A New Dimension to Quantum Chemistry: Analytic Derivative by Yukio Yamaguchi, John D. Goddard, Yoshihiro Osamura, Henry

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By Yukio Yamaguchi, John D. Goddard, Yoshihiro Osamura, Henry Schaefer

In sleek theoretical chemistry, the significance of the analytic assessment of power derivatives from trustworthy wave services can not often be over priced. This monograph offers the formula and implementation of analytical strength by-product tools in ab initio quantum chemistry. It features a systematic presentation of the mandatory algebraic formulae for all the derivations. The insurance is proscribed to by-product equipment for wave capabilities in accordance with the variational precept, particularly constrained Hartree-Fock (RHF), configuration interplay (CI) and multi-configuration self-consistent-field (MCSCF) wave services. The monograph is meant to facilitate the paintings of quantum chemists, and may function an invaluable source for graduate-level scholars of the sector.

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Extra info for A New Dimension to Quantum Chemistry: Analytic Derivative Methods in Ab Initio Molecular Electronic Structure Theory

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Q❯✤✯✘✙✛rts❃✉✲s✇✈①◗✭❝✏❯✤✯✘✙❲❤✪✜✤◗✪✗✶❙✘✖✐❚②❯✰✦✭❯✤✙◆✵ ❦④③ ❧❫⑤⑥❝❆❯✤✯✘✙❱✦✭❯✤◗✪❥⑦✣❬❚✏✣❬❙⑧✦€❥⑨✦◆❤✪❙✶✙❭❯✡✣✥✮❶⑩✘✙❍❩❬✖❷◗◆❝❆❸✶✵❹❸✶✱q❺✟✙❍❚✤❩❬✦✶✩◆⑩✢❙✶✖❻❯✡✯✘✙q❥⑨✦◆❤✪❙✶✙❭❯✡✣✥✮❉✙❭❙✘✙❍✜❜❤✪✣❬✙❭❚❼◗◆❝☎❯✡✯✶✙❘◗✪✜❜✣❬❤✪✣✥❙✢✦◆❩❬❩❽✧ ✖✘✙❍❤✪✙❭❙✘✙❍✜✤✦✭❯✡✙❷❾❣✈⑨❿♣✱✛❚②❯✰✦✭❯✤✙❍❚❭✵ ❾❣✵€➀➁❙✘✙❷✙❍❩❬✙❭✮❭❯✤✜✤◗✪❙❏❥❁◗✴➂✪✙❍❚€✣❬❙❏✦❋◗✪❙✶✙➃❵❨✖✶✣❬❥❁✙❍❙✘❚❜✣❬◗✪❙✢✦✭❩✟❚②✧❣❚❜❯✡✙❭❥➄✦◆❙✘✖✽❝④✙❭✙❍❩✟❯✡✯✘✙❻✣✥❙♠❯✡✙❍✜✤✦◆✮❭❯✤✣❬◗✪❙✬◗◆❝➅❯❨❳❘◗✻✦✭❯✤◗✪❥❁❚❍✵➁➆✝❴❛❵ ❴✶✜✤◗★❢❛✣❬❥⑨✦✭❯✡✙€❯✤✯✘✙❲✣❬❙♠❯✡✙❭✜✡✦◆✮➃❯✡✣✥◗✪❙ ③ ✙➃❯❨❳❘✙❭✙❍❙✐❯✤✯✘✙❲✙❍❩✥✙❍✮❭❯✤✜✤◗✪❙✶❚✝✦✭❙✘✖✻❯✤✯✘✙✛✦✭❯✡◗◆❥⑨❚q❳❪✣❽❯✡✯❫❯✡✯✘✙❲❴❆◗◆❯✡✙❭❙♠❯✡✣➇✦✭❩ ➈ ❦④➉ s➋➊❲❧➍➌➎s✕➏✏➐ ❦④➉ s❃➊❲❧➃➑ ❳❪✯✶✙❍✜✤✙✛➊➒✣❬❚q❯✡✯✶✙✛❴❆◗✪❚❜✣✥❯✡✣✥◗✪❙❫◗◆❝❞✦◆❙✐✦✭❯✡◗✪❥✻✵➅➓✕❚✤✙➔❯✡✯✘✙✛✦◆✖✶✣➇✦ ③ ✦→❯✡✣❬✮➁✦◆❴✘❴✘✜❜◗✴❢❛✣✥❥♦✦✭❯✤✣❬◗✪❙⑨❯✡◗ ❦ ✦♠❧✍➣❲✣❽➂✪✙❍❙❲❯✡✯✶✙➍❯❨❳❉◗✝✦✭❯✡◗✪❥❁❚❡✦◆✜❜✙➍❚✤✙❍❴✘✦◆✜✡✦✭❯✤✙❍✖ ③ ✧✛✦❪✖✶✣❬❚❜❯✡✦◆❙✘✮❭✙❶↔❣✩✴⑩✢❙✘✖✹✦q❯✡✜✡✦✭❙✘❚✤✮❭✙❍❙✘✖✘✙❭❙♠❯✰✦◆❩↕✙❍➙↕✗✢✦→❯✡✣❬◗◆❙✹✜❜✙❍❩➇✦→❯✡✣❬❙✶❤ ➛✻✦◆❙✶✖✐↔❷❳❪✯✶✙❍✜✤✙❲❯✡✯✶✙✛✙❭❩❬✙❭✮❭❯✡✜❜◗✪❙✘✣✥✮ ③ ✣❬❙✘✖✶✣❬❙✘❤⑧✙❭❙✘✙❍✜❜❤◆✧❫✣❬❚➁➝☎➜ ➞➟➛ ➞➃➠ ❦ ❾✭➡✻❧➟✵ ❦④③ ❧✍✚❞✣❬❙✘✖❫❯✤✯✘✙❲❴➢◗◆❯✤✙❍❙♠❯✡✣❬✦◆❩ ③ ✙❭❯❨❳❉✙❍✙❭❙✐❯✡✯✶✙❲❯❨❳❉◗❋✦→❯✡◗✪❥❁❚❱✦✭❯✕❚✤❥⑨✦◆❩✥❩✿↔❣✩ ➈ ❦ ↔❲➤ ❸♠❧➍➥ ➈ ❦ ↔✛➌➦❸♠❧❞s❃➧✟↔➨➑ ❯✡✯✢✦✭❯❉✣❬❚❭✩♠⑩✢❙✘✖ ➈ ❦ ↔❲➌➩❸✪❧➍✦✭❙✘✖❋➧❶✵➅➫➁◗✛❯✤✯✘✣❬❚ ③ ✧❁✙➃❢❛❴✢✦◆❙✶✖✘✣❬❙✘❤✛❯✡✯✘✙❪❯✡✜✤✦◆❙✘❚❜✮❍✙❍❙✶✖✘✙❍❙♠❯✰✦✭❩✿✙❍➙↕✗✢✦→❯✡✣❬◗◆❙♦✣❬❙➭❯✡✙❭✜✤❥❁❚ ◗◆❝€↔❣✵❃➯✝✣✥❙♠❯★➲✍✚❞✣✥✜✤❚❜❯❍✩❶⑩✘❙✘✖ ➈ ❦ ↔➳➌➄❸♠❧ ③ ✧❃❚✤◗✪❩❽➂❣✣❬❙✘❤✽❯✤✯✘✙❫❯✡✜✡✦✭❙✘❚✤✮❭✙❍❙✘✖✘✙❭❙♠❯✰✦◆❩✕✙❍➙↕✗✢✦✭❯✤✣❬◗✪❙➋❳❪✣❽❯✡✯❃↔➳➌➵❸❛✵ ❺❞✦◆➸✭✙➭✖✘✙❍✜❜✣✥➂✭✦✭❯✡✣❽➂✪✙❭❚➁◗◆❝➅❯✡✯✶✙❻❯✡✜✡✦✭❙✘❚✤✮❭✙❍❙✘✖✘✙❭❙♠❯✰✦◆❩➅✙❭➙❣✗✘✦✭❯✡✣✥◗✪❙✽❳❪✣✥❯✤✯✽✜✤✙❭❚✤❴❆✙❍✮❭❯❲❯✤◗❋↔❛✩➢❯✡✯✘✙❭❙✲❚❜◗✪❩✥➂◆✙❷❝④◗✪✜➔➺❣➛ ➠ ➺↕↔ ✦✭❯❪↔✛➌➦❸✶✩☎✦✭❙✘✖❫⑩✢❙✢✦◆❩✥❩✥✧♦⑩✘❙✘✖✬➺↕➻ ➠ ➺♠↔✹❯✡◗❁◗ ③ ❯✡✦◆✣❬❙✍➧❶✵ ❦ ✮✴❧✍✚❞✣❬❙✘✖❫❯✤✯✘✙❲❴➢◗◆❯✤✙❍❙♠❯✡✣❬✦◆❩ ③ ✙❭❯❨❳❉✙❍✙❭❙✐❯✡✯✶✙❲❯❨❳❉◗❋✦→❯✡◗✪❥❁❚❱✦✭❯✕❩➇✦✭✜✤❤✪✙➁↔❣✩ ➈ ❦ ↔❲➤ ➼➽❧❶➌⑦s✕➾€✙➃❢❛❴ ❦ s€❾✪➛♠➚➁↔◆❧➃➑ ❯✡✯✢✦✭❯❼✣❬❚❍✩→⑩✢❙✘✖⑧➾✟✵❼➯✕✣❬❙♠❯★➲✏➓✝❚❜✙❘⑩✢✜✤❚②❯➅◗✪✜❜✖✘✙❍✜❼❴❆✙❍✜②❯✡✗✘✜ ③ ✦✭❯✤✣❬◗✪❙❷❯✤✯✘✙❍◗◆✜❜✧✪✩↕✦✭❚✤❚✤✗✶❥⑨✣✥❙✘❤€❯✡✯✶✙q✗✘❙✘❴❆✙❍✜②❯✡✗✘✜ ③ ✙❭✖➭❳❘✦★➂✪✙ ❝④✗✘❙✘✮❭❯✤✣❬◗✪❙✍✣✥❚q❯✡✯✘✙ ③ ◗✪✗✘❙✘✖✻❚❜❯✡✦✭❯✡✙❲◗◆❝✟◗✪❙✶✙❲❳❉✙❍❩✥❩➪✩✶✦◆❙✘✖✍❯✡✯✘✙➔❴❆✙❍✜②❯✡✗✘✜ ③ ✦✭❯✡✣✥◗✪❙✍✣❬❚q❯✤✯✘✙➔✣❬❙♠❯✡✙❭✜✡✦◆✮➃❯✡✣✥◗✪❙❋❳❪✣✥❯✤✯✍❯✤✯✘✙ ❚✤✙❍✮❭◗✪❙✘✖✻❳❘✙❭❩❬❩➪✵ ✂✁☎✄✝✆✟✞✡✠☞☛ ✌✍✠✏✎✒✑✔✓✝✕ ✖✘✗✘✙✛✚✢✜✤✣✥✖✢✦★✧✪✩☎✫✬✦✭✜✤✮✰✯✬✱✳✲✵✴ ✶✸✷✺✹✼✻✾✽❀✿❁✻❃❂☎❄❆❅❈❇❉✻✾✶✛❊❋✽❍●❏■❑❅✢▲☎▲✟▼ ◆ ✴€❖◗✯✘❘❀❙❯❚✡✯✢✦❱❚❳❲❩❨ ❬✳❭✢❪❫❬❵❴✪❨ ❴❩❛❝❜ ❘✳✜❉✦✸❞❡❘◗❘✪❢❣❴ ✙❤✜✐❢✢✦✳✣❥✜❦❙❧✣♠❚✡✯♦♥q♣srt✣❥✉❉✈s✴❦✇①✉✤✙✝❚✤✯✘✙ ❜ ✦✳✮❤❚✐❚✤✯✢✦✭❚✐❚✡✯✘✙❧❙❡✦❀②✳✙ ❜ ✗✘③✵✮❤❚✡✣✥❘✪③ ④ ❘⑤✙❤✉❧✦✳✉✸⑥⑦✮❍❘✳✉❵⑥⑨⑧❶⑩★❷✳❸✏❪❹✮❍❘✪✉❀⑥⑨⑧✪❺❩❷✪❸❻❸✘❼✭❷ ✦❱❚✝❽❥✦✳✜ ④ ✙❳❷⑤✴ ✂✁☎✄✝✆✟✞✡✠☞☛ ✌✍✠✏✎✒✑✔✓✖✕ ✗✙✘✙✚✜✛✣✢✥✤✦✗✣✧✩★✫✪☎✬✭✧✮✢✥✯✱✰✳✲✫✴✶✵ ✷✹✸✻✺✽✼✿✾❁❀❂✼❄❃☎❅❇❆❉❈❊✼✿✷✜❋●✾■❍❑❏▲❆✣▼☎▼✟◆ ❖ ✵◗€❙❘❯❚✙❱✥✤✦✗✙✚■✢❲✧❨❳✣✧❯✢❬❩✡✤❭✯❫❪❭✚❴❘✮❵❜❛❝✧❯❱✥❱❡❞❢✧❯❚✙✗✍✯✱✰✣✧❯✢❤❣✫✚❥✐❦❛❂❘♠❧♥✤✦❚✙❣♦✤❭❚●❩✡✰✶✚❦♣rqtsr❳✙❪❭✧❯❚✙✚✉✘✙❚✶✗✙✚■✢❡❩✡✰✙✚❦✤✦❚✶✈✣✘✙✚❫❚✙✯■✚❦❘❯❵ ✧❨❛❝✧❯❣✫❚✙✚✇❩✡✤✦✯◗①✣✚■❪✦✗✳✤✦❚●❩✡✰✙✚✜②❂✗✙✤❭✢❤✚■✯❫❩✥✤❭❘✫❚✿✵④③⑤❣✫❚✙❘✫✢❤✚❦❛❝❘❯❩✥✤❭❘✫❚r✤❭❚⑥❩✡✰✙✚✜②♦✗✙✤❭✢❤✚■✯✇❩✡✤❭❘❯❚❉✵ ⑦ ✧⑨⑧✍⑩❶✰✙❘❁❷❸❩✡✰✙✧✮❩❹❩✡✰✙✚✉❧❯✚■✯❫❩✥❘✫✢❲❳❺❘❯❩✥✚■❚⑨❩✡✤❭✧❯❪❻✪ ❼❾❽➀❿ ➁ ⑦ ♣❡s➃➂ qts➄♣❇➂ ⑧✿➅ ✗✙✚■❱❤✯■✢✥✤✦➆❺✚❫❱◗✧❨❛❝✧❯❣✫❚✙✚✇❩✡✤✦✯❴①✣✚■❪✦✗✻✤✦❚⑥❩✡✰✙✚✜②♦✗✙✤❭✢❤✚■✯❫❩✥✤❭❘✫❚✿✵ ⑦ ➆☎⑧✍➇④➈❶❳✙✢❤✚■❱❤❱❲❩✥✰✙✚✉❧✫✚■✯✇❩✡❘✫✢❡❳❇❘❯❩✡✚❫❚⑨❩✡✤➉✧✮❪✿✤❭❚⑥✯✇★♥❪❭✤❭❚✶✗✙✢✥✤✦✯✩✧❯❪❺✯■❘♥❘✫✢✥✗✙✤✦❚✣✧✮❩✥✚■❱■✪♥❩✡✰✣✧➊❩❡✤❭❱➋✤✦❚✍❩✥✚■✢❤❛❝❱➋❘✮❵❜➌♥✪☎➍✟✪➄➌❨➂ ✧❯❚✙✗ ➍☞➂ ✵ ⑦ ✯❁⑧●➎➏✢❤✤✦❩✡✚❴❩✥✰✙✚✹⑩❶✯✱✰✙✢✩❘✫➐ ✗✙✤❭❚✶❣✫✚■✢❡✚■➑➒✘✣✧➊❩✡✤❭❘❯❚❉✪ ⑦➔➓ qt➁ ✐❁❼✍→❯➣❫⑧❬↔ ⑦ ➌♠➅➙➍❺⑧➛❽➝➜ ⑦ ➌♠➅➙➍❺⑧✇➅ ⑦❖⑧ ❞ ↕ ↕ ✤❭❚✍✯❫★♥❪❭✤✦❚✙✗✙✢❤✤❭✯✩✧✮❪✿✯■❘♥❘✫✢❤✗✙✤❭❚✣✧➊❩✡✚■❱❫✵ ⑦ ✗☎⑧✻⑩❶✰✙❘❁❷❸❩✡✰✙✧✮❩❲➞➛➟◗✯■❘❯❛❝❛➃✘❶❩✡✚■❱➋❷❡✤➠❩✡✰⑥❩✡✰✶✚✹➡✝✧❯❛❂✤❭❪✦❩✥❘✫❚✙✤❭✧❯❚❉✵ ⑦ ✚❁⑧⑥➢◗❱✥❱❤✘✙❛❂✤❭❚✙❣❨❩✡✰✶✚✜❱❤❘✫❪❭✘❶❩✡✤❭❘❯❚⑥✤❭❱❲✧❯❚✍✚■✤✦❣✫✚■❚✙❱❬❩✱✧✮❩✥✚❦❘❯❵④➞➛➟❲❷❡✤✦❩✡✰✍✚❫✤❭❣✫✚❫❚➒❧✮✧❯❪✦✘✙✚✉❞✽➥❉➤ ✪ ↕ ⑦ ➌♠➅➙➍✿⑧➄❽➦✐■➧➩➨❜➫♠➭ ➨ ⑦ ➌❯⑧✇➅ ✢✥✚❫❷❡✢❤✤✦❩✥✚❦❩✥✰✙✚✹⑩❶✯✱✰✙✢✩❘✫➐ ✗✙✤❭❚✶❣✫✚■✢❡✚■➑➒✘✣✧➊❩✡✤❭❘❯❚✍❵➔❘❯✢➋➭ ➨ ⑦ ➌❯⑧✇✵ ⑦ ❵✡⑧●➯◗➲❉➳❁➵♠➸ ❀ ➵➊➺♥➻✟➼➔➳✫➽➄⑩❶❘✫❪➠❧✫✚✉❵➔❘✫✢➋❩✡✰✶✚❦➭ ➨ ⑦ ➌❯⑧➋✧❯❚✙✗✍❩✡✰✙✚❦✚■✤✦❣✫✚■❚✶✚■❚✙✚❫✢✥❣✫✤✦✚■❱❹❵➔❘✫✢➋❩✡✰✶✚✜✯■✧❯❱✥✚❦❷❡✰✙✚❫✢✥✚❦❞➾❽➝✴❶✵ ➁ ✵◗€❙❘❯❚✙❱✥✤✦✗✙✚■✢r✧➚✯✱✰✣✧❯✢❤❣✫✚■✗➪✢❤✚■❪❭✧✮❩✡✤➠❧❶✤✦❱❤❩✥✤❭✯⑥❳✣✧❯✢❬❩✡✤✦✯■❪❭✚✻✤❭❚⑨❩✥✚■✢✡✧✮✯❫❩✡✤✦❚✙❣➶❷❡✤✦❩✡✰✂❩✡✰✙✚✳✚■❪❭✚❫✯❫❩✥✢✥❘✫❛❝✧❯❣✫❚✙✚✇❩✡✤✦✯✍①✙✚■❪❭✗✿✪❡✧❯❚✙✗➹✗✙✚➙➘ ❱❤✯■✢❤✤❭➆❇✚■✗✍➆⑨★⑥❩✡✰✙✚✜➴✉❪❭✚❫✤❭❚❶➘➬➷❦❘✫✢❤✗✙❘✫❚●✚❫➑➒✘✣✧✮❩✡✤✦❘✫❚❉✵ ➮ ⑦✃➱ ➥❇➤ ❐✫❒❺q❄✐♠❮❹⑧ ↔❜❰ ➣ ↔ ➥➤ ↔ ❐ Ï↔ qt❞ ↔ ➣✱Ð✥Ñ ⑦ ♣☞➅✥Ò❤⑧➄❽➦✴ ↕ Ó ✰✶✚✜✚❫❪❭✚❫✯❫❩✡✢❤❘✫❱❤❩✡✧✮❩✡✤✦✯✉❳❺❘✮❩✡✚■❚⑨❩✥✤➉✧❯❪☞❮Ô✤❭❱❹✤✦❪❭❪❭✘✶❱❤❩✡✢✥✧✮❩✡✚❫✗⑥✤❭❚●❩✥✰✙✚❦✗✙✤➉✧❯❣❯✢✡✧❯❛❾➆❺✚❫❪❭❘❁❷❦✵ E-mc 2 I.

Q❯✤✯✘✙✛rts❃✉✲s✇✈①◗✭❝✏❯✤✯✘✙❲❤✪✜✤◗✪✗✶❙✘✖✐❚②❯✰✦✭❯✤✙◆✵ ❦④③ ❧❫⑤⑥❝❆❯✤✯✘✙❱✦✭❯✤◗✪❥⑦✣❬❚✏✣❬❙⑧✦€❥⑨✦◆❤✪❙✶✙❭❯✡✣✥✮❶⑩✘✙❍❩❬✖❷◗◆❝❆❸✶✵❹❸✶✱q❺✟✙❍❚✤❩❬✦✶✩◆⑩✢❙✶✖❻❯✡✯✘✙q❥⑨✦◆❤✪❙✶✙❭❯✡✣✥✮❉✙❭❙✘✙❍✜❜❤✪✣❬✙❭❚❼◗◆❝☎❯✡✯✶✙❘◗✪✜❜✣❬❤✪✣✥❙✢✦◆❩❬❩❽✧ ✖✘✙❍❤✪✙❭❙✘✙❍✜✤✦✭❯✡✙❷❾❣✈⑨❿♣✱✛❚②❯✰✦✭❯✤✙❍❚❭✵ ❾❣✵€➀➁❙✘✙❷✙❍❩❬✙❭✮❭❯✤✜✤◗✪❙❏❥❁◗✴➂✪✙❍❚€✣❬❙❏✦❋◗✪❙✶✙➃❵❨✖✶✣❬❥❁✙❍❙✘❚❜✣❬◗✪❙✢✦✭❩✟❚②✧❣❚❜❯✡✙❭❥➄✦◆❙✘✖✽❝④✙❭✙❍❩✟❯✡✯✘✙❻✣✥❙♠❯✡✙❍✜✤✦◆✮❭❯✤✣❬◗✪❙✬◗◆❝➅❯❨❳❘◗✻✦✭❯✤◗✪❥❁❚❍✵➁➆✝❴❛❵ ❴✶✜✤◗★❢❛✣❬❥⑨✦✭❯✡✙€❯✤✯✘✙❲✣❬❙♠❯✡✙❭✜✡✦◆✮➃❯✡✣✥◗✪❙ ③ ✙➃❯❨❳❘✙❭✙❍❙✐❯✤✯✘✙❲✙❍❩✥✙❍✮❭❯✤✜✤◗✪❙✶❚✝✦✭❙✘✖✻❯✤✯✘✙✛✦✭❯✡◗◆❥⑨❚q❳❪✣❽❯✡✯❫❯✡✯✘✙❲❴❆◗◆❯✡✙❭❙♠❯✡✣➇✦✭❩ ➈ ❦④➉ s➋➊❲❧➍➌➎s✕➏✏➐ ❦④➉ s❃➊❲❧➃➑ ❳❪✯✶✙❍✜✤✙✛➊➒✣❬❚q❯✡✯✶✙✛❴❆◗✪❚❜✣✥❯✡✣✥◗✪❙❫◗◆❝❞✦◆❙✐✦✭❯✡◗✪❥✻✵➅➓✕❚✤✙➔❯✡✯✘✙✛✦◆✖✶✣➇✦ ③ ✦→❯✡✣❬✮➁✦◆❴✘❴✘✜❜◗✴❢❛✣✥❥♦✦✭❯✤✣❬◗✪❙⑨❯✡◗ ❦ ✦♠❧✍➣❲✣❽➂✪✙❍❙❲❯✡✯✶✙➍❯❨❳❉◗✝✦✭❯✡◗✪❥❁❚❡✦◆✜❜✙➍❚✤✙❍❴✘✦◆✜✡✦✭❯✤✙❍✖ ③ ✧✛✦❪✖✶✣❬❚❜❯✡✦◆❙✘✮❭✙❶↔❣✩✴⑩✢❙✘✖✹✦q❯✡✜✡✦✭❙✘❚✤✮❭✙❍❙✘✖✘✙❭❙♠❯✰✦◆❩↕✙❍➙↕✗✢✦→❯✡✣❬◗◆❙✹✜❜✙❍❩➇✦→❯✡✣❬❙✶❤ ➛✻✦◆❙✶✖✐↔❷❳❪✯✶✙❍✜✤✙❲❯✡✯✶✙✛✙❭❩❬✙❭✮❭❯✡✜❜◗✪❙✘✣✥✮ ③ ✣❬❙✘✖✶✣❬❙✘❤⑧✙❭❙✘✙❍✜❜❤◆✧❫✣❬❚➁➝☎➜ ➞➟➛ ➞➃➠ ❦ ❾✭➡✻❧➟✵ ❦④③ ❧✍✚❞✣❬❙✘✖❫❯✤✯✘✙❲❴➢◗◆❯✤✙❍❙♠❯✡✣❬✦◆❩ ③ ✙❭❯❨❳❉✙❍✙❭❙✐❯✡✯✶✙❲❯❨❳❉◗❋✦→❯✡◗✪❥❁❚❱✦✭❯✕❚✤❥⑨✦◆❩✥❩✿↔❣✩ ➈ ❦ ↔❲➤ ❸♠❧➍➥ ➈ ❦ ↔✛➌➦❸♠❧❞s❃➧✟↔➨➑ ❯✡✯✢✦✭❯❉✣❬❚❭✩♠⑩✢❙✘✖ ➈ ❦ ↔❲➌➩❸✪❧➍✦✭❙✘✖❋➧❶✵➅➫➁◗✛❯✤✯✘✣❬❚ ③ ✧❁✙➃❢❛❴✢✦◆❙✶✖✘✣❬❙✘❤✛❯✡✯✘✙❪❯✡✜✤✦◆❙✘❚❜✮❍✙❍❙✶✖✘✙❍❙♠❯✰✦✭❩✿✙❍➙↕✗✢✦→❯✡✣❬◗◆❙♦✣❬❙➭❯✡✙❭✜✤❥❁❚ ◗◆❝€↔❣✵❃➯✝✣✥❙♠❯★➲✍✚❞✣✥✜✤❚❜❯❍✩❶⑩✘❙✘✖ ➈ ❦ ↔➳➌➄❸♠❧ ③ ✧❃❚✤◗✪❩❽➂❣✣❬❙✘❤✽❯✤✯✘✙❫❯✡✜✡✦✭❙✘❚✤✮❭✙❍❙✘✖✘✙❭❙♠❯✰✦◆❩✕✙❍➙↕✗✢✦✭❯✤✣❬◗✪❙➋❳❪✣❽❯✡✯❃↔➳➌➵❸❛✵ ❺❞✦◆➸✭✙➭✖✘✙❍✜❜✣✥➂✭✦✭❯✡✣❽➂✪✙❭❚➁◗◆❝➅❯✡✯✶✙❻❯✡✜✡✦✭❙✘❚✤✮❭✙❍❙✘✖✘✙❭❙♠❯✰✦◆❩➅✙❭➙❣✗✘✦✭❯✡✣✥◗✪❙✽❳❪✣✥❯✤✯✽✜✤✙❭❚✤❴❆✙❍✮❭❯❲❯✤◗❋↔❛✩➢❯✡✯✘✙❭❙✲❚❜◗✪❩✥➂◆✙❷❝④◗✪✜➔➺❣➛ ➠ ➺↕↔ ✦✭❯❪↔✛➌➦❸✶✩☎✦✭❙✘✖❫⑩✢❙✢✦◆❩✥❩✥✧♦⑩✘❙✘✖✬➺↕➻ ➠ ➺♠↔✹❯✡◗❁◗ ③ ❯✡✦◆✣❬❙✍➧❶✵ ❦ ✮✴❧✍✚❞✣❬❙✘✖❫❯✤✯✘✙❲❴➢◗◆❯✤✙❍❙♠❯✡✣❬✦◆❩ ③ ✙❭❯❨❳❉✙❍✙❭❙✐❯✡✯✶✙❲❯❨❳❉◗❋✦→❯✡◗✪❥❁❚❱✦✭❯✕❩➇✦✭✜✤❤✪✙➁↔❣✩ ➈ ❦ ↔❲➤ ➼➽❧❶➌⑦s✕➾€✙➃❢❛❴ ❦ s€❾✪➛♠➚➁↔◆❧➃➑ ❯✡✯✢✦✭❯❼✣❬❚❍✩→⑩✢❙✘✖⑧➾✟✵❼➯✕✣❬❙♠❯★➲✏➓✝❚❜✙❘⑩✢✜✤❚②❯➅◗✪✜❜✖✘✙❍✜❼❴❆✙❍✜②❯✡✗✘✜ ③ ✦✭❯✤✣❬◗✪❙❷❯✤✯✘✙❍◗◆✜❜✧✪✩↕✦✭❚✤❚✤✗✶❥⑨✣✥❙✘❤€❯✡✯✶✙q✗✘❙✘❴❆✙❍✜②❯✡✗✘✜ ③ ✙❭✖➭❳❘✦★➂✪✙ ❝④✗✘❙✘✮❭❯✤✣❬◗✪❙✍✣✥❚q❯✡✯✘✙ ③ ◗✪✗✘❙✘✖✻❚❜❯✡✦✭❯✡✙❲◗◆❝✟◗✪❙✶✙❲❳❉✙❍❩✥❩➪✩✶✦◆❙✘✖✍❯✡✯✘✙➔❴❆✙❍✜②❯✡✗✘✜ ③ ✦✭❯✡✣✥◗✪❙✍✣❬❚q❯✤✯✘✙➔✣❬❙♠❯✡✙❭✜✡✦◆✮➃❯✡✣✥◗✪❙❋❳❪✣✥❯✤✯✍❯✤✯✘✙ ❚✤✙❍✮❭◗✪❙✘✖✻❳❘✙❭❩❬❩➪✵ ✂✁☎✄✝✆✟✞✡✠☞☛ ✌✍✠✏✎✒✑✔✓✝✕ ✖✘✗✘✙✛✚✢✜✤✣✥✖✢✦★✧✪✩☎✫✬✦✭✜✤✮✰✯✬✱✳✲✵✴ ✶✸✷✺✹✼✻✾✽❀✿❁✻❃❂☎❄❆❅❈❇❉✻✾✶✛❊❋✽❍●❏■❑❅✢▲☎▲✟▼ ◆ ✴€❖◗✯✘❘❀❙❯❚✡✯✢✦❱❚❳❲❩❨ ❬✳❭✢❪❫❬❵❴✪❨ ❴❩❛❝❜ ❘✳✜❉✦✸❞❡❘◗❘✪❢❣❴ ✙❤✜✐❢✢✦✳✣❥✜❦❙❧✣♠❚✡✯♦♥q♣srt✣❥✉❉✈s✴❦✇①✉✤✙✝❚✤✯✘✙ ❜ ✦✳✮❤❚✐❚✤✯✢✦✭❚✐❚✡✯✘✙❧❙❡✦❀②✳✙ ❜ ✗✘③✵✮❤❚✡✣✥❘✪③ ④ ❘⑤✙❤✉❧✦✳✉✸⑥⑦✮❍❘✳✉❵⑥⑨⑧❶⑩★❷✳❸✏❪❹✮❍❘✪✉❀⑥⑨⑧✪❺❩❷✪❸❻❸✘❼✭❷ ✦❱❚✝❽❥✦✳✜ ④ ✙❳❷⑤✴ ✂✁☎✄✝✆✟✞✡✠☞☛ ✌✍✠✏✎✒✑✔✓✖✕ ✗✙✘✙✚✜✛✣✢✥✤✦✗✣✧✩★✫✪☎✬✭✧✮✢✥✯✱✰✳✲✫✴✶✵ ✷✹✸✻✺✽✼✿✾❁❀❂✼❄❃☎❅❇❆❉❈❊✼✿✷✜❋●✾■❍❑❏▲❆✣▼☎▼✟◆ ❖ ✵◗€❙❘❯❚✙❱✥✤✦✗✙✚■✢❲✧❨❳✣✧❯✢❬❩✡✤❭✯❫❪❭✚❴❘✮❵❜❛❝✧❯❱✥❱❡❞❢✧❯❚✙✗✍✯✱✰✣✧❯✢❤❣✫✚❥✐❦❛❂❘♠❧♥✤✦❚✙❣♦✤❭❚●❩✡✰✶✚❦♣rqtsr❳✙❪❭✧❯❚✙✚✉✘✙❚✶✗✙✚■✢❡❩✡✰✙✚❦✤✦❚✶✈✣✘✙✚❫❚✙✯■✚❦❘❯❵ ✧❨❛❝✧❯❣✫❚✙✚✇❩✡✤✦✯◗①✣✚■❪✦✗✳✤✦❚●❩✡✰✙✚✜②❂✗✙✤❭✢❤✚■✯❫❩✥✤❭❘✫❚✿✵④③⑤❣✫❚✙❘✫✢❤✚❦❛❝❘❯❩✥✤❭❘✫❚r✤❭❚⑥❩✡✰✙✚✜②♦✗✙✤❭✢❤✚■✯✇❩✡✤❭❘❯❚❉✵ ⑦ ✧⑨⑧✍⑩❶✰✙❘❁❷❸❩✡✰✙✧✮❩❹❩✡✰✙✚✉❧❯✚■✯❫❩✥❘✫✢❲❳❺❘❯❩✥✚■❚⑨❩✡✤❭✧❯❪❻✪ ❼❾❽➀❿ ➁ ⑦ ♣❡s➃➂ qts➄♣❇➂ ⑧✿➅ ✗✙✚■❱❤✯■✢✥✤✦➆❺✚❫❱◗✧❨❛❝✧❯❣✫❚✙✚✇❩✡✤✦✯❴①✣✚■❪✦✗✻✤✦❚⑥❩✡✰✙✚✜②♦✗✙✤❭✢❤✚■✯❫❩✥✤❭❘✫❚✿✵ ⑦ ➆☎⑧✍➇④➈❶❳✙✢❤✚■❱❤❱❲❩✥✰✙✚✉❧✫✚■✯✇❩✡❘✫✢❡❳❇❘❯❩✡✚❫❚⑨❩✡✤➉✧✮❪✿✤❭❚⑥✯✇★♥❪❭✤❭❚✶✗✙✢✥✤✦✯✩✧❯❪❺✯■❘♥❘✫✢✥✗✙✤✦❚✣✧✮❩✥✚■❱■✪♥❩✡✰✣✧➊❩❡✤❭❱➋✤✦❚✍❩✥✚■✢❤❛❝❱➋❘✮❵❜➌♥✪☎➍✟✪➄➌❨➂ ✧❯❚✙✗ ➍☞➂ ✵ ⑦ ✯❁⑧●➎➏✢❤✤✦❩✡✚❴❩✥✰✙✚✹⑩❶✯✱✰✙✢✩❘✫➐ ✗✙✤❭❚✶❣✫✚■✢❡✚■➑➒✘✣✧➊❩✡✤❭❘❯❚❉✪ ⑦➔➓ qt➁ ✐❁❼✍→❯➣❫⑧❬↔ ⑦ ➌♠➅➙➍❺⑧➛❽➝➜ ⑦ ➌♠➅➙➍❺⑧✇➅ ⑦❖⑧ ❞ ↕ ↕ ✤❭❚✍✯❫★♥❪❭✤✦❚✙✗✙✢❤✤❭✯✩✧✮❪✿✯■❘♥❘✫✢❤✗✙✤❭❚✣✧➊❩✡✚■❱❫✵ ⑦ ✗☎⑧✻⑩❶✰✙❘❁❷❸❩✡✰✙✧✮❩❲➞➛➟◗✯■❘❯❛❝❛➃✘❶❩✡✚■❱➋❷❡✤➠❩✡✰⑥❩✡✰✶✚✹➡✝✧❯❛❂✤❭❪✦❩✥❘✫❚✙✤❭✧❯❚❉✵ ⑦ ✚❁⑧⑥➢◗❱✥❱❤✘✙❛❂✤❭❚✙❣❨❩✡✰✶✚✜❱❤❘✫❪❭✘❶❩✡✤❭❘❯❚⑥✤❭❱❲✧❯❚✍✚■✤✦❣✫✚■❚✙❱❬❩✱✧✮❩✥✚❦❘❯❵④➞➛➟❲❷❡✤✦❩✡✰✍✚❫✤❭❣✫✚❫❚➒❧✮✧❯❪✦✘✙✚✉❞✽➥❉➤ ✪ ↕ ⑦ ➌♠➅➙➍✿⑧➄❽➦✐■➧➩➨❜➫♠➭ ➨ ⑦ ➌❯⑧✇➅ ✢✥✚❫❷❡✢❤✤✦❩✥✚❦❩✥✰✙✚✹⑩❶✯✱✰✙✢✩❘✫➐ ✗✙✤❭❚✶❣✫✚■✢❡✚■➑➒✘✣✧➊❩✡✤❭❘❯❚✍❵➔❘❯✢➋➭ ➨ ⑦ ➌❯⑧✇✵ ⑦ ❵✡⑧●➯◗➲❉➳❁➵♠➸ ❀ ➵➊➺♥➻✟➼➔➳✫➽➄⑩❶❘✫❪➠❧✫✚✉❵➔❘✫✢➋❩✡✰✶✚❦➭ ➨ ⑦ ➌❯⑧➋✧❯❚✙✗✍❩✡✰✙✚❦✚■✤✦❣✫✚■❚✶✚■❚✙✚❫✢✥❣✫✤✦✚■❱❹❵➔❘✫✢➋❩✡✰✶✚✜✯■✧❯❱✥✚❦❷❡✰✙✚❫✢✥✚❦❞➾❽➝✴❶✵ ➁ ✵◗€❙❘❯❚✙❱✥✤✦✗✙✚■✢r✧➚✯✱✰✣✧❯✢❤❣✫✚■✗➪✢❤✚■❪❭✧✮❩✡✤➠❧❶✤✦❱❤❩✥✤❭✯⑥❳✣✧❯✢❬❩✡✤✦✯■❪❭✚✻✤❭❚⑨❩✥✚■✢✡✧✮✯❫❩✡✤✦❚✙❣➶❷❡✤✦❩✡✰✂❩✡✰✙✚✳✚■❪❭✚❫✯❫❩✥✢✥❘✫❛❝✧❯❣✫❚✙✚✇❩✡✤✦✯✍①✙✚■❪❭✗✿✪❡✧❯❚✙✗➹✗✙✚➙➘ ❱❤✯■✢❤✤❭➆❇✚■✗✍➆⑨★⑥❩✡✰✙✚✜➴✉❪❭✚❫✤❭❚❶➘➬➷❦❘✫✢❤✗✙❘✫❚●✚❫➑➒✘✣✧✮❩✡✤✦❘✫❚❉✵ ➮ ⑦✃➱ ➥❇➤ ❐✫❒❺q❄✐♠❮❹⑧ ↔❜❰ ➣ ↔ ➥➤ ↔ ❐ Ï↔ qt❞ ↔ ➣✱Ð✥Ñ ⑦ ♣☞➅✥Ò❤⑧➄❽➦✴ ↕ Ó ✰✶✚✜✚❫❪❭✚❫✯❫❩✡✢❤❘✫❱❤❩✡✧✮❩✡✤✦✯✉❳❺❘✮❩✡✚■❚⑨❩✥✤➉✧❯❪☞❮Ô✤❭❱❹✤✦❪❭❪❭✘✶❱❤❩✡✢✥✧✮❩✡✚❫✗⑥✤❭❚●❩✥✰✙✚❦✗✙✤➉✧❯❣❯✢✡✧❯❛❾➆❺✚❫❪❭❘❁❷❦✵ E-mc 2 I.

II.

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