Torsion Free Strain Calculation

Overview

A new function has been introduced to calculate the Torsion Free Strain, which combines torsional strain and an entropy-based component derived from statistical profiles. This allows users to assess how favorable a torsion is based on known conformational preferences.

Theory

The FreeStrain value is computed as:

FreeStrain = Strain + Entropy_Component

It is derived from statistical torsion profiles. For each torsion in a molecule, a probability is calculated based on the torsion's current value and its corresponding position in the profile:

Probability_Tors[i] = Sum( prof[k] * Exp(-d*d) )

Where:

• k ranges from 1 to 36 (corresponding to 10-degree bins over 360 degrees)
• d is the distance in bins between the current torsion angle and bin k

The cumulative torsional free strain is then calculated as:

Free_Strain = -Sum( Log(Probability_Tors[i]) )

A lower value indicates a more favorable (less strained) conformation.

Note: This method incorporates an entropy component. For example, if there are three equivalent minima, being confined to one of them incurs an entropy penalty for locking out the other two.

Graphical Interface (GUI) Access

This functionality is also accessible via the graphical user interface:

Chemistry > Calculate Torsion Free Strain

Selecting this option will compute and display the torsional free strain for the selected molecule(s) based on current conformations.

New Shell Function

A new shell function is available for use in scripts:

Score( <X_3Dn> torsion ) -> <R_n_free_strain>

Input: A set of 3D molecules with defined torsions
Output: A vector of torsion free strain values

This function evaluates each torsion in the molecule using the statistical profiles as described above and returns a cumulative strain score that includes entropy considerations.