晶格常数计算

晶格常数计算通常有两种方法，BM 方程拟合法和直接优化晶格常数（vasp-ISIF=3）.

Birch-Murnaghan 状态方程拟合

todo...

Ex33-35 晶格参数的确定（Birch-Murnaghan 状态方程）| LVTHW

直接优化晶格常数

ISIF=3，晶胞中原子的坐标，晶胞形状，以及体系都随着优化的过程发生变化。此时（计算是体积发生了变化）ENCUT 必须设置，而且要设置高一些，手册建议是$1.3 \times max(\text{ENCUT of each element})$。这是为了尽可能消除 Pulay stress（普莱应力）对计算的影响。

若只进行体积守恒的弛豫，通常可以忽略 Pulay stress，因为 pulay 应力几乎是均匀的。

这一步不得不增大 ENCUT，（但整个计算 ENCUT 轻易是不变的），是这一步例外，一旦计算完晶格常数，可以在这个基础上统一使用其他的 ENCUT。

POTCAR、KPOINTS、POSCAR 与单点计算一致就好。

Volume vs. energy, volume relaxations, Pulay Stress

If you are doing energy-volume calculations or cell shape and volume relaxations you must understand the Pulay stress, and related problems.

The Pulay stress arises from the fact that the plane wave basis set is not complete with respect to changes of the volume. Thus, unless absolute convergence with respect to the basis set has been achieved - the diagonal components of the stress tensor are incorrect. This error is often called "Pulay stress". The error is almost isotropic (i.e. the same for each diagonal component), and for a finite basis set it tends to decrease volume compared to fully converged calculations (or calculations with a constant energy cutoff).

The Pulay stress and related problems affect the behavior of VASP and any plane wave code in several ways: First it evidently affects the stress tensor calculated by VASP, i.e. the diagonal components of the stress tensor are incorrect, unless the energy cutoff is very large (ENMAX=1.3 * default is usually a safe setting to obtain a reliable stress tensor).

Ex36 晶格参数的确定（直接优化晶格常数）| LVTHW