Environment¶

Classes for the solvent environment overlay

Cavity¶

class Cavity : public mrcpp::RepresentableFunction<3>¶

Interlocking spheres cavity centered on the nuclei of the molecule. The Cavity class represents the following function Fosso-Tande2013.

\[\begin{split} C(\mathbf{r}) = 1 - \prod^N_{i=1} (1-C_i(\mathbf{r})) \\ C_i(\mathbf{r}) = 1 - \frac{1}{2}\left( 1 + \textrm{erf}\left(\frac{|\mathbf{r} - \mathbf{r}_i| - R_i}{\sigma_i}\right) \right) \end{split}\]

where \(\mathbf{r}\) is the coordinate of a point in 3D space, \(\mathbf{r}_i\) is the coordinate of the i-th nucleus, \(R_i\) is the radius of the i-th sphere, and \(\sigma_i\) is the width of the transition between the inside and outside of the cavity. The transition has a sigmoidal shape, such that the boundary is a smooth function instead of sharp boundaries often seen in other continuum models. This function is \(1\) inside and \(0\) outside the cavity.

The radii are computed as:

\[ R_{i} = \alpha_{i} R_{0,i} + \beta_{i}\sigma_{i} \]

where:

\(R_{0,i}\) is the atomic radius. By default, the van der Waals radius.
\(\alpha_{i}\) is a scaling factor. By default, 1.1
\(\beta_{i}\) is a width scaling factor. By default, 0.5
\(\sigma_{i}\) is the width. By default, 0.2

Public Functions

Cavity(const std::vector<mrcpp::Coord<3>> &coords, const std::vector<double> &R, const std::vector<double> &alphas, const std::vector<double> &betas, const std::vector<double> &sigmas)¶: Initializes the members of the class and constructs the analytical gradient vector of the Cavity.

Cavity(const std::vector<mrcpp::Coord<3>> &coords, const std::vector<double> &R, double sigma)¶

Initializes the members of the class and constructs the analytical gradient vector of the Cavity.

This CTOR applies a single width factor to the cavity and does not modify the radii. That is, in the formula:

\[ R_{i} = \alpha_{i} R_{0,i} + \beta_{i}\sigma_{i} \]

for every atom \(i\), \(\alpha_{i} = 1.0\) and \(\beta_{i} = 0.0\).

double evalf(const mrcpp::Coord<3> &r) const override¶

Evaluates the value of the cavity at a 3D point \(\mathbf{r}\).

Parameters: r – coordinate of 3D point at which the Cavity is to be evaluated at.
Returns: double value of the Cavity at point \(\mathbf{r}\)

inline std::vector<mrcpp::Coord<3>> getCoordinates() const¶: Returns centers.

inline std::vector<double> getOriginalRadii() const¶: Returns radii_0.

inline std::vector<double> getRadii() const¶: Returns radii.

inline std::vector<double> getRadiiScalings() const¶: Returns alphas.

inline std::vector<double> getWidths() const¶: Returns sigmas.

inline std::vector<double> getWidthScalings() const¶: Returns betas.

Protected Attributes

std::vector<double> radii_0¶: Contains the unscaled radius of each sphere in #Center.

std::vector<double> alphas¶: The radius scaling factor for each sphere.

std::vector<double> betas¶: The width scaling factor for each sphere.

std::vector<double> sigmas¶: The width for each sphere.

std::vector<double> radii¶: Contains the radius of each sphere in #Center. \(R_i = \alpha_{i} R_{0,i} + \beta_{i}\sigma_{i}\).

std::vector<mrcpp::Coord<3>> centers¶: Contains each of the spheres centered on the nuclei of the Molecule.

auto gradCavity(const mrcpp::Coord<3> &r, int index, const std::vector<mrcpp::Coord<3>> &centers, const std::vector<double> &radii, const std::vector<double> &widths) -> double¶

Constructs a single element of the gradient of the Cavity.

This constructs the analytical partial derivative of the Cavity \(C\) with respect to \(x\), \(y\) or \(z\) coordinates and evaluates it at a point \(\mathbf{r}\). This is given for \(x\) by

\[ \frac{\partial C\left(\mathbf{r}\right)}{\partial x} = \left(1 - C{\left(\mathbf{r} \right)}\right) \sum_{i=1}^{N} - \frac{\left(x-{x}_{i}\right)e^{- \frac{\operatorname{s_{i}}^{2}{\left(\mathbf{r} \right)}}{\sigma^{2}}}} {\sqrt{\pi}\sigma\left(0.5 \operatorname{erf}{\left(\frac{\operatorname{s_{i}}{\left(\mathbf{r} \right)}}{\sigma} \right)} + 0.5\right) \left| \mathbf{r} - \mathbf{r}_{i} \right|} \]

where the subscript \(i\) is the index related to each sphere in the cavity, and \(\operatorname{s}\) is the signed normal distance from the surface of each sphere.

Parameters

r – The coordinates of a test point in 3D space.
index – An integer that defines the variable of differentiation (0->x, 1->z and 2->z).
centers – A vector containing the coordinates of the centers of the spheres in the cavity.
radii – A vector containing the radii of the spheres.
width – A double value describing the width of the transition at the boundary of the spheres.

Returns

A double number which represents the value of the differential (w.r.t. x, y or z) at point r.

Permittivity¶

class Permittivity : public mrcpp::RepresentableFunction<3>¶

Permittivity function related to a substrate molecule and a solvent continuum. The Permittivity class represents the following function Fosso-Tande2013

\[ \epsilon(\mathbf{r}) = \epsilon_{in}\exp\left(\left(\log\frac{\epsilon_{out}}{\epsilon_{in}} \right) \left(1 - C(\mathbf{r})\right)\right) \]

where \(\mathbf{r}\) is the coordinate of a point in 3D space, \( C \) is the cavity function of the substrate, and \(\epsilon_{in}\) and \( \epsilon_{out} \) are the dielectric constants describing, respectively, the permittivity inside and outside the cavity of the substrate.

Public Functions

Permittivity(const Cavity cavity, double epsilon_in, double epsilon_out, std::string formulation)¶

Standard constructor. Initializes the cavity, epsilon_in and epsilon_out with the input parameters.

Parameters

cavity – interlocking spheres of Cavity class.
epsilon_in – permittivity inside the cavity.
epsilon_out – permittivity outside the cavity.
formulation – Decides which formulation of the Permittivity function to implement, only exponential available as of now.

double evalf(const mrcpp::Coord<3> &r) const override¶

Evaluates Permittivity at a point in 3D space with respect to the state of inverse.

Parameters: r – coordinates of a 3D point in space.
Returns: \(\frac{1}{\epsilon(\mathbf{r})}\) if inverse is true, and \( \epsilon(\mathbf{r})\) if inverse is false.

inline void flipFunction(bool is_inverse)¶: Changes the value of inverse.

inline auto isInverse() const¶: Returns the current state of inverse.

inline auto getCoordinates() const¶: Calls the Cavity::getCoordinates() method of the cavity instance.

inline auto getRadii() const¶: Calls the Cavity::getRadii() method of the cavity instance.

inline auto getGradVector() const¶: Calls the Cavity::getGradVector() method of the cavity instance.

inline auto getEpsIn() const¶: Returns the value of epsilon_in.

inline auto getEpsOut() const¶: Returns the value of epsilon_out.

inline Cavity getCavity() const¶: Returns the cavity.

inline std::string getFormulation() const¶: Returns the formulation.

void printParameters() const¶: Print parameters.

Private Members

bool inverse = false¶: State of evalf.

double epsilon_in¶: Dielectric constant describing the permittivity of free space.

double epsilon_out¶: Dielectric constant describing the permittivity of the solvent.

std::string formulation¶: Formulation of the permittivity function, only exponential is used as of now.

Cavity cavity¶: A Cavity class instance.

SCRF¶

class SCRF¶

class that performs the computation of the ReactionPotential, named Self Consistent Reaction Field.

Private Members

mrcpp::FunctionTreeVector<3> d_cavity¶: Vector containing the 3 partial derivatives of the cavity function.