stress vs. energy

[netscape88]

I am a new VASP users, and working on a test to understand the bulk optimization. My test system is Li bulk, using bcc structure, and exp. lattice constant 3.509 Ang.

There are two optimization ways that I used:
The first one: computing 31 different Li-bcc volumes by VASP with the same INCAR file and clean the directory after each calculation, I fit these energies by Murnaghan equation, and get the optimum constant is 3.44 Ang. During the calculations, I use the same ENCUT, and the ENCUT and K-mesh are highly converged to within few meV. Here is my INCAR file:
System = Li-bulk-bcc
ISTART = 0
ENCUT = 300
EDIFF = 0.1E-04
NELM = 100
ISMEAR = 1; SIGMA = 0.1

The second way to find the optimum lattice is using the ISIF-tag: ISIF=3, and keep other options as the same as in the INCAR of the first method. After running, it generate the optimum lattice: 3.418 Ang, and the "external pressure" in the OUTCAR is -5.71 kB.

My questions are coming:
1. I believe the first method is the best one. But both of methods use the same ENCUT, why they generate the different lattice constants? If it is because of "Pulay stress", all the Pulay stress in the second way are zero!

2. The Pulay stress is coming from the incomplete basis set in changing volume. Based on all my tests, it is always zero. I am wondering when and how can I get non-zero Pulay stress in the OUTCAR? :-)

3. In the second method, the extract "external pressure" in the OUTCAR is -1.64 kB, while the recalculate result based on the CONTCAR is -5.62 kB. What does the difference come from?

4. Normally, the smaller of total energy (in the optimum lattice constant", the smaller of the "external pressure". But in there, what I get is for these two "optimum" lattice:
a0 pressure energy
3.443 -8.65 -1.902478
3.418 -5.62 -1.902152

The lower energy structure has a large "external pressure". Why?

5. In order to understand this controversy, I use tetrahedral method without smearing (ISMEAR = -5) to redo above tests. I obtained the same optimum lattice constants for each method, and the same problems.

Thanks for your help

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