Ab_init stress perturbation theory - Department of Physics and ...

Design of development process (continued)
(2)
• Third stage – 0 H 0 :
2
1 ∂ EHxc
E = T + V +
2 ∂ λ ∂ λ
occ
( λ1λ
2) (0) ( λ1λ2)
( λ1λ
2)
(0)
non-var ∑ ψα
(
ext
) ψα
α
– Validate term-by-term with “frozen wave function” numerical strain
derivatives of stress components
– Diagonal and off-diagonal 2DTE’s
1 2
– Numerical strain derivatives of forces for internal strain mixed 2DTE’s
– Frozen wf strain derivatives of the electric polarization are zero, so there is
no contribution to piezoelectric tensor from these terms
• Note that the numerical derivatives of stress need factor for
2DTE comparison
2
∂ E el
∂
= Ω
∂η ∂η ∂η
αβ γδ αβ
σ
( σ
γδ )
Ω
n
(0)