Historical portraits Got a force constant

Finding the elements of matrices B and G is a purely geometrical problem. The force constant matrix F is now a 3 x 3 matrix over the stretching and bending internal coordinates. A little algebra shows that the corresponding secular equation is now 

This equation has three solutions for the X values corresponding to the same three nonzero vibrational frequencies obtained from equation 2.21, but is much more practical to work with. 

After going through the same steps as in equations 2.20-2.22, the solution of the secular equation 2.26 also yields the transformation from internal to normal coordinates, with a new set of coefficients  

For very large molecules finding the elements of the G matrix becomes hopelessly complicated. Alternatively, one prepares symmetry coordinates and then proceeds directly to the solution of the secular equation and to finding normal coordinates by trial and error. 

Circulation of computer codes had also begun to some extent. One time we received a printout of some 2,000 Fortran instruction, and, since there was no hope of getting a hardware copy of any sort, we set to the task of punching them one after another on the card puncher. An even bigger job was checking it out for misprints afterwards. 

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