Struct SlaterDeterminantSymmetryOrbit

pub struct SlaterDeterminantSymmetryOrbit<'a, G, T, SC>
where
    G: SymmetryGroupProperties,
    T: ComplexFloat + Debug + Lapack,
    SC: StructureConstraint + Display,
    SlaterDeterminant<'a, T, SC>: SymmetryTransformable,
{ /* private fields */ }

Structure to manage symmetry orbits (i.e. orbits generated by symmetry groups) of Slater determinants.

Implementations

impl<'a, G, T, SC> SlaterDeterminantSymmetryOrbit<'a, G, T, SC>

where G: SymmetryGroupProperties + Clone, T: ComplexFloat + Debug + Lapack, SC: StructureConstraint + Clone + Display, SlaterDeterminant<'a, T, SC>: SymmetryTransformable,

pub fn builder() -> SlaterDeterminantSymmetryOrbitBuilder<'a, G, T, SC>

Returns a builder for constructing a new Slater determinant symmetry orbit.

impl<'a, G, T, SC> SlaterDeterminantSymmetryOrbit<'a, G, T, SC>

where G: SymmetryGroupProperties, T: ComplexFloat + Debug + Lapack, SC: StructureConstraint + Display, SlaterDeterminant<'a, T, SC>: SymmetryTransformable,

pub fn action( &self, ) -> fn(&G::GroupElement, &SlaterDeterminant<'a, T, SC>) -> Result<SlaterDeterminant<'a, T, SC>, Error>

impl<'a, G, SC> SlaterDeterminantSymmetryOrbit<'a, G, f64, SC>

where G: SymmetryGroupProperties, SC: StructureConstraint + Display, SlaterDeterminant<'a, f64, SC>: SymmetryTransformable,

pub fn calc_xmat( &mut self, preserves_full_rank: bool, ) -> Result<&mut Self, Error>

Calculates the $\mathbf{X}$ matrix for real and symmetric overlap matrix $\mathbf{S}$ between the symmetry-equivalent Slater determinants in the orbit.

The resulting $\mathbf{X}$ is stored in the orbit.

Arguments

• preserves_full_rank - If true, when $\mathbf{S}$ is already of full rank, then $\mathbf{X}$ is set to be the identity matrix to avoid mixing the orbit determinants. If false, $\mathbf{X}$ also orthogonalises $\mathbf{S}$ even when it is already of full rank.

impl<'a, G, T, SC> SlaterDeterminantSymmetryOrbit<'a, G, Complex<T>, SC>

where G: SymmetryGroupProperties, T: Float + Scalar<Complex = Complex<T>>, Complex<T>: ComplexFloat<Real = T> + Scalar<Real = T, Complex = Complex<T>> + Lapack, SC: StructureConstraint + Display, SlaterDeterminant<'a, Complex<T>, SC>: SymmetryTransformable + Overlap<Complex<T>, Ix2>,

pub fn calc_xmat( &mut self, preserves_full_rank: bool, ) -> Result<&mut Self, Error>

Calculates the $\mathbf{X}$ matrix for complex and symmetric or Hermitian overlap matrix $\mathbf{S}$ between the symmetry-equivalent Slater determinants in the orbit.

The resulting $\mathbf{X}$ is stored in the orbit.

Arguments

• preserves_full_rank - If true, when $\mathbf{S}$ is already of full rank, then $\mathbf{X}$ is set to be the identity matrix to avoid mixing the orbit determinants. If false, $\mathbf{X}$ also orthogonalises $\mathbf{S}$ even when it is already of full rank.

Trait Implementations

impl<'a, G, T, SC> Clone for SlaterDeterminantSymmetryOrbit<'a, G, T, SC>

where G: SymmetryGroupProperties + Clone, T: ComplexFloat + Debug + Lapack + Clone, SC: StructureConstraint + Display + Clone, SlaterDeterminant<'a, T, SC>: SymmetryTransformable,

fn clone(&self) -> SlaterDeterminantSymmetryOrbit<'a, G, T, SC>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<'a, G, T, SC> Orbit<G, SlaterDeterminant<'a, T, SC>> for SlaterDeterminantSymmetryOrbit<'a, G, T, SC>

where G: SymmetryGroupProperties, T: ComplexFloat + Debug + Lapack, SC: StructureConstraint + Display, SlaterDeterminant<'a, T, SC>: SymmetryTransformable,

type OrbitIter = OrbitIterator<'a, G, SlaterDeterminant<'a, T, SC>>

Type of the iterator over items in the orbit.

fn group(&self) -> &G

The group generating the orbit.

fn origin(&self) -> &SlaterDeterminant<'a, T, SC>

The origin of the orbit.

fn iter(&self) -> Self::OrbitIter

An iterator over items in the orbit arising from the action of the group on the origin.

impl<'a, G> Projectable<G, SlaterDeterminant<'a, Complex<f64>, SpinConstraint>> for SlaterDeterminantSymmetryOrbit<'a, G, Complex<f64>, SpinConstraint>

where G: SymmetryGroupProperties + Clone,

type Projected<'p> = Result<MultiDeterminant<'p, Complex<f64>, OrbitBasis<'p, G, SlaterDeterminant<'p, Complex<f64>, SpinConstraint>>, SpinConstraint>, Error> where Self: 'p

The type of the result of the projection.

fn project_onto(&self, row: &G::RowSymbol) -> Self::Projected<'_>

Projects the orbit onto a symmetry subspace.

fn generate_orbit_algebra_terms<'a>( &'a self, row: &G::RowSymbol, ) -> impl Iterator<Item = Result<(&'a Character, I), Error>>

where I: 'a, G: 'a,

Returns an iterator containing each term in the projection summation and the accompanying character value (without complex conjugation).

impl<'a, G> Projectable<G, SlaterDeterminant<'a, Complex<f64>, SpinOrbitCoupled>> for SlaterDeterminantSymmetryOrbit<'a, G, Complex<f64>, SpinOrbitCoupled>

where G: SymmetryGroupProperties + Clone,

type Projected<'p> = Result<MultiDeterminant<'p, Complex<f64>, OrbitBasis<'p, G, SlaterDeterminant<'p, Complex<f64>, SpinOrbitCoupled>>, SpinOrbitCoupled>, Error> where Self: 'p

The type of the result of the projection.

fn project_onto(&self, row: &G::RowSymbol) -> Self::Projected<'_>

Projects the orbit onto a symmetry subspace.

fn generate_orbit_algebra_terms<'a>( &'a self, row: &G::RowSymbol, ) -> impl Iterator<Item = Result<(&'a Character, I), Error>>

where I: 'a, G: 'a,

Returns an iterator containing each term in the projection summation and the accompanying character value (without complex conjugation).

impl<'a, G> Projectable<G, SlaterDeterminant<'a, f64, SpinConstraint>> for SlaterDeterminantSymmetryOrbit<'a, G, f64, SpinConstraint>

where G: SymmetryGroupProperties + Clone,

type Projected<'p> = Result<MultiDeterminant<'p, f64, OrbitBasis<'p, G, SlaterDeterminant<'p, f64, SpinConstraint>>, SpinConstraint>, Error> where Self: 'p

The type of the result of the projection.

fn project_onto(&self, row: &G::RowSymbol) -> Self::Projected<'_>

Projects the orbit onto a symmetry subspace.

fn generate_orbit_algebra_terms<'a>( &'a self, row: &G::RowSymbol, ) -> impl Iterator<Item = Result<(&'a Character, I), Error>>

where I: 'a, G: 'a,

Returns an iterator containing each term in the projection summation and the accompanying character value (without complex conjugation).

impl<'a, G, T, SC> RepAnalysis<G, SlaterDeterminant<'a, T, SC>, T, Dim<[usize; 2]>> for SlaterDeterminantSymmetryOrbit<'a, G, T, SC>

where G: SymmetryGroupProperties, G::CharTab: SubspaceDecomposable<T>, T: Lapack + ComplexFloat<Real = <T as Scalar>::Real> + Debug + Mul<<T as ComplexFloat>::Real, Output = T>, <T as ComplexFloat>::Real: Debug + Zero + From<u16> + ToPrimitive + RelativeEq<<T as ComplexFloat>::Real> + AbsDiffEq<Epsilon = <T as Scalar>::Real>, SC: StructureConstraint + Eq + Display, SlaterDeterminant<'a, T, SC>: SymmetryTransformable,

fn analyse_rep( &self, ) -> Result<<<G as CharacterProperties>::CharTab as SubspaceDecomposable<T>>::Decomposition, DecompositionError>

Reduces the representation or corepresentation spanned by the determinants in the orbit to a direct sum of the irreducible representations or corepresentations of the generating symmetry group.

Returns

The decomposed result.

Errors

Errors if the decomposition fails, e.g. because one or more calculated multiplicities are non-integral, or also because the combination of group type, transformation type, and oddity of the number of electrons would not give sensible symmetry results. In particular, spin or spin-spatial symmetry analysis of odd-electron systems in unitary-represented magnetic groups is not valid.

fn set_smat(&mut self, smat: Array2<T>)

Sets the overlap matrix between the items in the orbit.

fn smat(&self) -> Option<&Array2<T>>

Returns the overlap matrix between the items in the orbit.

fn xmat(&self) -> &Array2<T>

Returns the transformation matrix $\mathbf{X}$ for the overlap matrix $\mathbf{S}$ between the items in the orbit.

fn norm_preserving_scalar_map(&self, i: usize) -> Result<fn(T) -> T, Error>

Returns the norm-preserving scalar map $f$ for every element of the generating group defined by

fn integrality_threshold(&self) -> <T as ComplexFloat>::Real

Returns the threshold for integrality checks of irreducible representation or corepresentation multiplicities.

fn eigenvalue_comparison_mode(&self) -> &EigenvalueComparisonMode

Returns the enumerated type specifying the comparison mode for filtering out orbit overlap eigenvalues.

fn calc_smat( &mut self, metric: Option<&Array<T, D>>, metric_h: Option<&Array<T, D>>, use_cayley_table: bool, ) -> Result<&mut Self, Error>

Calculates and stores the overlap matrix between items in the orbit, with respect to a metric of the basis in which these items are expressed.

fn normalise_smat(&mut self) -> Result<&mut Self, Error>

Normalises overlap matrix between items in the orbit such that its diagonal entries are unity.

fn calc_tmat(&self, op: &G::GroupElement) -> Result<Array2<T>, Error>

Computes the $\mathbf{T}(g)$ matrix for a particular element $g$ of the generating group.

fn calc_dmat(&self, op: &G::GroupElement) -> Result<Array2<T>, Error>

Computes the representation or corepresentation matrix $\mathbf{D}(g)$ for a particular element $g$ in the generating group in the basis of the orbit.

fn calc_character(&self, op: &G::GroupElement) -> Result<T, Error>

Computes the character of a particular element $g$ in the generating group in the basis of the orbit.

fn calc_characters( &self, ) -> Result<Vec<(<G as ClassProperties>::ClassSymbol, T)>, Error>

Computes the characters of the elements in a conjugacy-class transversal of the generating group in the basis of the orbit.

fn characters_to_string( &self, chis: &[(<G as ClassProperties>::ClassSymbol, T)], integrality_threshold: <T as ComplexFloat>::Real, ) -> String

where T: ComplexFloat + Lapack + Debug, <T as ComplexFloat>::Real: ToPrimitive,

Converts a slice of tuples of class symbols and characters to a nicely formatted table.