Spherical boundary conditions

NAMD provides spherical boundary conditions that consist of a single or two superimposed potential functions. The potential energy for these energies is given by

$$E_{\text{sphere}} = k_{\text{sphere}} {\left( \vert\vec{r}_{i... ...ter}}\vert - r_{\text{sphere}} \right)}^{exp_{\text{sphere}}}$$

if $\vert\vec{r}_{i} - \vec{r}_{\text{center}}\vert > r_0$ and $E_{\text{sphere}} = 0$ otherwise, where

• $k_{\text{sphere}}$ = force constant
• ${\vec{r}}_i$ = current position of atom i
• $\vec{r}_{\text{center}}$ = center of the spherical boundary
• $r_{\text{sphere}}$ = radius of the spherical boundary
• $exp_{\text{sphere}}$ = exponent for the potential function

The force applied by this potential is given by

$$\vec{F}_{\text{sphere}} = \left( exp_{\text{sphere}} k_{\tex... ...^{exp_{\text{sphere}} - 1} \right) \hat{r}_{i,\text{center}}$$

where

• $\hat{r}_{i,\text{center}}$ = the unit vector in the direction from atom i to the center of the sphere.

Thus a positive force constant will cause a force that moves atoms back in to the center of the sphere and a negative force constant will force atoms away from the sphere.

For simple harmonic boundary conditions, a single potential with an exponent of 2 or 4 may be used to obtain a potential like that shown in figure 5. It may be desirable, however, to simulate a surface tension affect, where a small harmonic well around the sphere boundary is desired. To obtain such an effect, two potentials of the form shown above can be superimposed. By combining a potential with a negative force constant and an exponent of two with a potential with a positive force constant and a exponent of four and a slightly larger raidus, a potential such as that shown in figure 6 can be obtained.

Currently, the spheres must be centered around the initial center of mass of the system. The force constant, radius, and exponents for each potential are defined in the configuration file using the options sphericalBCk1, sphericalBCr1, sphericalBCexp1, sphericalBCk2, sphericalBCr2, and sphericalBCexp2. These parameters are described in section 4.