Analytical form of pseudopotentials

The simplest and historically the first choice is the local ansatz [1] for AV in Eq. 26, however, such an ansatz is too inaccurate and therefore has soon been 

For scalar-quasirelativistic calculations, i.e., when spin-orbit coupling is neglected, a one-component form may be obtained by averaging over the spin 

The projection operator P refers now to the spherical harmonics centered at the core A 

If spin-orbit coupling is taken into account only at the correlated level, it is advantageous to separate space and spin 

PPs are a basic tool in Quantum Monte Carlo (QMC) calculations [146-150], The computational effort of QMC for an -electron system scales as 0 r ). It is estimated that for the additional Z- scaling with nuclear charge Z the exponent is reduced from jc 5.5 — 6.5 to jc 3.4 when the cores are replaced by PPs [151]. So-called soft PPs which avoid the 1/r and 1/r singularities in the effective one-electron potential have been derived at the nonrelativistic level for Be to Ne and A1 to Ar for use in QMC calculations by the group of Lester [152,153]. 

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