Intramolecular Interactions

The intramolecular interaction energy is the summation of the individual nonbonded interaction energies for pairs of atoms within the current molecular structure, e.g., a single molecule or a crystallographic asymmetric unit.

E_{ELEC} = {\sum_{i<j} f_{ELEC}(R_{ij})} + e_{14}\sum_{(i,j){\in}\{1-4\}}
\end{displaymath} (4.17)

E_{VDW} = {\sum_{i<j} f_{VDW}(R_{ij})} + \sum_{(i,j){\in}\{1-4\}}
\end{displaymath} (4.18)

The summation extends over all pairs of atoms ($i<j$) that satisfy the cutoff criteria specified by CUTNb and ATOM or GROUP (nbonds statement, see Section 3.2.1) and that are selected by the constraints interaction statement. The program's interpretation of the cutoff points depends on the type of cutoff used. For the group cutoff option, the program first executes a group-by-group centroid search to determine which centroids are within the particular cutoff value CUTNb of each other. Then the program calculates the energy using every atom in both groups. For the atom cutoff, the nonbonded interactions are included on an atom-by-atom basis. However, the pairwise search is computationally expensive. A great reduction in computational time is achieved by first searching for nearest neighbors among the nonbonded groups and then searching for atom pairs between selected group pairs.

The computational time is further reduced by introducing an approximation, storing the atomic pair indices ($i<j$) that satisfy $R_{ij} \leq R_{cut}$ in a list that is updated only when any atom has moved more than the amount specified by TOLErance. For both switched and shifted nonbonded options (see Section 3.2.1), the distance $R_{ij}$ at which the energy becomes zero is given by $R_{off}$. Thus, the nonbonded energy calculations become independent of the update frequencies if ${\rm CUTNB} \geq {\rm CTOFNB} +2 {\rm TOLErance}$.

There are a number of cases for nonbonded interactions that must not be computed, e.g., interactions between covalently bonded atoms. Covalently bonded exclusions are automatically generated by X-PLOR using information about atom connectivity. In addition, certain exclusions can be added manually by the EXCLude statement, which is an atom statement (see Section 3.1.1). The NBXMod statement (see Section 3.2.1) has several options for automatically excluding 1-2, 1-2 and 1-3, and 1-2, 1-3, and 1-4 interactions in the molecule. In the case of NBXMod=$\pm$5, the 1-4 interactions are treated in a special way. The electrostatic 1-4 interactions are scaled by $e_{14}$, and the van der Waals interactions use a special 1-4 set of parameters for ${\varepsilon}, {\sigma}, A$ and $B$. In the case of NBXMod$\char93 \pm$5, 1-4 interactions are treated as normal nonbonded interactions, and the second terms of the right-hand side of Eqs. 4.17 and 4.18 become zero.

Xplor-NIH 2023-11-10