ECOUB Subroutine

public subroutine ECOUB(CMOM, CMOM_INTERST, ECOU, CELL, DENSITY, SHAPEFUN, GAUNTSHAPE, LMAXATOM, LMAXD, NSPIN, NATOM, VM2Z, ZATOM, INS, IRMD, LMPOTD, LPOTD)

Attention : energy zero ---> electro static zero

Calculate the electrostatic potential-energies without the electron-nuclear interaction in the cell itself. the energy of the representive atom i is given by $$\begin{equation} E_\text{cou}(i) = \frac{1}{2} \int_{0}^{r_c}\sum_{l,m} dr' { vm2z(r',l,m,i)*rho2ns(r',l,m,i,1) } - z(i) * V_\text{mad} (r_i) \end{equation}$$ (see notes by B. Drittler)

vm2z is the coulomb potential of the atom without the nuclear potential of the atom rho2ns(...,1) is the real charge density times $r^2$

both developed into spherical harmonics. (see deck rholm)

z is the nuclear charge of the atom

vmad ( ri ) is a generalized madelung potential

$$\begin{equation} V_\text{mad} = \frac{1}{\sqrt{4\pi}} vm2z(irws,1,is)- 2\sqrt{4\pi} \frac{cmom(1,ipot)}{rws} \end{equation}$$

( <..> = spherical averaged )

modified for band structure code B. Drittler Jan. 1990 @note Warning this subroutine has to be called before the exchange correlation potential is added to the potential vm2. The energy calculated here is splitted into l-dependent parts to see the l -convergency.

@note Warning

 in case of shape corrections the contribution of the coulomb potential 
 the of the nucleus is analytically cancelled only in the muffin tin sphere
 in the interstial region it has to be taken into account ! see deck epotins

Arguments