A1 Appendix Matrix Operations

The second rule for isotopomer harmonic frequencies is the so-called Sum Rule which follows from Equation 3.A1.8. Equation 3.A1.8 relates the sum of the squares of all the frequencies to the sum of the diagonal matrix elements of the (FG) matrix diagonalized to obtain the frequencies. When mass weighted Cartesian displacement coordinates are used to calculate the vibration frequencies, this means that the sum of the A s (A = 4n2v12)can be found as follows (Equation3.51) 

The frequency sum here needs, of course, only to be taken over the 3N—6 (or 3N—5 for a linear molecule) non-zero frequencies of the molecule. 

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