coulomb/pairwise/schemes/

plain.rs

// Copyright 2023 Björn Stenqvist and Mikael Lund
//
// Converted to Rust with modification from the C++ library "CoulombGalore":
// https://zenodo.org/doi/10.5281/zenodo.3522058
//
// Licensed under the Apache license, version 2.0 (the "license");
// you may not use this file except in compliance with the license.
// You may obtain a copy of the license at
//
//     http://www.apache.org/licenses/license-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the license is distributed on an "as is" basis,
// without warranties or conditions of any kind, either express or implied.
// See the license for the specific language governing permissions and
// limitations under the license.

use crate::{pairwise::ShortRangeFunction, DebyeLength};

#[cfg(feature = "serde")]
use serde::{Deserialize, Deserializer, Serialize, Serializer};

/// Scheme for vanilla Coulomb interactions, $S(q)=1$.
///
/// See _Premier mémoire sur l’électricité et le magnétisme_ by Charles-Augustin de Coulomb,
/// <https://doi.org/msxd>.
#[derive(Clone, Debug, PartialEq)]
#[cfg_attr(
    feature = "serde",
    derive(Serialize, Deserialize),
    serde(deny_unknown_fields)
)]
pub struct Plain {
    /// Cut-off distance
    cutoff: f64,
    /// Optional inverse Debye length
    #[cfg_attr(
        feature = "serde",
        serde(
            rename = "debye",
            alias = "debye_length",
            alias = "debyelength",
            serialize_with = "serialize_reciprocal",
            deserialize_with = "deserialize_reciprocal",
            default
        )
    )]
    kappa: Option<f64>,
}

/// Convert from kappa to debye when serializing.
#[cfg(feature = "serde")]
fn serialize_reciprocal<S>(x: &Option<f64>, s: S) -> Result<S::Ok, S::Error>
where
    S: Serializer,
{
    match x.as_ref() {
        Some(&value) => s.serialize_some(&f64::recip(value)),
        None => s.serialize_none(),
    }
}

/// Convert from debye to kappa when serializing.
#[cfg(feature = "serde")]
fn deserialize_reciprocal<'de, D>(deserializer: D) -> Result<Option<f64>, D::Error>
where
    D: Deserializer<'de>,
{
    Ok(Option::deserialize(deserializer)?.map(f64::recip))
}

impl Default for Plain {
    /// The default is infinite cutoff radius and no screening
    fn default() -> Self {
        Self {
            cutoff: f64::INFINITY,
            kappa: None,
        }
    }
}

impl core::fmt::Display for Plain {
    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
        write!(f, "Plain Coulomb: 𝑟✂ = {:.1}", self.cutoff)?;
        if let Some(debye_length) = self.kappa.map(f64::recip) {
            write!(
                f,
                ", λᴰ = {:.1}, λᴰ/𝑟✂ = {:.1e}",
                debye_length,
                debye_length / self.cutoff
            )?;
        }
        write!(f, " <{}>", Self::url())?;
        Ok(())
    }
}

impl Plain {
    /// Create a plain Coulomb potential without a cutoff distance.
    pub fn without_cutoff() -> Self {
        Self::new(f64::INFINITY, None)
    }
    /// Create a new plain Coulomb scheme with a given cutoff and optional Debye length.
    pub fn new(cutoff: f64, debye_length: Option<f64>) -> Self {
        Self {
            cutoff,
            kappa: debye_length.map(f64::recip),
        }
    }
    /// Create a new plain Coulomb scheme with a given cutoff and no salt screening.
    pub fn new_without_salt(cutoff: f64) -> Self {
        Self::new(cutoff, None)
    }

    /// Create from medium. The Debye length is calculated from the medium's properties in units
    /// of angstrom. `cutoff` should be provided in angstrom.
    pub fn from_medium(cutoff: f64, medium: &crate::Medium) -> Self {
        Self::new(cutoff, medium.debye_length())
    }
}

impl crate::Cutoff for Plain {
    #[inline]
    fn cutoff(&self) -> f64 {
        self.cutoff
    }
}

impl DebyeLength for Plain {
    #[inline]
    fn kappa(&self) -> Option<f64> {
        self.kappa
    }
    fn set_debye_length(&mut self, debye_length: Option<f64>) -> crate::Result<()> {
        self.kappa = debye_length.map(f64::recip);
        Ok(())
    }
}

impl ShortRangeFunction for Plain {
    fn url() -> &'static str {
        "https://doi.org/msxd"
    }

    #[inline]
    fn short_range_f0(&self, _q: f64) -> f64 {
        1.0
    }
    #[inline]
    fn short_range_f1(&self, _q: f64) -> f64 {
        0.0
    }
    #[inline]
    fn short_range_f2(&self, _q: f64) -> f64 {
        0.0
    }
    #[inline]
    fn short_range_f3(&self, _q: f64) -> f64 {
        0.0
    }
}

#[test]
fn test_coulomb() {
    use super::test_utils::{assert_vec3_eq, assert_vec_x_equals_norm, assert_vec_zero};
    use crate::{NalgebraMatrix3 as Matrix3, NalgebraVector3 as Vector3};
    use approx::assert_relative_eq;

    use crate::pairwise::{MultipoleEnergy, MultipoleField, MultipoleForce, MultipolePotential};
    let cutoff: f64 = 29.0;
    let z1 = 2.0;
    let z2 = 3.0;
    let mu1 = Vector3::new(19.0, 7.0, 11.0);
    let mu2 = Vector3::new(13.0, 17.0, 5.0);
    let quad1 = Matrix3::new(3.0, 7.0, 8.0, 5.0, 9.0, 6.0, 2.0, 1.0, 4.0);
    let _quad2 = Matrix3::zeros();
    let r = Vector3::new(23.0, 0.0, 0.0);
    let rq = Vector3::new(
        5.75 * (6.0f64).sqrt(),
        5.75 * (2.0f64).sqrt(),
        11.5 * (2.0f64).sqrt(),
    );
    let rh = Vector3::new(1.0, 0.0, 0.0);

    let pot = Plain::new(cutoff, None);
    let eps = 1e-9;

    assert_eq!(
        pot.to_string(),
        "Plain Coulomb: 𝑟✂ = 29.0 <https://doi.org/msxd>"
    );

    // Test short-ranged function
    assert_eq!(pot.short_range_f0(0.5), 1.0);
    assert_eq!(pot.short_range_f1(0.5), 0.0);
    assert_eq!(pot.short_range_f2(0.5), 0.0);
    assert_eq!(pot.short_range_f3(0.5), 0.0);

    // Test potentials
    assert_eq!(pot.ion_potential(z1, cutoff + 1.0), 0.0);
    assert_relative_eq!(
        pot.ion_potential(z1, r.norm()),
        0.08695652173913043,
        epsilon = eps
    );
    assert_relative_eq!(
        pot.dipole_potential(mu1, (cutoff + 1.0) * rh),
        0.0,
        epsilon = eps
    );
    assert_relative_eq!(
        pot.dipole_potential(mu1, r),
        0.035916824196597356,
        epsilon = eps
    );
    assert_relative_eq!(
        pot.quadrupole_potential(quad1, rq),
        0.00093632817,
        epsilon = eps
    );

    // Test fields
    assert_vec_zero!(pot.ion_field(z1, (cutoff + 1.0) * rh), eps);
    assert_vec_x_equals_norm!(pot.ion_field(z1, r), 0.003780718336, eps);
    assert_vec_zero!(pot.dipole_field(mu1, (cutoff + 1.0) * rh), eps);
    assert_vec3_eq!(
        pot.dipole_field(mu1, r),
        [0.003123202104, -0.0005753267034, -0.0009040848196],
        eps
    );
    assert_vec3_eq!(
        pot.quadrupole_field(quad1, r),
        [-0.00003752130674, -0.00006432224013, -0.00005360186677],
        eps
    );

    // Test energies
    assert_relative_eq!(pot.ion_ion_energy(z1, z2, cutoff + 1.0), 0.0, epsilon = eps);
    assert_relative_eq!(
        pot.ion_ion_energy(z1, z2, r.norm()),
        z1 * z2 / r.norm(),
        epsilon = eps
    );
    assert_relative_eq!(
        pot.ion_dipole_energy(z1, mu2, (cutoff + 1.0) * rh),
        -0.0,
        epsilon = eps
    );
    assert_relative_eq!(
        pot.ion_dipole_energy(z1, mu2, r),
        -0.04914933837,
        epsilon = eps
    );
    assert_relative_eq!(
        pot.dipole_dipole_energy(mu1, mu2, (cutoff + 1.0) * rh),
        -0.0,
        epsilon = eps
    );
    assert_relative_eq!(
        pot.dipole_dipole_energy(mu1, mu2, r),
        -0.02630064930,
        epsilon = eps
    );
    assert_relative_eq!(
        pot.ion_quadrupole_energy(z2, quad1, rq),
        0.002808984511,
        epsilon = eps
    );

    // Test forces
    assert_vec_zero!(pot.ion_ion_force(z1, z2, (cutoff + 1.0) * rh), eps);
    assert_vec_x_equals_norm!(pot.ion_ion_force(z1, z2, r), 0.01134215501, eps);
    assert_vec_zero!(pot.ion_dipole_force(z2, mu1, (cutoff + 1.0) * rh), eps);
    assert_vec3_eq!(
        pot.ion_dipole_force(z2, mu1, r),
        [0.009369606312, -0.001725980110, -0.002712254459],
        eps
    );
    assert_vec_zero!(pot.dipole_dipole_force(mu1, mu2, (cutoff + 1.0) * rh), eps);
    assert_vec3_eq!(
        pot.dipole_dipole_force(mu1, mu2, r),
        [0.003430519474, -0.004438234569, -0.002551448858],
        eps
    );

    // Now test with a non-zero kappa
    let pot = Plain::new(cutoff, Some(23.0));

    assert_eq!(
        pot.to_string(),
        "Plain Coulomb: 𝑟✂ = 29.0, λᴰ = 23.0, λᴰ/𝑟✂ = 7.9e-1 <https://doi.org/msxd>"
    );

    assert_relative_eq!(pot.ion_potential(z1, cutoff + 1.0), 0.0, epsilon = eps);
    assert_relative_eq!(
        pot.ion_potential(z1, r.norm()),
        0.03198951663,
        epsilon = eps
    );
    assert_relative_eq!(
        pot.dipole_potential(mu1, (cutoff + 1.0) * rh),
        0.0,
        epsilon = eps
    );
    assert_relative_eq!(pot.dipole_potential(mu1, r), 0.02642612243, epsilon = eps);

    // Test fields
    assert_vec_zero!(pot.ion_field(z1, (cutoff + 1.0) * rh), eps);
    assert_vec_x_equals_norm!(pot.ion_field(z1, r), 0.002781697098, eps);
    assert_vec_zero!(pot.dipole_field(mu1, (cutoff + 1.0) * rh), eps);

    let field_scalar = pot.ion_field_scalar(z1, r.norm());
    let field: Vector3 = pot.ion_field(z1, r).into();
    assert_relative_eq!(field_scalar, field.norm(), epsilon = eps);

    assert_vec3_eq!(
        pot.dipole_field(mu1, r),
        [0.002872404612, -0.0004233017324, -0.0006651884364],
        eps
    );

    // Test ion-induced dipole energy
    let pot = Plain::new(cutoff, None);
    let alpha = 50.0;
    let charge = 1.0;
    let r_vec = Vector3::new(5.0, 0.0, 0.0);
    let energy = pot.ion_induced_dipole_energy(charge, alpha, r_vec);
    assert_relative_eq!(energy, -0.04, epsilon = eps);

    // Manually calculate the energy
    let r4 = r_vec.norm_squared().powi(2);
    assert_relative_eq!(energy, -0.5 * charge * charge * alpha / r4, epsilon = eps);

    // with non-zero kappa
    let pot = Plain::new(cutoff, Some(10.0));
    let energy = pot.ion_induced_dipole_energy(charge, alpha, r_vec);
    assert_relative_eq!(energy, -0.0331091497054298, epsilon = eps);
}

#[cfg(feature = "uom")]
#[test]
fn test_plain_si() {
    use crate::{
        pairwise::{MultipoleEnergySI, MultipoleFieldSI, MultipolePotentialSI},
        units::*,
    };
    use approx::assert_relative_eq;
    let eps = 1e-9; // Set epsilon for approximate equality
    let pot = Plain::without_cutoff();
    let z1 = ElectricCharge::new::<elementary_charge>(2.0);
    let z2 = ElectricCharge::new::<elementary_charge>(3.0);
    let r = Length::new::<nanometer>(2.3);
    let energy = pot.ion_ion_energy(z1, z2, r);
    assert_relative_eq!(
        energy.get::<kilojoule_per_mole>(),
        362.4403242896922,
        epsilon = eps
    );
    let potential = pot.ion_potential(z1, r);
    assert_relative_eq!(potential.get::<volt>(), 1.2521430850804929, epsilon = eps);

    let field = pot.ion_field(z1, r);
    assert_relative_eq!(
        field.get::<volt_per_micrometer>(),
        544.4100369915187,
        epsilon = eps
    );
}