Couldn't figure out the use of the Hessian matrix in computational chemistry.
Dear Gaurav
Generally Hessian is used for determining extrema of a function. Hessian determine local curvature of a function In the case of computational chemistry this function is potential energy surface. After optimization, you are standing on one point (stationary state) on PES , to find that the stationary state you have obtained is minimum, maximum or saddle point you need to calculate Hessian since sign of its eigen values shows the character of stationary point.
Hessian matrix is the double derivative of the energy functional. The algorithm used for geometry optimization in gaussian is based on Hessian matrix. It is known that for finding roots of a function the first derivative of the function has to be zero at those points and if the double derivative of the function is positive, then the roots corresponds to the points where the function attains its minimum value. Likewise, when the algorithm in gaussian searches for the minimum energy structures along the potential surface, the Hessian matrix provides a good direction since it is the double derivative of the energy functional.
Dear Gaurav
Generally Hessian is used for determining extrema of a function. Hessian determine local curvature of a function In the case of computational chemistry this function is potential energy surface. After optimization, you are standing on one point (stationary state) on PES , to find that the stationary state you have obtained is minimum, maximum or saddle point you need to calculate Hessian since sign of its eigen values shows the character of stationary point.
I agree with the answers you already got. Also the evaluation of the related second derivatives allows the prediction of vibrational frequencies (frequencies are related to the eigenvalues of the Hessian matrix). This will in turn allow you to find thermodynamic information of your molecule or system.
Yes, I agree with the above answers. Moreover, one can obtain the normal mode coordinates by calculating Hessian matrix followed by the Willson matrix.
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