Try to find translation + permutation for a given rotation.

Formula: d_central = (y_{i+1} - y_{i-1}) / (x_{i+1} - x_{i-1}) Example input: y_next=5.0, y_prev=1.0, dx_span=2.0 Example output: d_central=2.0

Calculate four-phi integral. Calculate the integral over the product of four all electron functions in the augmentation sphere, i.e.:

Calcualte PAW correction

Calculate density matrix term in LCAO

Calculate PAW-correction matrix elements of nabla. :: / _ _ d _ ~ _ d ~ _ | dr [phi (r) -- phi

This function calculates ground state forces in LCAO mode

Calculate Kinetic energy term in LCAO

Calculate PAW-correction matrix elements of r x nabla. :: / _ _ _ ~ _ ~ _ | dr [phi (r) O

Calculate potential term

Formula: f_q(r) = 4*pi*r^2*rho(r) Example input: r=2.0 bohr, rho=0.5 Example output: f_q(r)=25.1327412287

Formula: e_H(r) = 0.5 * 4*pi*r^2 * rho(r) * V_H(r) Example input: r=2.0 bohr, rho=0.25, V_H=1.5 Example output: e_H(r)=3.7699111843

Formula: f_s(r) = 4*pi*r*rho(r) Example input: r=2.0 bohr, rho=0.5 Example output: f_s(r)=12.5663706144

Fill the calc.wfs.kpt_[u].psit_nG arrays with useful data. Normally psit_nG is NOT used in lcao mode, but some extensions (like ase.d