Constrained degrees of freedom

Next, the saddle point and Hessian calculations can be narrowed to a subset of all coordinates. At a saddle point in the full dimensionality, the potential energy gradient equals zero with respect to all generalized coordinates. The same criterion holds for the flexible coordinates in a subset of the full dimensionality. For constrained degrees of freedom A=f + I,..., 3N, the stiff potential maintaining the constraints is of the form... 

This potential can be viewed as the free energy due to the entropy - i k In H associated with harmonic oscillators in the constrained degrees of freedom. 

Similar to the quasi-continuum Monte Carlo approach (see above), the CG potential energy is the PMF for the constrained degrees of freedom ... 

The subtraction of constrained degrees of freedom is necessary because geometrical constraints are characterized by a time-independent generalized coordinate associated with a vanishing generalized momentum (i.e., no kinetic energy). A more formal statistical-mechanical justification for the subtraction of the external degrees of... 

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