I apologize for asking this stupid question, but I am a bit confused with the ISIF tag. Doesn't a cell's shape and cell's volume depend on the atoms' positions? If so, why can the cell's volume/shape and atomic position change independently in the ISIF tag?
Doesn't a cell's shape and cell's volume depend on the atoms' positions?
Not really. The cell shape and size can be anything irrespective of atomic position. The cell is something that we repeat periodically in all the space dimensions. The atomic position doesn't have anything to do with it. I guess you are probably mistakenly assuming that the cell shape and size are determined by only the outer atoms! This is not the case.
VASP, like many other DFT codes such as Quantum ESPRESSO, CASTEP, etc., is a 3d-periodic code. That means the supercell you construct in these codes will get repeated in all 3 directions. You can always do calculation of systems with lower dimensionality within a supercell by making vacuum (large lattice parameters) accordingly.
We can think of 1D chain of monoatomic carbon, for instance. You can have one C atom in a tetragonal cell at
(0,0,0) with large lattice parameters
c. In this case, what you have is an isolated C atom (left figure). But if you choose
b to be large and
c to be small, then what you have is an infinite C chain (right figure). Notice that you didn't change any atomic position. Still the C atom has
(0,0,0) position. But since now you reduced the length of the cell in one direction (namely
c - along z-axis), the cell volume changed.
Why can the cell's volume/shape and atomic position change independently in the ISIF tag?
Just like in the previous example the cell volume and the shape changed (volume decreased, and shape became cubic from tetragonal) even though the atomic position didn't, the atomic positions can also be changed keeping cell shape and/or volume fixed. The shape or volume of the supercell do not depend on the atomic position. The only thing to notice is that the supercell will get repeated in 3D space.
ISIF tag, one controls how much degree of freedom one will allow in a relaxation calculations. For example, one may want to let the C chain system to be relaxed only along z-axis for which
ISIF=7 needs to be applied. Full reference for
ISIF tag is here. The same thing can be realized in Quantum ESPRESSO using the
cell_dofree parameter in
&CELL namecard reference.