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Collective motions in which substantial parts move as units relative to the rest play an important role in defining the function of a biomolecule. These processes involve the correlated motion of many atoms and are slower than local vibrations. They are difficult and costly to detect using classical molecular dynamics simulations, which motivates the use of normal modes dynamics. Normal modes are found by assuming that the potential energy can be approximated as a quadratic function of its variables and solving a generalized eigenvalue problem to give a closed analytical description of the motion. The eigenvalues give the frequencies of the modes and the eigenvectors give the details of the corresponding motions. At a critical point, the quadratic approximation is obtained by a Taylor expansion to the second order of the total potential energy. Computing normal modes therefore requires computing the second derivatives of the energy function. However, it is difficult to define a meaningful energy minimum for a system involving a large biomolecule in the midst of small water molecules since their geometric and physical properties are so different. We believe that this difficulty can be circumvented by using an implicit solvent model. Computing the Taylor expansion of the energy function including an implicit solvent model would require the second derivatives of the weighted surface area and/or volume of the biomolecule. We are currently developing analytical expressions for these second derivatives, following our recent work on the first derivatives, reported last year.