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High dimensional Function

For POTEntial=HIGH, a restraining function for stereospecifically assignable proton pairs is employed (Habazettl et al. 1990). This is useful for resolved but unassigned peaks involving methylene protons. The restraining function is given by


where S is the energy constant specified by the SCALe statement. Supppose that one observes 2n distance restraints involving the two protons a and b of a particular unassigned pair; this means that there are a total of 2n ASSIgn statements specified for this particular unassigned pair (NCOUnt has to match 2n). The function is then the product of two 2n-dimensional functions, each corresponding to one of the two possible stereospecific assignments:

where and are the distances from spin i to the unassigned spins a and b, respectively. When the corresponding ASSIgn statements contain multiple atom selections, averaged distances are computed; only center-averaging is allowed in combination with the high dimensional potential. and are lower bounds for the distances between spin i and spins a and b, respectively. and are upper bounds for the distances between spin i and spins a and b, respectively. and are the lower bounds and upper bounds for the distance difference y-x, respectively. These upper and lower bounds are specified through a group of 2n assignment statements:


where the terms should be understood as atom selections. are constants that are determined internally, such that the barrier height between the two minima of is given by BHIG. The functional forms of f and F are similar to the soft-square function (Section 18.3.3) with a linear asymptote, except that the switching region is symmetrically arranged:



where lim is set internally to 0.1.

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