70 the potential energy V is approximated by placing charges + 2/3 qe at each atom and qe at the middle of each bond. The potential energy V is then given by 

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