Electrostatics

Potential types

NESSie.PotentialType — Type

abstract type PotentialType end
struct SingleLayer <: PotentialType end
struct DoubleLayer <: PotentialType end

Enum-like representation of single and double layer potentials

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NESSie.SingleLayer — Type

abstract type PotentialType end
struct SingleLayer <: PotentialType end
struct DoubleLayer <: PotentialType end

Enum-like representation of single and double layer potentials

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NESSie.DoubleLayer — Type

abstract type PotentialType end
struct SingleLayer <: PotentialType end
struct DoubleLayer <: PotentialType end

Enum-like representation of single and double layer potentials

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Locality assumption

NESSie.LocalityType — Type

abstract type LocalityType end
struct NonlocalES <: LocalityType end
struct LocalES    <: LocalityType end

Enum-like representation of locality assumption:

Local electrostatics: Complete independence of solvent molecules
Nonlocal electrostatics: Allow solvent molecule correlation effects (with area-of-effect radius λ)

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NESSie.LocalES — Type

abstract type LocalityType end
struct NonlocalES <: LocalityType end
struct LocalES    <: LocalityType end

Enum-like representation of locality assumption:

Local electrostatics: Complete independence of solvent molecules
Nonlocal electrostatics: Allow solvent molecule correlation effects (with area-of-effect radius λ)

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NESSie.NonlocalES — Type

abstract type LocalityType end
struct NonlocalES <: LocalityType end
struct LocalES    <: LocalityType end

Enum-like representation of locality assumption:

Local electrostatics: Complete independence of solvent molecules
Nonlocal electrostatics: Allow solvent molecule correlation effects (with area-of-effect radius λ)

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Potentials

Molecular potentials

NESSie.φmol — Function

φmol(
    ξ        ::Vector{T},
    charges  ::Vector{Charge{T}};
    # kwargs
    tolerance::T                 = T(1e-10)
)

Computes and returns the molecular potential of the given system of point charges in a structureless medium for the given observation point ξ:

\[φ_{mol}(ξ) = \frac{1}{4π ε_0 ε_Ω} \sum_i \frac{qᵢ}{|rᵢ-ξ|}\]

If $|rᵢ-ξ|$ is smaller than the given tolerance, the value is replaced by tolerance for the affected charge.

Note

The return value is premultiplied by $4π ⋅ ε₀ ⋅ ε_Ω$

Return type

T

Aliases

φmol{T}(
    Ξ        ::Vector{Vector{T}},
    charges  ::Vector{Charge{T}};
    # kwargs
    tolerance::T                 = T(1e-10)
)

Computes the molecular potentials for a list of observation points.

φmol{T}(
    model    ::Model{T, Triangle{T}};
    # kwargs
    tolerance::T                     = T(1e-10)
)

Computes the molecular potentials for the given surface model, using each triangle center as observation point.

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NESSie.∂ₙφmol — Function

∂ₙφmol(ξ::Triangle{T}, charges::Vector{Charge{T}})

Computes and returns the normal derivative of the given system's molecular potential in a structureless medium, using the given triangle's center as observation point and the triangle's normal as reference normal.

\[∂ₙφ_{mol}(ξ) = -\frac{1}{4π ε_0 ε_Ω} \sum_i \frac{qᵢ}{|rᵢ-ξ|³} (rᵢ-ξ) ⋅ n\]

Note

The return value is premultiplied by $4π ⋅ ε₀ ⋅ ε_Ω$

Return type

T

Aliases

∂ₙφmol(model::Model{T, Triangle{T}})

Computes the normal derivatives of the molecular potentials for the given surface model, using each triangle center and normal as observation point.

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NESSie.∇φmol — Function

∇φmol(ξ::Vector{T}, charges::Vector{Charge{T}})

Computes and returns the gradient of the given system's molecular potential in a structureless medium for the given observation point ξ.

\[∇φ_{mol}(ξ) = -\frac{1}{4π ε_0 ε_Ω} \sum_i \frac{qᵢ}{|rᵢ-ξ|³} (rᵢ-ξ)\]

Note

The return value is premultiplied by $4π ⋅ ε₀ ⋅ ε_Ω$

Return type

Vector{T}

Aliases

∇φmol(Ξ::Vector{Vector{T}})

Computes the molecular potential gradients for a list of observation points.

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Interior potentials

NESSie.BEM.φΩ — Function

φΩ(
    Ξ         ::Vector{Vector{T}},
    bem       ::BEMResult{T}
)

Computes the local or nonlocal interior electrostatic potential $φ_Ω$ for the given set of observation points Ξ.

Warning

This function does not verify whether all points in Ξ are located in $Ω$!

Unit

$V = \frac{C}{F}$

Return type

Vector{T}

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NESSie.TestModel.φΩ — Function

φΩ(
       ::Type{<: LocalityType},
    ξ  ::Vector{T},
    ion::BornIon{T},
    opt::Option{T} = defaultopt(T)
)

Computes the interior local or nonlocal electrostatic potential $φ_Ω$ for the given observation point $ξ$.

Unit

$V = \frac{C}{F}$

Return type

T

Warning

This function does not verify whether ξ is located inside of the sphere!

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function φΩ(
    ξ    ::Vector{T},
    model::NonlocalXieModel1{T}
)

Computes the interior nonlocal electrostatic potential $φ_Ω$ for the given observation point $ξ$.

Unit

$V = \frac{C}{F}$

Return type

T

Warning

This function does not verify whether ξ is located inside of the sphere!

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Exterior potentials

NESSie.BEM.φΣ — Function

φΣ(
    Ξ         ::Vector{Vector{T}},
    bem       ::BEMResult{T}
)

Computes the local or nonlocal exterior electrostatic potential $φ_Σ$ for the given set of observation points Ξ.

Warning

This function does not verify whether all points in Ξ are located in $Σ$!

Unit

$V = \frac{C}{F}$

Return type

Vector{T}

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NESSie.TestModel.φΣ — Function

φΣ(
       ::Type{<: LocalityType},
    ξ  ::Vector{T},
    ion::BornIon{T},
    opt::Option{T} = defaultopt(T)
)

Computes the exterior local or nonlocal electrostatic potential $φ_Σ$ for the given observation point $ξ$.

Unit

$V = \frac{C}{F}$

Return type

T

Warning

This function does not verify whether ξ is located outside of the sphere!

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function φΣ(
    ξ    ::Vector{T},
    model::NonlocalXieModel1{T}
)

Computes the exterior nonlocal electrostatic potential $φ_Σ$ for the given observation point $ξ$.

Unit

$V = \frac{C}{F}$

Return type

T

Warning

This function does not verify whether ξ is located outside of the sphere!

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Energies

NESSie.BEM.rfenergy — Function

rfenergy(::BEMResult{T})

Computes the local or nonlocal reaction field energy W* as

\[W^* = ∫φ^* ρ \quad dΩ\]

where $φ^*$ is the reaction field and $ρ$ is the corresponding charge distribution.

Unit

$\frac{kJ}{mol}$

Return type

T

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