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GIPAW – Linear response in the presence of
QE developers’ mee7ng Linear Response Trieste, January 18 – 21, 2016 GIPAW – Linear response in the presence of magne7c fields Uwe Gerstmann University of Paderborn, Germany Davide Ceresoli Emine Kucukbenli Ari Parvo Seitsonen Originally aimed to calculate NMR chemical shiBs, later also the EPR electronic g-‐tensor, ... Standard version: qe-gipaw-5.3.tar @ qe-‐forge QE developers’ mee7ng Linear Response Trieste, January 18 – 21, 2016 GIPAW – Linear Magne7c Response Uwe Gerstmann University of Paderborn, Germany Davide Ceresoli Emine Kucukbenli Ari Parvo Seitsonen Originally aimed to calculate NMR chemical shiBs, later also the EPR electronic g-‐tensor, ... Standard version: qe-gipaw-5.3.tar @ qe-‐forge QE developers’ mee7ng Linear Response Trieste, January 18 – 21, 2016 GIPAW – Linear Magne7c Response Originally aimed to calculate NMR chemical shiBs, later also the EPR electronic g-‐tensor,... GIPAW rouOnes/pseudopoten7als are also used for -‐ X-‐ray spectra (Xspectra): XANES, (XMCD) -‐ orbital magneOzaOon, converse NMR-‐approach -‐ SOC including two component noncolinear scheme using scalar-‐relaOvisOc GIPAW pseudos GIPAW-‐ Linear Magne7c Response QE Developers’ MeeOng, Trieste, January 18 – 21, 2016 EssenOal: B-‐field brings the phase of the wfc into play (to insure translaOonal invariance within PBC) The PAW augmentaOon scheme has to be extended in a Gauge Including way: à GIPAW GIPAW-‐ Linear Magne7c Response QE Developers’ MeeOng, Trieste, January 18 – 21, 2016 Basic quan7ty for NMR (EPR): (spin) currents induced by the B-‐field EPR: spin-‐currents à Green‘s funcOon required GIPAW-‐ Linear Magne7c Response QE Developers’ MeeOng, Trieste, January 18 – 21, 2016 Basic quan7ty for NMR (EPR): (spin) currents induced by the B-‐field r
‘-‐ r
NMR: Bind(r‘) = ... 3 ... |r‘-‐ r|
EPR: spin-‐currents à Green‘s funcOon required GIPAW-‐ Linear Magne7c Response QE Developers’ MeeOng, Trieste, January 18 – 21, 2016 Central rou7ne: greenfunction.f90
Green‘s funcOon@k+q to be applied on a modified version of the unperturbed wfc: Gk+q |psi > = Gk+q { Vk+q,k|evc>}; q = {0, ± Δq ei with i=x,y,z} Similar to solve_linter.f90 in PH, it calls cgsolve_all.f90 iteraOve solver of linear systems cg_psi.f90 for (simple) precondiOoning (via diagonals of H), ch_psi_all.f90 for applicaOon of H-‐eS+P_cv orthogonalize.f90 for compuOng P_cv ( h_psi_q.f90 for BAND parallelzaOon only; otherwize: h_psi, calbec, s_psi ) GIPAW-‐ Linear Magne7c Response QE Developers’ MeeOng, Trieste, January 18 – 21, 2016 Central rou7ne: greenfunction.f90
Green‘s funcOon@k+q to be applied on a modified version of the unperturbed wfc: Gk+q |psi > = Gk+q { Vk+q,k|evc>}; q = {0, ± Δq ei with i=x,y,z} Similar to solve_linter.f90 in PH, it calls cgsolve_all.f90 iteraOve solver of linear systems cg_psi.f90 for (simple) precondiOoning (via diagonals of H), ch_psi_all.f90 for applicaOon of H-‐eS+P_cv orthogonalize.f90 for compuOng P_cv ( h_psi_q.f90 for BAND parallelzaOon only; instead: h_psi, calbec, s_psi ) GIPAW-‐ Linear Magne7c Response QE Developers’ MeeOng, Trieste, January 18 – 21, 2016 Central rou7ne: greenfunction.f90
Gk+q |psi > = Gk+q { Vk+q,k|evc>}; q = {0, ± Δq ei with i=x,y,z} in addiOon: apply_operators.f90 , e.g. apply Vk+q,k to rhs compute_u_kq.f90 prepares unperturbed wfc@k+q NEW: Speed-‐up for small Δq: resuse Gk+q |psi > from previous q, ch_psi.f90 only for q=0. Includes all things for precondiOoning, e.g. also small parts from phq_init.f90:
eprec = 1.35*zdotc(evq,work)
GIPAW-‐ Linear Magne7c Response QE Developers’ MeeOng, Trieste, January 18 – 21, 2016 Central rou7ne: greenfunction.f90
Gk+q |psi > = Gk+q { Vk+q,k|evc>}; q = {0, ± Δq ei with i=x,y,z} in addiOon: apply_operators.f90 , e.g. apply Vk+q,k to rhs compute_u_kq.f90 prepares unperturbed wfc@k+q Specific topics: -‐ quanOOes at k and k+q must have the same G-‐vector ordering; we call gk_sort only for k, not for k+q. -‐ symmetry operaOons that do not map cartesian axes might be – in principle – removed (as done in 5.3.0), but: NEW: it works also with full symmetry, if symmetrizaOon is applied at the very end (onto the full tensors) excusively. GIPAW-‐ Linear Magne7c Response QE Developers’ MeeOng, Trieste, January 18 – 21, 2016 LR related rou7nes (as a general observa6on): LR in GIPAW has very few dependencies, can be easily decoupled from the code, and can be „librarized“ away (into LR_Modules). As my present personal opinion: greenfunction.f90 (or something like that) should be either kept GIPAW-‐specific or solve_linter.f90 should be reorganized, split-‐up into less PH-specific logical subrouOnes, may be all of them kept within the same file. interface between GIPAW/LR_Modules can be changed accordingly. GIPAW-‐ Linear Magne7c Response QE Developers’ MeeOng, Trieste, January 18 – 21, 2016 Open Ques7on (loosely related to LR):
-‐ Where to put the Berry-‐phase rouOnes applicable onto NMR/EPR, GIPAW-‐tree or (parOally) PW-‐core? -‐ orbital magneOzaOon as a more general quanOty (MTM analogue to MTM, suggesOng PW), but to compute accurate du/dk: greenfunction.f90 Proposal: keep it close to “NMR/EPR“, should be found in GIPAW, e.g.: Work in progress, perspec7ves:
-‐ Zero-‐Field Spliqng (ZFS) of EPR, both DS-‐S and DSO! -‐ NMR/EPR for hybrid funcOonals -‐ NMR with spin-‐orbit coupling, colinear & non-‐colinear based on relaOvisOc & scalar relaOvisOc (GI)PAW pseudos -‐ Circular Dichroism of X-‐ray AdsorpOon (XMCD) (Mateo Calandra, UG) Thanks for your aZen7on! GIPAW-‐ Linear Magne7c Response QE Developers’ MeeOng, Trieste, January 18 – 21, 2016 Orbital magne7za7on EPR 2nd method: beyond perturba7on theory htp://www.quantum-‐espresso.org Orbital magne7za7on EPR 2nd method: beyond perturba7on theory htp://www.quantum-‐espresso.org Calcula7ng the g-‐tensor – two different methods Both methods are now applicable also on metallic systems, e.g. electrons trapped by the conducOon band minimum in Si bulk: Strongly delocalized states: conducOon band electrons in Si: gexp = 1.9995 Young et al., PRB 55, 16245 (1997) cc unit cell (2 atoms), (24 × 24 × 24) MP k-‐point set: gDFT 1 = 1.9991 (Berry phase) gDFT 2 = 1.9990 (non-‐eq. GIPAW) Efficient relativistic DFT calculations
Bi(111) bilayer 2
scalar-‐rela/vis/c pseudopoten/als: -‐ RelaOvisOc kineOc energy -‐ spin-‐orbit (SO) coupling neglected 1.5
1
0.5
EF
0
E [eV]
-0.5
-1
-1.5
-2
-2.5
-3
-3.5
-4
scalar-rel.
-4.5
M
K
M
18 Efficient relativistic DFT calculations
Bi(111) bilayer E [eV]
scalar-‐rela/vis/c pseudopoten/als: -‐ RelaOvisOc kineOc energy -‐ spin-‐orbit (SO) coupling neglected full-‐rela7vis7c approach: large SO coupling effects, but: factor-‐of-‐40 more computaOonal costs 2
1.5
1
0.5
EF
0
-0.5
-1
-1.5
-2
-2.5
-3
-3.5
full-rel.
-4
scalar-rel.
-4.5
M
K
M
19 Efficient relativistic DFT calculations
Bi(111) bilayer 1.5
1
0.5
EF
0
-0.5
E [eV]
scalar-‐rela/vis/c pseudopoten/als: -‐ RelaOvisOc kineOc energy -‐ spin-‐orbit (SO) coupling neglected alterna7ve rela7vis7c approach: PAW-‐reconstruc7on of SO coupling 2
-1
-1.5
-2
-2.5
-3
-3.5
full-rel.
-4
Pauli
scalar-rel.
-4.5
M
K
M
20 Efficient relativistic DFT calculations
Bi(111) bilayer 2
1.5
1
0.5
EF
0
-0.5
E [eV]
scalar-‐rela/vis/c pseudopoten/als: -‐ RelaOvisOc kineOc energy -‐ spin-‐orbit (SO) coupling neglected alterna7ve rela7vis7c approach: PAW-‐reconstruc7on of SO coupling -1
-1.5
-2
-2.5
-3
-3.5
full-rel.
ZORA
Pauli
scalar-rel.
-4
-4.5
M
Γ
K
M
ZORA: 21 Efficient relativistic DFT calculations
Bi(111) bilayer 2
1.5
1
0.5
EF
0
-0.5
E [eV]
scalar-‐rela/vis/c pseudopoten/als: -‐ RelaOvisOc kineOc energy -‐ spin-‐orbit (SO) coupling neglected alterna7ve rela7vis7c approach: PAW-‐reconstruc7on of SO coupling -1
-1.5
-2
-2.5
-3
-3.5
full-rel.
ZORA
Pauli
scalar-rel.
-4
-4.5
M
Γ
K
M
iden7cal results ! 22 Efficient relativistic DFT calculations
efficient „reconstruc6on-‐only“ approach: rela7vis7c calcula7ons for large systems (500 atoms) possible: 23
