s rt rs srs - - PowerPoint PPT Presentation

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

❆s❦ ❍❥♦rt❤ ▲❛rs❡♥ ❛s❦❧❛rs❡♥❅❣♠❛✐❧✳❝♦♠

◆❛♥♦✲❜✐♦ ❙♣❡❝tr♦s❝♦♣② ●r♦✉♣ ❛♥❞ ❊❚❙❋ ❙❝✐❡♥t✐✜❝ ❉❡✈❡❧♦♣♠❡♥t ❈❡♥tr❡ ❯♥✐✈❡rs✐❞❛❞ ❞❡❧ P❛ís ❱❛s❝♦ ❯P❱✴❊❍❯

▼❛② ✸✶✱ ✷✵✶✼

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

• P❆❲

◮ ❉❡♥s✐t② ❢✉♥❝t✐♦♥❛❧ t❤❡♦r② ❝♦❞❡ ✇r✐tt❡♥ ✐♥ P②t❤♦♥ ❛♥❞ ❈ ◮ ❤tt♣s✿✴✴✇✐❦✐✳❢②s✐❦✳❞t✉✳❞❦✴❣♣❛✇✴ ◮ Pr♦❥❡❝t♦r ❛✉❣♠❡♥t❡❞ ✇❛✈❡ ♠❡t❤♦❞ ✭❇❧ö❝❤❧ P❤②s✳ ❘❡✈✳ ❇ ✺✵✱

✶✼✾✺✸✱ ✶✾✾✹✮

◮ ❈❛❧❝✉❧❛t✐♦♥s ❛r❡ ✇r✐tt❡♥ ❛s P②t❤♦♥ s❝r✐♣ts ✉s✐♥❣ ❆❙❊ ◮ ❚❤r❡❡ ❝❛❧❝✉❧❛t✐♦♥ ♠♦❞❡s✿ ❋❉✱ ▲❈❆❖✱ P❲ ◮ P❛r❛❧❧❡❧✐③❛t✐♦♥ ✇✐t❤ ▼P■❀ ❤✐❣❤❧② s❝❛❧❛❜❧❡ ✭❡①❝❡♣t P❲✮ ◮ P②t❤♦♥ ✐♥t❡r❢❛❝❡s ❢♦r ✐♠♣♦rt❛♥t ❢✉♥❝t✐♦♥s ❢r♦♠ ▼P■✱ ❇▲❆❙✱

▲❆P❆❈❑✱ ❙❝❛▲❆P❆❈❑

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

❚❤❡ ❝❛s❡ ❢♦r P②t❤♦♥ ✐♥ ❉❋❚ ❝♦❞❡s

◮ Pr♦❜❛❜❧② ♠♦r❡ t❤❛♥ ✾✵ ✪ ♦❢ ❈P❯ t✐♠❡ ✐s s♣❡♥t ✐♥ ❧❡ss t❤❛♥

✶✵ ✪ ♦❢ t❤❡ ❝♦❞❡

◮ ❲r✐t❡ ✾✵ ✪ ✐♥ ❛ ♥✐❝❡ ❧❛♥❣✉❛❣❡ ❛♥❞ ✶✵ ✪ ✐♥ ❈✴❋♦rtr❛♥ ◮ ❉❋❚ ❝♦❞❡s ❞♦ ♠❛♥② ♥♦♥✲❝♦♠♣✉t❛t✐♦♥❛❧ t❤✐♥❣s✿

◮ ●❧✉❡ ❝♦♠♣♦♥❡♥ts t♦❣❡t❤❡r ✭P♦✐ss♦♥✱ ❡✐❣❡♥s♦❧✈❡r✱ ♠✐①✐♥❣✱ ❡t❝✳✮ ◮ ❘❡❛❞ ❛♥❞ ✇r✐t❡ ❞❛t❛ ◮ ❙tr✐♥❣ ♣r♦❝❡ss✐♥❣ ✭♣❛rs❡ ♣s❡✉❞♦♣♦t❡♥t✐❛❧s✱ ❢♦r♠❛t ♦✉t♣✉t✱ ✳✳✳✮ ◮ P❛r❛❧❧❡❧ ♦♣❡r❛t✐♦♥s ✭t✐♠❡ s♣❡♥t ✇❛✐t✐♥❣ ❢♦r ❤❛r❞✇❛r❡✮

◮ ❉✐s❛❞✈❛♥t❛❣❡✿ ▼✐①✐♥❣ ❧❛♥❣✉❛❣❡s ❞♦❡s ❤❛✈❡ s♦♠❡ ❡①tr❛

❝♦♠♣❧❡①✐t②

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

P❆❲ ❛♥❞ t❤❡ q✉❡st ❢♦r s♠♦♦t❤ ✇❛✈❡❢✉♥❝t✐♦♥s

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Distance from atom [Bohr] −0.5 0.0 0.5 1.0 1.5 2.0 2.5 φ(r) [arb. units]

Fe 4s AE Fe 3d AE Fe 4s HGH Fe 3d HGH Fe 4s PAW Fe 3d PAW ◮ ❲❛✈❡❢✉♥❝t✐♦♥s ♦s❝✐❧❧❛t❡ ❛♥❞ ❛r❡ ❡①♣❡♥s✐✈❡ t♦ r❡♣r❡s❡♥t ◮ ❘❡♠♦✈❡ ❝♦r❡ ❡❧❡❝tr♦♥s✱ r❡♣❧❛❝❡ ♥✉❝❧❡✐ ✇✐t❤ ♣s❡✉❞♦♣♦t❡♥t✐❛❧s ◮ P❆❲✿ ❊①t❡♥s✐♦♥ t♦ ♣s❡✉❞♦♣♦t❡♥t✐❛❧s✳ ❆✈♦✐❞s

♥♦r♠✲❝♦♥s❡r✈❛t✐♦♥✱ ❛♥❞ r❡t❛✐♥s ✏❛❧❧✲❡❧❡❝tr♦♥✑ ✐♥❢♦r♠❛t✐♦♥

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

❚❤❡ ♣r♦❥❡❝t♦r ❛✉❣♠❡♥t❡❞ ✇❛✈❡ ♠❡t❤♦❞

◮ ❱❛❧❡♥❝❡ st❛t❡s r❡♣r❡s❡♥t❡❞ ❜② |ψ = ˆ

T | ˜ ψ

◮ P❆❲ tr❛♥s❢♦r♠❛t✐♦♥✿ ˆ

T = 1 +

• ai

(|φa

i − |˜

φa

i ) ˜

pa

i | ◮ ●✐✈❡♥ ❛t♦♠✐❝ st❛t❡s φa i (r)✱ ❝❤♦♦s❡ s♠♦♦t❤ ❢✉♥❝t✐♦♥s ˜

φa

i (r) ❛♥❞

❧♦❝❛❧✐③❡❞ ✏♣r♦❥❡❝t♦rs✑ ˜ pa

i (r)❀ t❤✐s ❞❡✜♥❡s ˆ

T ✳

◮ P❆❲ tr❛♥s❢♦r♠❛t✐♦♥ ♠❛♣s ♥✐❝❡ s♠♦♦t❤ ♣s❡✉❞♦✇❛✈❡❢✉♥❝t✐♦♥s

t♦ ✉❣❧② ♦s❝✐❧❧❛t✐♥❣ ❛❧❧✲❡❧❡❝tr♦♥ ✇❛✈❡❢✉♥❝t✐♦♥s

◮ ❈❛❧❝✉❧❛t❡ q✉❛♥t✐t✐❡s ❢r♦♠ s♠♦♦t❤ ❢✉♥❝t✐♦♥s ♣❧✉s ❛t♦♠✐❝

❝♦♥tr✐❜✉t✐♦♥s✿ φ| ˆ O|ψ = ˜ φ| ˆ O| ˜ ψ

• ✸❉ ❣r✐❞

+

• ai

˜ φ|˜ pa

i

❛t♦♠✐❝ ♣r♦♣❡rt✐❡s

• ❙②st❡♠ ✐♥❞❡♣❡♥❞❡♥t

˜ pa

i | ˜

ψ

◮ Pr♦❥❡❝t♦r ❢✉♥❝t✐♦♥s ❝♦✉♣❧❡ ✸❉ ❝❛❧❝✉❧❛t✐♦♥ t♦ ❛t♦♠✐❝ ❝♦rr❡❝t✐♦♥s

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

• P❆❲

❯♥✐❢♦r♠ r❡❛❧✲s♣❛❝❡ ❣r✐❞s

◮ ❆❝❝✉r❛t❡✱ ♣❛r❛❧❧❡❧✐③❡s ✈❡r② ✇❡❧❧ ◮ ●r✐❞ ❝❛✉s❡s ✏❡❣❣✲❜♦①✑ ❡✛❡❝t

◆✉♠❡r✐❝ ❛t♦♠✐❝ ♦r❜✐t❛❧s

◮ ❱❡r② ❢❛st ✕ ❡❛s② t♦ ❞♦ t❤♦✉s❛♥❞s ♦❢ ❛t♦♠s ◮ ◆♦t ❛s ❛❝❝✉r❛t❡❀ ❝❛♥♥♦t ❡❛s✐❧② r❡❛❝❤ ❝♦♠♣❧❡t❡ ❜❛s✐s s❡t

P❧❛♥❡✇❛✈❡ ♠♦❞❡

◮ ❋❛st ❢♦r s♠❛❧❧ s②st❡♠s ✭❝r②st❛❧s✮ ◮ P❧❛♥❡✇❛✈❡s ♥✉♠❡r✐❝❛❧❧② ✇❡❧❧✲❜❡❤❛✈❡❞ ◮ ◆♦t s❝❛❧❛❜❧❡

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

❘❡❛❧✲s♣❛❝❡ ✭✏❋❉✑✮ ♠♦❞❡

◮ ●P❆❲✭♠♦❞❡❂✬❢❞✬✱ ❤❂✵✳✶✽✮ ◮ ■t❡r❛t✐✈❡ ❡✐❣❡♥s♦❧✈❡rs ✭s♦❧✈❡ ✏❛ ❜✐t✑ ❡✈❡r② ✐t❡r❛t✐♦♥✮ ◮ ✸❉ ♠❛✐♥ ❈P❯ ♠❡s❤✿ ❞✐str✐❜✉t❡ ψkn(r) ♦✈❡r s♣✐♥s✴k✲♣♦✐♥ts✱

❞♦♠❛✐♥s ❛♥❞ ❜❛♥❞s

◮ ❲❛✈❡ ❢✉♥❝t✐♦♥s ♦♥ ❝♦❛rs❡ ❣r✐❞✱ ❞❡♥s✐t②✴♣♦t❡♥t✐❛❧ ♦♥ ✜♥❡ ❣r✐❞ ◮ ▼✉❧t✐❣r✐❞✿ ❙♦❧✈❡ ✷①✷①✷ ❣r✐❞❀ t❤❡♥ ♦♥ ✹①✹①✹ ❣r✐❞❀ t❤❡♥ ♦♥

✽①✽①✽ ❣r✐❞❀ ❡t❝✳

◮ ❋❡❛t✉r❡s✿ ❘❡❛❧✲t✐♠❡ ❚❉❉❋❚✱ ▲✐♥❡❛r r❡s♣♦♥s❡ ❚❉❉❋❚

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

❙t❡♥❝✐❧s

◮ ❉✐✛❡r❡♥t✐❛❧ ♦♣❡r❛t♦rs r❡♣r❡s❡♥t❡❞ ❜② ✜♥✐t❡✲❞✐✛❡r❡♥❝❡ st❡♥❝✐❧s ◮ ˆ

O ˜ ψ(x, y, z) =

• ijk

wijk ˜ ψ(x + i dx, y + j dy, z + k dz) ① ① ① ① ① ① ① ① ① ▼♦r❡ ♥❡❛r❡st ♥❡✐❣❤❜♦✉rs → ❤✐❣❤❡r ♦r❞❡r → ❜❡tt❡r ❝♦♥✈❡r❣❡♥❝❡

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

P❲ ♠♦❞❡

◮ ●P❆❲✭♠♦❞❡❂P❲✭✹✵✵✮✮ ◮ ❙❛♠❡ ❡✐❣❡♥s♦❧✈❡rs ❛s ❋❉ ♠♦❞❡ ✭✐t❡r❛t✐✈❡✮ ◮ ✭❆❧♠♦st✮ ♥♦ ❡❣❣✲❜♦① ❡✛❡❝t ◮ P❛r❛❧❧❡❧✐③❡ ♦✈❡r s♣✐♥s✴k✲♣♦✐♥ts ❛♥❞ st❛t❡s ✭✏❜❛♥❞s✑✮ ◮ ❖♥❧② ♠♦❞❡ s✉♣♣♦rt✐♥❣ str❡ss❡s ◮ ❋❡❛t✉r❡s✿ ❘P❆ ❧✐♥❡❛r r❡s♣♦♥s❡✱ G0W0 ✭♥♦t s❡❧❢❝♦♥s✐st❡♥t ❜✉t

✉♥❞❡r ❞❡✈❡❧♦♣♠❡♥t✮✱ ❇❡t❤❡✕❙❛❧♣❡t❡r ❡q✉❛t✐♦♥

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

▲❈❆❖ ♠♦❞❡

◮ ●P❆❲✭♠♦❞❡❂✬❧❝❛♦✬✱ ❜❛s✐s❂✬❞③♣✬✱ ❤❂✵✳✶✽✮ ◮ ❲❛✈❡❢✉♥❝t✐♦♥s r❡♣r❡s❡♥t❡❞ ❛s | ˜

ψn =

• µ

|Φµ cµn

◮ |Φµ ❛r❡ ❧♦❝❛❧✐③❡❞ ❢✉♥❝t✐♦♥s ❜❛s❡❞ ♦♥ ❛t♦♠✐❝ ♦r❜✐t❛❧s ◮ ❙♠❛❧❧ ❜❛s✐s s❡t ✭∼ ✺✕✷✵ ❢✉♥❝t✐♦♥s ♣❡r ❛t♦♠✮ ❛❧❧♦✇s ❞✐r❡❝t

❞✐❛❣♦♥❛❧✐③❛t✐♦♥

◮ ❑♦❤♥✕❙❤❛♠ ❡q✉❛t✐♦♥s ❡①♣❧✐❝✐t❧② s♦❧✈❡❞ ❛s ❣❡♥❡r❛❧✐③❡❞

❡✐❣❡♥✈❛❧✉❡ ♣r♦❜❧❡♠✿

• ν

HµνCνn =

• ν

SµνCνnǫn

◮ P❛r❛❧❧❡❧✐③❡ ♦✈❡r s♣✐♥s✴k✲♣♦✐♥ts✱ ❞♦♠❛✐♥s✱ ♦r❜✐t❛❧s ◮ P❛r❛❧❧❡❧✐③❡ ❧✐♥❡❛r ❛❧❣❡❜r❛ ✇✐t❤ ❇▲❆❈❙✴❙❝❛▲❆P❆❈❑ ◮ ❋❡❛t✉r❡s✿ ❚✐♠❡✲♣r♦♣❛❣❛t✐♦♥ ❚❉❉❋❚ ✭▲❈❆❖✲❚❉❉❋❚✮

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

▲♦❝❛❧✐③❡❞ ❜❛s✐s s❡ts

1 2 3 4 5 6 7 8 r [Bohr] 0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ˜ φr

Basis functions: Au dzp 6s-sz confin 5d-sz confin 6s-dz split- 5d-dz split- p-type Gauss

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

P❛r❛❧❧❡❧ s❝❛❧✐♥❣

◮ P❛r❛❧❧❡❧ ♣❡r❢♦r♠❛♥❝❡ ♦❢ ●P❆❲✴▲❈❆❖ ◮ ❚✐♠✐♥❣ ♣❡r ❙❈❋ st❡♣ ◮ ✷✺✵✵✕✶✵✵✵✵ ❛t♦♠s

1 / 1 6 2 / 3 2 4 / 6 4 8 / 1 2 8 1 6 / 2 5 6

Number of nodes/cores

101 102 103 104

Time [s] 1N 3N SCF 2N 4N diag

10 10 10 10

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

P❛r❛❧❧❡❧ s❝r✐♣t✐♥❣

◮ ●P❆❲ ❝♦♠♣✐❧❡s ▼P■✲❡♥❛❜❧❡❞ ✐♥t❡r♣r❡t❡r ❣♣❛✇✲♣②t❤♦♥ ◮ ♠♣✐r✉♥ ✲♥♣ ✹ ❣♣❛✇✲♣②t❤♦♥ s❝r✐♣t✳♣② ◮ ❊❛❝❤ ❝♦r❡ ❤❛s ❞✐st✐♥❝t ✏r❛♥❦✑ ❜✉t r✉♥s t❤❡ s❛♠❡ ❝♦❞❡

✐♠♣♦rt ♥✉♠♣② ❛s ♥♣ ❢r♦♠ ❣♣❛✇✳♠♣✐ ✐♠♣♦rt ✇♦r❧❞ ♣r✐♥t✭✬❤❡❧❧♦ ④⑥✴④⑥ ✬✳❢♦r♠❛t✭✇♦r❧❞✳r❛♥❦ ✱ ✇♦r❧❞✳s✐③❡ ✮✮ ❛rr❛② ❂ ♥♣✳♦♥❡s ✭✸✮ ✯ ✇♦r❧❞✳r❛♥❦ ❜✐❣❴❛rr❛② ❂ ◆♦♥❡ ✐❢ ✇♦r❧❞✳r❛♥❦ ❂❂ ✵✿ ❜✐❣❴❛rr❛② ❂ ♥♣✳③❡r♦s ✭✸ ✯ ✇♦r❧❞✳s✐③❡✮ ✇♦r❧❞✳❣❛t❤❡r✭❛rr❛② ✱ ✵✱ ❜✐❣❴❛rr❛② ✮ ✐❢ ✇♦r❧❞✳r❛♥❦ ❂❂ ✵✿ ♣r✐♥t✭❜✐❣❴❛rr❛② ✮ ✇♦r❧❞✳s✉♠✭❛rr❛②✮ ♣r✐♥t✭❛rr❛②✮

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

❆❙❊

◮ ❲❡❜ ♣❛❣❡✿ ❤tt♣s✿✴✴✇✐❦✐✳❢②s✐❦✳❞t✉✳❞❦✴❛s❡✴ ◮ ▼❛✐❧✐♥❣ ❧✐st✿ ❛s❡✲✉s❡rs❅❧✐sts❡r✈✳❢②s✐❦✳❞t✉✳❞❦ ◮ ❣✐t✿ ❤tt♣s✿✴✴❣✐t❧❛❜✳❝♦♠✴❛s❡✴❛s❡ ◮ ■❘❈✿ ★❛s❡ ♦♥ ✐r❝✳❢r❡❡♥♦❞❡✳♥❡t ◮ ▲✐❝❡♥s❡✿ ▲●P▲✈✷✳✶✰

• P❆❲

◮ ❲❡❜ ♣❛❣❡✿ ❤tt♣s✿✴✴✇✐❦✐✳❢②s✐❦✳❞t✉✳❞❦✴❣♣❛✇✴ ◮ ▼❛✐❧✐♥❣ ❧✐st✿ ❣♣❛✇✲✉s❡rs❅❧✐sts❡r✈✳❢②s✐❦✳❞t✉✳❞❦ ◮ ❣✐t✿ ❤tt♣s✿✴✴❣✐t❧❛❜✳❝♦♠✴❣♣❛✇✴❣♣❛✇ ◮ ■❘❈✿ ★❣♣❛✇ ♦♥ ✐r❝✳❢r❡❡♥♦❞❡✳♥❡t ◮ ▲✐❝❡♥s❡✿ ●P▲✈✸✰

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

❈♦♥tr✐❜✉t❡ t♦ ❆❙❊✦

◮ ❤tt♣s✿✴✴✇✐❦✐✳❢②s✐❦✳❞t✉✳❞❦✴❛s❡✴❞❡✈❡❧♦♣♠❡♥t✴

❝♦♥tr✐❜✉t❡✳❤t♠❧

◮ ❈r❡❛t❡ ❛❝❝♦✉♥t ♦♥ ●✐t❧❛❜ ◮ ❈❧♦♥❡ ❆❙❊ ✭❛♥❞ ❧❡❛r♥ ❣✐t✳✳✳✮ ◮ ❍❛❝❦ ◮ P✉s❤ ❝❤❛♥❣❡s t♦ ②♦✉r ♦✇♥ ❜r❛♥❝❤ ♦♥ ●✐t❧❛❜ ◮ ❈r❡❛t❡ ♠❡r❣❡ r❡q✉❡st

❚❤✐♥❣s t♦ ❞♦

◮ ❘❡♣♦rt ❛♥❞ ✜① ❜✉❣s ◮ ❆❞❞ ②♦✉r ❢❛✈♦✉r✐t❡ ❝❛❧❝✉❧❛t♦r ◮ ❆❞❞ ②♦✉r ❢❛✈♦✉r✐t❡ ✜❧❡ ❢♦r♠❛t ◮ ❚r❛♥s❧❛t❡ ❆❙❊ ●❯■ ✐♥t♦ ❈❛t❛❧❛♥

• P❆❲

❲r❛♣♣✐♥❣ ✉♣

❆s❦ ♥♦t ✇❤❛t ❢r❡❡ s♦❢t✇❛r❡ ❝❛♥ ❞♦ ❢♦r ②♦✉❀ ❛s❦ ✇❤❛t ②♦✉ ❝❛♥ ❞♦ ❢♦r ❢r❡❡ s♦❢t✇❛r❡✦ ✖ ◆♦t q✉✐t❡ ❏❋❑