❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❖ ❈❊❆❘➪ ❈❊◆❚❘❖ ❉❊ ❈■✃◆❈■❆❙
❉❊P❆❘❚❆▼❊◆❚❖ ❉❊ ❋❮❙■❈❆
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❋❮❙■❈❆
▼❆❯❘■❙❆◆ ❆▲❱❊❙ ▲■◆❖
▼❆●◆❊❚■❙▼❖ ❊▼ ◆❆◆❖❈❘■❙❚❆■❙ ❉❖P❆❉❖❙ ❈❖▼ ■▼P❯❘❊❩❆❙ ◆➹❖ ▼❆●◆➱❚■❈❆❙ ❊ P❘❖P❘■❊❆❉❆❉❊❙ ❊❙❚❘❯❚❯❘❆■❙✱
❊▲❊❚❘Ô◆■❈❆❙ ❊ ÓP❚■❈❆❙ ❉❊ P❖◆❚❖❙ ◗❯➶◆❚■❈❖❙ ❉❊ ❋Ó❙❋❖❘❖ ◆❊●❘❖
▼❆❯❘■❙❆◆ ❆▲❱❊❙ ▲■◆❖
▼❆●◆❊❚■❙▼❖ ❊▼ ◆❆◆❖❈❘■❙❚❆■❙ ❉❖P❆❉❖❙ ❈❖▼ ■▼P❯❘❊❩❆❙ ◆➹❖ ▼❆●◆➱❚■❈❆❙ ❊ P❘❖P❘■❊❆❉❆❉❊❙ ❊❙❚❘❯❚❯❘❆■❙✱ ❊▲❊❚❘Ô◆■❈❆❙ ❊ ÓP❚■❈❆❙
❉❊ P❖◆❚❖❙ ◗❯➶◆❚■❈❖❙ ❉❊ ❋Ó❙❋❖❘❖ ◆❊●❘❖
❚❡s❡ ❞❡ ❉♦✉t♦r❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá✱ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❛ ❛ ♦❜✲ t❡♥çã♦ ❞♦ ❚ít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❋ís✐❝❛✳ ➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦✿ ❋ís✐❝❛ ❞❛ ▼❛tér✐❛ ❈♦♥❞❡♥✲ s❛❞❛✳
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❏❡❛♥❧❡① ❙♦❛r❡s ❞❡ ❙♦✉s❛✳
Dados Internacionais de Catalogação na Publicação Universidade Federal do Ceará
Biblioteca Universitária
Gerada automaticamente pelo módulo Catalog, mediante os dados fornecidos pelo(a) autor(a)
L73m Lino, Maurisan Alves.
Magnetismo em nanocristais dopados com impurezas não magnéticas e propriedades estruturais, eletrônicas e ópticas de pontos quânticos de fósforo negro / Maurisan Alves Lino. – 2017.
106 f. : il. color.
Tese (doutorado) – Universidade Federal do Ceará, Centro de Ciências, Programa de Pós-Graduação em Física , Fortaleza, 2017.
Orientação: Prof. Dr. Jeanlex Soares de Sousa.
1. Nanocristais. 2. Pontos quânticos. 3. Teoria do funcional da densidade. 4. Excitons. 5. Fósforo negro. I. Título.
▼❆❯❘■❙❆◆ ❆▲❱❊❙ ▲■◆❖
▼❆●◆❊❚■❙▼❖ ❊▼ ◆❆◆❖❈❘■❙❚❆■❙ ❉❖P❆❉❖❙ ❈❖▼ ■▼P❯❘❊❩❆❙ ◆➹❖ ▼❆●◆➱❚■❈❆❙ ❊ P❘❖P❘■❊❆❉❆❉❊❙ ❊❙❚❘❯❚❯❘❆■❙✱ ❊▲❊❚❘Ô◆■❈❆❙ ❊ ÓP❚■❈❆❙
❉❊ P❖◆❚❖❙ ◗❯➶◆❚■❈❖❙ ❉❊ ❋Ó❙❋❖❘❖ ◆❊●❘❖
❚❡s❡ ❞❡ ❉♦✉t♦r❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá✱ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❛ ❛ ♦❜✲ t❡♥çã♦ ❞♦ ❚ít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❋ís✐❝❛✳ ➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦✿ ❋ís✐❝❛ ❞❛ ▼❛tér✐❛ ❈♦♥❞❡♥✲ s❛❞❛✳
❆♣r♦✈❛❞❛ ❡♠ ✵✶✴✶✷✴✷✵✶✼✳
❇❆◆❈❆ ❊❳❆▼■◆❆❉❖❘❆
Pr♦❢✳ ❉r✳ ❏❡❛♥❧❡① ❙♦❛r❡s ❞❡ ❙♦✉s❛ ✭❖r✐❡♥t❛❞♦r✮ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ✭❯❋❈✮
Pr♦❢✳ ❉r✳❘❛✐♠✉♥❞♦ ◆♦❣✉❡✐r❛ ❞❛ ❈♦st❛ ❋✐❧❤♦ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ✭❯❋❈✮
Pr♦❢✳ ❉r✳ ❏♦ã♦ ▼✐❧t♦♥ P❡r❡✐r❛ ❏ú♥✐♦r ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ✭❯❋❈✮
Pr♦❢✳ ❉r✳ ❊✇❡rt♦♥ ❲❛❣♥❡r ❙❛♥t♦s ❈❛❡t❛♥♦ ■♥st✐t✉t♦ ❋❡❞❡r❛❧ ❞❡ ❊❞✉❝❛çã♦✱ ❈✐ê♥❝✐❛ ❡ ❚❡❝♥♦❧♦❣✐❛ ❞♦
❈❡❛rá ✭■❋❈❊✮
Pr♦❢❛✳ ❉r❛✳ ❙✐❧✈✐❛ ❍❡❧❡♥❛ ❘♦❜❡rt♦ ❞❡ ❙❡♥❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❛ ■♥t❡❣r❛çã♦ ■♥t❡r♥❛❝✐♦♥❛❧ ❞❛ ▲✉s♦❢♦♥✐❛
➚ ♠✐♥❤❛ ❡s♣♦s❛✱ ■s❛❜❡❧ ❈r✐st✐♥❛✱ ♣♦r ❡st❛r ❛♦ ♠❡✉ ❧❛❞♦ ❞✉r❛♥t❡ t♦❞♦s ❡ss❡s ❛♥♦s ❞❡
❉♦✉t♦r❛❞♦✳
➚ ♠✐♥❤❛ ♠ã❡✱ ♠❡✉ ❛✈ô ❡ ❛✈ó ❏ú❧✐❛ ✭■♥ ▼❡♠♦r✐❛♠✮✱ sá❜✐❛ ♠✉❧❤❡r s❡♠✐❛♥❛❧❢❛❜❡t❛✱
❆●❘❆❉❊❈■▼❊◆❚❖❙
❆♦ Pr♦❢❡ss♦r ❏❡❛♥❧❡① ❙♦❛r❡s ❞❡ ❙♦✉s❛✱ ♣❡❧❛ ❛♠✐③❛❞❡✱ ♣❛❝✐ê♥❝✐❛✱ ❝♦♥✜❛♥ç❛ ❡ ♦r✐❡♥t❛çã♦ r❡s♣♦♥sá✈❡❧ ❞✉r❛♥t❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ss❛ ❚❡s❡✳
❆♦s Pr♦❢❡ss♦r❡s ❡ ❡st✉❞❛♥t❡s ❞♦ ❣r✉♣♦ ●❚▼❈ ♣❡❧❛s s✉❣❡stõ❡s✱ ❝rít✐❝❛s ❡ ♣♦r ❡st❛r❡♠ s❡♠♣r❡ ❡♠ ❜✉s❝❛ ❞❡ ♠❡❧❤♦r❛r ❛ ✐♥❢r❛❡str✉t✉r❛ ❞♦ ▲❛❜♦r❛tór✐♦✳
➚ ♠✐♥❤❛ ❡s♣♦s❛ ■s❛❜❡❧ ❈r✐st✐♥❛ ♣❡❧♦ ❝♦♠♣❛♥❤❡✐r✐s♠♦✱ ❝❛r✐♥❤♦✱ ❛♠♦r ❡ ♣r✐♥❝✐✲ ♣❛❧♠❡♥t❡ ♣♦r ❡st❛r tr❛③❡♥❞♦ ♥♦ss♦ ✜❧❤♦ ❈r✐st✐♥♦✳
❆♦s ♠❡✉s ❢❛♠✐❧✐❛r❡s✿ ✐r♠ã ✭❊❧❛♥❡✮✱ ♣❛❞r✐♥❤♦ ✭❋r❛♥❝✐♥é✮✱ ♣r✐♠❛ ✭❆♥❞r❡❛♥❡✮✱ ♠✐♥❤❛ ♠ã❡ ✭▲ú❝✐❛✮✱ ❛✈ó ❏ú❧✐❛ ✭■♥ ▼❡♠♦r✐❛♠✮ ❡ ❛✈ô ❏♦sé ♣♦r ❡st❛r❡♠ s❡♠♣r❡ ♦❢❡r❡❝❡♥❞♦ ❢♦rç❛s ❡ ❡stí♠✉❧♦✳
➚ ♠✐♥❤❛ s♦❣r❛ ❆♥❛ ■s❛❜❡❧✱ q✉❡ ❞❡s❡♠♣❡♥❤❛ ♦ ♣❛♣❡❧ ❞❡ ✉♠❛ s❡❣✉♥❞❛ ♠ã❡✳ ❆♦ ♠❡✉ ✐r♠ã♦ ❆♥❞ré✱ ♣❡❧❛s ✈❛❧✐♦s❛s ❞✐s❝✉ssõ❡s ❡ ❝♦♥tr✐❜✉✐çõ❡s ❞✉r❛♥t❡ ♥♦ss❛ tr❛❥❡tór✐❛ ❡st✉❞❛♥t✐❧ ❡ ♣r♦✜ss✐♦♥❛❧✳
❆♦s ♠❡✉s ❝✉♥❤❛❞♦s ♣❡❧♦ ❡stí♠✉❧♦ ❡ ❛♠✐③❛❞❡✳ ❆♦s s♦❜r✐♥❤♦s✱ s♦❜r✐♥❤❛s ❡ ❛✜❧❤❛❞♦s ♣❡❧♦ ❝❛r✐♥❤♦✳
❆♦s ❛♠✐❣♦s ❞❡ ❧♦♥❣❛ ❞❛t❛✿ ❆❧❡①✱ ❆❧❡①❛♥❞r❡ ●✉t❡♥❜❡r❣✱ ▼❡❞❡rã♦✱ ❍é❧✐q✉❡s✱ ■r✐s♠❛r✱ ❏♦♥❛s✱ ❑❛❣✐♠✉r❛ ❡ ❏♦♥❛t❤❛♥ ♣♦r ❡st❛r ❞✐s♣♦♥í✈❡❧ ♥❛s ❞✐✜❝✉❧❞❛❞❡s ❝♦♠♣✉t❛❝✐♦✲ ♥❛✐s✱ ❡ ♦✉tr♦s ♣❡❧❛ ❛♠✐③❛❞❡ ❡ ♠♦♠❡♥t♦s ❛❣r❛❞á✈❡✐s✳
❆♦s ♣r♦❢❡ss♦r❡s q✉❡ t✐✈❡ ♥❡ss❡s ❛♥♦s ❞❡ ❡st✉❞♦ ♥♦ ❉♦✉t♦r❛❞♦✱ ♣❡❧❛ ❢♦r♠❛çã♦ ❛❝❛❞ê♠✐❝❛ ❡ ♣❡❧♦ ❡①❡♠♣❧♦ ♣r♦✜ss✐♦♥❛❧✳
❆♦ ♣❡ss♦❛❧ ❞❛ s❡❝r❡t❛r✐❛ ❞❛ ❋ís✐❝❛✱ ♣❡❧♦s s❡r✈✐ç♦s ♣r❡st❛❞♦s✳
➚ ❈❆P❊❙✱ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦ ❞✉r❛♥t❡ ❛ r❡❛❧✐③❛çã♦ ❞❡st❛ ♣❡sq✉✐s❛✳
➚ ❯❋P■ ♣♦r t❡r ❝♦♥❝❡❞✐❞♦ ♠❡✉ ❛❢❛st❛♠❡♥t♦ ❞❛s ❛t✐✈✐❞❛❞❡s ❞♦❝❡♥t❡ ❞✉r❛♥t❡ ♦ ♣❡rí♦❞♦ ❞❡❞✐❝❛❞♦ ❛♦ ❉♦✉t♦r❛❞♦✳
❘❊❙❯▼❖
◆❛ ♣r✐♠❡✐r❛ ♣❛rt❡ ❞❡ss❛ t❡s❡✱ ✐♥✈❡st✐❣❛♠♦s ♥❛♥♦❝r✐st❛✐s ❞❡ ❙✐❧í❝✐♦✱ ❈❛r❜♦♥♦ ❡ ●❡r♠â♥✐♦ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ❡s❢ér✐❝♦s✱ ♣✉r♦s ❡ ❞♦♣❛❞♦s ❝♦♠ ✐♠♣✉r❡③❛s ♥ã♦ ♠❛❣♥ét✐❝❛s ✭❇♦r♦ ♦✉ ❋ós❢♦r♦ ✮ ❡ ❞✐â♠❡tr♦s ❡♥tr❡ ✼✱✸➴ ❡ ✸✺➴✳ ❚♦❞♦s ♦s ❝á❧❝✉❧♦s ❢♦r❛♠ r❡❛❧✐③❛❞♦s ✉s❛♥❞♦ ❚❡♦r✐❛ ❞♦ ❋✉♥❝✐♦♥❛❧ ❞❡ ❉❡♥s✐❞❛❞❡ ✭❉❋❚✮✱ ✐♠♣❧❡♠❡♥t❛❞♦ ♥♦ ♣r♦❣r❛♠❛ ❙■❊❙❚❆✳ ◆♦ss♦s r❡s✉❧t❛❞♦s ♠♦str❛♠ q✉❡ ♦s ♥❛♥♦❝r✐st❛✐s ❞♦♣❛❞♦s ❡①✐❜❡♠ ♠❛❣♥❡t✐s♠♦ q✉❡ ❞❡♣❡♥❞❡ ❞♦ ❞✐â♠❡tr♦✱ s❡♥❞♦ r❡❞✉③✐❞♦ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞♦s ❞✐â♠❡tr♦s✳ ❆ t❛①❛ ❞❡ r❡❞✉çã♦ ❞♦ ♠♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ❝♦♠ ♦ ❞✐â♠❡tr♦ ♠✉❞❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ t✐♣♦ ❞❡ ♥❛♥♦❝r✐st❛❧✳ ❊♠ t♦❞♦s ♦s ❝❛s♦s✱ ❛ s✐♠✉❧❛çã♦ ❝♦♠ s✉♣❡r❝é❧✉❧❛s ❞♦ ❜✉❧❦ ❞♦♣❛❞❛s r❡s✉❧t❛ ❡♠ ♠♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ♥✉❧♦✳ ❆❧é♠ ❞♦s ❝á❧❝✉❧♦s ❝♦♠ ❛ ❞♦♣❛❣❡♠ ♥♦ ❝❡♥tr♦✱ r❡❛❧✐③❛♠♦s ❝á❧❝✉❧♦s ♠✉❞❛♥❞♦ ❛ ♣♦s✐çã♦ ❞❛s ❞♦♣❛❣❡♥s ❛♦ ❧♦♥❣♦ ❞♦ r❛✐♦ ♥♦s ♥❛♥♦❝r✐st❛✐s ❞❡ ❙✐❧í❝✐♦ ❝♦♠ ❞✐â♠❡tr♦ ❞❡ ✷✵ ➴ ❡ ✷✺ ➴ ❡ ♥♦s ♥❛♥♦❝r✐st❛✐s ❞❡ ●❡r♠â♥✐♦ ❝♦♠ ♦s ❞✐â♠❡tr♦s ✶✽ ➴ ❡ ✷✸✱✻ ➴✱ ♦♥❞❡ ❡♥❝♦♥tr❛♠♦s ♦s❝✐❧❛çõ❡s ♥♦s ♠♦♠❡♥t♦s ♠❛❣♥ét✐❝♦s✳ ◆❛ s❡❣✉♥❞❛ ♣❛rt❡✱ ❛♣r❡s❡♥t❛♠♦s ✉♠ ❡st✉❞♦ t❡ór✐❝♦ ❞♦ ❡❢❡✐t♦ ❝❛✉s❛❞♦ ♣❡❧❛ ✐♥s❡rçã♦ ❞❡ ❡❧étr♦♥s ❡♠ ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡ ❢ós❢♦r♦ ♥❡❣r♦ ✭P◗❋◆s✮ ❝♦♠ ✉♠❛ ❡ ❞✉❛s ❝❛♠❛❞❛s✱ ❛❧❝❛♥ç❛♥❞♦ ❞✐â♠❡tr♦s ❞❡ ✷ ♥♠ ❡ ✸ ♥♠✳ ❉❡♠♦♥str❛♠♦s q✉❡ ♦s ♣♦♥t♦s q✉â♥t✐❝♦s sã♦ ❝❛♣❛③❡s ❞❡ ❛r♠❛③❡♥❛r ✉♠ ♥ú♠❡r♦ ♠á①✐♠♦ ❞❡ ❡❧étr♦♥s ✭◆♠❛①✮ q✉❡ ❞❡♣❡♥❞❡ ❞♦ t❛♠❛♥❤♦ ❧❛t❡r❛❧ ❡ ❞♦ ♥ú♠❡r♦ ❞❡ ❝❛♠❛❞❛s✱ ❞❡ ❢♦r♠❛ q✉❡ ❛♣ós ❡ss❡ ✭◆♠❛①✮ s✉r❣❡♠ ✐♥st❛❜✐❧✐❞❛❞❡s ❡str✉t✉r❛✐s✳ ❖ ♣♦♥t♦ q✉â♥t✐❝♦ ❝♦♠ ✉♠❛ ❝❛♠❛❞❛ ❞❡ ✸ ♥♠ ♣❛ss✐✈❛❞♦ ❝♦♠ ❤✐❞r♦❣ê♥✐♦s✱ ♣♦r ❡①❡♠♣❧♦✱ ♣♦❞❡ ❛r♠❛③❡♥❛r ♥♦ ♠á①✐♠♦ ✶✻ ❡❧étr♦♥s✱ ❡ ✉♠ ❡❧étr♦♥ ❛❞✐❝✐♦♥❛❧ ❝❛✉s❛ ❛ r❡♣✉❧sã♦ ❞♦s át♦♠♦s ❞❡ ❤✐❞r♦❣ê♥✐♦ ❞❛ ❜♦r❞❛✱ ❡ ❛❧❣✉♠❛s r❡♣✉❧sõ❡s ❞♦s ❤✐❞r♦❣ê♥✐♦s ❝♦♠ át♦♠♦s ❞❡ ❢ós❢♦r♦✳ ❈❛❧❝✉❧❛♠♦s ♦ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣✐❛ ❛❞✐❝✐♦♥❛❧ ✭❊❆✮✱ ♦♥❞❡ ♣❛r❛ ♣♦♥t♦s q✉â♥t✐❝♦s ❝♦♠ ✉♠❛ ❝❛♠❛❞❛ ❞❡ ✷ ♥♠ ❡ ✸ ♥♠ ❛ ✭❊❆✮ ✜❝❛ ❡♠ t♦r♥♦ ❞❡ ✵✱✹ ❡❱ ❡ ✵✱✸ ❡❱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ P❛r❛ ❞✉❛s ❝❛♠❛❞❛s ❝♦♠ ♦s ♠❡s♠♦ t❛♠❛♥❤♦s✱ ❛ ♠é❞✐❛ ❞❛ ✭❊❆✮ é ❡♥t♦r♥♦ ❞❡ ✵✱✷✺ ❡❱ ❡ ✵✱✷ ❡❱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❊ss❛s ❡♥❡r❣✐❛s sã♦ ♠✉✐t♦ ♠❛✐♦r❡s q✉❡ ❛ ❡♥❡r❣✐❛ tér♠✐❝❛ ❡♠ t❡♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡ ✭≈✸✵ ♠❡❱✮✱ s❛t✐s❢❛③❡♥❞♦ ❛ ❝♦♥❞✐çã♦ ❞♦ ❡❢❡✐t♦ ❜❧♦q✉❡✐♦ ❞❡ ❝♦✉❧♦♠❜✳ ❊ss❡s r❡s✉❧t❛❞♦s t♦r♥❛♠✲s❡ ✐♠♣♦rt❛♥t❡s ♣❛r❛ ❢✉t✉r♦s ❡st✉❞♦s ❡①♣❡r✐♠❡♥t❛✐s✱ ❛✜♠ ❞❡ ♦t✐♠✐③❛r ♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❡ ♥♦✈♦s ❞✐s♣♦s✐t✐✈♦s✳ ■♥✈❡st✐❣❛♠♦s t❛♠❜é♠ ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❞♦s P◗❋◆s ❞❡♣♦s✐t❛❞♦s ❡♠ s✉❜str❛t♦s ❞❡SiO2 ❡ Si✱ ♦♥❞❡ ♦s r❡s✉❧t❛❞♦s ❞❡✐①❛♠ ❝❧❛r♦ ♦ ❡❢❡✐t♦ ❞r❛♠át✐❝♦ ❞♦s s✉❜str❛t♦s ❡ ❞♦ ♥ú♠❡r♦ ❞❡ ❝❛♠❛❞❛s ❞♦s P◗❋◆s ♥♦ ❣❛♣ ❡ ❡s♣❡❝tr♦ ❡①❝✐tô♥✐❝♦✳
❆❇❙❚❘❆❈❚
❚❤❡ ✜rst ♣❛rt ♦❢ t❤✐s t❤❡s✐s ❛✐♠s t♦ st✉❞② ♦❢ ❙✐❧✐❝♦♥✱ ❈❛r❜♦♥ ❛♥❞ ●❡r♠❛♥✐✉♠ ♥❛♥♦❝r②st❛❧s ❞♦♣❡❞ ✇✐t❤ ❛ s✐♥❣❧❡ ✐♠♣✉r✐t② ✭❇♦r♦♥ ♦r P❤♦s♣❤♦r✉s✮ ❝♦♠ s✐③❡s r❛♥❣✐♥❣ ❜❡t✇❡❡♥ ✼✳✸➴ ❡ ✸✺➴✳ ❚❤❡ ❝❛❧❝✉❧❛t✐♦♥s ✇❡r❡ ♣❡r❢♦r♠❡❞ ✉s✐♥❣ ❉❡♥s✐t② ❋✉♥❝t✐♦♥❛❧ ❚❤❡♦r② ❛s ✐♠♣❧❡♠❡♥t❡❞ ✐♥ ❙■❊❙❚❆ ❝♦❞❡✳ ❖✉r r❡s✉❧ts s❤♦✇ t❤❛t t❤❡ ❞♦♣❡❞ ♥❛♥♦❝r②st❛❧s ❡①❤✐❜✐t s✐③❡✲❞❡♣❡♥❞❡♥t ♠❛❣♥❡t✐❝ ❞✐♣♦❧❡ ♠♦♠❡♥ts✱ ✈❛♥✐s❤✐♥❣ ❢♦r ❧❛r❣❡ ♥❛♥♦❝r②st❛❧ ❞✐❛♠❡t❡rs✳ ❚❤❡ r❛t❡ ♦❢ ❞✐♣♦❧❡ ♠♦♠❡♥t r❡❞✉❝t✐♦♥ ❞❡♣❡♥❞s ♦♥ t❤❡ ♥❛♥♦❝r②st❛❧ s♣❡❝✐♠❡♥✳ ■♥ ❛❧❧ ❝❛s❡s✱ t❤❡ ❜✉❧❦ ❝❛❧❝✉❧❛t✐♦♥s ♣r♦✈✐❞❡❞ ③❡r♦ ♠❛❣♥❡t✐❝ ❞✐♣♦❧❡ ♠♦♠❡♥t✳ ❲❡ ❛❧s♦ ♣❡r❢♦r♠❡❞ ❝❛❧❝✉❧❛t✐♦♥s ✇❤❡r❡ t❤❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ ✐♠♣✉r✐t② ✐s ❝❤❛♥❣❡❞ ✇✐t❤✐♥ t❤❡ ♥❛♥♦❝r②st❛❧ ♦❢ s✐❧✐❝♦♥ ❛♥❞ ❣❡r♠❛♥✐✉♠✱ ❛♥❞ ✇❡ ♦❜t❛✐♥❡❞ str♦♥❣ ♦s❝✐❧❧❛t✐♦♥ ♦❢ t❤❡ ♠❛❣♥❡t✐❝ ❞✐♣♦❧❡ ♠♦♠❡♥t✳ ■♥ t❤❡ s❡❝♦♥❞ ♣❛rt ✇❡ ♣r❡s❡♥t ❛ t❤❡♦r❡t✐❝❛❧ st✉❞② ♦❢ t❤❡ ❝❤❛r❣✐♥❣ ❡✛❡❝ts ✐♥ s✐♥❣❧❡ ❛♥❞ ❞♦✉❜❧❡ ❧❛②❡r ❜❧❛❝❦ ♣❤♦s♣❤♦r✉s q✉❛♥t✉♠ ❞♦ts ✭❇P◗❉s✮ ✇✐t❤ ❧❛t❡r❛❧ s✐③❡s ♦❢ ✷ ♥♠ ❛♥❞ ✸ ♥♠✳ ❲❡ ❞❡♠♦♥str❛t❡ t❤❛t t❤❡ ❝❤❛r❣✐♥❣ ♦❢ ❇P◗❉s ❛r❡ ❛❜❧❡ t♦ st♦r❡ ✉♣ t♦ ❛♥ ◆ ♠❛① ❡❧❡❝tr♦♥ ✭t❤❛t ❞❡♣❡♥❞s ♦♥ t❤❡ ❧❛t❡r❛❧ s✐③❡ ❛♥❞ ♥✉♠❜❡r ♦❢ ❧❛②❡rs ✐♥ t❤❡ ◗❉✮✱ ❛❢t❡r ✇❤✐❝❤ str✉❝t✉r❛❧ ✐♥st❛❜✐❧✐t✐❡s ❛r✐s❡s✳ ❋♦r ❡①❛♠♣❧❡✱ ✸ ♥♠ ✇✐❞❡ ❤②❞r♦❣❡♥✲♣❛ss✐✈❛t❡❞ s✐♥❣❧❡ ❧❛②❡r ❇P◗❉s ❝❛♥ ❤♦❧❞ ❛ ♠❛①✐♠✉♠ ♦❢ ✶✻ ❡❧❡❝tr♦♥s✱ ❛♥❞ ❛♥ ❛❞❞✐t✐♦♥❛❧ ❡❧❡❝tr♦♥ ❝❛✉s❡s t❤❡ ❡①♣❡❧❧✐♥❣ ♦❢ ❤②❞r♦❣❡♥ ❛t♦♠s ❢r♦♠ t❤❡ ◗❉ ❜♦r❞❡rs✳ ❲❡ ❛❧s♦ ❝❛❧❝✉❧❛t❡❞ t❤❡ ❛❞❞✐t✐♦♥ ❡♥❡r❣② ✭❊❆✮ s♣❡❝tr✉♠✳ ❋♦r s✐♥❣❧❡ ❧❛②❡r ◗❉s ✇✐t❤ ✷ ❛♥❞ ✸ ♥♠ ♦❢ ❧❛t❡r❛❧ s✐③❡s✱ t❤❡ ❛✈❡r❛❣❡ ❊❆ ✐s ❛r♦✉♥❞ ✵✳✹ ❡❱ ❛♥❞ ✵✳✸ ❡❱✱ r❡s♣❡❝t✐✈❡❧②✳ ❋♦r ❞♦✉❜❧❡ ❧❛②❡r ◗❉s ✇✐t❤ t❤❡ s❛♠❡ s✐③❡s✱ t❤❡ ❛✈❡r❛❣❡ ❊❆ ✐s ❛r♦✉♥❞ ✵✳✷✺ ❡❱ ❛♥❞ ✵✳✷ ❡❱✱ r❡s♣❡❝t✐✈❡❧②✳ ❚❤❡s❡ ❡♥❡r❣✐❡s ❛r❡ ♠✉❝❤ ❧❛r❣❡r t❤❛♥ t❤❡ t❤❡r♠❛❧ ❡♥❡r❣② ❛t r♦♦♠ t❡♠♣❡r❛t✉r❡ ✭≈ 30 ♠❡❱✮✱ s❛t✐s❢②✐♥❣ t❤❡ ❝♦♥❞✐t✐♦♥ ♦❢ t❤❡ ❡✛❡❝t ❈♦✉❧♦♠❜ ❜❧♦❝❦❛❞❡✳ ❚❤❡s❡ r❡s✉❧ts ❛r❡
✐♠♣♦rt❛♥t ❢♦r ❢✉t✉r❡ ❡①♣❡r✐♠❡♥t❛❧ st✉❞✐❡s✱ ✐♥ ♦r❞❡r t♦ ♦♣t✐♠✐③❡ t❤❡ ♦♣❡r❛t✐♦♥ ♦❢ ♥❡✇ ❞❡✈✐❝❡s✳ ❲❡ ❛❧s♦ ✐♥✈❡st✐❣❛t❡❞ t❤❡ ♦♣t✐❝❛❧ ♣r♦♣❡rt✐❡s ♦❢ P◗❋◆s ❞❡♣♦s✐t❡❞ ♦♥ s✉❜str❛t❡s ♦❢ SiO2 ❛♥❞ Si✱ ✇❤❡r❡ t❤❡ r❡s✉❧ts ♠❛❦❡ ❝❧❡❛r t❤❡ ❞r❛♠❛t✐❝ ❡✛❡❝t ♦❢ s✉❜str❛t❡s ❛♥❞ t❤❡ ♥✉♠❜❡r ♦❢ ❧❛②❡rs ♦❢ ❇P◗❉s ✐♥ t❤❡ ❡①❝✐t♦♥✐❝ ❣❛♣s ❛♥❞ ❡①❝✐t♦♥✐❝ s♣❡❝tr✉♠✳
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
❋✐❣✉r❛ ✶ ✕ ❈✐❝❧♦ ❛✉t♦❝♦♥s✐st❡♥t❡ ❞❛ ❉❋❚✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ❋✐❣✉r❛ ✷ ✕ ■❧✉str❛çã♦ ❞❡ ♣s❡✉❞♦✲♣♦t❡♥❝✐❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ❋✐❣✉r❛ ✸ ✕ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛ sí♥t❡s❡ ❞❡ ◆❈s❙✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ❋✐❣✉r❛ ✹ ✕ ■♠❛❣❡♥s ❢❡✐t❛s ♣♦r ❚❊▼ ❞❡ ◆❈s❙✐ ♣r♦❞✉③✐❞♦s ♣♦r ✭❛✮ r❡❞✉çã♦ ❞❡ s❛✐s ❞❡
❤❛❧♦❣❡♥❡t♦s✱ ✭❜✮ tr❛t❛♠❡♥t♦ tér♠✐❝♦ ❞❡ ❍❙◗ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ❋✐❣✉r❛ ✺ ✕ ■♠❛❣❡♠ ❋❧✉♦r❡s❝❡♥t❡ ❞❡ ❝❡❧✉❧❛s ❍❡▲❛ ✉s❛♥❞♦ ◆❈s❙✐ ❡♠✐ss♦r ❞❡ ▲✉③ ❛③✉❧✳ ✸✶ ❋✐❣✉r❛ ✻ ✕ ■♠❛❣❡♠ ♦❜t✐❞❛ ♣♦r ❚❊▼ ❞❡ ◆❈s●❡ ♣r❡♣❛r❛❞♦s ❝♦♠ ♦ ♣r❡❝✉rs♦r GeCl4
r❡❞✉③✐❞♦ ♣♦r LiAlH4 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ❋✐❣✉r❛ ✼ ✕ ❋✐❣✉r❛ ✐❧✉str❛♥❞♦ ❛ ❝â♠❛r❛ ♠❡tá❧✐❝❛ ♦♥❞❡ ♦❝♦rr❡ ♦ ♣r♦❝❡ss♦ ❞❡ ❞❡t♦♥❛çã♦
❞❡ ❡①♣❧♦s✐✈♦s q✉❡ ❢♦r♠❛♠ ♥❛♥♦❝r✐st❛✐s ❞❡ ❝❛r❜♦♥♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ❋✐❣✉r❛ ✽ ✕ ❆rr❛♥❥♦ ❡str✉t✉r❛❧ ❛✮ ◆❈❙✐ ❝♦♠ ❞✐â♠❡tr♦ ✶✵➴ ❡ ❜✮ ◆❈❙✐ ❝♦♠ ❞✐â♠❡tr♦
✷✺➴✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ❋✐❣✉r❛ ✾ ✕ ▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ❡♠ ❢✉♥çã♦ ❞♦ ❞✐â♠❡tr♦ ❞♦s ◆❈s ❞❡ ❈❛r❜♦♥♦ ✭◆❈s❈✮✱
❙✐❧í❝✐♦ ✭◆❈s❙✐✮ ❡ ●❡r♠â♥✐♦ ✭◆❈s●❡✮ ❝♦♠ ❞♦♣❛❣❡♥s ❇ ❡ P ♥♦ ❝❡♥tr♦✳ ✳ ✳ ✳ ✸✼ ❋✐❣✉r❛ ✶✵ ✕❉❡♥s✐❞❛❞❡s ❞❡ ❡st❛❞♦s ❞♦s ◆❈s ❞❡ ❈❛r❜♦♥♦ ✭◆❈s❈✮ ♣✉r♦s ❡ ❞♦♣❛❞♦s ❝♦♠
❇ ❡ P✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ❋✐❣✉r❛ ✶✶ ✕❉❡♥s✐❞❛❞❡s ❞❡ ❡st❛❞♦s t♦t❛❧ ❡ ♣♦r át♦♠♦s ❞♦s ◆❈s❈ ❝♦♠ ❞✐â♠❡tr♦ ✼✱✸
➴✭❞✼✱✸✮ ❞♦♣❛❞♦s ❝♦♠ ❇ ❡ P✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ❋✐❣✉r❛ ✶✷ ✕❉❡♥s✐❞❛❞❡s ❞❡ ❡st❛❞♦s ❞♦s ◆❈s ❞❡ ❙✐❧í❝✐♦ ✭◆❈s❙✐✮ ♣✉r♦s ❡ ❞♦♣❛❞♦s ❝♦♠
❇ ❡ P✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ❋✐❣✉r❛ ✶✸ ✕❉❡♥s✐❞❛❞❡s ❞❡ ❡st❛❞♦s t♦t❛❧ ❡ ♣♦r át♦♠♦s ❞♦s ◆❈s❙✐ ❝♦♠ ❞✐â♠❡tr♦ ✶✵
➴✭❞✶✵✮ ❞♦♣❛❞♦s ❝♦♠ ❇ ❡ P✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ❋✐❣✉r❛ ✶✹ ✕❉❡♥s✐❞❛❞❡s ❞❡ ❡st❛❞♦s ❞♦s ◆❈s ❞❡ ●❡r♠â♥✐♦ ✭◆❈s●❡✮ ♣✉r♦s ❡ ❞♦♣❛❞♦s
❝♦♠ ❇ ❡ P✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ❋✐❣✉r❛ ✶✺ ✕❉❡♥s✐❞❛❞❡s ❞❡ ❡st❛❞♦s t♦t❛❧ ❡ ♣♦r át♦♠♦s ❞♦s ◆❈s●❡ ❝♦♠ ❞✐â♠❡tr♦ ✶✶✱✸
➴ ✭❞✶✶✱✸✮ ❞♦♣❛❞♦s ❝♦♠ ❇ ❡ P✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ❋✐❣✉r❛ ✶✻ ✕❚❛❜❡❧❛ ❝♦♠ ♦s ♠♦♠❡♥t♦s ♠❛❣♥ét✐❝♦s ♠s ✭❞♦ ♦r❜✐t❛❧ s✮ ❡ ♠♣ ✭❞♦ ♦r❜✐t❛❧
♣✮ ❡♠ µB ❞♦s át♦♠♦s ♥♦s ◆❈s ❞❡ ❈❛r❜♦♥♦✱ ❙✐❧í❝✐♦ ❡ ●❡r♠â♥✐♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
❋✐❣✉r❛ ✶✼ ✕■❧✉str❛çã♦ ❞❛s ♣♦s✐çõ❡s ❞❛s ❞♦♣❛❣❡♥s ♥♦ ◆❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ❋✐❣✉r❛ ✶✽ ✕▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ❡ ♣♦s✐çã♦ r❛❞✐❛❧ ❞❛ ❞♦♣❛❣❡♠ ❇ ❡ P ♥♦ ◆❈❙✐ ❞❡
❋✐❣✉r❛ ✶✾ ✕❊♥❡r❣✐❛ ❞❡ ❋♦r♠❛çã♦ ❡♠ ❢✉♥çã♦ ❞❛ ♣♦s✐çã♦ ❞❛ ❞♦♣❛❣❡♠ ♥♦ ◆❈❙✐ ❞❡ ✷✵ ➴ ✭❞✷✵✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ❋✐❣✉r❛ ✷✵ ✕▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ❡ ♣♦s✐çã♦ r❛❞✐❛❧ ❞❛ ❞♦♣❛❣❡♠ ❇ ❡ P ♥♦ ◆❈❙✐ ❞❡ ✷✺
➴ ✭❞✷✺✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ❋✐❣✉r❛ ✷✶ ✕❊♥❡r❣✐❛ ❞❡ ❋♦r♠❛çã♦ ❡♠ ❢✉♥çã♦ ❞❛ ♣♦s✐çã♦ ❞❛ ❞♦♣❛❣❡♠ ♥♦ ◆❈❙✐ ❞❡ ✷✺
➴ ✭❞✷✺✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ❋✐❣✉r❛ ✷✷ ✕▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ❡ ♣♦s✐çã♦ r❛❞✐❛❧ ❞❛ ❞♦♣❛❣❡♠ ❇ ❡ P ♥♦ ◆❈●❡ ❞❡ ✶✽
➴ ✭❞✶✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ❋✐❣✉r❛ ✷✸ ✕❊♥❡r❣✐❛ ❞❡ ❋♦r♠❛çã♦ ❡♠ ❢✉♥çã♦ ❞❛ ♣♦s✐çã♦ ❞❛ ❞♦♣❛❣❡♠ ♥♦ ◆❈●❡ ❞❡ ✶✽
➴ ✭❞✶✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ❋✐❣✉r❛ ✷✹ ✕▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ❡ ♣♦s✐çã♦ r❛❞✐❛❧ ❞❛ ❞♦♣❛❣❡♠ ❇ ❡ P ♥♦ ◆❈●❡ ❞❡ ✷✸✱✻
➴ ✭❞✷✸✱✻✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ❋✐❣✉r❛ ✷✺ ✕❊♥❡r❣✐❛ ❞❡ ❋♦r♠❛çã♦ ❡♠ ❢✉♥çã♦ ❞❛ ♣♦s✐çã♦ ❞❛ ❞♦♣❛❣❡♠ ♥♦ ◆❈●❡ ❞❡ ✷✸✱✻
➴ ✭❞✷✸✱✻✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ❋✐❣✉r❛ ✷✻ ✕■❧✉str❛çã♦ ❞❛s ♣♦s✐çõ❡s ♣❛r❛ ❞✉❛s ❞♦♣❛❣❡♥s s✐♠✉❧tâ♥❡❛s ♥♦ ◆❈❙✐ ❞✷✵✳ ✳ ✳ ✹✾ ❋✐❣✉r❛ ✷✼ ✕❛✮ ❆rr❛♥❥♦ ❡str✉t✉r❛❧ ❞❡ ❞✉❛s ❝❛♠❛❞❛s ❞❡ ❢♦s❢♦r❡♥♦ ❡ ❜✮ ❛s ❞✐r❡çõ❡s ③✐❣③❛❣
❡ ❛r♠❝❤❛✐r ❞❡ ✉♠❛ ❝❛♠❛❞❛ ❞❡ ❢♦s❢♦r❡♥♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ❋✐❣✉r❛ ✷✽ ✕❛✮ ❋♦t♦❣r❛✜❛ ❡ ✐❧✉str❛çã♦ ❞♦ ❞✐s♣♦s✐t✐✈♦ ❞❡ ♠❡♠ór✐❛ ✢❡①í✈❡❧ ❢❛❜r✐❝❛❞♦✳
❜✮❈❛r❛❝t❡r✐③❛çã♦ ■✲❱ ❞❡ ✉♠ ❞✐s♣♦s✐t✐✈♦ ❞❡ ♠❡♠ór✐❛ ❜❛s❡❛❞♦ ♥♦ P◗❋◆ ❬✻✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ❋✐❣✉r❛ ✷✾ ✕❉✐❛❣r❛♠❛ ❞❡ ✉♠ ❞✐s♣♦s✐t✐✈♦ ❙❊❚ ❜❛s❡❛❞♦ ♥♦ ♣♦♥t♦ q✉â♥t✐❝♦ ✭P◗✮✳ ✳ ✳ ✳ ✺✹ ❋✐❣✉r❛ ✸✵ ✕✭❛✮ ❉✐❛❣r❛♠❛ ❞❡ ❡♥❡r❣✐❛ ❞❡ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦ ♥♦ r❡❣✐♠❡ ❞♦ ❜❧♦q✉❡✐♦ ❞❡
❈♦✉❧♦♠❜✱ ✭❜✮ ■❧✉str❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛ ❝♦rr❡♥t❡ IP Q ❛tr❛✈és ❞♦ P◗ ❡♠
❢✉♥çã♦ ❞❛ ✈♦❧t❛❣❡♠ ♣♦rt❛ VP✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
❋✐❣✉r❛ ✸✶ ✕●❡♦♠❡tr✐❛s r❡♣r❡s❡♥t❛♥❞♦ ♦s P◗❋◆s ✉s❛❞♦s ♥♦s ❝á❧❝✉❧♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ❋✐❣✉r❛ ✸✷ ✕❊♥❡r❣✐❛ t♦t❛❧ ❞❛s ♠♦♥♦❝❛♠❛❞❛s ❡ ❜✐❝❛♠❛❞❛s ❡♠ ❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡
❡❧étr♦♥s ◆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ❋✐❣✉r❛ ✸✸ ✕❱✐sã♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ ◆ ♥❛ ♠♦♥♦❝❛♠❛❞❛
❞❡ ✸ ♥♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ❋✐❣✉r❛ ✸✹ ✕❊s♣❡❝tr♦ ❞❛ ❡♥❡r❣✐❛ ❛❞✐❝✐♦♥❛❧ ❡♠ ❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ❡❧étr♦♥s ◆✳ ✳ ✳ ✳ ✺✽ ❋✐❣✉r❛ ✸✺ ✕❉❡♥s✐❞❛❞❡ t♦t❛❧ ❞❡ ❡st❛❞♦s ✭❉❖❙✮ ❞❛ ♠♦♥♦❝❛♠❛❞❛ ❡ ❜✐❝❛♠❛❞❛ ♣❛r❛ ❞✐✲
❢❡r❡♥t❡s ❡st❛❞♦s ❞❡ ❝❛r❣❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ❋✐❣✉r❛ ✸✻ ✕✭❛✲❜✮ ❱❛r✐❛çã♦ ❞♦ ❞✐â♠❡tr♦ ♣❛r❛ ♠♦♥♦❝❛♠❛❞❛s ❞❡ P◗❋◆s ❡ ✭❝✮ s❡♣❛r❛✲
❋✐❣✉r❛ ✸✼ ✕❊str✉t✉r❛ ❛tô♠✐❝❛ ❞❡ ✉♠❛ ♠♦♥♦❝❛♠❛❞❛ ❞♦ P◗❋◆ ❝♦♠ ❞✐â♠❡tr♦ ❛♣r♦①✐✲ ♠❛❞❛♠❡♥t❡ ❞❡ ✷♥♠✱ ❛ ❞✐r❡çã♦ ❛r♠❝❤❛✐r ❛❧✐♥❤❛❞❛ ❝♦♠ ♦ ❡①✐♦ ① ❡ ❛ ❞✐r❡çã♦ ③✐❣③❛❣ ❝♦♠ ♦ ❡✐①♦ ②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ❋✐❣✉r❛ ✸✽ ✕❊s♣❡❝tr♦ ❞❡ ❡♥❡r❣✐❛ ❞❡ ♣❛rtí❝✉❧❛ ú♥✐❝❛ ♣❛r❛ ♦s P◗❋◆s ✐s♦❧❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ❋✐❣✉r❛ ✸✾ ✕●❛♣ ❞❡ ♣❛rtí❝✉❧❛ ú♥✐❝❛Eg✱ ❣❛♣s ❡①❝✐tô♥✐❝♦s EX ❡ ❡♥❡r❣✐❛ ❞❡ ❧✐❣❛çã♦ EB
❞❡♣❡♥❞❡♥t❡ ❞♦ t❛♠❛♥❤♦ ❞♦ P◗❋◆ ❡♠ ❞✐❢❡r❡♥t❡s s✉❜str❛t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ❋✐❣✉r❛ ✹✵ ✕❊s♣❡❝tr♦ ❡①❝✐tô♥✐❝♦ ❞❡♣❡♥❞❡♥t❡ ❞♦ t❛♠❛♥❤♦ ❝❛❧❝✉❧❛❞♦ ❝♦♠ ♦ ❢♦r♠❛❧✐s♠♦
❈■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ❋✐❣✉r❛ ✹✶ ✕●❛♣s ❞❡ ❡♥❡r❣✐❛ ❞❡♣❡♥❞❡♥t❡s ❞♦ t❛♠❛♥❤♦ ❞♦ P◗ ❡ ❞♦ s✉❜str❛t♦ ❝❛❧❝✉❧❛❞♦s
❝♦♠ ♦ ♠ét♦❞♦ ❈■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ❋✐❣✉r❛ ✹✷ ✕❈♦♠♣♦♥❡♥t❡s r❡❛❧ ❡ ✐♠❛❣✐♥ár✐❛ ❞❛ ❢✉♥çã♦ ❞✐❡❧étr✐❝❛ε ♣❛r❛ ❛s ♠✉❧t✐❝❛♠❛✲
❞❛s ❞❡ ❋◆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ❋✐❣✉r❛ ✹✸ ✕●❛♣ ❞❡ ♣❛rtí❝✉❧❛ ú♥✐❝❛ ✭❛✮ ❡ ❡①❝✐tô♥✐❝♦ ❞❛s ♠✉❧t✐❝❛♠❛❞❛s ❞❡ P◗❋◆s
❞❡♣♦s✐t❛❞❛s ♥♦s s✉❜str❛t♦s ❞❡ SiO2 ✭❜✮ ❡ Si✭❝✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ❋✐❣✉r❛ ✹✹ ✕❊♥❡r❣✐❛ ❞❡ ❧✐❣❛çã♦ ❞♦ ❡①❝✐t♦♥ ❞❡♣❡♥❞❡♥t❡ ❞♦ t❛♠❛♥❤♦ ❞❛s ♠✉❧t✐❝❛♠❛❞❛s
❙❯▼➪❘■❖
✶ ■◆❚❘❖❉❯➬➹❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷ ▼❊❚❖❉❖▲❖●■❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✶ ❆ ❛♣r♦①✐♠❛çã♦ ❞❡ ❇♦r♥✲❖♣♣❡♥❤❡✐♠❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✷ ❆ ❚❡♦r✐❛ ❞♦ ❋✉♥❝✐♦♥❛❧ ❞❛ ❉❡♥s✐❞❛❞❡ ✲ ❉❋❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✸ ❆s ❡q✉❛çõ❡s ❞❡ ❑♦❤♥✲❙❤❛♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✹ ❖ ❚❡♦r❡♠❛ ❞❡ ❍❡❧❧♠❛♥♥✲❋❡②♥♠❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✺ ❆ ❚❡♦r✐❛ ❞♦s Ps❡✉❞♦s✲P♦t❡♥❝✐❛✐s✿ ❛♣r♦①✐♠❛çã♦ ♣❛r❛ ✐♥t❡r❛çã♦
❡❧étr♦♥✲♥ú❝❧❡♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✻ ❖ ❙■❊❙❚❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✻✳✶ ❖r❜✐t❛✐s ❆tô♠✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼
✸ ◆❆◆❖❈❘■❙❚❆■❙ ❉❊ ❙■▲í❈■❖✱ ❈❆❘❇❖◆❖ ❊ ●❊❘▼➶◆■❖
P❯❘❖❙ ❊ ❉❖P❆❉❖❙ ❈❖▼ ❇❖❘❖ ✭❇✮ ❊ ❋Ó❙❋❖❘❖ ✭P✮ ✳ ✳ ✷✾ ✸✳✶ ◆❛♥♦❝r✐st❛✐s ❞❡ ❙✐❧í❝✐♦ ✲ ◆❈s❙✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✷ ◆❛♥♦❝r✐st❛✐s ❞❡ ●❡r♠â♥✐♦ ✲ ◆❈s●❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✸ ◆❛♥♦❝r✐st❛✐s ❞❡ ❈❛r❜♦♥♦ ✲ ◆❈s❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸✳✹ ❘❡s✉❧t❛❞♦s ❡ ❞✐s❝✉ssõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✹✳✶ ▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ❡♠ ❢✉♥çã♦ ❞♦ ❞✐â♠❡tr♦ ❞♦s ◆❛♥♦❝r✐st❛✐s
✭◆❈s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✹✳✷ ▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ❡♠ ❢✉♥çã♦ ❞❛ ♣♦s✐çã♦ ❞❛ ❞♦♣❛❣❡♠ ♥♦s
◆❛♥♦❝r✐st❛✐s ❞❡ ❙✐❧í❝✐♦ ❡ ●❡r♠â♥✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✹ P❖◆❚❖❙ ◗❯➶◆❚■❈❖❙ ❉❊ ❋Ó❙❋❖❘❖ ◆❊●❘❖ ✭P◗❋◆❙✮ ✳ ✺✵
✹✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✷ P♦♥t♦s ◗✉â♥t✐❝♦s ❞❡ ❋ós❢♦r♦ ◆❡❣r♦ ✲ P◗❋◆s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✸ P♦♥t♦ ◗✉â♥t✐❝♦ ❝♦♠♦ ❚r❛♥s✐st♦r ❞❡ Ú♥✐❝♦ ❊❧étr♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✹ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✹✳✶ ❊♥❡r❣✐❛ t♦t❛❧ ❡♠ ❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ❡❧étr♦♥s ❛❞✐❝✐♦♥❛❞♦s ♥♦s
P◗❋◆s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✹✳✷ ❊s♣❡❝tr♦ ❞❡ ❡♥❡r❣✐❛ ❛❞✐❝✐♦♥❛❧ ✭❊A✮ ♥♦s P◗❋◆s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✺ P❘❖P❘■❊❉❆❉❊❙ ÓP❚■❈❆❙ ❉❊ P❖◆❚❖❙ ◗❯➶◆❚■❈❖❙ ❉❊
❋Ó❙❋❖❘❖ ◆❊●❘❖ ❉❊P❖❙■❚❆❉❖❙ ❊▼ ❙❯❇❙❚❘❆❚❖❙ ✳ ✳ ✻✶
✺✳✶✳✷ ▼♦❞❡❧♦ ❞❡ ❜❧✐♥❞❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✺✳✷ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✺✳✷✳✶ ❊s♣❡❝tr♦ ❞❡ ♣❛rtí❝✉❧❛ ú♥✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✺✳✷✳✷ ❊s♣❡❝tr♦ ❊①❝✐tô♥✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✺✳✷✳✸ ●❛♣s ❡①❝✐tô♥✐❝♦s ❡ ❡♥❡r❣✐❛s ❞❡ ❧✐❣❛çã♦ ❞❡ ❡①❝✐t♦♥ ❡♠ ♠✉❧t✐❝❛✲
♠❛❞❛s ❞❡ P◗❋◆s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✻ ❈❖◆❈▲❯❙Õ❊❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ❘❊❋❊❘✃◆❈■❆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ❆P✃◆❉■❈❊ ❆ ✲✲ P❯❇▲■❈❆➬➹❖ ❈❆❘❘❊●❆◆❉❖ ❖❙ P◗❋◆❙
❈❖▼ ❊▲➱❚❘❖◆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ❆P✃◆❉■❈❊ ❇ ✲✲ P❯❇▲■❈❆➬➹❖ ❉❖❙ ❊❋❊■❚❖❙ ❊❳❈■❚Ô◆■✲
❈❖❙ ❊▼ ▼❖◆❖❈❆▼❆❉❆❙ ❉❊ P◗❋◆❙ ✭❈❖▲❆❇❖❘❆❉❖❘✮ ✾✶
✶✸
✶ ■◆❚❘❖❉❯➬➹❖
❆ ❝♦♠♣r❡❡♥sã♦ ❡ ♦ ❝♦♥tr♦❧❡ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ❞♦s ♠❛t❡r✐❛✐s é ❝r✉❝✐❛❧ ♣❛r❛ ♠❡❧❤♦r❛r ❛ t❡❝♥♦❧♦❣✐❛ ❞❛ ✐♥❢♦r♠❛çã♦ ❡♠ q✉❡ ❛ ♥♦ss❛ ✈✐❞❛ ♠♦❞❡r♥❛ é ❝♦♥str✉í❞❛✳ P❛r❛ ✐ss♦✱ ❛s t❡♦r✐❛s ❛ss✉♠❡♠ ✉♠ ♣❛♣❡❧ ❝❡♥tr❛❧✱ ♣♦✐s ♦❢❡r❡❝❡♠ ✉♠❛ ❝♦♠♣r❡❡♥sã♦ ❞❛ ♠❛tér✐❛ ❡♠ ♥í✈❡❧ ♠✐❝rós❝♦♣✐❝♦✳ ■st♦ ♣❡r♠✐t❡ ♣r❡✈❡r ❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s✱ ❡❧❡trô♥✐❝❛s ❡ ❡str✉t✉r❛✐s ❞❡ ♥♦✈♦s ♠❛t❡r✐❛✐s ❛tr❛✈és ❞❡ ♠ét♦❞♦s t❡ór✐❝♦s ❞❡ ♣r✐♠❡✐r♦s ♣r✐♥❝í♣✐♦s✳ ❆t✉❛❧♠❡♥t❡✱ ❛ ✐♥✈❡st✐❣❛çã♦ t❡ór✐❝❛ ❞❡ ♥♦✈♦s ♠❛t❡r✐❛✐s r❡♣r❡s❡♥t❛ ✉♠ ♣❛ss♦ ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ❛ ✐♥♦✈❛çã♦✱ ❡❧❛❜♦r❛çã♦ ❡ ❢❛❜r✐❝❛çã♦ ❞❡ ♥♦✈♦s ❞✐s♣♦s✐t✐✈♦s✳
✶✹
♣♦s✐❝✐♦♥❛❞❛s ♣ró①✐♠❛s ❞❛ s✉♣❡r❢í❝✐❡✱ ❝♦♥✜r♠❛♥❞♦ ♦s r❡s✉❧t❛❞♦s ♦❜s❡r✈❛❞♦s ❡①♣❡r✐♠❡♥t❛❧✲ ♠❡♥t❡✳ ◗✉❛♥❞♦ ♥♦s r❡❢❡r✐♠♦s ❛♦s ◆❈❈s✱ ❡ss❡s t❛♠❜é♠ ♣♦❞❡♠ t❡r s✉❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s✱ ❛ss✐♠ ❝♦♠♦ q✉í♠✐❝❛s ❡ ❡❧❡trô♥✐❝❛s ❝♦♥tr♦❧❛❞❛s ♣♦r ❞♦♣❛❣❡♥s ❞❡ ❖①✐❣ê♥✐♦ ❡ ◆✐tr♦✲ ❣ê♥✐♦ ❬✽❪✳ ◆❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s✱ ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ú♥✐❝❛ q✉❡ ♦s ❞✐st✐♥❣✉❡ ❞♦s ♦✉tr♦s ♥❛♥♦♠❛t❡r✐❛✐s ❛❧ótr♦♣♦s ❞❡ ❝❛r❜♦♥♦ é ❛ ♣r❡s❡♥ç❛ ❞❡ ❝❡♥tr♦s ❞❡ ❞❡❢❡✐t♦s ✢✉♦r❡s❝❡♥t❡s✱ ♦♥❞❡ ♦ ❞❡❢❡✐t♦ ❞❡ ❝❡♥tr♦ ♠❛✐s ❝♦♠✉♠ é ♦ ◆✐tr♦❣ê♥✐♦✲❱❛❝â♥❝✐❛ ✭◆✲❱✮✱ s❡♥❞♦ ❝♦♠♣♦st♦ ♣♦r ❞♦✐s t✐♣♦s✿ ♦ ♥❡✉tr♦ ◆✲❱0 ❝♦♠ ❡♠✐ssã♦ ✢✉♦r❡s❝❡♥t❡ ❡♠ ✺✼✻♥♠ ❡ ♦ ♥❡❣❛t✐✈❛♠❡♥t❡ ❝❛rr❡❣❛❞♦ ◆✲❱− ❝♦♠ ❡♠✐ssã♦ ❡♠ ✻✸✽ ♥♠✳ ❊ss❛s ❡str✉t✉r❛s tê♠ s❡ ❛♣r❡s❡♥t❛❞♦ ❛❧t❛♠❡♥t❡ ❝♦♠♣❛tí✲
✈❡✐s ❡ ♥ã♦ tó①✐❝❛s ♣❛r❛ t❡❝✐❞♦s✱ ♦r❣❛♥✐s♠♦s ❜✐♦❧ó❣✐❝♦s ❡ ❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ❧✐❣❛çõ❡s ♣❡♥❞❡♥t❡s ♥❛s s✉❛s s✉♣❡r❢í❝✐❡s ❢❛❝✐❧✐t❛♠ ❢✉♥❝✐♦♥❛❧✐③❛çõ❡s s❡♠ ❛❢❡t❛r ❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐✲ ❝❛s ✐♥trí♥s❡❝❛s ❞♦s ❝❡♥tr♦s ❞❡ ❞❡❢❡✐t♦s ♥♦ ♥ú❝❧❡♦ ❞♦ ◆❈✱ t♦r♥❛♥❞♦✲❛s ✈✐á✈❡✐s ♣❛r❛ ✈ár✐❛s ❛♣❧✐❝❛çõ❡s ❜✐♦♠é❞✐❝❛s ❬✾❪✳ ❆❧é♠ ❞❡ss❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s✱ r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❥á ❞❡♠♦str❛r❛♠ q✉❡ é ♣♦ssí✈❡❧ ❞❡t❡❝t❛r ❝❛♠♣♦s ♠❛❣♥ét✐❝♦s ❞❡ ❜❛✐①❛ ✐♥t❡♥s✐❞❛❞❡ ✉s❛♥❞♦ ♥❛♥♦❝r✐st❛✐s ❞❡ ❞✐❛♠❛♥t❡ ❝♦♠ ❡ss❡s ❞❡❢❡✐t♦s ❞❡ ❝❡♥tr♦ ❬✶✵❪✳ ◆❛ ❧✐t❡r❛t✉r❛✱ ❛✐♥❞❛ ♥ã♦ ❡♥✲ ❝♦♥tr❛♠♦s r❡s✉❧t❛❞♦s r❡❧❛❝✐♦♥❛❞♦s ❛♦s ◆❈❈s ❞♦♣❛❞♦s ❝♦♠ ❇ ❡ P✱ ♣♦rt❛♥t♦✱ ♥❡ss❡ s❡♥t✐❞♦✱ ✈❛♠♦s s✐♠✉❧❛r ♦s ◆❈❈s ❝♦♠ ❛s ❞♦♣❛❣❡♥s ❇ ♦✉ P ✈❡r✐✜❝❛♥❞♦ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ❡❢❡✐t♦s ♠❛❣♥ét✐❝♦s ✈❛r✐❛♥❞♦ ♦s s❡✉s ❞✐â♠❡tr♦s✳ ◆♦ ❝❛♣ít✉❧♦ ✸✱ ❛♣r❡s❡♥t❛r❡♠♦s ✉♠❛ ❛❜♦r❞❛❣❡♠ ♠❛✐s ❡①t❡♥s❛ ❞❡ r❡s✉❧t❛❞♦s ♠♦str❛♥❞♦ ❛ sí♥t❡s❡ ❞❡ss❡s ◆❈s✳ ◗✉❛♥❞♦ ♥♦s ❞✐r❡❝✐♦♥❛♠♦s ❛♦ ●❡r♠â♥✐♦ ✭●❡✮✱ ✈✐♠♦s q✉❡ ❡❧❡ é ✉♠ ♠❛t❡r✐❛❧ ♣❛rt✐❝✉❧❛r♠❡♥t❡ ❛tr❛t✐✈♦ ❡♠ ❛♣❧✐❝❛çõ❡s ❞❡ ♦♣t♦❡❧❡trô♥✐❝❛ ♣♦r ❝♦♠❜✐♥❛r s❡✉ ❡str❡✐t♦ ❣❛♣ ❞❡ ❡♥❡r❣✐❛ ❝♦♠ s✉❛ ❛❧t❛ ♠♦❜✐❧✐❞❛❞❡ ❞❡ ♣♦rt❛❞♦r❡s✱ ❡ q✉❡ ♦s tr❛❜❛❧❤♦s ❡①♣❡r✐♠❡♥t❛✐s ❡stã♦ ❞✐r❡❝✐♦♥❛❞♦s ♣❛r❛ ❛ sí♥t❡s❡ ❞❡ ♥❛♥♦❡s✲ tr✉t✉r❛s ✈♦❧t❛❞❛s ♣❛r❛ ♣♦ssí✈❡✐s ❛♣❧✐❝❛çõ❡s ♥♦ ❝❛♠♣♦ t❡❝♥♦❧ó❣✐❝♦✳ ▼❛✐s ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ◆❈s●❡ s❡rã♦ ❡♥❢❛t✐③❛❞❛s t❛♠❜é♠ ♥♦ ❝❛♣ít✉❧♦ ✸✳
◆❛ s❡❣✉♥❞❛ ♣❛rt❡ ❞❡ss❛ ❚❡s❡✱ tr❛❜❛❧❤❛♠♦s ❝♦♠ ♥❛♥♦❡str✉t✉r❛s ❞❡ ❢ós❢♦r♦ ♥❡✲ ❣r♦ ✭❋◆✮ ❞❡ ♣♦✉❝❛s ❝❛♠❛❞❛s ♦❜t✐❞♦s r❡❝❡♥t❡♠❡♥t❡ ❡♠ ✷✵✶✹✳ ❆ ♠♦♥♦❝❛♠❛❞❛ ❞❡ ❋◆✱ t❛♠❜é♠ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❢♦s❢♦r❡♥♦✱ ❝♦♥s✐st❡ ❡♠ ✉♠ ♠❛t❡r✐❛❧ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❝✉❥❛s ♣r♦♣r✐✲ ❡❞❛❞❡s ❢ís✐❝❛s ❡ q✉í♠✐❝❛s sã♦ ✐♥t❡r❡ss❛♥t❡s ❬✶✶❪✳ ❉❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ♦ ❣r❛❢❡♥♦✱ ❡ss❡ ♠❛t❡r✐❛❧ s❡♠✐❝♦♥❞✉t♦r ♣♦❞❡ s❡r ♦❜t✐❞♦ ❡s❢♦❧✐❛♥❞♦ ♦ ❢ós❢♦r♦ ♥❡❣r♦ ♣❛r❛ s❡ ♦❜t❡r ❢♦❧❤❛s ❛t♦✲ ♠✐❝❛♠❡♥t❡ ✜♥❛s✱ ❝♦♠ ♦ ❣❛♣ ❞❡ ❡♥❡r❣✐❛ ✈❛r✐❛♥❞♦ ❞❡ ✵✱✸ ❡❱ ✭♣❛r❛ ♦ ❝r✐st❛❧✮ ❛té ♦ ✈❛❧♦r ❞❡ ✷✱✵ ❡❱ ✭♣❛r❛ ❛ ♠♦♥♦❝❛♠❛❞❛✮ ❬✶✷❪✳ ❊ss❡ ❢❛✐①❛ ❞❡ ✈❛❧♦r❡s ❛❧❝❛♥ç❛❞♦s ♣❡❧♦ ❣❛♣ ❞❡ ❡♥❡r❣✐❛ t♦r♥❛ ♦ ❢ós❢♦r♦ ♥❡❣r♦ ❡s♣❡❝✐❛❧♠❡♥t❡ ❛❞❡q✉❛❞♦ ♣❛r❛ ❛♣❧✐❝❛çõ❡s ❡♠ ✐♠❛❣❡♥s tér♠✐❝❛s ✭q✉❡ ♥♦r♠❛❧♠❡♥t❡ ❡①✐❣❡♠ s❡♠✐❝♦♥❞✉t♦r❡s ❝♦♠ ❣❛♣s ❞❡ ❡♥❡r❣✐❛ ❝♦♠♣r❡❡♥❞✐❞♦s ❡♥tr❡ ✭✵✱✶ ❡ ✶✱✵ ❡❱✮✱ ❡♠ ❣❡r❛çã♦ ❞❡ ❡♥❡r❣✐❛ t❡r♠♦❡❧étr✐❝❛ ✭✉s❛♠ ♠❛t❡r✐❛✐s ❝♦♠ ❣❛♣s ❞❡ ❡♥❡r❣✐❛ ❞❛ ♦r❞❡♠ ❞❡ ✵✱✷ ❛ ✵✱✸ ❡❱✮✱ ❡♠ ✜❜r❛s ❞❡ t❡❧❡❝♦♠✉♥✐❝❛çõ❡s ✭q✉❡ ❡♠♣r❡❣❛♠ ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♦♥❞❛ ♥♦ ❛❧❝❛♥❝❡ ❞❡ ✶✱✷ µ♠ ✲ ✶✱✺ µ♠✱ ❝♦rr❡s♣♦♥❞❡♥❞♦ ❛ ❡♥❡r❣✐❛s ❞❡ ❢ót♦♥s ❞❡ ✵✱✽ ❡❱ ❛té ✶✱✵
✶✺
❣❛♣s ❞❡ ❡♥❡r❣✐❛ ❡♥tr❡ ✶✳✷ ❡❱ ✲ ✶✳✻ ❡❱ ✮ ❬✶✸❪✳ ❈♦♠ ♦ ❛✈❛♥ç♦ ♥❛s té❝♥✐❝❛s ❡①♣❡r✐♠❡♥t❛✐s✱ ♦✉tr❛s ♥❛♥♦❡str✉t✉r❛s ❜❛s❡❛❞❛s ♥♦ ❢ós❢♦r♦ ♥❡❣r♦✱ ❝❤❛♠❛❞❛s ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡ ❢ós❢♦r♦ ♥❡❣r♦ ✭P◗❋◆✮✱ r❡❝❡♥t❡♠❡♥t❡ t✐✈❡r❛♠ s✉❛s sí♥t❡s❡s ❡st❛❜❡❧❡❝✐❞❛s✳ ❙❡✉s t❛♠❛♥❤♦s ✈❛r✐❛♠ ❞❡ ✷✱✶ ♥♠ ❛té ✷✵✵ ♥♠ ❝♦♠ ♠ú❧t✐♣❧❛s ❝❛♠❛❞❛s✱ ❡①✐❜✐♥❞♦ ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❡ ❡❧❡trô♥✐✲ ❝❛s ú♥✐❝❛s ❞❡✈✐❞♦ ❛♦ ❝♦♥✜♥❛♠❡♥t♦ q✉â♥t✐❝♦ ❡ ❛♦s ❡❢❡✐t♦s ❞❡ ❜♦r❞❛✱ t❡♥❞♦ ❝♦♠♦ ❛♣❧✐❝❛çã♦ ♣rát✐❝❛ ❛ ❢❛❜r✐❝❛çã♦ ❞❡ ❞✐s♣♦s✐t✐✈♦s ❞❡ ♠❡♠ór✐❛ ❝♦♠ ❜❛✐①❛ ♣♦tê♥❝✐❛ ❞❡ ♦♣❡r❛çã♦ ❬✶✹✱ ✶✺❪✳ ▼❡s♠♦ ❞✐❛♥t❡ ❞❡ss❛ ✈❛st❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ❛♣❧✐❝❛çã♦✱ ✐♥✈❡st✐❣❛r❡♠♦s ❛tr❛✈és ❞❡ ❝á❧❝✉❧♦s ❞❡ ♣r✐♠❡✐r♦s ♣r✐♥❝í♣✐♦s ❛✐♥❞❛ ❛ ✈✐❛❜✐❧✐❞❛❞❡ ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡ ❢ós❢♦r♦ ♥❡❣r♦ ✭P◗❋◆s✮ ❢✉♥❝✐♦♥❛r❡♠ ❝♦♠♦ ❞✐s♣♦s✐t✐✈♦s ❜❛s❡❛❞♦s ♥♦ ❡❢❡✐t♦ ❞♦ ❜❧♦q✉❡✐♦ ❞❡ ❈♦✉❧♦♠❜✱ ❞❡t❡r♠✐♥❛♥❞♦ ✉♠ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣✐❛ ❛❞✐❝✐♦♥❛❧ ♣❛r❛ ✉♠❛ ❡ ❞✉❛s ❝❛♠❛❞❛s ❛tr❛✈és ❞❛ ❛❞✐çã♦ ❞❡ ❡❧étr♦♥s✱ ♦♥❞❡ ❝♦♥s✐❞❡r❛♠♦s ❡ss❡s P◗❋◆s ❝♦♠♦ ♥❛♥♦❡str✉t✉r❛s ♦❜t✐❞❛s ❛ ♣❛rt✐r ❞❛s ❝❛♠❛❞❛s q✉❡ ❢♦r♠❛♠ ♦ ❜✉❧❦ ❞❡ ❢ós❢♦r♦ ❢❡❣r♦✳ ❆❧é♠ ❞♦s tr❛❜❛❧❤♦s ❡①♣❡r✐♠❡♥t❛✐s ❝✐t❛❞♦s ❛♥t❡s✱ ❡①✐st❡♠ ✈ár✐♦s ♦✉tr♦s ✈♦❧t❛❞♦s ♣❛r❛ ❛ sí♥t❡s❡ ❞❡ss❡s ♠❛t❡r✐❛✐s✱ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❝♦♥tr♦❧❛r s✉❛s ❡s♣❡ss✉r❛s ❡ t❛♠❛♥❤♦s ❧❛t❡r❛✐s✱ ♦♥❞❡ ♦s ❞❡t❛❧❤❡s s❡rã♦ ♠❡♥❝✐♦♥❛❞♦s ♥❛s s❡çõ❡s ❢✉t✉r❛s✳ ❱❛❧❡ r❡ss❛❧t❛r q✉❡ ❛s ❡str✉t✉r❛s ✉s❛❞❛s ♥❛s s✐♠✉❧❛çõ❡s ❡stã♦ ❜❛s❡❛❞❛s ♥❛s ❞✐♠❡♥sõ❡s ❡①✲ ♣❡r✐♠❡♥t❛✐s✳ P♦rt❛♥t♦✱ ♦s r❡s✉❧t❛❞♦s ❛♣r❡s❡♥t❛❞♦s ♣❛r❛ ♦s ❡s♣❡❝tr♦s ❞❡ ❡♥❡r❣✐❛ ❛❞✐❝✐♦♥❛❧ ♥♦s ♣❡r♠✐t✐rá ❛✈❛❧✐❛r ❛s ❝♦♥❞✐çõ❡s ♥❡❝❡ssár✐❛s ♣❛r❛ q✉❡ ❡ss❡s P◗❋◆s ♣♦ss❛♠ ❢✉t✉r❛♠❡♥t❡ s❡r ✉t✐❧✐③❛❞♦s ❝♦♠♦ ❞✐s♣♦s✐t✐✈♦s ❙❊❚ ✭❚r❛♥s✐st♦r ❞❡ ú♥✐❝♦ ❊❧étr♦♥✮✱ ❡ ♣♦r ❝♦♥s❡q✉ê♥❝✐❛ ♥❛ ❢❛❜r✐❝❛çã♦ ❞❡ ❞✐s♣♦s✐t✐✈♦s ❞❡ ♠❡♠ór✐❛✳ ❊♠ ♦✉tr❛ ♣❛rt❡ ❞❡ss❛ ❚❡s❡✱ ♠♦str❛♠♦s q✉❡ ♠✉❞❛♥ç❛s ❝♦♥s✐❞❡rá✈❡✐s ♦❝♦rr❡♠ ♥❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❞♦s P◗❋◆s ❝♦♠ ❞✐❢❡r❡♥t❡s t❛✲ ♠❛♥❤♦s ❞❡♣♦s✐t❛❞♦s ❡♠ ❞✐❢❡r❡♥t❡s s✉❜str❛t♦s✱ ♦ q✉❡ ♥♦s ❢❛③ ❝❤❡❣❛r à ❝♦♥❝❧✉sã♦ ❞❡ q✉❡ ♦s ❡s♣❡❝tr♦s ❞❡ ❡♥❡r❣✐❛ ❛❞✐❝✐♦♥❛❧✱ ❝❛❧❝✉❧❛❞♦s ♣❛r❛ ♦s P◗❋◆s ✐s♦❧❛❞♦s ♣♦❞❡♠ s♦❢r❡r ♠✉❞❛♥ç❛s ❞❡♣❡♥❞❡♥❞♦ ❞♦ t✐♣♦ ❞❡ s✉❜str❛t♦ ✉s❛❞♦ ♣❛r❛ ❛ ❞❡♣♦s✐çã♦✱ ✜❝❛♥❞♦ ❡ss❛ ❛♥á❧✐s❡ ♣❛r❛ ✉♠ ♠♦♠❡♥t♦ ♣♦st❡r✐♦r✳
✶✻
✷ ▼❊❚❖❉❖▲❖●■❆
❖ ❡st✉❞♦ r❡❛❧✐③❛❞♦ ♥❡ss❛ t❡s❡ ❞❡ ❞♦✉t♦r❛❞♦ ❢♦✐ ❜❛s❡❛❞♦ ❡♠ ❝á❧❝✉❧♦s ❞❡ ♣r✐✲ ♠❡✐r♦s ♣r✐♥❝í♣✐♦s✱ q✉❡ sã♦ ❝á❧❝✉❧♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❞❡r✐✈❛❞♦s ❞✐r❡t❛♠❡♥t❡ ❞❡ ♣r✐♥❝í♣✐♦s t❡ór✐❝♦s s❡♠ ❛ ✐♥❝❧✉sã♦ ❞❡ ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s✱ ♣❛rt✐♥❞♦ ❛♣❡♥❛s ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦s ❞❡ ▼❡❝â♥✐❝❛ ◗✉â♥t✐❝❛✳ P❛r❛ ♦❜t❡r♠♦s ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ❛ ❡str✉t✉r❛ ❡❧❡trô♥✐❝❛ ❞❡ ✉♠ s✐s✲ t❡♠❛✱ ♥❡❝❡ss✐t❛♠♦s ❞❡ ❝♦♥❤❡❝❡r s✉❛s ❢✉♥çõ❡s ❞❡ ♦♥❞❛ ❡ ♣❛r❛ ❝♦♥s❡❣✉✐r♠♦s t❛✐s ❢✉♥çõ❡s✱ ♣r❡❝✐s❛♠♦s ❡♥❝♦♥tr❛r ❛ s♦❧✉çã♦ ❞❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r ✐♥❞❡♣❡♥❞❡♥t❡ ❞♦ t❡♠♣♦ ♣❛r❛ ✉♠ s✐st❡♠❛ ❝♦♠♣♦st♦ ❞❡ ◆ ❡❧étr♦♥s ❡ ▼ ♥ú❝❧❡♦s✱ ❝✉❥❛ ❛ ❢♦r♠❛ é ❞❛❞❛ ♣❡❧❛ ❡q✉❛çã♦2.1❬✶✻❪✱
♦♥❞❡|Ψié ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❞♦ s✐st❡♠❛✱ε é ❛ ❛✉t♦❡♥❡r❣✐❛ ❡H é ♦ ♦♣❡r❛❞♦r ❍❛♠✐❧t♦♥✐❛♥♦
❞♦ ♣r♦❜❧❡♠❛✳
H|Ψi=ε|Ψi. ✭✷✳✶✮
◆♦ ❝❛s♦ ❞❡ át♦♠♦s✱ ♠♦❧é❝✉❧❛s ❡ só❧✐❞♦s q✉❡ sã♦ s✐st❡♠❛s q✉â♥t✐❝♦s ❞❡ ♥♦ss♦ ✐♥t❡r❡ss❡✱ ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛|Ψis❡rá ❢✉♥çã♦ ❞❡ t♦❞❛s ❛s ❝♦♦r❞❡♥❛❞❛s ♥✉❝❧❡❛r❡s ❡ ❡❧❡trô♥✐❝❛s ✭✐♥❞✐❝❛❞❛s ♣♦r R~ ❡ ~r✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✮✳ ❖ ❍❛♠✐❧t♦♥✐❛♥♦ H ♣❛r❛ ✉♠ s✐st❡♠❛ ♣♦❞❡ s❡r
❡s❝r✐t♦ ❝♦♠♦✿
H =−
N X i=1 1 2∇ 2 i − M X A=1 1
2MA
∇2A−
N X i=1 M X A=1 ZA riA + N X i=1 N X j>1 1 rij + M X A=1 M X B>A ZAZB
RAB
, ✭✷✳✷✮
♥❛ q✉❛❧ MA ❡ ZA sã♦ ❛ ♠❛ss❛ ❡ ♦ ♥ú♠❡r♦ ❛tô♠✐❝♦ ❞♦ ♥ú❝❧❡♦ ❆✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❖s
♦♣❡r❛❞♦r❡s ∇2
i ❡ ∇2A ❡♥✈♦❧✈❡♠ ❞✐❢❡r❡♥❝✐❛çõ❡s ❡♠ r❡❧❛çã♦ às ❝♦♦r❞❡♥❛❞❛s ❡❧❡trô♥✐❝❛s ❡
♥✉❝❧❡❛r❡s ♥❡ss❛ ♦r❞❡♠✱ ❞❡ t❛❧ ♠❛♥❡✐r❛ q✉❡ ♦ ♣r✐♠❡✐r♦ t❡r♠♦ r❡♣r❡s❡♥t❛ ♦ ♦♣❡r❛❞♦r ❞❡ ❡♥❡r❣✐❛ ❝✐♥ét✐❝❛ ❞♦s ❡❧étr♦♥s✱ ♦ s❡❣✉♥❞♦ t❡r♠♦ r❡❢❡r❡✲s❡ ❛♦ ♦♣❡r❛❞♦r ❞❡ ❡♥❡r❣✐❛ ❝✐♥ét✐❝❛ ❞♦s ♥ú❝❧❡♦s✳ ❖ t❡r❝❡✐r♦ ❝♦rr❡s♣♦♥❞❡ à ❛tr❛çã♦ ❝♦✉❧♦♠❜✐❛♥❛ ❡♥tr❡ ♦s ❡❧étr♦♥s ❡ ♥ú❝❧❡♦s ❡ riA = |r~i −R~A|✳ ❖ q✉❛rt♦ ❡ q✉✐♥t♦ t❡r♠♦s r❡♣r❡s❡♥t❛♠ ❛s r❡♣✉❧sõ❡s ❡❧étr♦♥✲❡❧étr♦♥ ❡
♥ú❝❧❡♦✲♥ú❝❧❡♦ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❊ss❛ ❡q✉❛çã♦✱ ❡s❝r✐t❛ ❡♠ ✉♥✐❞❛❞❡s ❛tô♠✐❝❛s✱ ♦♥❞❡¯h, e, me
✶✼
❛ s✐♠♣❧✐✜❝❛çã♦ ❞❛s ❞✐✜❝✉❧❞❛❞❡s ❝r✐❛❞❛s ♣❡❧♦s ❛❝♦♣❧❛♠❡♥t♦s ❞❛s ✈❛r✐á✈❡✐s ❡♥✈♦❧✈✐❞❛s✳ ◆❛s s❡çõ❡s s❡❣✉✐♥t❡s✱ s❡rã♦ ♠❡♥❝✐♦♥❛❞❛s ❡ ❞✐s❝✉t✐❞❛s ❛s ❛♣r♦①✐♠❛çõ❡s ✉s❛❞❛s ♥❛ r❡s♦❧✉çã♦ ❞❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r✳
✷✳✶ ❆ ❛♣r♦①✐♠❛çã♦ ❞❡ ❇♦r♥✲❖♣♣❡♥❤❡✐♠❡r
❆ s♦❧✉çã♦ ❞❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r(2.1)t♦r♥❛✲s❡ ✐♥✈✐á✈❡❧ ❞❡✈✐❞♦ ❛♦s ✐♥ú♠❡✲
r♦s ❛❝♦♣❧❛♠❡♥t♦s ❡①✐st❡♥t❡s ♥♦ s✐st❡♠❛✳ ❉❡ss❛ ❢♦r♠❛✱ ❢❛③✲s❡ ♥❡❝❡ssár✐♦ r❡❝♦rr❡r ❛ ❛♣r♦✲ ①✐♠❛çõ❡s ♣❛r❛ q✉❡ s❡❥❛ ♣♦ssí✈❡❧ r❡s♦❧✈ê✲❧❛✳ ❆ ♣r✐♠❡✐r❛ ❞❡❧❛s é ❛ ❛♣r♦①✐♠❛çã♦ ❞❡ ❇♦r♥✲ ❖♣♣❡♥❤❡✐♠❡r ❬✶✻❪✱ r❡s♣♦♥sá✈❡❧ ♣❡❧❛ s❡♣❛r❛çã♦ ❞♦s ♠♦✈✐♠❡♥t♦s ❞♦s ❡❧étr♦♥s ❡ ❞♦s ♥ú❝❧❡♦s✳ ❇❛s✐❝❛♠❡♥t❡✱ ❡❧❛ ♣❛rt❡ ❞♦ ♣r✐♥❝í♣✐♦ ❞❡ q✉❡ ♦s ❡❧étr♦♥s ♠♦✈❡♠✲s❡ ❜❡♠ ♠❛✐s r❛♣✐❞❛♠❡♥t❡ q✉❡ ♦s ♥ú❝❧❡♦s✱ ❞❡ ♠❛♥❡✐r❛ q✉❡ ❡st❡s ♣♦❞❡♠ s❡r ❝♦♥s✐❞❡r❛❞♦s ❝♦♠♦ ✜①♦s✳ P♦rt❛♥t♦✱ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞♦s ❡❧étr♦♥s✱ é ✉♠❛ ❜♦❛ ❛♣r♦①✐♠❛çã♦ ❝♦♥s✐❞❡rá✲❧♦s s♦❜ ✉♠ ❝❛♠♣♦ ❞❡ ♥ú✲ ❝❧❡♦s ✜①♦s ❡ s✉❛s ♣♦s✐çõ❡s ❞❡♣❡♥❞❡r❡♠ ❞❛s ❞✐❢❡r❡♥t❡s ❝♦♥✜❣✉r❛çõ❡s ❞❡ss❡s ♥ú❝❧❡♦s✳ ❈♦♠ ✐ss♦✱ ❛♥✉❧❛✲s❡ ❛ ❡♥❡r❣✐❛ ❝✐♥ét✐❝❛ ❞♦s ♥ú❝❧❡♦s ♥❛ ❡q✉❛çã♦ (2.2) ❡ ❛ r❡♣✉❧sã♦ ♥ú❝❧❡♦✲♥ú❝❧❡♦
t♦r♥❛✲s❡ ✉♠❛ ❝♦♥st❛♥t❡✳ ❖ ❍❛♠✐❧t♦♥✐❛♥♦ r❡s✉❧t❛♥t❡ é ♦ ❍❛♠✐❧t♦♥✐❛♥♦ ❡❧❡trô♥✐❝♦ q✉❡ ❞❡s✲ ❝r❡✈❡ ♦ ♠♦✈✐♠❡♥t♦ ❞❡ N ❡❧étr♦♥s ♥♦ ❝❛♠♣♦ ❞❡ M ♥ú❝❧❡♦s ✜①♦s✱ ❞❛❞♦ ♣♦r✿
Helec =− N X i=1 1 2∇ 2 i − N X i=1 M X A=1 ZA riA + 1 2 N X i=1 N X j>1 1 rij . ✭✷✳✸✮
❆ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❡❧❡trô♥✐❝❛ |Ψeleci✱ s♦❧✉çã♦ ❞❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r ♣❛r❛
❡ss❡ ❍❛♠✐❧t♦♥✐❛♥♦✱ ❞❡♣❡♥❞❡rá ❡①♣❧✐❝✐t❛♠❡♥t❡ ❞❛s ❝♦♦r❞❡♥❛❞❛s ❡❧❡trô♥✐❝❛sr~i ❡ ♣❛r❛♠❡tr✐✲
❝❛♠❡♥t❡ ❞❛s ❝♦♦r❞❡♥❛❞❛s ♥✉❝❧❡❛r❡s R~A✱ |Ψeleci = Ψ(~ri;R~A)✳ ❯♠❛ ❞❡♣❡♥❞ê♥❝✐❛ ♣❛r❛♠é✲
tr✐❝❛ s✐❣♥✐✜❝❛ q✉❡ |Ψeleci é ✉♠❛ ❢✉♥çã♦ ❞❛s ❝♦♦r❞❡♥❛❞❛s ❡❧❡trô♥✐❝❛s q✉❡ é ❞✐❢❡r❡♥t❡ ♣❛r❛ ❝❛❞❛ ❝♦♥✜❣✉r❛çã♦ ❞❛s ♣♦s✐çõ❡s ♥✉❝❧❡❛r❡s✳ ❊♠ t❡r♠♦s ♣rát✐❝♦s✱ ❛ s♦❧✉çã♦ ❞❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r ❡♥✈♦❧✈❡ ♦ ❍❛♠✐❧t♦♥✐❛♥♦ ❡❧❡trô♥✐❝♦✱
Helec|Ψeleci=εelec|Ψeleci, ✭✷✳✹✮
❡ ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❡❧❡trô♥✐❝❛✱
|Ψeleci= Ψ(r~i;R~A). ✭✷✳✺✮
❆ ❡♥❡r❣✐❛ t♦t❛❧✱ εtotal✱ ♣❛r❛ ✉♠❛ ❝♦♥✜❣✉r❛çã♦ ♥✉❝❧❡❛r R~A é ❞❛❞❛ ♣♦r✿
εtotal(R~A) = εelec(~ri, ~RA) + 1 2 M X A=1 M X B>A ZAZB
RAB
. ✭✷✳✻✮
P❛r❛ ♦ ♠♦✈✐♠❡♥t♦ ♥✉❝❧❡❛r ❬✶✼❪✱ ♥❛ ❛♣r♦①✐♠❛çã♦ ❞❡ ❇♦r♥✲❖♣♣❡♥❤❡✐♠❡r✱ t❡♠♦s
✶✽
Hnuclear=
M
X
A=1
1
2MA
▽2A+εtotal(R~A). ✭✷✳✼✮
❉❡ss❡ ♠♦❞♦✱ ♦ ♥ú❝❧❡♦ ♠♦✈❡✲s❡ ❡♠ ✉♠ ♣♦t❡♥❝✐❛❧ ♦❜t✐❞♦ ❞❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❡❧❡trô✲ ♥✐❝♦✳ ❆ s♦❧✉çã♦ ❞❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r ❝♦♥s✐❞❡r❛♥❞♦ ♦ ❍❛♠✐❧t♦♥✐❛♥♦ ♥✉❝❧❡❛rHnuclear✱
❞❡s❝r❡✈❡ ❛ ✈✐❜r❛çã♦✱ r♦t❛çã♦ ❡ tr❛♥s❧❛çã♦ ❞❛ ❡str✉t✉r❛ ❡♠ ❝♦♥s✐❞❡r❛çã♦✱ ♣♦ré♠ ♥♦ss♦ ✐♥✲ t❡r❡ss❡ é s♦♠❡♥t❡ ♥♦ ♣r♦❜❧❡♠❛ ❡❧❡trô♥✐❝♦✱ ✐st♦ é✱ ❡♠ r❡s♦❧✈❡r ❛ ❡q✉❛çã♦2.4✳ ◆♦ ❡♥t❛♥t♦✱
♣❛r❛ t❡r♠♦s ✉♠❛ ❞❡s❝r✐çã♦ ❝♦♠♣❧❡t❛ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ◆ ❡❧étr♦♥s✱ ♥❡❝❡ss✐t❛♠♦s ❛❧é♠ ❞❛s ❝♦♦r❞❡♥❛❞❛s ❡s♣❛❝✐❛✐s ~ri✱ ❡s♣❡❝✐✜❝❛r♠♦s ❛s ❝♦♦r❞❡♥❛❞❛s ❞❡ s♣✐♥ σi ❡ ❝♦♠ ✐ss♦ ❡♥❝♦♥tr❛r
❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❡❧❡trô♥✐❝❛ ♥ã♦ é ✉♠ ♣r♦❜❧❡♠❛ ❢á❝✐❧✱ ♠❡s♠♦ ❡❧✐♠✐♥❛♥❞♦ ❛ ❛✈❛❧✐❛çã♦ ❞❛s ❝♦♦r❞❡♥❛❞❛s ♥✉❝❧❡❛r❡s✳ ❖ ♣r♦❜❧❡♠❛ ♥ã♦ ❛❞♠✐t❡ s♦❧✉çã♦ ❛♥❛❧ít✐❝❛ ❡ ❛ ❛❧t❡r♥❛t✐✈❛ ❞❡ s♦❧✉✲ çã♦ ♥✉♠ér✐❝❛ t♦r♥❛✲s❡ ✐♥✈✐á✈❡❧ ❛ ♠❡❞✐❞❛ q✉❡ ♦ ♥ú♠❡r♦ ❞❡ ❡❧étr♦♥s ❛✉♠❡♥t❛✳ ◆❛ ❜✉s❝❛ ❞❡ ❝♦♥t♦r♥❛r t♦❞♦s ❡ss❡s ❡❢❡✐t♦s✱ ♦✉tr♦s ♠ét♦❞♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ♠❛✐s ❡✜❝✐❡♥t❡s ♣❛ss❛r❛♠ ❛ s❡r ❞❡s❡♥✈♦❧✈✐❞♦s✱ ❞❡♥tr❡ ❡❧❡s✱ ❛ ❚❡♦r✐❛ ❞♦ ❋✉♥❝✐♦♥❛❧ ❞❛ ❉❡♥s✐❞❛❞❡ ✭❉❋❚✮✱ ♦♥❞❡ ❛ ❣r❛♥✲ ❞❡③❛ ❢✉♥❞❛♠❡♥t❛❧ ❞♦ s✐st❡♠❛ ♥ã♦ é ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛✱ ♠❛s s✐♠ s✉❛ ❞❡♥s✐❞❛❞❡ ❡❧❡trô♥✐❝❛✱ q✉❡ ❞❡♣❡♥❞❡ ❛♣❡♥❛s ❞❡ ✸ ✈❛r✐á✈❡✐s✱ ❝♦♠♦ ✈❡r❡♠♦s ❛ s❡❣✉✐r✳
✷✳✷ ❆ ❚❡♦r✐❛ ❞♦ ❋✉♥❝✐♦♥❛❧ ❞❛ ❉❡♥s✐❞❛❞❡ ✲ ❉❋❚
❊ss❛ t❡♦r✐❛ t❡✈❡ ✐♥í❝✐♦ ❝♦♠ ♦s tr❛❜❛❧❤♦s ❞❡ ❍✳ ▲✳ ❚❤♦♠❛s ❡ ❊♥r✐❝♦ ❋❡r♠✐ ❡♠ ✶✾✷✼✱ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❛ ❛♣r♦①✐♠❛çã♦ ❞❡ ❚❤♦♠❛s✲❋❡r♠✐ ❬✶✽❪✱ ♦♥❞❡ ❡❧❡s ❝♦♥s✐❞❡r❛♠ ❛ ❞❡♥s✐❞❛❞❡ ❡❧❡trô♥✐❝❛ ❞♦ s✐st❡♠❛ ρ(~r) ❛♦ ✐♥✈és ❞❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛✱ ❡ ❛ ❡♥❡r❣✐❛ t♦t❛❧ E é
❡s❝r✐t❛ ❝♦♠♦ ✉♠ ❢✉♥❝✐♦♥❛❧ ❞❡ ρ(~r)✱ ♦✉ s❡❥❛✱E[ρ(~r)]✳ ❊ss❛ ❢♦r♠❛ ❞❡ ❞❡✜♥✐r ♦ ♣r♦❜❧❡♠❛ ❞❡
♠✉✐t♦s ❡❧étr♦♥s ♣❡r♠✐t✐✉ ✉♠❛ ❡♥♦r♠❡ s✐♠♣❧✐✜❝❛çã♦✱ ♣♦✐s ❛ ❡q✉❛çã♦ ♣❛r❛ ✉♠ s✐st❡♠❛ ❞❡ ◆ ❡❧étr♦♥s ❡ ♣♦rt❛♥t♦✱ ❝♦♠ ✸◆ ❝♦♦r❞❡♥❛❞❛s ✐♥❞❡♣❡♥❞❡♥t❡s é r❡❞✉③✐❞❛ ❛ ✉♠ ♣r♦❜❧❡♠❛ ❝♦♠ ✸ ❞✐♠❡♥sõ❡s✳ ◆♦ ❡♥t❛♥t♦✱ s♦♠❡♥t❡ ❡♠ ✶✾✻✹✱ ❝♦♠ ❛ ♣✉❜❧✐❝❛çã♦ ❞♦ tr❛❜❛❧❤♦ ❞❡ ❍♦❤❡♥❜❡r❣ ❡ ❑♦❤♥ ✐♥t✐t✉❧❛❞♦ ■♥❤♦♠♦❣❡♥❡♦✉s ❡❧❡❝tr♦♥ ❣❛s ❬✶✾❪✱ ❛ ❉❋❚ ❣❛♥❤♦✉ s✉❛ ❢♦r♠❛ ❞❡✜♥✐❞❛✱ ♦♥❞❡ ❢♦✐ ❞❡♠♦♥str❛❞♦ ✉♠ ♣r✐♠❡✐r♦ ✐♠♣♦rt❛♥t❡ t❡♦r❡♠❛✿
❚❡♦r❡♠❛ ✶✿ ❊♠ ✉♠ s✐st❡♠❛ ❞❡ ♣❛rtí❝✉❧❛s ✐♥t❡r❛❣❡♥t❡s✱ ♦ ♣♦t❡♥❝✐❛❧vext(~r)q✉❡
❛❣❡ s♦❜r❡ ♦ s✐st❡♠❛ é ❞❡t❡r♠✐♥❛❞♦ ❞❡ ❢♦r♠❛ ✉♥í✈♦❝❛✱ ❛ ♠❡♥♦s ❞❡ ✉♠❛ ❝♦♥st❛♥t❡ ❛❞✐t✐✈❛✱ ♣❡❧❛ ❞❡♥s✐❞❛❞❡ ❡❧❡trô♥✐❝❛ ❞♦ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧✳
P♦st❡r✐♦r♠❡♥t❡ ❡♠ ✶✾✻✺✱ ❝♦♠ ♦ tr❛❜❛❧❤♦ ❙❡❧❢✲❝♦♥s✐st❡♥t ❡q✉❛t✐♦♥s ✐♥❝❧✉❞✐♥❣ ❡①❝❤❛♥❣❡ ❛♥❞ ❝♦rr❡❧❛t✐♦♥ ❡✛❡❝ts✱ ❑♦❤♥ ❡ ❙❤❛♠ ♣r♦♣✉s❡r❛♠ ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ ❝❛♣❛③ ❞❡ ❞❡t❡r♠✐♥❛r ❛ ❞❡♥s✐❞❛❞❡ ❡❧❡trô♥✐❝❛ρ(~r)❬✷✵❪ ✉t✐❧✐③❛♥❞♦ ♣r♦❝❡❞✐♠❡♥t♦s ❜❛s❡❛❞♦s ♥♦ ♠ét♦❞♦
✈❛r✐❛❝✐♦♥❛❧✱ r❡s✉❧t❛♥❞♦ ❡♠ ✉♠ s❡❣✉♥❞♦ t❡♦r❡♠❛✿
❚❡♦r❡♠❛ ✷✿ ❖ ✈❛❧♦r ♠í♥✐♠♦ ❞♦ ❢✉♥❝✐♦♥❛❧ ❡♥❡r❣✐❛E[ρ] é ❛ ❡♥❡r❣✐❛ ❞♦ ❡st❛❞♦
✶✾
❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧✳
❆ ♠❡t♦❞♦❧♦❣✐❛ ❜❛s❡❛❞❛ ♥❡ss❡s t❡♦r❡♠❛s r❡❝❡❜❡ ❛ ❞❡♥♦♠✐♥❛çã♦ ❞❡ ❚❡♦r✐❛ ❞♦ ❋✉♥❝✐♦♥❛❧ ❞❡ ❉❡♥s✐❞❛❞❡ ✭❉❋❚✮✳ ❈❛❜❡ r❡ss❛❧t❛r q✉❡ ❛ ✈✐❛❜✐❧✐❞❛❞❡ ❞❛ ❉❋❚ ❞❡♣❡♥❞❡ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞♦ ❢✉♥❝✐♦♥❛❧E[ρ(~r)]q✉❡ ❡①♣r❡ss❛ ❛ ❡♥❡r❣✐❛ t♦t❛❧ E ❞♦ s✐st❡♠❛ ❡♠ ❢✉♥çã♦
❞❡ρ(~r)✳
P❡❧♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ss❡s tr❛❜❛❧❤♦s✱ ❛ ❝♦♠✉♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛ ♠✉♥❞✐❛❧ r❡❝♦✲ ♥❤❡❝❡✉ q✉❡ ❛ ❉❋❚ ♣r♦♣♦r❝✐♦♥♦✉ ✉♠ ❛✈❛♥ç♦ s✐❣♥✐✜❝❛t✐✈♦ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ❝✐ê♥❝✐❛ ❡ ♥♦ ❛♥♦ ❞❡ ✶✾✾✽✱ ❲❛❧t❡r ❑♦❤♥ r❡❝❡❜❡✉ ♦ ♣rê♠✐♦ ♥♦❜❡❧ ❡♠ ◗✉í♠✐❝❛ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❏♦❤♥ ❆✳ P♦♣❧❡ ♣♦r s✉❛ ❝♦♥tr✐❜✉✐çã♦ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♠ét♦❞♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❡♠ q✉í♠✐❝❛ q✉â♥t✐❝❛✳
❉❡ss❛ ❢♦r♠❛✱ ❝♦♠ ❡ss❡s ❞♦✐s t❡♦r❡♠❛s ❍♦❤❡♥❜❡r❣ ❡ ❑♦❤♥ ❣❛r❛♥t❡♠ q✉❡ é ♣♦ssí✲ ✈❡❧ ♦❜t❡r ❛ ❡♥❡r❣✐❛ ❢✉♥❞❛♠❡♥t❛❧ ❞❡ ✉♠ s✐st❡♠❛ s❡♠ q✉❡ s❡ t❡♥❤❛ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛✳ ❊♥tr❡t❛♥t♦✱ ❛✐♥❞❛ é ♥❡❝❡ssár✐♦ q✉❡ s❡ t❡♥❤❛ ✉♠❛ ❢♦r♠❛ ❞❡ ♦❜t❡r ❡ss❛ ❞❡♥s✐✲ ❞❛❞❡ ❞♦ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧✱ ❡ss❛ ❢♦r♠❛ ❢♦✐ ❡♥❝♦♥tr❛❞❛ ❛tr❛✈és ❞❛s ❡q✉❛çõ❡s q✉❡ s❡rã♦ ❞✐s❝✉t✐❞❛s ♥❛ s❡çã♦ s❡❣✉✐♥t❡✳
✷✳✸ ❆s ❡q✉❛çõ❡s ❞❡ ❑♦❤♥✲❙❤❛♠
❆ ✐❞é✐❛ ❝❤❛✈❡ ❞❡ ❑♦❤♥ ❡ ❙❤❛♠ ❢♦✐ ♦ ♠❛♣❡❛♠❡♥t♦ ❞❡ ✉♠ ❝♦♠♣❧✐❝❛❞♦ s✐st❡♠❛ ❞❡ ♠✉✐t♦s ❝♦r♣♦s ✐♥t❡r❛❣❡♥t❡s ❡♠ ✉♠ s✐st❡♠❛ ❛✉①✐❧✐❛r q✉❡ ♣♦❞❡ s❡r r❡s♦❧✈✐❞♦ ♠❛✐s ❢❛❝✐❧♠❡♥t❡✱ ❛ss✉♠✐♥❞♦ q✉❡ ❛ ❞❡♥s✐❞❛❞❡ ❡①❛t❛ ❞♦ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧ ❞♦ s✐st❡♠❛ ✐♥t❡r❛❣❡♥t❡ ♣♦❞❡ s❡r r❡♣r❡s❡♥t❛❞❛ ♣❡❧❛ ❞❡♥s✐❞❛❞❡ ❞❡ ✉♠ s✐st❡♠❛ ❛✉①✐❧✐❛r ❞❡ ♣❛rtí❝✉❧❛s ♥ã♦ ✐♥t❡r❛❣❡♥t❡s✱ r❡s✉❧t❛♥❞♦ ❡♠ ❡q✉❛çõ❡s ❞❡ ♣❛rtí❝✉❧❛s ✐♥❞❡♣❡♥❞❡♥t❡s ♣❛r❛ ♦ s✐st❡♠❛ ♥ã♦ ✐♥t❡r❛❣❡♥t❡✱ ❝♦♠ t♦❞♦s ♦s t❡r♠♦s ❞❡ ♠✉✐t♦s ❝♦r♣♦s ✐♥❝❧✉í❞♦s ❡♠ ✉♠ ❢✉♥❝✐♦♥❛❧ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ tr♦❝❛ ❡ ❝♦rr❡❧❛çã♦✳ ❆ss✐♠ ❛ ❡♥❡r❣✐❛ t♦t❛❧ ❞♦ s✐st❡♠❛ ♣♦❞❡ s❡r ❞❡✜♥✐❞❛ ❝♦♠♦ ✉♠ ❢✉♥❝✐♦♥❛❧ ❞❛ ❞❡♥s✐❞❛❞❡ ρ(~r)✿
E[ρ] =Ts[ρ(~r)] + 1 2
Z ρ(~r)ρ(~r′)
|~r−~r′| d~rd~r ′+
Z
vext(~r)ρ(~r)d~r+Eσ
xc(~r,[ρ]), ✭✷✳✽✮
♦♥❞❡✿
• ❖ ♣r✐♠❡✐r♦ t❡r♠♦ Ts[ρ] = −1
2 N X i Z Ψ∗
i(~r)∇2Ψi(~r)d~r é ❛ ❡♥❡r❣✐❛ ❝✐♥ét✐❝❛ ❞❡ ✉♠
s✐st❡♠❛ ✜❝tí❝✐♦ ❞❡ N ❡❧étr♦♥s ♥ã♦ ✐♥t❡r❛❣❡♥t❡s✱ ❝♦♠ ❛ ♠❡s♠❛ ❞❡♥s✐❞❛❞❡ ❡❧❡trô♥✐❝❛
❞♦ s✐st❡♠❛ ♦r✐❣✐♥❛❧✳
✷✵
• ❖ q✉❛rt♦ t❡r♠♦ é ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ♣♦t❡♥❝✐❛❧ ❞❡ tr♦❝❛✲❝♦rr❡❧❛çã♦ ✭❳❈✮✱ ❛t✉❛♥❞♦ s♦❜r❡ ♦ ❡❧étr♦♥ ❞❡ s♣✐♥ σ ♥❛ ❝♦♦r❞❡♥❛❞❛~r✳ ❖ ❡❢❡✐t♦ ❞❡ tr♦❝❛ ❡stá r❡❧❛❝✐♦♥❛❞♦ ❛♦ ♣r✐♥❝í♣✐♦
❞❡ ❡①❝❧✉sã♦ ❛♣❧✐❝❛❞♦ ❛ ❡❧étr♦♥s ❞❡ s♣✐♥ ♣❛r❛❧❡❧♦s✱ ❡♥q✉❛♥t♦s ♦s ❡❢❡✐t♦s ❞❡ ❝♦rr❡❧❛çã♦✱ ❡stã♦ ❛ss♦❝✐❛❞♦s ❛♦ ❢❛t♦ ❞❡ ❡❧étr♦♥s ❝♦♠ s♣✐♥s ❛♥t✐♣❛r❛❧❡❧♦s t❡r❡♠ s❡✉s ♠♦✈✐♠❡♥t♦s ❝♦rr❡❧❛❝✐♦♥❛❞♦s✱ ♦ q✉❡ ❝♦rr✐❣❡ t❛♠❜é♠ ❛ ❡♥❡r❣✐❛ ❝✐♥ét✐❝❛ ❞♦ ♠♦❞❡❧♦ ❞❡ ♣❛rtí❝✉❧❛s ✐♥❞❡♣❡♥❞❡♥t❡s✳
P♦r ú❧t✐♠♦✱ ❛ ❞❡♥s✐❞❛❞❡ ❞♦ s✐st❡♠❛ ❛✉①✐❧✐❛r é ❞❛❞❛ ♣♦r✿
ρ(~r) = N
X
i Ψ∗
i(~r)Ψi(~r), ✭✷✳✾✮
s❡♥❞♦Ψi(~r) ❛s ❢✉♥çõ❡s ❞❡ ♦♥❞❛ ❞❡ ♣❛rtí❝✉❧❛ ú♥✐❝❛ ♣❛r❛ ♦ s✐st❡♠❛ ❛✉①✐❧✐❛r✳
❈♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛ ❞♦s t❡♦r❡♠❛s ❞❡ ❍♦❤❡♥❜❡r❣ ❡ ❑♦❤♥✱ ❛ ❡♥❡r❣✐❛ ❡❧❡trô♥✐❝❛ ❞♦ s✐st❡♠❛ ♥♦ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧ s❡ ♦❜té♠ ♠✐♥✐♠✐③❛♥❞♦ ♦ ❢✉♥❝✐♦♥❛❧ ❞❛ ❡q✉❛çã♦ ✷✳✽✱ ✈❛r✐❛♥❞♦✲s❡ ρ(~r)✱ s✉❥❡✐t♦ ❛ r❡str✐çã♦ ❞❡ ♠❛♥t❡r ✜①♦ ♦ ♥ú♠❡r♦ ❞❡ ♣❛rtí❝✉❧❛s✱ ♦✉ s❡❥❛✱
R
ρ(~r)d~r =N✳ ❖ ♣r♦❜❧❡♠❛ ❞❛ ♠✐♥✐♠✐③❛çã♦ é r❡s♦❧✈✐❞❛ ❛♣❧✐❝❛♥❞♦✲s❡ ❛ té❝♥✐❝❛ ❞♦s ♠✉❧t✐✲
♣❧✐❝❛❞♦r❡s ❞❡ ▲❛❣r❛♥❣❡✿
δ
δρ{E[ρ]−εi( Z
ρ(~r)d~r−N)}= 0, ✭✷✳✶✵✮
♦♥❞❡εi é ♦ ♠✉❧t✐♣❧✐❝❛❞♦r ❞❡ ▲❛❣r❛♥❣❡✳
❆ ❞❡r✐✈❛❞❛ ❢✉♥❝✐♦♥❛❧ ❞❡E[ρ]♥❛ ❡q✉❛çã♦ ✷✳✽✱ é ❝❛❧❝✉❧❛❞❛ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛ ✭♦
í♥❞✐❝❡σ s❡rá ♦♠✐t✐❞♦✮✿ δE[ρ]
δρ =
δTs[ρ]
δρ +
Z ρ(~r′)
|~r−~r′|d~r
′ +vext(~r) + δExc(~r,[ρ])
δρ . ✭✷✳✶✶✮
❖ ❝á❧❝✉❧♦ ❞❛ ❞❡r✐✈❛❞❛ ❢✉♥❝✐♦♥❛❧ ❞❡ Ts[ρ]é ❞❛❞♦ ♣♦r✿ δTs[ρ]
δρ =
δTs[ρ] δΨ∗
i δΨ∗
i δρ =−
1 Ψi
∇2
2 Ψi, ✭✷✳✶✷✮
✉s❛♥❞♦ ❡ss❡ r❡s✉❧t❛❞♦ ♥❛ ❡q✉❛çã♦ ✷✳✶✶✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛ ❝♦♥❞✐çã♦ ❞❡ ❡①tr❡♠♦ ❞❛❞❛ ♣❡❧❛ ❡q✉❛çã♦ ✷✳✶✵✱ ♦❜t❡♠♦s ❛s ❡q✉❛çõ❡s ❞❡ ❑♦❤♥✲❙❤❛♠ ✭❑❙✮✿
"
−1
2∇
2
i +
Z ρ(~r′)
|~r−~r′|d~r
′+vext(~r) + δExc[ρ] δρ
#
Ψi =εiΨi, e i= 1,2, ..., N. ✭✷✳✶✸✮
❉❡ss❛ ❢♦r♠❛✱ ❛s ❡q✉❛çõ❡s ❞❡ ❑♦❤♥✲❙❤❛♠ r❡♣r❡s❡♥t❛♠ ♦ ♠❛♣❡❛♠❡♥t♦ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ♠✉✐t♦s ❡❧étr♦♥s ✐♥t❡r❛❣❡♥t❡s ❡♠ ✉♠ s✐st❡♠❛ ❞❡ ❡❧étr♦♥s ♥ã♦ ✐♥t❡r❛❣❡♥t❡s✱ ♠♦✈❡♥❞♦✲s❡ ❡♠ ✉♠ ♣♦t❡♥❝✐❛❧ ❡❢❡t✐✈♦ ❞❡✈✐❞♦ ❛ t♦❞♦s ♦s ♦✉tr♦s ❡❧étr♦♥s✱ ❞❛❞♦ ♣♦r✿
vef(~r) =
Z ρ(~r′)
|~r−~r′|d~r
′+vext(~r) + δExc[ρ]
✷✶
❆ ❡q✉❛çã♦ ✷✳✶✸ ♣♦❞❡ s❡r r❡❡s❝r✐t❛ ❝♦♠♦✿
−1
2∇
2
i +vef(~r)
Ψi =εiΨi. ✭✷✳✶✺✮
❊ss❛s ❡q✉❛çõ❡s ❞❡✈❡♠ s❡r r❡s♦❧✈✐❞❛s ❞❡ ❢♦r♠❛ ❛✉t♦✲❝♦♥s✐st❡♥t❡✿ ♣r✐♠❡✐r❛♠❡♥t❡ ♣❛rt❡✲s❡ ❞❡ ✉♠❛ ❞❡♥s✐❞❛❞❡ ❡❧❡trô♥✐❝❛ ✐♥✐❝✐❛❧✱ ♣❛r❛ q✉❡ ♦ ♣♦t❡♥❝✐❛❧ s❡❥❛ ❝♦♥str✉í❞♦ ❡ ♦❜t❡♥❤❛✲s❡ ♦ ❍❛♠✐❧t♦♥✐❛♥♦ ❞❡ ✭❑❙✮✱ q✉❡ é ❞✐❛❣♦♥❛❧✐③❛❞♦ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦s ❛✉t♦✈❛✲ ❧♦r❡s ❡ ❛✉t♦✈❡t♦r❡s✱ ✉♠❛ ♥♦✈❛ ❞❡♥s✐❞❛❞❡ ❡❧❡trô♥✐❝❛ é ♦❜t✐❞❛ ❡ ❝♦♠♣❛r❛❞❛ ❝♦♠ ❛ ❞❡♥s✐❞❛❞❡ ✐♥✐❝✐❛❧✳ ❙❡ ❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❡❧❛s ❛t❡♥❞❡r ✉♠ ❝❡rt♦ ❝r✐tér✐♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛✱ ❛❞♠✐t✐♠♦s q✉❡ ❛ ❞❡♥s✐❞❛❞❡ ❡♥❝♦♥tr❛❞❛ é ❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✳
◆❛ ✜❣✉r❛ ✶✱ ✐❧✉str❛♠♦s ❝♦♠♦ ❛ ❡q✉❛çã♦ ❞❡ ❑❙ ♣♦❞❡ s❡r r❡s♦❧✈✐❞❛✳
