Overview
The net non-bonded force of each particle is produced by summing all the non-bonded forces of neighboring particles on the basis of a neighbor list that lists the interacting particles for each particle, built beforehand. Because of the independence of parallel CUDA threads, a pair of interacting particles is inevitably included independently in neighbor list in the mode that one thread calculates and sums all non-bonded forces of a particle. The common non-bonded potential energy functions are included.
Description:
\begin{eqnarray*} V_{\mathrm{LJ}}(r) = & 4 \epsilon \left[ \left( \frac{\sigma}{r} \right)^{12} - \alpha \left( \frac{\sigma}{r} \right)^{6} \right] & r < r_{\mathrm{cut}} \\ = & 0 & r \ge r_{\mathrm{cut}} \\ \end{eqnarray*}The following coefficients must be set per unique pair of particle types:
- \epsilon - epsilon (in energy units)
- \sigma - sigma (in distance units)
- \alpha - alpha (unitless)
- r_{\mathrm{cut}} - r_cut (in distance units) - optional: defaults to the global r_cut specified in the pair command
.. py:class:: LJForce(all_info, nlist, r_cut)
The constructor of LJ interaction calculation object.
:param AllInfo all_info: The system information.
:param NeighborList nlist: The neighbor list.
:param float r_cut: The cut-off radius.
.. py:function:: setParams(string type1, string type2, float epsilon, float sigma, float alpha)
specifies the LJ interaction parameters with type1, type2, epsilon, sigma, and alpha.
.. py:function:: setParams(string type1, string type2, float epsilon, float sigma, float alpha, float r_cut)
specifies the LJ interaction parameters with type1, type2, epsilon, sigma, alpha, and cut-off of radius.
.. py:function:: setEnergy_shift()
calls the function to shift LJ potential to be zero at cut-off point.
.. py:function:: setDispVirialCorr(bool open)
switches the dispersion virial correction.
Example::
lj = gala.LJForce(all_info, neighbor_list, 3.0)
lj.setParams('A', 'A', 1.0, 1.0, 1.0)
lj.setEnergy_shift()
app.add(lj) # Note: adds this object to the application.
Description:
\begin{eqnarray*} V_{\mathrm{SLJ}}(r)=&4 \epsilon \left[ \left( \frac{\sigma }{r-\Delta } \right)^{12}-\alpha \left( \frac{\sigma }{r-\Delta } \right)^{6} \right] & r<(r_{\mathrm{cut}}+\Delta ) \\ = & 0 & r \ge (r_{\mathrm{cut}}+\Delta ) \\ \end{eqnarray*}The following coefficients must be set per unique pair of particle types:
- \epsilon - epsilon (in energy units)
- \sigma - sigma (in distance units)
- \alpha - alpha (unitless) - optional: defaults to 1.0
- \Delta = (d_{i} + d_{j})/2 - \sigma - (in distance units); d_{i} and d_{j} are the diameter of particle i and j which can be input from XML file.
- r_{\mathrm{cut}} - r_cut (in distance units) - optional: defaults to the global r_cut specified in the pair command
.. py:class:: SLJForce(all_info, nlist, r_cut)
The constructor of shift LJ interaction calculation object.
:param AllInfo all_info: The system information.
:param NeighborList nlist: The neighbor list.
:param float r_cut: The cut-off radius.
.. py:function:: setParams(string type1, string type2, float epsilon, float sigma, float alpha)
specifies the shift LJ interaction parameters with type1, type2, epsilon, sigma, and alpha.
.. py:function:: setParams(string type1, string type2, float epsilon, float sigma, float alpha, float r_cut)
specifies the shift LJ interaction parameters with type1, type 2, epsilon, sigma, alpha, and cut-off of radius.
.. py:function:: setEnergy_shift()
calls the function to shift LJ potential to be zero at the cut-off point.
Example::
slj = gala.SLJForce(all_info, neighbor_list, 3.0)
slj.setParams('A', 'A', 1.0, 1.0, 1.0)
slj.setEnergy_shift()
app.add(slj)
An attractive potential to mimic \pi-\pi interactions of rod segments. Reference: Y.-L. Lin, H.-Y. Chang, and Y.-J. Sheng, Macromolecules 2012, 45, 7143-7156.
Description:
\begin{eqnarray*} V_{\mathrm{\pi-\pi}}(r, \theta)=&-\epsilon \cos^{2}\theta (1-r) & r<r_{\mathrm{cut}} \\ = & 0 & r \ge r_{\mathrm{cut}} \\ \end{eqnarray*}
- \theta - (in radians) the angle between two linear molecules
- r_{\mathrm{cut}} - r_cut (in distance units) - optional: defaults to the global r_cut
The following coefficients must be set per unique pair of particle types:
- \epsilon - epsilon (in energy units)
The transitional forces are added between the center particles of linear molcules. A group of the center particles are needed for :py:class:`CenterForce`. The rotational forces are added on the two neighbor particles of a center particle.
.. py:class:: CenterForce(all_info, nlist, group, r_cut, epsilon)
The constructor of a pi-pi interaction calculation object for linear molecules.
:param AllInfo all_info: The system information.
:param NeighborList nlist: The neighbor list.
:param ParticleSet group: The group of center particles.
:param float r_cut: The cut-off radius.
:param float epsilon: the depth of the potential well.
.. py:function:: setPreNextShift(int prev, int next)
sets the previous particle and next particle of center particle with shift ID value, the default value is -1 and 1, respectively.
Example::
groupC = gala.ParticleSet(all_info, 'C')
cf = gala.CenterForce(all_info,neighbor_list, groupC, 1.0, 2.0)
app.add(cf)
Description:
\begin{eqnarray*}\phi(r)=&\epsilon\text{ exp}\left[-\left(\frac{r}{\sigma}\right)^{n}\right] & r<r_{\mathrm{cut}} \\ = & 0 & r \ge r_{\mathrm{cut}} \\ \end{eqnarray*}The following coefficients must be set per unique pair of particle types:
- \epsilon - epsilon (in energy units)
- \sigma - sigma (in distance units)
- n - power exponent n
- r_{\mathrm{cut}} - r_cut (in distance units) - optional: defaults to the global r_cut
.. py:class:: GEMForce(all_info, nlist, r_cut)
The constructor of a generalized exponential model object.
:param AllInfo all_info: The system information.
:param NeighborList nlist: The neighbor list.
:param float r_cut: The cut-off radius.
.. py:function:: setParams(string type1, string type2, float epsilon, float sigma, float n)
specifies the GEM interaction parameters with type1, type2, epsilon, sigma, and n.
.. py:function:: setParams(string type1, string type2, float epsilon, float sigma, float n, float r_cut)
specifies the GEM interaction parameters with type1, type2, epsilon, sigma, n, and cut-off radius.
Example::
gem = gala.GEMForce(all_info, neighbor_list, 2.0)
gem.setParams('A', 'A', 1.0, 1.0, 4.0) # epsilon, sigma, n
app.add(gem)
Description:
\begin{eqnarray*} V(r_{ij}) = & 4 \epsilon \left[ \left( \frac{\sigma}{r_{ij}} \right)^{12} - \alpha \left( \frac{\sigma}{r_{ij}} \right)^{6} \right] +\frac{f}{\epsilon_{r}}\frac{{q}_{i}{q}_{j}\mbox{erfc} \left(\kappa{r}_{ij}\right)}{{r}_{ij}} & r < r_{\mathrm{cut}}\\ = & 0 & r \ge r_{\mathrm{cut}} \\\end{eqnarray*}The following coefficients must be set per unique pair of particle types:
- \epsilon - epsilon (in energy units)
- \sigma - sigma (in distance units)
- \alpha - alpha (unitless)
- \kappa - kappa (unitless)
- r_{\mathrm{cut}} - r_cut (in distance units) - optional: defaults to the global r_cut specified in the pair command
.. py:class:: LJEwaldForce(all_info, nlist, r_cut)
The constructor of LJ + Ewald in real space interaction calculation object. The :math:`\kappa` parameter could be derived
automatically.
:param AllInfo all_info: The system information.
:param NeighborList nlist: The neighbor list.
:param float r_cut: The cut-off radius.
.. py:function:: setParams(string type1, string type2, float epsilon, float sigma, float alpha)
specifies the LJ interaction parameters with type1, type2, epsilon, sigma, and alpha.
.. py:function:: setParams(string type1, string type2, float epsilon, float sigma, float alpha, float r_cut)
specifies the LJ interaction parameters with type1, type2, epsilon, sigma, alpha, and cut-off of radius.
.. py:function:: setEnergy_shift()
calls the function to shift LJ potential to be zero at cut-off point.
.. py:function:: setDispVirialCorr(bool open)
switches the dispersion virial correction.
Example::
lj = gala.LJEwaldForce(all_info, neighbor_list, 0.9)
lj.setParams('OW', 'OW', 0.648520, 0.315365, 1.0)
lj.setParams('HW', 'HW', 0.0, 0.47, 1.0)
lj.setParams('MW', 'MW', 0.0, 0.47, 1.0)
lj.setParams('OW', 'HW', 0.0, 0.47, 1.0)
lj.setParams('OW', 'MW', 0.0, 0.47, 1.0)
lj.setParams('HW', 'MW', 0.0, 0.47, 1.0)
lj.setEnergy_shift()
lj.setDispVirialCorr(True)
app.add(lj)
Description:
\begin{eqnarray*} V(r) = & 6.75 \epsilon \left[ \left( \frac{\sigma}{r} \right)^{9} - \alpha \left( \frac{\sigma}{r} \right)^{6} \right] & r < r_{\mathrm{cut}} \\ = & 0 & r \ge r_{\mathrm{cut}} \\ \end{eqnarray*}The following coefficients must be set per unique pair of particle types:
- \epsilon - epsilon (in energy units)
- \sigma - sigma (in distance units)
- \alpha - alpha (unitless)
- r_{\mathrm{cut}} - r_cut (in distance units)
Description:
\begin{eqnarray*} V_{\mathrm{harmonic}}(r)=&\frac{1}{2}\alpha \left(1-\frac{r}{r_{cut}} \right)^{2} & r < r_{\mathrm{cut}} \\ = & 0 & r \ge r_{\mathrm{cut}} \\ \end{eqnarray*}The following coefficients must be set per unique pair of particle types:
- \alpha - alpha (in energy units)
- r_{\mathrm{cut}} - r_cut (in distance units)
Description:
\begin{eqnarray*} V_{\mathrm{Gaussion}}(r)=& \epsilon \exp \left[ -\frac{1}{2}{\left( \frac{r}{\sigma} \right)}^{2} \right] & r < r_{\mathrm{cut}} \\ = & 0 & r \ge r_{\mathrm{cut}} \\ \end{eqnarray*}The following coefficients must be set per unique pair of particle types:
- \epsilon - epsilon (in energy units)
- \sigma - sigma (in distance units)
- r_{\mathrm{cut}} - r_cut (in distance units)
Description:
\begin{eqnarray*} V_{\mathrm{IPL}}(r)=&\epsilon \left(\frac{\sigma}{r} \right)^{n} & r < r_{\mathrm{cut}} \\ = & 0 & r \ge r_{\mathrm{cut}} \\ \end{eqnarray*}The following coefficients must be set per unique pair of particle types:
- \epsilon - epsilon (in energy units)
- \sigma - sigma (in distance units)
- n - n (unitless)
- r_{\mathrm{cut}} - r_cut (in distance units)
Description:
\begin{eqnarray*} U\left( r \right)=&\frac{\alpha}{r} & r < r_{\mathrm{cut}} \\ = & 0 & r \ge r_{\mathrm{cut}} \\ \end{eqnarray*}The following coefficients must be set per unique pair of particle types:
- \alpha = f\frac{q_{i} q_{j}}{\epsilon_{r}} - alpha - (in energy*distance unit): f= 1/4\pi \epsilon_0=138.935\text{ }kJ\text{ }mol^{-1}\text{ }nm\text{ }e^{-2}
- r_{\mathrm{cut}} - r_cut (in distance units)
.. py:class:: PairForce(all_info, nlist)
The constructor of pair interaction calculation object.
:param AllInfo all_info: The system information.
:param NeighborList nlist: The neighbor list.
.. py:function:: setParams(string type1, string type2, float param0, float param1, float param2, float r_cut, PairFunc function)
specifies the interaction and its parameters with type1, type2, parameter0, parameter1, parameter2, cut-off radius, and potential type.
.. py:function:: setShiftParams(string type1, string type2, float param0, float param1, float param2, float r_cut, float r_shift, PairFunc function)
specifies the interaction and its parameters with type1, type2, parameter0, parameter1, parameter2, cut-off radius, shift radius, and potential type.
This method employs a shift function introduced by GROMACS by which potential and force are smoothed at the boundaries.
============== ========== ========== ==========
Function types Parameter0 Parameter1 Parameter2
============== ========== ========== ==========
lj12_6 epsilon sigma alpha
lj9_6 epsilon sigma alpha
harmonic alpha
gauss epsilon sigma
ipl epsilon sigma n
Coulomb alpha
============== ========== ========== ==========
Example::
pair = gala.PairForce(all_info, neighbor_list)
pair.setParams('A', 'A', 100.0, 0.0, 0.0, 1.0, gala.PairFunc.harmonic)
pair.setParams('A', 'B', 10.0, 1.0, 0.0, 1.0, gala.PairFunc.gauss)
pair.setParams('B', 'B', 10.0, 1.0, 2, 1.0, gala.PairFunc.ipl)
app.add(pair)