Struct qsym2::target::determinant::SlaterDeterminant

pub struct SlaterDeterminant<'a, T>
where
    T: ComplexFloat + Lapack,
{ /* private fields */ }

Structure to manage single-determinantal wavefunctions.

Implementations

impl<'a, T> SlaterDeterminant<'a, T>

where T: ComplexFloat + Clone + Lapack,

pub fn builder() -> SlaterDeterminantBuilder<'a, T>

Returns a builder to construct a new SlaterDeterminant.

pub fn complex_symmetric(&self) -> bool

Returns the complex-symmetric flag of the determinant.

pub fn spin_constraint(&self) -> &SpinConstraint

Returns the spin constraint imposed on the coefficients.

pub fn bao(&self) -> &BasisAngularOrder<'_>

Returns the basis angular order information of the basis set in which the coefficients are expressed.

pub fn mol(&self) -> &Molecule

Returns the molecule associated with this Slater determinant.

pub fn energy(&self) -> Result<&T, &String>

Returns the determinantal energy.

pub fn mo_energies(&self) -> Option<&Vec<Array1<T>>>

Returns the molecular-orbital energies.

pub fn occupations(&self) -> &Vec<Array1<<T as ComplexFloat>::Real>>

Returns the occupation patterns of the molecular orbitals.

pub fn coefficients(&self) -> &Vec<Array2<T>>

Returns a shared reference to a vector of coefficient arrays.

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

Returns the threshold with which determinants are compared.

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

where <T as ComplexFloat>::Real: Sum + From<u16>,

Returns the total number of electrons in the determinant.

pub fn to_generalised(&self) -> Self

Augments the encoding of coefficients in this Slater determinant to that in the corresponding generalised spin constraint.

Returns

The equivalent Slater determinant with the coefficients encoded in the generalised spin constraint.

pub fn to_orbitals(&self) -> Vec<Vec<MolecularOrbital<'a, T>>>

Extracts the molecular orbitals in this Slater determinant.

Returns

A vector of the molecular orbitals constituting this Slater determinant. In the restricted spin constraint, the identical molecular orbitals across different spin spaces are only given once. Each molecular orbital does contain an index of the spin space it is in.

impl<'a> SlaterDeterminant<'a, f64>

pub fn to_densities(&'a self) -> Result<DensitiesOwned<'a, f64>, Error>

Constructs a vector of real densities, one for each spin space in a Slater determinant.

For restricted and unrestricted spin constraints, spin spaces are well-defined. For generalised spin constraints, each spin-space density is constructed from the corresponding diagonal block of the overall density matrix.

Occupation numbers are also incorporated in the formation of density matrices.

Returns

A vector of real densities, one for each spin space.

impl<'a, T> SlaterDeterminant<'a, Complex<T>>

where T: Float + FloatConst + Lapack, Complex<T>: Lapack,

pub fn to_densities(&'a self) -> Result<DensitiesOwned<'a, Complex<T>>, Error>

Constructs a vector of complex densities, one from each coefficient matrix in a Slater determinant.

For restricted and unrestricted spin constraints, spin spaces are well-defined. For generalised spin constraints, each spin-space density is constructed from the corresponding diagonal block of the overall density matrix.

Occupation numbers are also incorporated in the formation of density matrices.

Arguments

• sd - A Slater determinant.

Returns

A vector of complex densities, one for each spin space.

Trait Implementations

impl<'a, T> Clone for SlaterDeterminant<'a, T>

where T: ComplexFloat + Lapack + Clone,

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<'a, T> ComplexConjugationTransformable for SlaterDeterminant<'a, T>

where T: ComplexFloat + Lapack,

fn transform_cc_mut(&mut self) -> Result<&mut Self, TransformationError>

Performs a complex conjugation in-place.

fn transform_cc(&self) -> Result<Self, TransformationError>

Performs a complex conjugation and returns the complex-conjugated result.

impl<'a, T> Debug for SlaterDeterminant<'a, T>

where T: Debug + ComplexFloat + Lapack, <T as ComplexFloat>::Real: Sum + From<u16> + Debug,

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

Formats the value using the given formatter.

impl<'a, T> Display for SlaterDeterminant<'a, T>

where T: Display + ComplexFloat + Lapack, <T as ComplexFloat>::Real: Sum + From<u16> + Display,

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

Formats the value using the given formatter.

impl<'a, T> From<SlaterDeterminant<'a, T>> for SlaterDeterminant<'a, Complex<T>>

where T: Float + FloatConst + Lapack, Complex<T>: Lapack,

fn from(value: SlaterDeterminant<'a, T>) -> Self

Converts to this type from the input type.

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

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

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

Type of the iterator over items in the orbit.

fn group(&self) -> &G

The group generating the orbit.

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

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, T> Overlap<T, Dim<[usize; 2]>> for SlaterDeterminant<'a, T>

where T: Lapack + ComplexFloat<Real = <T as Scalar>::Real> + Debug + Mul<<T as ComplexFloat>::Real, Output = T>, <T as ComplexFloat>::Real: Debug + RelativeEq<<T as ComplexFloat>::Real> + AbsDiffEq<Epsilon = <T as Scalar>::Real>,

fn overlap( &self, other: &Self, metric: Option<&Array2<T>>, metric_h: Option<&Array2<T>>, ) -> Result<T, Error>

Computes the overlap between two Slater determinants.

Determinants with fractional electrons are currently not supported.

When one or both of the Slater determinants have been acted on by an antiunitary operation, the correct Hermitian or complex-symmetric metric will be chosen in the evalulation of the overlap.

Arguments

• metric - The atomic-orbital overlap matrix with respect to the conventional sesquilinear inner product.
• metric_h - The atomic-orbital overlap matrix with respect to the bilinear inner product.

Panics

Panics if self and other have mismatched spin constraints or numbers of coefficient matrices, or if fractional occupation numbers are detected.

fn overlap_definition(&self) -> String

Returns the mathematical definition of the overlap between two Slater determinants.

fn complex_symmetric(&self) -> bool

If true, the inner product is bilinear and $\hat{\iota} = \hat{\kappa}$. If false, the inner product is sesquilinear and $\hat{\iota} = \mathrm{id}$.

impl<'a, T> PartialEq for SlaterDeterminant<'a, T>

where T: ComplexFloat<Real = f64> + Lapack,

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

This method tests for self and other values to be equal, and is used by ==.

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

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

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

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>, SlaterDeterminant<'a, T>: 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.

impl<'a, T> SpatialUnitaryTransformable for SlaterDeterminant<'a, T>

where T: ComplexFloat + LinalgScalar + ScalarOperand + Copy + Lapack, f64: Into<T>,

fn transform_spatial_mut( &mut self, rmat: &Array2<f64>, perm: Option<&Permutation<usize>>, ) -> Result<&mut Self, TransformationError>

Performs a spatial transformation in-place.

fn transform_spatial( &self, rmat: &Array2<f64>, perm: Option<&Permutation<usize>>, ) -> Result<Self, TransformationError>

Performs a spatial transformation and returns the transformed result.

impl<'a, T> SpinUnitaryTransformable for SlaterDeterminant<'a, Complex<T>>

where T: Clone, Complex<T>: ComplexFloat<Real = T> + LinalgScalar + ScalarOperand + Lapack + Mul<Complex<T>, Output = Complex<T>> + Mul<Complex<f64>, Output = Complex<T>>,

fn transform_spin_mut( &mut self, dmat: &Array2<Complex<f64>>, ) -> Result<&mut Self, TransformationError>

Performs a spin transformation in-place.

Arguments

• dmat - The two-dimensional representation matrix of the transformation in the basis of the $\{ \alpha, \beta \}$ spinors (i.e. decreasing $m$ order).

Panics

Panics if the spin constraint is not generalised. Spin transformations can only be performed with generalised spin constraint.

fn transform_spin( &self, dmat: &Array2<Complex<f64>>, ) -> Result<Self, TransformationError>

Performs a spin transformation and returns the transformed result.

impl<'a> SpinUnitaryTransformable for SlaterDeterminant<'a, f64>

fn transform_spin_mut( &mut self, dmat: &Array2<Complex<f64>>, ) -> Result<&mut Self, TransformationError>

Performs a spin transformation in-place.

Arguments

• dmat - The two-dimensional representation matrix of the transformation in the basis of the $\{ \alpha, \beta \}$ spinors (i.e. decreasing $m$ order).

fn transform_spin( &self, dmat: &Array2<Complex<f64>>, ) -> Result<Self, TransformationError>

Performs a spin transformation and returns the transformed result.

impl<'a, T> SymmetryTransformable for SlaterDeterminant<'a, T>

where T: ComplexFloat + Lapack, SlaterDeterminant<'a, T>: SpatialUnitaryTransformable + SpinUnitaryTransformable + TimeReversalTransformable,

fn sym_permute_sites_spatial( &self, symop: &SymmetryOperation, ) -> Result<Permutation<usize>, TransformationError>

Determines the permutation of sites (e.g. atoms in molecules) due to the action of a symmetry operation.

fn sym_transform_spatial_mut( &mut self, symop: &SymmetryOperation, ) -> Result<&mut Self, TransformationError>

Performs a spatial transformation according to a specified symmetry operation in-place.

fn sym_transform_spatial( &self, symop: &SymmetryOperation, ) -> Result<Self, TransformationError>

Performs a spatial transformation according to a specified symmetry operation and returns the transformed result.

fn sym_transform_spatial_with_spintimerev_mut( &mut self, symop: &SymmetryOperation, ) -> Result<&mut Self, TransformationError>

Performs a spatial transformation according to a specified symmetry operation in-place, but with spin-including time reversal.

fn sym_transform_spatial_with_spintimerev( &self, symop: &SymmetryOperation, ) -> Result<Self, TransformationError>

Performs a spatial transformation according to a specified symmetry operation but with spin-including time reversal and returns the transformed result.

fn sym_transform_spin_mut( &mut self, symop: &SymmetryOperation, ) -> Result<&mut Self, TransformationError>

Performs a spin transformation according to a specified symmetry operation in-place.

fn sym_transform_spin( &self, symop: &SymmetryOperation, ) -> Result<Self, TransformationError>

Performs a spin transformation according to a specified symmetry operation and returns the transformed result.

fn sym_transform_spin_spatial_mut( &mut self, symop: &SymmetryOperation, ) -> Result<&mut Self, TransformationError>

Performs a coupled spin-spatial transformation according to a specified symmetry operation in-place.

fn sym_transform_spin_spatial( &self, symop: &SymmetryOperation, ) -> Result<Self, TransformationError>

Performs a coupled spin-spatial transformation according to a specified symmetry operation and returns the transformed result.

impl<'a, T> DefaultTimeReversalTransformable for SlaterDeterminant<'a, T>

where T: ComplexFloat + Lapack,

impl<'a, T> Eq for SlaterDeterminant<'a, T>

where T: ComplexFloat<Real = f64> + Lapack,