Struct HamiltonianAO

pub struct HamiltonianAO<'a, T, SC, F>
where
    T: ComplexFloat + Lapack,
    SC: StructureConstraint + Clone,
    F: Fn(&Array2<T>) -> Result<(Array2<T>, Array2<T>), Error> + Clone,
{ /* private fields */ }

Structure for managing the electronic Hamiltonian integrals in an atomic-orbital basis.

Implementations

impl<'a, T, SC, F> HamiltonianAO<'a, T, SC, F>

where T: ComplexFloat + Lapack, SC: StructureConstraint + Clone, F: Fn(&Array2<T>) -> Result<(Array2<T>, Array2<T>), Error> + Clone,

pub fn builder() -> HamiltonianAOBuilder<'a, T, SC, F>

Returns a builder for HamiltonianAO.

pub fn enuc(&self) -> T

Returns the nuclear repulsion energy.

pub fn onee(&'a self) -> &'a ArrayView2<'a, T>

Returns the one-electron integrals in an atomic-orbital basis (with respect to the specified structure constraint).

pub fn twoe(&self) -> Option<&ArrayView4<'a, T>>

Returns the two-electron integrals in an atomic-orbital basis (with respect to the specified structure constraint).

pub fn get_jk(&self) -> Option<&F>

impl<'a, T, SC, F> HamiltonianAO<'a, T, SC, F>

where T: ComplexFloat + Lapack + ScalarOperand + FromPrimitive, <T as ComplexFloat>::Real: LowerExp, SC: StructureConstraint + Display + PartialEq + Clone, F: Fn(&Array2<T>) -> Result<(Array2<T>, Array2<T>), Error> + Clone,

pub fn calc_hamiltonian_matrix_element_contributions( &self, det_w: &SlaterDeterminant<'_, T, SC>, det_x: &SlaterDeterminant<'_, T, SC>, sao: &ArrayView2<'_, T>, thresh_offdiag: <T as ComplexFloat>::Real, thresh_zeroov: <T as ComplexFloat>::Real, ) -> Result<(T, T, T), Error>

Calculates the zero-, one-, and two-electron contributions to the matrix element of the electronic Hamiltonian between two possibly non-orthogonal Slater determinants.

The matrix element is given by

    \braket{\hat{\iota} ^{w}\Psi | \hat{\mathscr{H}} | ^{x}\Psi}

where $\hat{\iota}$ is an involutory operator that is either the identity or the complex-conjugation operator, which depends on whether the specified determinants have been defined with the SlaterDeterminant::complex_symmetric boolean set to false or true, respectively.

Arguments

• det_w - The determinant $^{w}\Psi$.
• det_x - The determinant $^{x}\Psi$.
• sao - The atomic-orbital overlap matrix.
• thresh_offdiag - Threshold for determining non-zero off-diagonal elements in the orbital overlap matrix between $^{w}\Psi$ and $^{x}\Psi$ during Löwdin pairing.
• thresh_zeroov - Threshold for identifying zero Löwdin overlaps.

Returns

A tuple containing the zero-, one-, and two-electron contributions to the matrix element.

pub fn calc_hamiltonian_matrix( &self, dets: &[&SlaterDeterminant<'_, T, SC>], sao: &ArrayView2<'_, T>, thresh_offdiag: <T as ComplexFloat>::Real, thresh_zeroov: <T as ComplexFloat>::Real, ) -> Result<Array2<T>, Error>

Calculates the Hamiltonian matrix in the basis of non-orthogonal Slater determinants.

Each matrix element is given by

    \braket{\hat{\iota} ^{w}\Psi | \hat{\mathscr{H}} | ^{x}\Psi}

where $\hat{\iota}$ is an involutory operator that is either the identity or the complex-conjugation operator, which depends on whether the specified determinants have been defined with the SlaterDeterminant::complex_symmetric boolean set to false or true, respectively.

Arguments

• dets - A sequence of Slater determinants to be used as the basis for the Hamiltonian matrix.
• sao - The atomic-orbital overlap matrix.
• thresh_offdiag - Threshold for determining non-zero off-diagonal elements in the orbital overlap matrix between $^{w}\Psi$ and $^{x}\Psi$ during Löwdin pairing.
• thresh_zeroov - threshold for identifying zero Löwdin overlaps.

Returns

The Hamiltonian matrix.

Trait Implementations

impl<'a, T, SC, F> OrbitMatrix<'a, T, SC> for &HamiltonianAO<'a, T, SC, F>

where T: ComplexFloat + Lapack + ScalarOperand + FromPrimitive, <T as ComplexFloat>::Real: LowerExp, SC: StructureConstraint + Clone + Display + PartialEq, SlaterDeterminant<'a, T, SC>: SymmetryTransformable, F: Fn(&Array2<T>) -> Result<(Array2<T>, Array2<T>), Error> + Clone,

type MatrixElement = T

The type of the matrix elements.

fn calc_matrix_element( &self, det_w: &SlaterDeterminant<'_, T, SC>, det_x: &SlaterDeterminant<'_, T, SC>, sao: &ArrayView2<'_, T>, thresh_offdiag: <T as ComplexFloat>::Real, thresh_zeroov: <T as ComplexFloat>::Real, ) -> Result<T, Error>

Calculates the matrix element between two Slater determinants.

fn t(x: &T) -> T

Computes the transpose of a matrix element.

fn conj(x: &T) -> T

Computes the complex conjugation of a matrix element.

fn zero(&self) -> T

Returns the zero matrix element.

fn norm_preserving_scalar_map<'b, G>( &self, i: usize, orbit_basis: &'b OrbitBasis<'b, G, SlaterDeterminant<'a, T, SC>>, ) -> Result<fn(&Self::MatrixElement) -> Self::MatrixElement, Error>

where G: SymmetryGroupProperties + Clone, 'a: 'b,

Returns the norm-presearving scalar map connecting diagonally-symmetric elements in the matrix.

fn calc_orbit_matrix<'g, G>( &self, orbit_basis: &'g OrbitBasis<'g, G, SlaterDeterminant<'a, T, SC>>, use_cayley_table: bool, sao: &ArrayView2<'_, T>, thresh_offdiag: <T as ComplexFloat>::Real, thresh_zeroov: <T as ComplexFloat>::Real, ) -> Result<Array2<Self::MatrixElement>, Error>

where G: SymmetryGroupProperties + Clone, T: Sync + Send, <T as ComplexFloat>::Real: Sync, SlaterDeterminant<'a, T, SC>: Sync, Self: Sync, Self::MatrixElement: Send + LowerExp + Clone, 'a: 'g,

Computes the entire matrix of matrix elements in an orbit basis, making use of group closure for optimisation.

impl<'a, T, SC, F> OrbitMatrix<'a, T, SC> for HamiltonianAO<'a, T, SC, F>

where T: ComplexFloat + Lapack + ScalarOperand + FromPrimitive, <T as ComplexFloat>::Real: LowerExp, SC: StructureConstraint + Clone + Display + PartialEq, SlaterDeterminant<'a, T, SC>: SymmetryTransformable, F: Fn(&Array2<T>) -> Result<(Array2<T>, Array2<T>), Error> + Clone,

type MatrixElement = T

The type of the matrix elements.

fn calc_matrix_element( &self, det_w: &SlaterDeterminant<'_, T, SC>, det_x: &SlaterDeterminant<'_, T, SC>, sao: &ArrayView2<'_, T>, thresh_offdiag: <T as ComplexFloat>::Real, thresh_zeroov: <T as ComplexFloat>::Real, ) -> Result<T, Error>

Calculates the matrix element between two Slater determinants.

fn t(x: &T) -> T

Computes the transpose of a matrix element.

fn conj(x: &T) -> T

Computes the complex conjugation of a matrix element.

fn zero(&self) -> T

Returns the zero matrix element.

fn norm_preserving_scalar_map<'b, G>( &self, i: usize, orbit_basis: &'b OrbitBasis<'b, G, SlaterDeterminant<'a, T, SC>>, ) -> Result<fn(&Self::MatrixElement) -> Self::MatrixElement, Error>

where G: SymmetryGroupProperties + Clone, 'a: 'b,

Returns the norm-presearving scalar map connecting diagonally-symmetric elements in the matrix.

fn calc_orbit_matrix<'g, G>( &self, orbit_basis: &'g OrbitBasis<'g, G, SlaterDeterminant<'a, T, SC>>, use_cayley_table: bool, sao: &ArrayView2<'_, T>, thresh_offdiag: <T as ComplexFloat>::Real, thresh_zeroov: <T as ComplexFloat>::Real, ) -> Result<Array2<Self::MatrixElement>, Error>

where G: SymmetryGroupProperties + Clone, T: Sync + Send, <T as ComplexFloat>::Real: Sync, SlaterDeterminant<'a, T, SC>: Sync, Self: Sync, Self::MatrixElement: Send + LowerExp + Clone, 'a: 'g,

Computes the entire matrix of matrix elements in an orbit basis, making use of group closure for optimisation.