There are quite a few differences between PAW and Norm-Conserving (NC) PP:

1) In PAW the pseudized wavefunction is transformed to the all-electron wavefunction. So, that we have, in principle, all-electron precision.

2) In PAW, we have ultra-soft pseudo potentials, so that we usually require lower energy-cutoffs to converge than we do within NCPP.

3) In PAW, the on-site quantities, close to the atoms, are treated separately. Usually with an atomic-orbitals basis. Outside the atoms, another basis is used, such as plane-waves or wavelets (as in ABINIT).

Hence, in the PAW formalism there are more terms to be evaluated (such as on-site densities, compensation densities, etc..)

We start with thinking about the core wavefunctions, which are almost perfectly confined to a sphereical environment so that we can we lift them out of the calculation and treat them separately, either beforehand to yield a fixed core density (frozen core approximation) or by updating the core wavefunctions self-consistently. Now imagine that you try to solve the Kohn-Sham equations for, say, Si using the potential resulting from all the core (1s,2s,2p states) and valence electrons. You are supposed to find the lowest energy eigenvalue, but we all know the name of that one, right? It is the Si 1s wavefunction and then follows the 2s and 2p wavefunctions. But we had all of these in the core! So: all electronic structure methods need that do not want to treat ALL the electrons as valence electrons (which is definitely not a good idea using plane waves) need some mechanism to select an energy window and to constrain the valence wavefunctions to only energies within that window.

Basically, the implementation of this constraint to some energy window is all that differs between different electronic structure methods (there are some other aspects too, but the mostly it is just this). This is also referred to as the "orthogonalization to the core states", since this is how we generally enforce the energy window: by forcing the valence states to be orthogonal to the core states, thus pushing them up in energy to the right position.

Plane-wave/pseudopotential methods are descended from the orthogonalized plane wave method, which used to orthogonalize the plane waves directly to the core states. It was later realized that this could be more easily achieved by simply interpreting the orthogonalization as a change in the potential that pushed valence electrons out of the core region, in other words, you enforce the energy window by direct addition of a constraining potential. This levels the deep potential wells near the nuclei producing something closer to a constant potential, which obviously requires a lot less plane waves. It can be done beforehand for each element, but you may need to beware that transferring your "pseudopotential" from one system to the next might be tricky.

PAW instead handles the orthogonalization by adding site-local functions, projectors, to the plane-wave basis, and these are designed to maintain the orthogonality to the core states, still in a pseudized atomic environment. As Tonatiuh explained above, the formalism is such that it is in principle possible to transform yourself between the all-electron wavefunction and the pseudized wavefunction (although in practice the implementations do not really allow for this to any extent). PAW is like PS methods typically implemented in the frozen core approximation and require pre-calculated datasets storing the core density and the projectors.

PAW datasets tends to have somewhat better transferability from one system to the next than PS datasets, which makes them popular and somewhat more reliable in my opinion. I would go with PAW if you have no specific reason to do otherwise.

Thank you so much both of you Tonatiuh and Torbjorn.

To be specific and as a layman, I did calculation (Sorry, I do experimental condensed matter and do not have depth understanding code and ) for DOS and pDOS for orthorhombic LaCrO3, by invoking non-colinear spin arrangement by including SO coupling which results in weak ferromagnetism in the system consistent with magnetic measurements but wrong (small) band gap (http://www.scientific.net/AMR.585.274). On the other hand DFT +U (spin polarized but SO coupling NOT included) results in correct band gap but wrong (zero total magnetization) magnetization and also delocalized Cr 3d orbitals. For both calculations following PP are used.

The calculation was performed Using Quantum Espresso 4.2 by running pw.x.

If I am not wrongly understood by above discussion, I not did the PAW based calculation as it does not 'add site-local functions, projectors, to the plane-wave basis'. If I am wrong please clarify me (sorry if it so silly). Can you please suggest how can I improve band gap maintaining weak ferromagnetism in LaCrO3.

(As I recently started learning ABINIT, if it can help in this regard I ll try run this system).

For La,

http://www.quantum-espresso.org/wp-content/uploads/upf_files/La.pbe-nsp-van.UPF

La.pbe-nsp-van.UPF

Pseudopotential type: ULTRASOFT

Method: Vanderbilt ultrasoft

Functional type: Perdew-Burke-Ernzerhof (PBE) exch-corr

Nonlinear core correction

scalar relativistic

For Cr,

http://www.quantum-espresso.org/wp-content/uploads/upf_files/Cr.pbe-sp-van.UPF

Cr.pbe-sp-van.UPF

Pseudopotential type: ULTRASOFT

Method: Vanderbilt ultrasoft

Functional type: Perdew-Burke-Ernzerhof (PBE) exch-corr

Semi-core state in valence

scalar relativistic

For O,

http://www.quantum-espresso.org/wp-content/uploads/upf_files/O.pbe-rrkjus.UPF

O.pbe-rrkjus.UPF

Pseudopotential type: ULTRASOFT

Method: Rappe Rabe Kaxiras Joannopoulos

Functional type: Perdew-Burke-Ernzerhof (PBE) exch-corr

scalar relativistic

Thank you

What is the Pseudopotential approximation?