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A 3N * 3N force constant matrix can be very confusing so HyperChem, like MOPAC, gives an N * N force constant matrix describing the atom-atom interaction forces. This N * N force constant matrix is formed from the 3N * 3N force constant matrix by calculating the norm of the tensor of each atom.
You may reconstruct the 3N * 3N force constant matrix from HyperChem log file output using the matrix equation:
F C = C E
where F is the MASS-WEIGHTED force constant matrix (3N * 3N), C is the eigenvector (normal coordinate) matrix and E is the eigenvalue diagonal matrix. You can get C and E from the log file (with QuantumPrintLevel=9) or script output, you can calculate the matrix F by multiplying on the right by the inverse of C.
The relationship between an eigenvalue Ei in E and the vibrational frequency f is:
f = SQRT(Ei) / (2*PI*c)
where c is the speed of light.
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