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

Design of development process (continued)
• Fourth stage –
2
– Use strain-perturbation wave functions
– is Cartesian strain or reduced atomic displacement
λ 1
• Electric field is special case –
occ
( λ 1 λ 2) ( 2) ( 1) ( 1) ( 1) (0)
non-stat
= ∑ ψ
λ ( λ λ λ
α
+
ext
+
Hxc0)
ψα
α
( λ )
ψ α
E T V H
∂ E 2Ω
∑
∂E ! !
∂
2 occ
( k!
el
j ) ( η )
=
iψ
3
m
ψ
αβ
m
d
j
ηαβ
(2 π )
∫ k k
k
BZ m
– Field and d/dk first-order wave function in reduced coordinates
Non-selfconsistent
• Validate using numerical strain derivatives of GS stresses, forces, and
polarization
– Use converged strained wave functions
– No subtractions since non-variational contributions are already validated
– For polarization, numerical derivatives have to be corrected to give “proper”
piezoelectric tensor (see Infos/theory/lr.pdf)
– Need to use finite-difference d/dk wf’s in RF calculation for accurate
comparison