Functions to do molecular mechanics. More...

#include "model_mechanics.h"
#include "model_poly.h"
#include "model_shell.h"
#include "model_transform.h"
#include "model_util.h"
#include "math_util.h"
#include "random_numbers.h"
#include "symmetry.h"
#include "Vector3.h"
#include "linked_list.h"
#include "utilities.h"

Macros
#define	ETERMS 16

Functions
double	model_mechanics (Bmodel *model, Bmodparam &md, int mm_type, int max_iter, double max_shift, double velocitylimit)
	Minimizes the energy of a model. More...

int	model_minimize (Bmodel *model, double max_shift)
	Move components random distances down the energy gradient. More...

double	model_verlet (Bmodel *model, double timestep, double Kfriction, double velocitylimit)
	Model dynamics using the velocity verlet integrator. More...

double	component_harmonic_potential (Bcomponent comp1, Bcomponent comp2, double d0, double Kd)

double	component_soft_potential (Bcomponent comp1, Bcomponent comp2, double d0, double Kd)

double	component_lennard_jones_potential (Bcomponent comp1, Bcomponent comp2, double d0, double Kd)

double	component_morse_potential (Bcomponent comp1, Bcomponent comp2, double d0, double Kd)

double	component_angular_potential (Bcomponent comp, Bcomponent comp1, Bcomponent *comp2, double a0, double Ka)

double	component_radial_potential (Bcomponent *comp, Vector3< double > point, double d0, double Kradial)

double	component_distance_potential (Bcomponent comp1, Bcomponent comp2, double Kd, int type)

double	component_electrostatic_potential (Bcomponent comp1, Bcomponent comp2, double q1, double q2, double Ke, double cutoff)

double	model_electrostatic_energy (Bmodel *model, Bmodparam &md)
	Calculates the electrostatic potentials between components. More...

double	model_distance_energy (Bmodel *model, Bmodparam &md)
	Calculates the distance-related potentials between components. More...

double	model_grid_distance_energy (Bmodel *model, Bmodparam &md)
	Calculates the non-bonded forces and energy. More...

double	model_neighbor_distance_energy (Bmodel *model, Bmodparam &md)
	Calculates the distance-related potentials between components and their neighbors. More...

double	model_soft_sphere_energy (Bmodel *model, double Kd, double d0)
	Calculates the soft sphere potential between components. More...

double	model_lennard_jones_energy (Bmodel *model, double Kd, double d0)
	Calculates the Lennard-Jones potential between components. More...

double	model_morse_energy (Bmodel *model, double Kd, double d0)
	Calculates the Morse potential between components. More...

double	model_link_energy (Bmodel *model, Bmodparam &md)
	Calculates the model link energy. More...

double	model_link_energy (Bmodel *model, double Klink)
	Calculates the model link energy. More...

double	model_angle_energy (Bmodel *model, Bmodparam &md)
	Calculates the model angular energy. More...

double	model_polygon_angle_energy (Bmodel *model, double Kpolyangle)
	Calculates the link angular forces and energy. More...

double	model_polygon_energy (Bmodel *model, double linklength, double Kpoly)
	Calculates the polygon regularity. More...

double	model_polygon_energy (Bmodel *model, double Kpoly)
	Calculates the polygon regularity energy and forces. More...

double	model_polygon_plane_energy (Bmodel *model, double Kpolyplane)
	Calculates the polygon planarity energy and forces. More...

double	model_neighbor_plane_energy (Bmodel *model, double Kplane)
	Calculates the planarity energy and forces with respect to neighbors. More...

double	model_point_force (Bmodel *model, Vector3< double > point, double Kpoint, double decay)
	Calculates the forces and energy resulting from a single point force. More...

double	model_radial_energy (Bmodel *model, Vector3< double > point, double d0, double Kradial)
	Calculates the potential between a components and a point. More...

double	model_guide_energy (Bmodel *model, Bmodparam &md)
	Calculates the potential with respect to a guide model. More...

double	model_polyhedron_guide_energy (Bmodel model, Bmodel gmod, double Kguide)
	Calculates the potential with respect to a guide polyhedron. More...

double	model_map_energy (Bmodel model, Bimage map, double Kmap)
	Energy calculation of a model into a map. More...

double	model_map_gradient_energy (Bmodel model, Bimage map, double Kmap)

double	model_map_energy (Bmodel model, Bimage map, double Kmap, double sigma)

int	model_zero_forces (Bmodel *model)
	Zeroes the component forces. More...

int	model_calculate_deviations (Bmodel *model)
	Calculates the deviations from regularity in a polyhedral model. More...

int	model_calculate_deviations (Bmodel *model, Bmodparam &md)

double	model_average_linklength (Bmodel *model)

int	model_regularize (Bmodel *model, int max_iter, double distance, double Kdistance, double Klink, double Kpolyangle, double Kpolygon, double Kpolyplane, double Kpoint, double decay)
	Regularizes a model. More...

Variables
int	verbose

Detailed Description

Functions to do molecular mechanics.

Author: Bernard Heymann

Date: Created: 20010828; Modified: 20210318

Macro Definition Documentation

◆ ETERMS

#define ETERMS 16

Function Documentation

◆ component_angular_potential()

double component_angular_potential	(	Bcomponent *	comp,
		Bcomponent *	comp1,
		Bcomponent *	comp2,
		double	a0,
		double	Ka
	)

◆ component_distance_potential()

double component_distance_potential	(	Bcomponent *	comp1,
		Bcomponent *	comp2,
		double	Kd,
		int	type
	)

◆ component_electrostatic_potential()

double component_electrostatic_potential	(	Bcomponent *	comp1,
		Bcomponent *	comp2,
		double	q1,
		double	q2,
		double	Ke,
		double	cutoff
	)

◆ component_harmonic_potential()

double component_harmonic_potential	(	Bcomponent *	comp1,
		Bcomponent *	comp2,
		double	d0,
		double	Kd
	)

◆ component_lennard_jones_potential()

double component_lennard_jones_potential	(	Bcomponent *	comp1,
		Bcomponent *	comp2,
		double	d0,
		double	Kd
	)

◆ component_morse_potential()

double component_morse_potential	(	Bcomponent *	comp1,
		Bcomponent *	comp2,
		double	d0,
		double	Kd
	)

◆ component_radial_potential()

double component_radial_potential	(	Bcomponent *	comp,
		Vector3< double >	point,
		double	d0,
		double	Kradial
	)

◆ component_soft_potential()

double component_soft_potential	(	Bcomponent *	comp1,
		Bcomponent *	comp2,
		double	d0,
		double	Kd
	)

◆ model_angle_energy()

double model_angle_energy	(	Bmodel *	model,
		Bmodparam &	md
	)

Calculates the model angular energy.

Parameters

*model	model structure.
&md	model parameters with reference angle specifications.

Returns

double angular energy.

The angular potential is a harmonic function:
    E = Ka*(a - a0)^2
The force is zero when a = reference angle (a0).
Only the first model in the linked list is used.

◆ model_average_linklength()

double model_average_linklength ( Bmodel * model )

◆ model_calculate_deviations() [1/2]

int model_calculate_deviations ( Bmodel * model )

Calculates the deviations from regularity in a polyhedral model.

Parameters

*model model structure.

Returns

int 0.

Link deviation:
    d = sqrt(sum((l - l0)^2)/n)
where l is the length and l0 is the reference length.
Angle deviation:
    d = sqrt(sum((a - a0)^2)/n)
where a is the angle between two links and a0 is the reference angle:
    a0 = PI*(1 - 2/v)
where v is the number of vertices in the associated polygon.
Only the first model in the linked list is used.

◆ model_calculate_deviations() [2/2]

int model_calculate_deviations	(	Bmodel *	model,
		Bmodparam &	md
	)

◆ model_distance_energy()

double model_distance_energy	(	Bmodel *	model,
		Bmodparam &	md
	)

Calculates the distance-related potentials between components.

Parameters

*model	model structure.
&md	model parameters with distance interactions specifications.

Returns

double distance energy.

Distance potential types:
    0   none
    1   harmonic - only for explicit links
    2   soft
    3   Lennard-Jones
    4   Morse
Only the first model in the linked list is used.

◆ model_electrostatic_energy()

double model_electrostatic_energy	(	Bmodel *	model,
		Bmodparam &	md
	)

Calculates the electrostatic potentials between components.

Parameters

*model	model structure.
&md	model parameters with distance interactions specifications.

Returns

double electrostatic energy.

Electrostaic potential:
    E = Ke*q1*q2/d
Only the first model in the linked list is used.

◆ model_grid_distance_energy()

double model_grid_distance_energy	(	Bmodel *	model,
		Bmodparam &	md
	)

Calculates the non-bonded forces and energy.

Parameters

*model	model structure.
&md	model parameters with distance interactions specifications.

Returns: double distance energy.

Distance potential types:
    0   none
    1   harmonic - only for explicit links
    2   soft
    3   Lennard-Jones
    4   Morse

◆ model_guide_energy()

double model_guide_energy	(	Bmodel *	model,
		Bmodparam &	md
	)

Calculates the potential with respect to a guide model.

Parameters

*model	model structure.
&md	model aparameters.

Returns

double energy.

Only the first model in the linked list is used.

◆ model_lennard_jones_energy()

double model_lennard_jones_energy	(	Bmodel *	model,
		double	Kd,
		double	d0
	)

Calculates the Lennard-Jones potential between components.

Parameters

*model	model structure.
Kd	distance force constant (Kd).
d0	reference distance between components (d0).

Returns

double distance energy.

The Lennard-Jones potential is given by:
    E = Kd*((d0/d)^12 - 2*(d0/d)^6)
The force is zero when d = d0.
The potential is set to zero for d > 3*d0;
Only the first model in the linked list is used.

◆ model_link_energy() [1/2]

double model_link_energy	(	Bmodel *	model,
		Bmodparam &	md
	)

Calculates the model link energy.

Parameters

*model	model structure.
&md	model parameters with distance interactions specifications.

Returns

double distance energy.

The link potential is a harmonic function:
    E = Kl*(d - l0)^2
The force is zero when d = reference link length (l0).
Only the first model in the linked list is used.

◆ model_link_energy() [2/2]

double model_link_energy	(	Bmodel *	model,
		double	Klink
	)

Calculates the model link energy.

Parameters

*model	model structure.
Klink	link force constant (Kl).

Returns

double link energy.

The link potential is a harmonic function:
    E = Kl*(d - l0)^2
The force is zero when d = reference link length (l0).
Only the first model in the linked list is used.

◆ model_map_energy() [1/2]

double model_map_energy	(	Bmodel *	model,
		Bimage *	map,
		double	Kmap
	)

Energy calculation of a model into a map.

Parameters

*model	model structure.
*map	map.
Kmap	map force constant.

Returns

double energy.

The map must be possitive density.
Only the first model in the linked list is used.

◆ model_map_energy() [2/2]

double model_map_energy	(	Bmodel *	model,
		Bimage *	map,
		double	Kmap,
		double	sigma
	)

◆ model_map_gradient_energy()

double model_map_gradient_energy	(	Bmodel *	model,
		Bimage *	map,
		double	Kmap
	)

◆ model_mechanics()

double model_mechanics	(	Bmodel *	model,
		Bmodparam &	md,
		int	mm_type,
		int	max_iter,
		double	max_shift,
		double	velocitylimit
	)

Minimizes the energy of a model.

Parameters

*model	model structure.
&md	model parameters.
mm_type	type of mechanics: 0=minimization, 1=dynamics
max_iter	number of minimization iterations.
max_shift	maximum shift per iteration.
velocitylimit	limit on velocity per time step.

Returns

double final energy.

The inclusion of energy terms is based on positive K-constants in the 
model parameter structure.
Only the first model in the linked list is used.

◆ model_minimize()

int model_minimize	(	Bmodel *	model,
		double	max_shift
	)

Move components random distances down the energy gradient.

Parameters

*model	model structure.
max_shift	maximum shift for each component.

Returns

int number of components.

The distance of movement is limited to the maximum shift.
Only the first model in the linked list is used.

◆ model_morse_energy()

double model_morse_energy	(	Bmodel *	model,
		double	Kd,
		double	d0
	)

Calculates the Morse potential between components.

Parameters

*model	model structure.
Kd	distance force constant (Kd).
d0	reference distance between components (d0).

Returns

double distance energy.

The Morse potential is given by:
    E = Kd*((1-exp((a/d0)*(d0-d)))^2 - 1)
The width of the energy well is given by a, set here to 6.
The force is zero when d = d0.
The potential is set to zero for d > 3*d0;
Only the first model in the linked list is used.

◆ model_neighbor_distance_energy()

double model_neighbor_distance_energy	(	Bmodel *	model,
		Bmodparam &	md
	)

Calculates the distance-related potentials between components and their neighbors.

Parameters

*model	model structure.
&md	model parameters with distance interactions specifications.

Returns

double distance energy.

Distance potential types:
    0   none
    1   harmonic - only for explicit links
    2   soft
    3   Lennard-Jones
    4   Morse
Only the first model in the linked list is used.

◆ model_neighbor_plane_energy()

double model_neighbor_plane_energy	(	Bmodel *	model,
		double	Kplane
	)

Calculates the planarity energy and forces with respect to neighbors.

Parameters

*model	model structure.
Kplane	neighbor planarity constant.

Returns

double neighbor planar energy.

A plane is fit through the neigbor locations and the normal calculated from:
    n•p = d
where n is the normal vector, p is a point in the plane, and d is the offset.
The deviation of a component location from the neighbor plane is calculated
and converted to a harmonic energy and force.
Only the first model in the linked list is used.

◆ model_point_force()

double model_point_force	(	Bmodel *	model,
		Vector3< double >	point,
		double	Kpoint,
		double	decay
	)

Calculates the forces and energy resulting from a single point force.

Parameters

*model	model structure.
point	center of point force.
Kpoint	point force constant.
decay	energy decay with distance.

Returns

double point force energy.

The energy is defined as an exponential decay over distance from the 
center of the point force:
    Ep = Kp * exp(-decay*dist)
The force is the derivative of the energy:
    Fp = Kp * decay * dir * exp(-decay*dist)
where Kp is the point force constant, dist is the distance of the component 
from the center of the point force, decay is the energy decay with distance
from the point force center, and dir is the normalized direction vector
pointing from the point force center to the component, indicating the direction
of force.
Only the first model in the linked list is used.

◆ model_polygon_angle_energy()

double model_polygon_angle_energy	(	Bmodel *	model,
		double	Kpolyangle
	)

Calculates the link angular forces and energy.

Parameters

*model	model structure.
Kpolyangle	angle force constant (Ka).

Returns

double total link angle energy.

The energy is defined as a harmonic function around the reference 
link angle, a0:
    Ea = Ka*(cos(a0)-r1*r2/(|r1|*|r2|))^2
    Ea = Ka*(a0 - a)^2
The force is the derivative of the energy on the first and last atoms:
    Fa1 = 2*Ka*(cos(a0)-r1*r2/(|r1|*|r2|))/(|r1|*|r2|) * ((r1*r2/|r1|)*r1-r2)
    Fa3 = 2*Ka*(cos(a0)-r1*r2/(|r1|*|r2|))/(|r1|*|r2|) * ((r1*r2/|r2|)*r2-r1)
where r1 is the vector from atom 2 to atom 1, r2 is the vector from
atom 2 to atom 3, and Ka is the link angle force constant.
Only the first model in the linked list is used.

◆ model_polygon_energy() [1/2]

double model_polygon_energy	(	Bmodel *	model,
		double	Kpoly
	)

Calculates the polygon regularity energy and forces.

Parameters

*model	model structure.
Kpoly	polygon regularity constant (Kp).

Returns

double polygon energy.

Given the distances of all the vertices from the polygon center, the
polygon regularity is defined as the deviation of these distances
from the average distance:
    E = Kp*(d - d0)
Only the first model in the linked list is used.

◆ model_polygon_energy() [2/2]

double model_polygon_energy	(	Bmodel *	model,
		double	linklength,
		double	Kpoly
	)

Calculates the polygon regularity.

Parameters

*model	model structure.
linklength	reference link length (l0).
Kpoly	polygon regularity constant (Kp).

Returns

double polygon energy.

Given the distances of all the vertices from the polygon center, the
polygon regularity is defined as the deviation of these distances
from the reference distance:
    E = Kp*(d - d0)
where the reference distance is calculated from the link length:
    d0 = l0/sqrt(2*(1-cos(2PI/n))
where n is the polygon order.
Only the first model in the linked list is used.

◆ model_polygon_plane_energy()

double model_polygon_plane_energy	(	Bmodel *	model,
		double	Kpolyplane
	)

Calculates the polygon planarity energy and forces.

Parameters

*model	model structure.
Kpolyplane	polygon planarity constant.

Returns

double polygon planar energy.

A plane is fit through the polygon vertices and the normal calculated from:
    n•p = d
where n is the normal vector, p is a point in the plane, and d is the offset.
The polygon plane energy is calculated as a harmonic deviation from 
the fitted plane.
Only the first model in the linked list is used.

◆ model_polyhedron_guide_energy()

double model_polyhedron_guide_energy	(	Bmodel *	model,
		Bmodel *	gmod,
		double	Kguide
	)

Calculates the potential with respect to a guide polyhedron.

Parameters

*model	model structure.
*gmod	guide polyhedron model.
Kguide	guide polyhedron force constant.

Returns

double energy.

Only the first model in the linked list is used.

◆ model_radial_energy()

double model_radial_energy	(	Bmodel *	model,
		Vector3< double >	point,
		double	d0,
		double	Kradial
	)

Calculates the potential between a components and a point.

Parameters

*model	model structure.
point	reference point = radial center.
d0	reference distance between component and point.
Kradial	radial force constant.

Returns

double energy.

The radial potential is given by:
    E = Kd*(d - d0)^2
The force is zero when d = d0.
Only the first model in the linked list is used.

◆ model_regularize()

int model_regularize	(	Bmodel *	model,
		int	max_iter,
		double	distance,
		double	Kdistance,
		double	Klink,
		double	Kpolyangle,
		double	Kpolygon,
		double	Kpolyplane,
		double	Kpoint,
		double	decay
	)

Regularizes a model.

Parameters

*model	model structure.
max_iter	maximum number of iterations.
distance	reference distance.
Kdistance	distance strength constant.
Klink	link strength constant.
Kpolyangle	angle strength constant.
Kpolygon	polygon regularity constant.
Kpolyplane	polygon planarity constant.
Kpoint	force away from the center-of-mass.
decay	point force decay constant.

Returns

int 0.

Only the first model in the linked list is used.

◆ model_soft_sphere_energy()

double model_soft_sphere_energy	(	Bmodel *	model,
		double	Kd,
		double	d0
	)

Calculates the soft sphere potential between components.

Parameters

*model	model structure.
Kd	distance force constant.
d0	reference distance between components.

Returns

double distance energy.

The soft sphere potential is given by:
    E = Kd*(d0/d)^12
The potential is set to zero for d > 3*d0;
Only the first model in the linked list is used.

◆ model_verlet()

double model_verlet	(	Bmodel *	model,
		double	timestep,
		double	Kfriction,
		double	velocitylimit
	)

Model dynamics using the velocity verlet integrator.

Parameters

*model	model structure.
timestep	dynamics time step.
Kfriction	friction coefficient.
velocitylimit	limit on velocity per time step.

Returns

double kinetic energy.

Leapfrog integration for any coordinate x, velocity vx and force Fx:
    x(t+1) = x(t) + vx(t+1) * dt
    vx(t+1) = (Fx(t) * dt/m + vx(t)) * kf
    where
        kf: friction constant (1=no friction)
        dt: time step
        m: atomic mass
The velocity is limited each time step to damp chaotic oscillations.
Only the first model in the linked list is used.

◆ model_zero_forces()

int model_zero_forces ( Bmodel * model )

Zeroes the component forces.

Parameters

*model model.

Returns

int number of components.

Only the first model in the linked list is used.

Variable Documentation

◆ verbose

int verbose

extern

Macros

Functions

Variables

Detailed Description

Macro Definition Documentation

◆ ETERMS

Function Documentation

◆ component_angular_potential()

◆ component_distance_potential()

◆ component_electrostatic_potential()

◆ component_harmonic_potential()

◆ component_lennard_jones_potential()

◆ component_morse_potential()

◆ component_radial_potential()

◆ component_soft_potential()

◆ model_angle_energy()

◆ model_average_linklength()

◆ model_calculate_deviations() [1/2]

◆ model_calculate_deviations() [2/2]

◆ model_distance_energy()

◆ model_electrostatic_energy()

◆ model_grid_distance_energy()

◆ model_guide_energy()

◆ model_lennard_jones_energy()

◆ model_link_energy() [1/2]

◆ model_link_energy() [2/2]

◆ model_map_energy() [1/2]

◆ model_map_energy() [2/2]

◆ model_map_gradient_energy()

◆ model_mechanics()

◆ model_minimize()

◆ model_morse_energy()

◆ model_neighbor_distance_energy()

◆ model_neighbor_plane_energy()

◆ model_point_force()

◆ model_polygon_angle_energy()

◆ model_polygon_energy() [1/2]

◆ model_polygon_energy() [2/2]

◆ model_polygon_plane_energy()

◆ model_polyhedron_guide_energy()

◆ model_radial_energy()

◆ model_regularize()

◆ model_soft_sphere_energy()

◆ model_verlet()

◆ model_zero_forces()

Variable Documentation

◆ verbose