local_occupation.h File Reference

The C interface for LOSC local occupation number. More...

#include <c_losc/matrix.h>
#include <stddef.h>

Go to the source code of this file.

Functions
losc_matrix *	losc_local_occupation (const losc_matrix *C_lo, const losc_matrix *S, const losc_matrix *D)
	Create the local occupation matrix. More...

Detailed Description

The C interface for LOSC local occupation number.

Function Documentation

losc_matrix* losc_local_occupation	(	const losc_matrix *	C_lo,
		const losc_matrix *	S,
		const losc_matrix *	D
	)

Create the local occupation matrix.

Parameters

[in]	C_lo	LO coefficient matrix with dimension [nbasis, nlo].
[in]	S	AO overlap matrix with dimension [nbasis, nbasis].
[in]	D	Spin density matrix under AO with dimension [nbasis, nbasis].

Returns

Create a local occupation matrix with dimension [nlo, nlo] and return the pointer.

See also

LoscLocalizerBase.lo: Obtain the LOs' coefficient matrix.

Note

The local occupation matrix is defined as \(\displaystyle \lambda_{ij} = \langle \phi_i|\rho|\phi_j \rangle \), where \( \lambda_{ij} \) is the local occupation matrix element, \( \phi_i \) and \( \phi_j \) are the i-th and j-th localized orbital and \( \rho \) is the spin density operator. In matrix form, local occupation matrix \( L \) is expressed as \( L = C_{\rm{LO}}^T S D S C_{\rm{LO}} \).