Data Structures
struct	potential
Defines
#define	potential_err_ok 0
#define	potential_err_null -1
#define	potential_err_malloc -2
#define	potential_err_bounds -3
#define	potential_err_nyi -4
#define	potential_err_ivalsmax -5
#define	potential_degree 5
#define	potential_chunk (potential_degree+3)
#define	potential_ivalsa 1
#define	potential_ivalsb 10
#define	potential_N 100
#define	potential_align 64
#define	potential_align 64
#define	potential_ivalsmax 320
#define	potential_escale (0.079577471545947667882)
#define	potential_flag_none 0
#define	potential_flag_LJ126 1
#define	potential_flag_Ewald 2
#define	potential_flag_Coulomb 4
#define	potential_flag_single 6
Functions
void	potential_clear (struct potential *p)
	Free the memory associated with the given potential.
int	potential_init (struct potential p, double(f)(double), double(fp)(double), double(f6p)(double), FPTYPE a, FPTYPE b, FPTYPE tol)
	Construct a potential from the given function.
int	potential_getcoeffs (double(f)(double), double(fp)(double), FPTYPE xi, int n, FPTYPE c, FPTYPE *err)
	Compute the interpolation coefficients over a given set of nodes.
double	potential_getalpha (double(*f6p)(double), double a, double b)
	Compute the parameter $\alpha$ for the optimal node distribution.
struct potential *	potential_create_LJ126 (double a, double b, double A, double B, double tol)
	Creates a potential representing a 12-6 Lennard-Jones potential.
struct potential *	potential_create_LJ126_Ewald (double a, double b, double A, double B, double q, double kappa, double tol)
	Creates a potential representing the sum of a 12-6 Lennard-Jones potential and the real-space part of an Ewald potential.
struct potential *	potential_create_LJ126_Coulomb (double a, double b, double A, double B, double q, double tol)
	Creates a potential representing the sum of a 12-6 Lennard-Jones potential and a shifted Coulomb potential.
struct potential *	potential_create_Ewald (double a, double b, double q, double kappa, double tol)
	Creates a potential representing the real-space part of an Ewald potential.
struct potential *	potential_create_Coulomb (double a, double b, double q, double tol)
	Creates a potential representing a shifted Coulomb potential.
struct potential *	potential_create_harmonic (double a, double b, double K, double r0, double tol)
	Creates a harmonic bond potential.
struct potential *	potential_create_harmonic_angle (double a, double b, double K, double theta0, double tol)
	Creates a harmonic angle potential.
struct potential *	potential_create_harmonic_dihedral (double K, int n, double delta, double tol)
	Creates a harmonic dihedral potential.
double	potential_LJ126 (double r, double A, double B)
	A basic 12-6 Lennard-Jones potential.
double	potential_LJ126_p (double r, double A, double B)
	A basic 12-6 Lennard-Jones potential (first derivative).
double	potential_LJ126_6p (double r, double A, double B)
	A basic 12-6 Lennard-Jones potential (sixth derivative).
double	potential_Ewald (double r, double kappa)
	The short-range part of an Ewald summation.
double	potential_Ewald_p (double r, double kappa)
	The short-range part of an Ewald summation (first derivative).
double	potential_Ewald_6p (double r, double kappa)
	The short-range part of an Ewald summation (sixth derivative).
double	potential_Coulomb (double r)
	The Coulomb potential.
double	potential_Coulomb_p (double r)
	The Coulomb potential (first derivative).
double	potential_Coulomb_6p (double r)
	TheCoulomb potential (sixth derivative).
Variables
int	potential_err
struct potential	potential_null

Define Documentation

#define potential_align 64

#define potential_chunk (potential_degree+3)

#define potential_degree 5

#define potential_err_bounds -3

#define potential_err_ivalsmax -5

#define potential_err_malloc -2

#define potential_err_null -1

#define potential_err_nyi -4

#define potential_err_ok 0

#define potential_escale (0.079577471545947667882)

#define potential_flag_Coulomb 4

#define potential_flag_Ewald 2

#define potential_flag_LJ126 1

#define potential_flag_none 0

#define potential_flag_single 6

#define potential_ivalsa 1

#define potential_ivalsb 10

#define potential_ivalsmax 320

#define potential_N 100

Function Documentation

void potential_clear ( struct potential * p )

Free the memory associated with the given potential.

Parameters:

p	Pointer to the potential to clear.

double potential_Coulomb ( double r ) [inline]

The Coulomb potential.

Parameters:

r	The interaction radius.

Returns:: The potential $\frac{1}{4\pi r}$ evaluated at r.

double potential_Coulomb_6p ( double r ) [inline]

TheCoulomb potential (sixth derivative).

Parameters:

r	The interaction radius.

Returns:: The sixth derivative of the potential $\frac{1}{4\pi r}$ evaluated at r.

double potential_Coulomb_p ( double r ) [inline]

The Coulomb potential (first derivative).

Parameters:

r	The interaction radius.

Returns:: The first derivative of the potential $\frac{1}{4\pi r}$ evaluated at r.

struct potential* potential_create_Coulomb	(	double	a,
		double	b,
		double	q,
		double	tol
	)		`[read]`

Creates a potential representing a shifted Coulomb potential.

Parameters:

a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
q	The charge scaling of the potential.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential $\frac{1}{4\pi r}$ in or NULL on error (see potential_err).

struct potential* potential_create_Ewald	(	double	a,
		double	b,
		double	q,
		double	kappa,
		double	tol
	)		`[read]`

Creates a potential representing the real-space part of an Ewald potential.

Parameters:

a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
q	The charge scaling of the potential.
kappa	The screening distance of the Ewald potential.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential $q\frac{\mbox{erfc}(\kappa r}{r}$ in or NULL on error (see potential_err).

struct potential* potential_create_harmonic	(	double	a,
		double	b,
		double	K,
		double	r0,
		double	tol
	)		`[read]`

Creates a harmonic bond potential.

Parameters:

a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
K	The energy of the bond.
r0	The minimum energy distance.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential in or NULL on error (see potential_err).

struct potential* potential_create_harmonic_angle	(	double	a,
		double	b,
		double	K,
		double	theta0,
		double	tol
	)		`[read]`

Creates a harmonic angle potential.

Parameters:

a	The smallest angle for which the potential will be constructed.
b	The largest angle for which the potential will be constructed.
K	The energy of the angle.
theta0	The minimum energy angle.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential $K(\arccos(r)-r_0)^2$ in or NULL on error (see potential_err).

struct potential* potential_create_harmonic_dihedral	(	double	K,
		int	n,
		double	delta,
		double	tol
	)		`[read]`

Creates a harmonic dihedral potential.

Parameters:

K	The energy of the dihedral.
n	The multiplicity of the dihedral.
delta	The minimum energy dihedral.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential $K(1 + \cos(n\arccos(r)-delta)$ in or NULL on error (see potential_err).

struct potential* potential_create_LJ126	(	double	a,
		double	b,
		double	A,
		double	B,
		double	tol
	)		`[read]`

Creates a potential representing a 12-6 Lennard-Jones potential.

Parameters:

a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
A	The first parameter of the Lennard-Jones potential.
B	The second parameter of the Lennard-Jones potential.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential $\left( \frac{A}{r^{12}} - \frac{B}{r^6} \right)$ in or NULL on error (see potential_err).

struct potential* potential_create_LJ126_Coulomb	(	double	a,
		double	b,
		double	A,
		double	B,
		double	q,
		double	tol
	)		`[read]`

Creates a potential representing the sum of a 12-6 Lennard-Jones potential and a shifted Coulomb potential.

Parameters:

a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
A	The first parameter of the Lennard-Jones potential.
B	The second parameter of the Lennard-Jones potential.
q	The charge scaling of the potential.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential $\left( \frac{A}{r^{12}} - \frac{B}{r^6} \right)$ in or NULL on error (see potential_err).

struct potential* potential_create_LJ126_Ewald	(	double	a,
		double	b,
		double	A,
		double	B,
		double	q,
		double	kappa,
		double	tol
	)		`[read]`

Creates a potential representing the sum of a 12-6 Lennard-Jones potential and the real-space part of an Ewald potential.

Parameters:

a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
A	The first parameter of the Lennard-Jones potential.
B	The second parameter of the Lennard-Jones potential.
q	The charge scaling of the potential.
kappa	The screening distance of the Ewald potential.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential $\left( \frac{A}{r^{12}} - \frac{B}{r^6} \right)$ in or NULL on error (see potential_err).

double potential_Ewald	(	double	r,
		double	kappa
	)		`[inline]`

The short-range part of an Ewald summation.

Parameters:

r	The interaction radius.
kappa	The screening length of the Ewald summation.

Returns:: The potential $\frac{\mbox{erfc}( \kappa r )}{r}$ evaluated at r.

double potential_Ewald_6p	(	double	r,
		double	kappa
	)		`[inline]`

The short-range part of an Ewald summation (sixth derivative).

Parameters:

r	The interaction radius.
kappa	The screening length of the Ewald summation.

Returns:: The sixth derivative of the potential $\frac{\mbox{erfc}( \kappa r )}{r}$ evaluated at r.

double potential_Ewald_p	(	double	r,
		double	kappa
	)		`[inline]`

The short-range part of an Ewald summation (first derivative).

Parameters:

r	The interaction radius.
kappa	The screening length of the Ewald summation.

Returns:: The first derivative of the potential $\frac{\mbox{erfc}( \kappa r )}{r}$ evaluated at r.

double potential_getalpha	(	double(*)(double)	f6p,
		double	a,
		double	b
	)

Compute the parameter $\alpha$ for the optimal node distribution.

Parameters:

f6p	Pointer to a function representing the 6th derivative of the interpoland.
a	Left limit of the interpolation.
b	Right limit of the interpolation.

Returns:: The computed value for $\alpha$ .

The value $\alpha$ is computed using Brent's algortihm to 4 decimal digits.

int potential_getcoeffs	(	double(*)(double)	f,
		double(*)(double)	fp,
		FPTYPE *	xi,
		int	n,
		FPTYPE *	c,
		FPTYPE *	err
	)

Compute the interpolation coefficients over a given set of nodes.

Parameters:

f	Pointer to the function to be interpolated.
fp	Pointer to the first derivative of `f`.
xi	Pointer to an array of nodes between whicht the function `f` will be interpolated.
n	Number of nodes in `xi`.
c	Pointer to an array in which to store the interpolation coefficients.
err	Pointer to a floating-point value in which an approximation of the interpolation error, relative to the maximum of f in each interval, is stored.

Returns:: potential_err_ok or < 0 on error (see potential_err).

Compute the coefficients of the function f with derivative fp over the n intervals between the xi and store an estimate of the maximum locally relative interpolation error in err.

The array to which c points must be large enough to hold at least potential_degree x n values of type #FPTYPE.

int potential_init	(	struct potential *	p,
		double(*)(double)	f,
		double(*)(double)	fp,
		double(*)(double)	f6p,
		FPTYPE	a,
		FPTYPE	b,
		FPTYPE	tol
	)

Construct a potential from the given function.

Parameters:

p	A pointer to an empty potential.
f	A pointer to the potential function to be interpolated.
fp	A pointer to the first derivative of `f`.
f6p	A pointer to the sixth derivative of `f`.
a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
tol	The absolute tolerance to which the interpolation should match the exact potential.

Returns:: potential_err_ok or <0 on error (see potential_err).

Computes an interpolated potential function from f in [a,b] to the locally relative tolerance tol.

The sixth derivative f6p is used to compute the optimal node distribution. If f6p is NULL, the derivative is approximated numerically.

The zeroth interval contains a linear extension of f for values < a.

double potential_LJ126	(	double	r,
		double	A,
		double	B
	)		`[inline]`

A basic 12-6 Lennard-Jones potential.

Parameters:

r	The interaction radius.
A	First parameter of the potential.
B	Second parameter of the potential.

Returns:: The potential $\left( \frac{A}{r^{12}} - \frac{B}{r^6} \right)$ evaluated at r.

double potential_LJ126_6p	(	double	r,
		double	A,
		double	B
	)		`[inline]`

A basic 12-6 Lennard-Jones potential (sixth derivative).

Parameters:

r	The interaction radius.
A	First parameter of the potential.
B	Second parameter of the potential.

Returns:: The sixth derivative of the potential $\left( \frac{A}{r^{12}} - \frac{B}{r^6} \right)$ evaluated at r.

double potential_LJ126_p	(	double	r,
		double	A,
		double	B
	)		`[inline]`

A basic 12-6 Lennard-Jones potential (first derivative).

Parameters:

r	The interaction radius.
A	First parameter of the potential.
B	Second parameter of the potential.

Returns:: The first derivative of the potential $\left( \frac{A}{r^{12}} - \frac{B}{r^6} \right)$ evaluated at r.

Variable Documentation

int potential_err

ID of the last error.

The last error

struct potential potential_null

Fictitious null potential.

Data Structures

Defines

Functions

Variables

Define Documentation

Function Documentation

Variable Documentation