Energy Minima, Force Constants and Structure Correlation

1 Energy Minima, Force Constants and Structure Correlation 

A convenient way to represent an energy surface in the neighborhood of an arbitrary point Dq of configuration space, is in terms of a Taylor expansion about this point. 

For a fixed deformation energy V Do,Dq)-V(PQ), this equation represents an equipotential hyperellipsoidal surface with principal axes along the eigenvectors As an example, consider the bond-stretching deformations of a symmetric I3 fragment with distance deformations d and di- 

The choice of a symmetric reference structure Dq implies /, = fn. The mixed element/) 2 says that changing both bond lengths in the same sense does not require the same deformation energy as increasing one and decreasing the other. In matrix representation we obtain 

For a positive value of/i 2 a symmetric stretch ( +cf2)/V is more costly in 

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