Struct qsym2::target::orbital::MolecularOrbital

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

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

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

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

Returns a builder to construct a new MolecularOrbital.

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pub fn to_generalised(&self) -> Self

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

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

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

Returns a shared reference to the coefficient array.

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pub fn spin_constraint(&self) -> &SpinConstraint

Returns a shared reference to the spin constraint.

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

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

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pub fn mol(&self) -> &Molecule

Returns the molecule associated with this molecular orbital.

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pub fn complex_symmetric(&self) -> bool

Returns the complex-symmetric flag of the molecular orbital.

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

Returns the threshold with which molecular orbitals are compared.

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

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

Constructs the total density of the molecular orbital.

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impl<'a, T> MolecularOrbital<'a, Complex<T>>
where T: Float + FloatConst + Lapack + From<u16>, Complex<T>: Lapack,

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

Constructs the total density of the molecular orbital.

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

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

Returns a copy of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl<'a, T> ComplexConjugationTransformable for MolecularOrbital<'a, T>
where T: ComplexFloat + Lapack,

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

Performs a complex conjugation in-place.
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fn transform_cc(&self) -> Result<Self, TransformationError>

Performs a complex conjugation and returns the complex-conjugated result. Read more
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impl<'a, T> Debug for MolecularOrbital<'a, T>
where T: Debug + ComplexFloat + Lapack,

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

Formats the value using the given formatter. Read more
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impl<'a, T> Display for MolecularOrbital<'a, T>
where T: Display + ComplexFloat + Lapack,

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

Formats the value using the given formatter. Read more
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impl<'a, T> From<MolecularOrbital<'a, T>> for MolecularOrbital<'a, Complex<T>>
where T: Float + FloatConst + Lapack, Complex<T>: Lapack,

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

Converts to this type from the input type.
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impl<'a, G, T> Orbit<G, MolecularOrbital<'a, T>> for MolecularOrbitalSymmetryOrbit<'a, G, T>

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

Type of the iterator over items in the orbit.
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fn group(&self) -> &G

The group generating the orbit.
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fn origin(&self) -> &MolecularOrbital<'a, T>

The origin of the orbit.
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fn iter(&self) -> Self::OrbitIter

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

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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.

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

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fn overlap_definition(&self) -> String

Returns the mathematical definition of the overlap between two orbitals.

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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 $\hat{\iota} = \mathrm{id}$.
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impl<'a, T> PartialEq for MolecularOrbital<'a, T>
where T: ComplexFloat<Real = f64> + Lapack,

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

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

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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.

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The decomposed result.

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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.

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

Sets the overlap matrix between the items in the orbit. Read more
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fn smat(&self) -> Option<&Array2<T>>

Returns the overlap matrix between the items in the orbit.
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fn xmat(&self) -> &Array2<T>

Returns the transformation matrix $\mathbf{X}$ for the overlap matrix $\mathbf{S}$ between the items in the orbit. Read more
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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 Read more
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fn integrality_threshold(&self) -> <T as ComplexFloat>::Real

Returns the threshold for integrality checks of irreducible representation or corepresentation multiplicities.
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fn eigenvalue_comparison_mode(&self) -> &EigenvalueComparisonMode

Returns the enumerated type specifying the comparison mode for filtering out orbit overlap eigenvalues.
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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. Read more
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fn normalise_smat(&mut self) -> Result<&mut Self, Error>

Normalises overlap matrix between items in the orbit such that its diagonal entries are unity. Read more
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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. Read more
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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. Read more
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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. Read more
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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. Read more
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impl<'a, T> SpatialUnitaryTransformable for MolecularOrbital<'a, T>
where T: ComplexFloat + LinalgScalar + ScalarOperand + Copy + Lapack, f64: Into<T>,

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

Performs a spatial transformation in-place. Read more
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fn transform_spatial( &self, rmat: &Array2<f64>, perm: Option<&Permutation<usize>>, ) -> Result<Self, TransformationError>

Performs a spatial transformation and returns the transformed result. Read more
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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>>,

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

Performs a spin transformation in-place. Read more
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fn transform_spin( &self, dmat: &Array2<Complex<f64>>, ) -> Result<Self, TransformationError>

Performs a spin transformation and returns the transformed result. Read more
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impl<'a> SpinUnitaryTransformable for MolecularOrbital<'a, f64>

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

Performs a spin transformation in-place. Read more
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fn transform_spin( &self, dmat: &Array2<Complex<f64>>, ) -> Result<Self, TransformationError>

Performs a spin transformation and returns the transformed result. Read more
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impl<'a, T> SymmetryTransformable for MolecularOrbital<'a, T>

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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. Read more
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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. Read more
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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. Read more
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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. Read more
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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. Read more
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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. Read more
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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. Read more
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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. Read more
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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. Read more
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impl<'a, T> DefaultTimeReversalTransformable for MolecularOrbital<'a, T>
where T: ComplexFloat + Lapack,

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impl<'a, T> Eq for MolecularOrbital<'a, T>
where T: ComplexFloat<Real = f64> + Lapack,

Auto Trait Implementations§

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impl<'a, T> Freeze for MolecularOrbital<'a, T>
where <T as ComplexFloat>::Real: Freeze, T: Freeze,

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

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impl<'a, T> Send for MolecularOrbital<'a, T>
where <T as ComplexFloat>::Real: Send, T: Send,

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impl<'a, T> Sync for MolecularOrbital<'a, T>
where <T as ComplexFloat>::Real: Sync, T: Sync,

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impl<'a, T> Unpin for MolecularOrbital<'a, T>
where <T as ComplexFloat>::Real: Unpin, T: Unpin,

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

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Gets the TypeId of self. Read more
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default unsafe fn clone_to_uninit(&self, dst: *mut T)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dst. Read more
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fn transform_timerev_mut(&mut self) -> Result<&mut T, TransformationError>

Performs a time-reversal transformation in-place.

The default implementation of the time-reversal transformation for any type that implements SpinUnitaryTransformable and ComplexConjugationTransformable is a spin rotation by $\pi$ about the space-fixed $y$-axis followed by a complex conjugation.

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

Performs a time-reversal transformation and returns the time-reversed result. Read more
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