mod_overlap Module

Calculates the overlap integral of test function PHI with regular or irregular wavefunction (PZ, QZ: spherical part of the large component, PQNS: nonspherical part of the large component) for LDA+U. The overlap is given out in array RESULT

In the inner region the non-spherical wavefunctions are approximated as:

• The regular one (ir < irmin = irws-irns) : $$\begin{equation} pns\left(ir,lm1,lm2\right) = pz\left(ir,l1\right) ar\left(lm1,lm2\right) \end{equation}$$ where $pz$ is the regular wavefunction of the spherically symmetric part of the potential and $ar$ the alpha matrix (see sub. regns)

• The irregular one (ir < irmin) : $$\begin{equation} qns\left(ir,lm1,lm2\right) = pz\left(ir,l1\right) cr\left(lm1,lm2\right) + qz\left(ir,l1\right) * dr\left(lm1,lm2\right) \end{equation}$$ where $pz$ is the regular and $qz$ is the irregular wavefunction of the spherically symmetric part of the potential and $cr$, $dr$ the matrices calculated at the point $irmin$ (see sub. irwns)

The integrand is convoluted with the shape functions: $$\begin{equation} Result = \int \bar{phi_l} \sum_{L''L'''} R_L''L' Theta_L''' GAUNT_LL''L''' \end{equation}$$ Finally, the result should then be transformed to complex spherical harmonics basis!