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The Born interpretation of the wavefunction leads to boundary conditions in each spatial degree of freedom, which then leads to quantum numbers when solving the Schrodinger equation. That is only certain solutions of the S.E. obey the boundary conditions, and these solutions have a quantum number that falls out of the math. For example, a 1D particle in a box (no spin) has 1 quantum number, n, such that the wavefunction is zero at the walls: psi(x) = 1/sqrt(2Pi) * sin ( n Pi x / L).
For the spin, we do not know what the spin operator or spin coordinate looks like, but we know it behaves like orbital angular momentum, giving another quantum number.
So for each quantum particle, there are 3 spatial degrees of freedom (which we can describe mathematically) and 1 spin coordinate (which we cannot describe mathematically but is there), so 4 degrees of freedom for each quantum particle.
From the Murnaghan equation, B_0 has units of pressure and B_1 is unitless. B_1 is unitless since derivative of a pressure with respect to pressure is unitless. Total energy values from QE are given in Ry, while lattice parameters are in Angstrom. So, some unit conversions are necessary to get B_0 in GPa. Your value of B_0 = 0.0811 is in Ry/Ang^3, so your value in GPa would be 177 GPa. I believe the expected is around 175 GPa.
I think we still bother with wave functions is that there is a prescription for getting the exact result given the computational resources. For example, the post HF methods are a prescribed way to get to the exact answer. For DFT, since we do not know the XC functional, we do not have the prescribed method for getting the exact result.
Thank you Ruben… It’s a good point. No, I did not do convergence tests with both potentials. But I did do convergence tests for the halite task using a different pseudo potential for Na and Cl (the one provided in the SSSP-precision download), and I still got considerable differences in the total stress. Perhaps I need to revisit.
