#include <lowdin_orthogonalization.hpp>

Public Attributes
std::vector< Real >	eigenvalues

std::vector< Complex >	eigenvectors

std::vector< Complex >	inverse_square_root

int	number_of_orbitals = 0

Detailed Description

S^{-1/2} for one orbital set, together with the eigendecomposition it was built from.

The eigenpairs are kept rather than discarded because the derivative of S^{-1/2} cannot be recovered from S^{-1/2} alone: dS and S^{-1/2} do not commute, so d(S^{-1/2}) is the solution of a Lyapunov equation that is diagonal only in S's own eigenbasis (see lowdin_inverse_square_root_derivative). DFT+U forces with ortho-atomic projectors need exactly that, and re-diagonalizing S per displaced atom and Cartesian direction to get it back would be both wasteful and a second definition of the same transform.

Both matrices are column-major – element (row, column) at row + column * number_of_orbitals. eigenvectors is ZHEEV's own output (column k is eigenvector k); inverse_square_root is Hermitian, so its layout only fixes which index is written first.

Definition at line 50 of file lowdin_orthogonalization.hpp.