kubo_projected Module Reference

Finite projected-Hamiltonian current in a nonorthogonal, possibly spinor AO basis. More...

Functions/Subroutines
subroutine, public	projected_current (h, s, positions, energies, current, status)
	Compute C^dagger (H S^-1 X - X S^-1 H) C without forming S^-1.
subroutine, public	projected_eigensystem (h, s, energies, c, status)
	Complete generalized eigensystem with a positive, well-conditioned AO metric.

Detailed Description

Finite projected-Hamiltonian current in a nonorthogonal, possibly spinor AO basis.

Author

Thomas D. Kuehne, tkueh.nosp@m.ne@c.nosp@m.p2k.o.nosp@m.rg

Function/Subroutine Documentation

projected_current()

subroutine, public kubo_projected::projected_current	(	complex(dp), dimension(:, :), intent(in)	h,
		complex(dp), dimension(:, :), intent(in)	s,
		complex(dp), dimension(:, :, :), intent(in)	positions,
		real(dp), dimension(:), intent(out)	energies,
		complex(dp), dimension(:, :, :), intent(out)	current,
		integer, intent(out)	status )

Compute C^dagger (H S^-1 X - X S^-1 H) C without forming S^-1.

Parameters

h	Complete scalar/spinor covariant Hamiltonian, not an occupied-state projection
s	Positive definite overlap, with explicit spin blocks when applicable
positions	Three analytic covariant Cartesian first moments
energies	Eigenvalues of H C = S C E
current	Anti-Hermitian commutators in the eigenbasis; velocity is i*current in atomic units
status	0 success; -1 invalid matrices; -2 ill-conditioned metric; positive LAPACK failure

Note

This is the commutator of projected operators. It is not the projection of the continuum commutator in an incomplete basis, nor a periodic Berry velocity.

Definition at line 33 of file kubo_projected.F.

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projected_eigensystem()

subroutine, public kubo_projected::projected_eigensystem	(	complex(dp), dimension(:, :), intent(in)	h,
		complex(dp), dimension(:, :), intent(in)	s,
		real(dp), dimension(:), intent(out)	energies,
		complex(dp), dimension(:, :), intent(out)	c,
		integer, intent(out)	status )

Complete generalized eigensystem with a positive, well-conditioned AO metric.

Parameters

h	Hermitian covariant Hamiltonian
s	Hermitian positive definite overlap
energies	Complete spectrum
c	Metric-orthonormal eigenvectors
status	0 success; -1 invalid matrices; -2 metric failure; positive LAPACK failure

Definition at line 77 of file kubo_projected.F.

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