Struct qsym2::target::orbital::MolecularOrbital

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

Structure to manage molecular orbitals. Each molecular orbital is essentially a one-electron Slater determinant.

Implementations

impl<'a, T> MolecularOrbital<'a, T>

where T: ComplexFloat + Clone + Lapack,

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

Returns a builder to construct a new MolecularOrbital.

pub fn to_generalised(&self) -> Self

Augments the encoding of coefficients in this molecular orbital to that in the corresponding generalised spin constraint.

Returns

The equivalent molecular orbital with the coefficients encoded in the generalised spin constraint.

pub fn coefficients(&self) -> &Array1<T>

Returns a shared reference to the coefficient array.

pub fn spin_constraint(&self) -> &SpinConstraint

Returns a shared reference to the spin constraint.

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

Returns a shared reference to the BasisAngularOrder description of the basis in which the orbital coefficients are written.

pub fn mol(&self) -> &Molecule

Returns the molecule associated with this molecular orbital.

pub fn complex_symmetric(&self) -> bool

Returns the complex-symmetric flag of the molecular orbital.

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

Returns the threshold with which molecular orbitals are compared.

impl<'a> MolecularOrbital<'a, f64>

pub fn to_total_density(&'a self) -> Result<Density<'a, f64>, Error>

Constructs the total density of the molecular orbital.

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

where T: Float + FloatConst + Lapack + From<u16>, Complex<T>: Lapack,

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

Constructs the total density of the molecular orbital.

Trait Implementations

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

where T: ComplexFloat + Lapack + Clone,

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

where T: Debug + ComplexFloat + Lapack,

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

Formats the value using the given formatter.

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

where T: Display + ComplexFloat + Lapack,

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

Formats the value using the given formatter.

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

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

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

Converts to this type from the input type.

impl<'a, G, T> Orbit<G, MolecularOrbital<'a, T>> for MolecularOrbitalSymmetryOrbit<'a, G, T>

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

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

Type of the iterator over items in the orbit.

fn group(&self) -> &G

The group generating the orbit.

fn origin(&self) -> &MolecularOrbital<'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 MolecularOrbital<'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 molecular orbitals.

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

Panics

Panics if self and other have mismatched spin constraints or coefficient array lengths.

fn overlap_definition(&self) -> String

Returns the mathematical definition of the overlap between two orbitals.

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 MolecularOrbital<'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, MolecularOrbital<'a, T>, T, Dim<[usize; 2]>> for MolecularOrbitalSymmetryOrbit<'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 + RelativeEq<<T as ComplexFloat>::Real> + AbsDiffEq<Epsilon = <T as Scalar>::Real>, MolecularOrbital<'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 molecular orbitals 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 and transformation type would not give sensible symmetry results for a single-electron orbital. In particular, spin or spin-spatial symmetry analysis in unitary-represented magnetic groups is not valid for one-electron orbitals.

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 MolecularOrbital<'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 MolecularOrbital<'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.

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

Performs a spin transformation and returns the transformed result.

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

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

Performs a spin transformation in-place.

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 MolecularOrbital<'a, T>

where T: ComplexFloat + Lapack, MolecularOrbital<'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 MolecularOrbital<'a, T>

where T: ComplexFloat + Lapack,

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

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