Testing of Numerical Procedures

After a series of numerical methods has been investigated in the previous sections, the questions arise  

Are these methods appropriate to quantum chemical purposes  

Which of them is to be preferred when a certain class of problems is investigated  

Today both questions can only be decided by experimentation. That is to say, each procedure has to be tested on a variety of test problems which has been chosen to represent the different features which might occur in PES calculations. Clearly experimentation can never give a guarantee of good performance in the sense of a mathematical proof. 

The choice of the test functions may considerably affect the test result. Therefore, they should be chosen with care. The better a test problem is adapted to the characteristics of a numerical procedure, the better the test result will be. Thus, a serious testing should not only rely on one (artificial, well-adapted) test function, but on some different molecular systems of different size (number of nuclei) with different characteristic (deep minima, clear saddles, flat minima/saddles, etc.). 

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