https://mazziotti.uchicago.edu/qcdictionary/h_terms/hessian_matrix/index.html The Hessian matrix is a mathematical concept widely used in many different fields, including computational chemistry. In quantum mechanics, the Hessian matrix is relevant to calculating vibrational frequencies. The Hessian is also used in molecular mechanics methods, especially to obtain force constants for molecular dynamics experiments. Calculation of the Hessian generally involves first optimizing a structure until a stationary point is reached and then finding the pairwise second derivatives for every degree of freedom. Hugo en-us