[CPMD-list] "True" Eigenvalues

[Salomon Billeter]

Dear Eun-Gun,

a term you might want to have a look at is the G=0 (uniform) component of
the Hartree energy. It arises from the use of Gaussian core charge
distributions and therefore depends on the width of the Gaussian core
charge distribution (RAGGIO). When the total energy is calculated from the
band-structure-energy,
Etot = \sum E_i + Exc - \int dx*n(x)Vxc(x) + Ecorecore - Ehartree, (E_i are
the KS eigenenergies),
the integral of this term over the total electron distribution is added to
the core-core energy for the reciprocal-space based Poisson solvers (CPMD:
periodic, Mortensen, Tuckerman) as NEL*VPLOC (see vofrhoa.F or vofrhot.F:
EHII = DREAL(EI)*OMEGA + NEL*VPLOC). Note that this term does not affect
the energies from real-space based Poisson solvers (CPMD: Hockney for
isolated systems).

A short note about the vacuum reference electrostatic energy: since the
vacuum reference energy is usually defined at infinite separation from the
system, the condition to have no density at the point you probe is not
sufficient owing to the slow decay of the electrostatic potential. Even in
the case of an uncharged system with the leading term being caused by a
dipole moment of 1 Debye, the potential at 5 A separation would still be
0.3934302/(5/0.5291772083)^2*27.211384 eV = 0.120 eV.

Best regards,
Salomon