CI::CSF2

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Two-electron configuration state function (CSF).

A CSF is an antisymmetrised two-electron basis state with definite total angular momentum ( \( J^2 \), \( J_z \)) and parity, built from a pair of single-particle relativistic orbitals. Only two-electron CSFs are implemented.

Each CSF2 stores the indices of its two constituent orbitals (always sorted to avoid double-counting) and the total parity, which is the product of the parities of the two single-particle states.

Note

The orbital pair is stored as a sorted array of DiracSpinor::Index (uint16_t) rather than DiracSpinor references, so CSF2 objects are cheap to copy and store. There is a limit to maximum n<=256 - see Angular::nk_to_index

#include <CSF.hpp>

Public Member Functions
	CSF2 (const DiracSpinor &a, const DiracSpinor &b)
DiracSpinor::Index	state (std::size_t i) const
	Index (nk_index) of the ith constituent orbital (i = 0 or 1)
int	parity () const
	Parity of the CSF, +/-1.
std::string	config (bool relativistic=false) const
	Single-particle configuration as a string, in relativistic or non-rel form.

Static Public Member Functions
static int	num_different (const CSF2 &A, const CSF2 &B)
	Returns the number of orbitals that differ between two CSFs (0, 1, or 2).
static std::array< DiracSpinor::Index, 2 >	diff_1_na (const CSF2 &V, const CSF2 &X)
	For two CSFs differing by exactly one orbital, returns {n, a} where V contains orbital n and X contains orbital a.
static DiracSpinor::Index	same_1_j (const CSF2 &A, const CSF2 &B)
	Returns the orbital index shared by two CSFs that differ by exactly one orbital.

Public Attributes
std::array< DiracSpinor::Index, 2 >	states

Friends
bool	operator== (const CSF2 &A, const CSF2 &B)
bool	operator!= (const CSF2 &A, const CSF2 &B)

Member Function Documentation

state()

DiracSpinor::Index CI::CSF2::state

(

std::size_t

i

)

const

Index (nk_index) of the ith constituent orbital (i = 0 or 1)

num_different()

int CI::CSF2::num_different ( const CSF2 &  A, const CSF2 &  B  )

static

Returns the number of orbitals that differ between two CSFs (0, 1, or 2).

Used to select the appropriate Slater-Condon rule when evaluating CI matrix elements: 0 – diagonal; 1 – single substitution; 2 – double substitution; >2 – zero by orthogonality.

diff_1_na()

std::array< DiracSpinor::Index, 2 > CI::CSF2::diff_1_na ( const CSF2 &  V, const CSF2 &  X  )

static

For two CSFs differing by exactly one orbital, returns {n, a} where V contains orbital n and X contains orbital a.

Identifies the "particle" index n (in V but not X) and the "hole" index a (in X but not V), as needed to apply the single-substitution Slater-Condon rule: \( \langle V | \hat{O} | X \rangle \) where \( |V\rangle = \hat{a}^\dag_n \hat{a}_a |X\rangle \).

Warning

Result is undefined if V and X do not differ by exactly one orbital; check with num_different() first.

same_1_j()

DiracSpinor::Index CI::CSF2::same_1_j ( const CSF2 &  A, const CSF2 &  B  )

static

Returns the orbital index shared by two CSFs that differ by exactly one orbital.

Extracts the common (spectator) orbital needed for single-substitution matrix elements.

Warning

Assumes A and B differ by exactly one orbital.

parity()

int CI::CSF2::parity

(

)

const

Parity of the CSF, +/-1.

config()

std::string CI::CSF2::config

(

bool

relativistic = false

)

const

Single-particle configuration as a string, in relativistic or non-rel form.

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The documentation for this class was generated from the following files:

• CI/CSF.hpp
• CI/CSF.cpp