VisitModelInnerTable

class VisitModelInnerTable : public feasst::VisitModelInner

Represent anisotropic sites using a tabular potential that is precomputed and read from a file.

The relative position and orientation of an arbitrary rigid body is given by 5 orientational degrees of freedom and the radial distance, r between the centers of the two bodies.

The spherical coordinate azimuthal angle [0, 2pi] and polar angle [0, pi] are denoted s1 and s2, and are as described in the Position class. Note that there is increased resolution at the poles. While something resembling a Fibonacci lattice could more uniformly represent a spherical surface, interpolation would be more complicated.

The Euler angles, [e1, e2, e3], in order, are as described in the Euler class.

The radial distance, r, is transformed into z which varies from z=0 at the hard contact distance, r_h, to z=1 at the cutoff, r_c. A stretching parameter, \(\gamma\), increases the resolution at shorter distances when negative.

\(z=[(r^\gamma - r_h^\gamma)/(r_c^\gamma - r_h^\gamma)]\).

The format of the tabular potential stored in a file is as follows.

The first line should be ‘site_types’ followed by the number of site types and then the identity of each of those site types in order of the tables given below. (e.g., “site_types n i” where n is the number of site types and each following number is the type of each anisotropic site.)

There is a table for each unique pair of site types. For example, if the first line is as follows: “site_types 2 1 7” then the first table will be for interactions of site type 1 with site type 1 (i.e., 1-1), the second table will be for 1-7 interactions, and the third table will be for 7-7 interactions.

For each pair of site types, i <= j, a table is given by the following lines.

  1. “num_orientations_per_pi [value]” is used to determine the resolution of all 5 orientational degrees of freedom.

  2. ”gamma [value]” is the expononent for the definition of z. But, if gamma==0, then use a square well potential.

  3. ”delta [value]” is the distance between the hard particle inner cutoff and the outer cutoff when the potential goes to zero (e.g., delta = r_c - r_h).

  4. ”num_z [value]” is the number of energy values along the z parameter.

  5. ”smoothing_distance [value]” is the distance to linearly interpolate the energy to zero. Specifically, r_c - smoothing_distance is the z=1 value. If smoothing_distance is <= 0, then it is not used at all.

  6. The remaining lines are for each unique set of the five angles separated by spaces. The outer loop is s1, with range [-pi, pi]. If i == j, the range is [0, pi] for i-j swap symmetry (e.g., swap i and j if s1 < 0). The next loop is s2 in [0, pi], then e1 in [-pi, pi], e2 and [0, pi], and finally e3 in [-pi, pi]. The number of lines should be (k+1)^3(2k+1)^2 for i==j, and (k+1)^2(2k+1)^3 lines for i!=j, where k=num_orientations_per_pi. Each line then reports the contact distance, r_h, followed by num_z values of the potential energy uniformly in the z range of [0, 1]. If the orientation is duplicate, then the first number is -1 and the second is the integer number of the orientation that it is a duplicate of.

Subclassed by feasst::VisitModelInnerNN

Public Functions

bool is_energy_table(const std::vector<std::vector<std::shared_ptr<Table6D>>> &energy) const

Return true if there is an energy table.

double second_virial_coefficient(const Configuration &config, argtype args = argtype()) const

Compute the second virial coefficient between anisotropic sites by table integration. See https://doi.org/10.1063/1.5040252 For the hard particle interaction, see Eq D5.

For the Jacobian in integration, see https://doi.org/10.1021%2Facs.jpcb.9b06808 https://doi.org/10.1063/1.432162 (missing alpha integration?) https://doi.org/10.1098/rspa.1948.0009 https://doi.org/10.1063/1.4961541

args:

  • site_type1: type of first site (default: 0).

  • site_type2: type of second site (default: 0).

  • expand_t: increase orientation points by this factor (default: 1).

  • expand_z: increase translation points by this factor (default: 1).

  • beta: see ThermoParams (default: 1).

Arguments

  • table_file: table file with format described above.

  • ignore_energy: do not read the energy table (default: false).