Struct SalvatDhfs 

pub struct SalvatDhfs { /* private fields */ }

The three-term analytic screening function of Salvat, Martinez, Mayol & Parellada, Phys. Rev. A 36, 467 (1987), doi:10.1103/PhysRevA.36.467: V(r) = -(Z/r) sum_i A_i exp(-alpha_i r) with sum_i A_i = 1 (neutral atom), r in bohr.

The form is the paper’s Eq. (11) (screening function) inserted in its Eq. (1); its Eq. (12) gives the electron density used by ElectronDensity. Both were checked (issue #91) in the open copy of the paper in the University of Barcelona repository (diposit.ub.edu; the publisher’s copy is closed). SalvatDhfs::for_element returns the paper’s Table I coefficients for Z = 1..92 (pp. 470-471, transcribed in #130, see salvat_table.rs and docs/data-provenance.md); SalvatDhfs::from_coefficients takes caller-supplied ones.

Rows marked with an asterisk in Table I (H..P, Ca, Sc, Se, Br, Kr, Xe) have A_3 = 0 and no alpha_3 (p. 471); they are held as two-term potentials, so no alpha_3 value enters ScreenedPotential::energy, ElectronDensity::density or ScreenedPotential::length_scale.

Some amplitudes are negative (H, He: A_1; S, Cl, Ar: A_2). For H (A_1 = -184.39, A_2 = 185.39, nearly equal alphas) the two terms cancel to about 1 part in 370 near the nucleus, so phi(r) there keeps roughly 13 significant digits in f64 rather than 16.

Implementations

impl SalvatDhfs

pub fn from_coefficients( z: u32, a: [f64; 3], alpha: [f64; 3], ) -> Result<Self, ElasticError>

Build from caller-supplied coefficients (a dimensionless summing to 1 within 1e-6, alpha in 1/bohr and positive).

pub fn from_two_terms( z: u32, a: [f64; 2], alpha: [f64; 2], ) -> Result<Self, ElasticError>

Build a two-term potential (A_3 = 0, the form of the asterisked rows of Salvat et al. (1987) Table I): a sums to 1 within 1e-6, alpha in 1/bohr and positive.

pub fn for_element(z: u32) -> Result<Self, ElasticError>

The Salvat et al. (1987) Table I potential of element z (pp. 470-471, A_3 = 1 - A_1 - A_2; two-term for the asterisked rows). ElasticError::ScreeningCoefficientsUnavailable outside Z = 1..92.

pub fn amplitudes(&self) -> &[f64]

Amplitudes A_i of the terms in use (2 or 3).

pub fn alphas(&self) -> &[f64]

Screening constants alpha_i (1/bohr) of the terms in use (2 or 3).

Trait Implementations

impl Clone for SalvatDhfs

fn clone(&self) -> SalvatDhfs

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for SalvatDhfs

impl Debug for SalvatDhfs

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl ElectronDensity for SalvatDhfs

Poisson density of the analytic screening function, Salvat et al. (1987) Eq. (12): rho(r) = (Z/(4 pi r)) sum_i A_i alpha_i^2 exp(-alpha_i r), summed over the terms in use (two for the asterisked, A_3 = 0 rows of Table I).

fn density(&self, r: f64) -> f64

Electron number density at radius r bohr, electrons per bohr^3 (>= 0).

fn density_source(&self) -> String

Where the density comes from (recorded in the result metadata).

impl PartialEq for SalvatDhfs

fn eq(&self, other: &SalvatDhfs) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl ScreenedPotential for SalvatDhfs

fn energy(&self, r: f64) -> f64

Potential energy V(r) of the electron, hartree, at radius r bohr. Attractive potentials are negative.

fn nuclear_charge(&self) -> f64

Coefficient Z of the point-Coulomb singularity V -> -Z/r at the origin (0 for a regular potential). Selects the series used to start the integration.

fn length_scale(&self) -> f64

A length over which V changes appreciably, bohr. It caps the step.

fn breakpoints(&self) -> Vec<f64>

Radii at which V is discontinuous; the integrator restarts there.

fn bound_energy_ev(&self) -> Option<f64>

The kinetic energy (eV) this potential was built for, when it depends on one (such as CorrectedPotential, whose exchange and polarization cutoff use the energy). ElasticSolver::new rejects any other solver energy. The default, None, accepts every energy.

fn correction_metadata(&self) -> CorrectionMetadata

Which corrections the potential includes; copied into ElasticResult::corrections by solve. The default reports both off.

fn matching_radius(&self, threshold: f64) -> f64

Radius beyond which the potential is neglected: the smallest radius on a geometric grid (ratio 1.05, from length_scale) with |r V(r)| < threshold that also lies beyond every breakpoint.

impl StructuralPartialEq for SalvatDhfs