Vibrational frequency calculation holds a key that can decide whether the obtained optimized structure is a minimum or a transition state or some thing else. I always wanted a simplistic adaptation with minimal understandable and required information that in a matter of minutes can help a new person understand the concept as easily as possible. Finally I found this link: http://openmopac.net/manual/Hessian_Matrix.html which makes it really easy for anybody. So, what we least need to know when you submit a frequency calculation. In frequency calculation also called force calculation, we are solving a hessian matrix. What is a Hessian matrix? The Hessian matrix is the matrix of second derivative s of the energy with respect to geometry. What is the trouble in frequency calculation? Although first derivatives are relatively easy to calculate, second derivatives are not. To overcome this problem, the double derivative is evaluated in terms of first der
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