Harmonic constraints

Harmonic constraints provide a mechanism for holding certain parts of a molecule relatively immobile during a simulation. It allows specific atoms to be held to a reference position. The energy for an atom i that is constrained is

$$E_{\text{constraint}} = k_i {\left(\vert{\vec{r}}_i - {\vec{r}}_{\text{ref}}\vert\right)}^e$$

where

• k_i = force constant defined for atom i
• ${\vec{r}}_i$ = current position of atom i
• $\vec{r}_{\text{ref}}$ = reference position atom i is constrained to
• e = exponent defined for all constraints

The reference positions, force constaints, exponent, and atoms which are constrained are defined by the user using several configuration options. For more details, see the description of the options constraints, consexp, conskfile, conskcol, and consref in section 4.

NOTE: NAMD actually calculates the constraints potential with E = k (x-x₀)^d and the force with F = -d k (x-x₀)^d-1, where d is the exponent consexp. The result is that a force constant k specified in the PDB file is effectively the force constant d k in calculations (usually d = 2).