Gaussianを用いた分子モデリングと量子化学計算

ǹïǋǝ4lȮȗȳȸȇǣ ŦlCoĹĔ ıįİĴĭĵĭıĵħİİĹįįĬİİĹĴį đıį^ź4lĹĔÍĉoăĎŃ ǈź4lȌȫȰȵȺȌȱȸǧǝǰǧȑȣȘǿȀǼ-Ūǉ ¿ÇŻ/ ŧÙioŻio¯ĨŬøȹ©ȐȸȒȺ ¯Ĩ©ȌȎȖȬăĎšŪǄ2¯¤
ĪĜ 2 1X ³ÃÞ îÍÃX ė\X´ TXÞ Ďº ƟƎƦƝ 3 'J ;G),/I ¾ŃǧÉĳɄŋµǳǵɆ Ǆ Őǅź4lăĎǧ4ťǦǎǋǡǱĹĔÍȌȫȰȵȺ ȌȱȸǧÝïǐǒĽǮǴǷǡǎǵǅȉȸȢȰȺȒȞȺșǿ ȀǼǧŗÐǣ0ǦǅhËǥȑȣȘǿȀǼǐ/ŬǗǷǡǋ ǭǙǆǘǏǘǅź4lǹuŅǣǙǶǣĸǢĸǞǡǱǅ KǅÊŖǅÍĩǥǤuŅǨŴǦh{ǦǸǝǵǅMǶ ǬǑȌȫȰȵȺȌȱȸÚǅïǋǶǬǑȑȣȘǿȀǼǧúĄ ǥŠ ǐĳǣǥǵǅǏǴǹǔǡǋǋǧǏǸǏǴ ǥǋǣǋǌ³ǇǱhǋǣǋǭǙǆȹȹȹ ǃŻ️ĹĔĉoȹȌȫȰȵȺȌȱȸĉoǫǧĩȹ¼ ǃŻìŁǧ;ĚǣǅĘǧůôǅřiǥĹĔȉȎȘȹȹȹ

¾Ńǧüú ǄŦlCoĹĔȥȶȇȲȬ ǹïǋǅ4lŌŚÚ ǎǳǪt×Ů°ÚǦǳǶ4lȮȗȳȸȇǧcĆǅsŰ ǧĹĔǦǎǔǶȩǾȸȘǹķľǙǶ •  :śüÌɃ – ȄȺȷȺșǹǱǣǦ ĳǥÉǹǅǟǏǯ
– 4lǧÊŖȹæȹKǧłĳěǦǟǋǡǅŦlC oǧŝïPĩǥĖ_ǣǜǧůôǦǟǋǡľ¶ǢǑǶ – 4lȮȗȳȸȇǧ ǹǱǣǦǅïǢǑǶ ċV1XƝŽrƌƭƬƊƚž ųlèǐǸǏǶ !  ĳǥdǨǅc¾úǦGlȹ4lǧ6¼ÊŖ ȼÌȽǧǮ !  sŹȠȲȭȺȒǦǳǴǚǅđGìȼab initioȽúǦ ķǒǖǣǐǢǑǶ !  ųlèǏǴǅ¹ŝǥÊŖǅȁȜȴȅȺǅ4læǅ CoKǹ áǙǶǖǣǐǢǑǶ ȥȲȔȘȣȂȺȬǧfC ź!ǥȷȺȆȎȖȺȌȱȸǧġ¡ȹĕìǣǅĹĔȉȎȘ →ǄÒŎúp!ǥȭțȺȉǼPCǅȎȘȵȺȍȹȭȮȳ →Ǆi4lęǦǱħǍǌǶìŁȹȑȣȘǿȀǼŬø 6 ³óǤǧǥź'VøĂ§ĨňŊ§ĩŵ ńŢŧťţřŨŘŧŞţŢħŧţħňţŠŚŘŨŠŖťħŊťŗŞŧŖŠħňŚŧŝţř 7 ŎŘŝťůřŞŢŜŚťÅm • hųlęǧSchrödinger³Č ĤΨ=EΨ →GlÆǧŘBǹ`r(Born-OppenheimerŐ) →ąÓúþïǧäĵ Ǆ1ųlǐGlÆǣǧųlǏǴNǔǶȩȖȸȌȯȴǧ ǢŘBȼbeŐǅ1ųlŐǭǝǨéĐųlȮȗȴȽǆ 8 2 1 1 ˆ 2 1 ˆ( ) A i i A i i j i iA ij i i j i ij Z H r r h i r > > = − ∇ + + = + ∑ ∑∑ ∑∑ ∑ ∑∑ 1ųlȞȫȴȘțǼȸǣ ųlŭKøȩȖȸȌȯȴ

ŎŠŖŧŚťä(m • ųlÛBŮ° →ųlǧ¨ǦǟǋǡKuĊǹâǝǙ →Ƞǿȳǧ¥<ǹâǝǙ •  m ƞ1, 2, …, 2nƟŻěVlr
1 ,r 2 , …, r 2n ƞ¸ï 9 ψ(1,2,!,2n) = φ1 (1) φ1 (1) φ2 (1) φ2 (1) ! φn (1) φn (1) φ1 (2) φ1 (2) φ2 (2) φ2 (2) ! φn (2) φn (2) ! ! ! ! ! ! ! φ1 (2n) φ1 (2n) φ2 (2n) φ2 (2n) ! φn (2n) φn (2n) φn φ2 φ1 2n ūÑųlŢĥǧɃŻȾųlŮ°φn (x)Ǩ4lŌŚ ¤Ó4Vƞ4VøĂƞo¯Ĩİĩ ļŧţšŞŘħŊťŗŞŧŖŠħħıŤūøĂƞ 11 ƜƂŻƙƮƯƸƨƭƮŻƦƲƩŻƙƂŻƠƸƼƸƯƮƀŻ ŻƉƅŻżƄƌƋƈŽŻƅƃƉƂ ¤Ó4Vƞ4VøĂƞo¯Ĩıĩ ļŧţšŞŘħŊťŗŞŧŖŠħĲřøĂƞ 12 ƗƂŻƟƭƮưƪƀŻ ŻƌƄŻżƅƃƄƇŽŻƄƊƆƌƂ 4lŌŚǧƚƑƏƜŐǅƠƑƔĹĔ • GlŌŚ(AO)ǧĢğR(Linear Combination) GlŌŚχǧĢğRǢ4lŌŚǹıǸǙɃLCAO ȁȜȴȅȺ¼)ǹÖǰǶǝǰǦLCAOǧ4lč4ǹķǒ ķǒǬǑÕ³ČǨHartree-Fock-Roothaan³Čǣǥǵ Ǆİ5F,S,cǐĂÿǐäǒǥǶǭǢĹĔǹĤǵőǙ →Īä«āǥeǄself-consistent field(SCF)ĹĔ 1 m i ri r r c φ χ = = ∑ ˆ E H d Ψ Ψ τ ∗ = ∫ ( ) 0 i i i − = F S c e xŬǙǶcŮ°ǧŠ f4ÚǦǳǶȁȜȴȅȺ¹vC ȁȜȴȅȺLÀǧȓȀȔȆǄ→ǄMOǅ4læ SCFǹķǒ³ÚŁǧŠ 13

'VøĂîÍĨŃŖťŧťŚŚĬŁţŘş§ĩƝƩƖƘsƪƭƬxO ź¤'Vƞ Ɩ Ɩ Ɯ ƖƜƛƜ ƚƢƛƜ ųlÑǣųlŌŚ ɈÑ
Ƅƶ ɉÑ ƅƶŻŻŻŻŻŻŻŻƅƴŻŻŻƅƴŻŻƅƴŻ 4lŌŚżƛƜŽŻƍŻƽ ŌŚȁȜȴȅȺƍŻ 4lŌŚÚǧ4Ÿ •  ŴĞŹú³Ú non empirical –  ǙǬǡǧ4lč4ǹĀõǥǘǦİǌ = ab initioÚǣǱZǩǷǶǆ –  ªBÚǅŢĥŭþïǦǳǵǅǈųlþŮǉǧAÄǹMǵŏ ǯǖǣǐǢǑǅęĠúǦĘǹǕǶǖǣǐǢǑǶǆ –  ȑȣȘǿȀǼɃGaussian, Spartan, GAMESS, NWChemǥǤ •  EĞŹú³Ú semi-empirical –  !ųlǧǮǹMǵǋǅč4ǹȠȲȭȺȒCǘǝǵĀõǙǶ –  ȑȣȘǿȀǼɃMOPAC(AM1, PM3, MOZYMEÚǥǤ) •  ĞŹú³Ú empirical –  HückelŐǢǨǅπųlǧǮǹǋǅĞŹȠȲȭȺȒǹïǋǶ •  t×Ů°(DF)ÚǄdensity functional –  ųltǹc¾f°ǣǘǝKohn-Sham³ČǦǘǝǐǌǆų lþŮǹºAúǦMǵŏǯǐǅĹĔȉȎȘǨHartree-FockŐ ǣTČǢàǯǆŐǅûǺǦïǋǴǷǡǋǶǆ 15 ĝÖĤ»'VøĂ§ƞǋƶǛǝƸǢ •  ěVď6ºƞĠƯŻß'RƞěVƅƗƇƬh JƞPƚƍƘûƏƬǤ°ÈÏVǖǄǝǥƝƩƖƘƀƬ –  û÷ęƞěVď6ºƞāTðǪ0»ěV½Đ –  ěVĉÜƞƶǈǝƹǢ©ƞûǪĝ0»ěV½Đ –  "ŃŁ§ƞŎľŁƞ×ƟŻuƐ¾ƞƶǈǝƹǢƞƝſƬǣ •  ěV½ĐƞÝzƝƩƬÑØ»ƜÐk< –  ňŰŠŠŚťĬŋŠŚŦŦŚŧƝƩƬ0§ħňŋħŤŚťŧŨťŗŖŧŞţŢħŧŝŚţťŬǪŵ ĨňŋıĩŻǤňŋĲǥŻCǤňŋĳǥ –  ĉÜď½µħľţŢśŞŜŨťŖŧŞţŢħńŢŧŚťŖŘŧŞţŢħĨľńǥǪŵ ſƪƮƝƒƭƓƭƞěV/öĉÜƯÝzŻSĉÜ§ƚƧ@ơŵ ľńŎĨǧěV/öĉÜƣƙĩŻŻľńŎĿŻľńŎĿŏŻľńŎĿŏŌǡǡǡŁľń –  ×:ƺǛƾǀǢ§ħľţŨŤŠŚřħľŠŨŦŧŚťǪźǉǔǝǅǇƱǠƢªÍVƯÛ ƫúƥźǩěV/öĉÜƣƙÝzƍƔľľŎĿĨŏĩƜƛ 16 ³ÚŁǅcŮ°ęȼŒȽǦuǙǶǂ ĹĔȉȎȘǣuGl° •  ³ÚŁǣcŮ°ęǧŠ ǧǝǰǦǨɇ –  ĹĔǘǝǋęǨuGl°ǦLǭǞǡǋǶǏ –  ¼ǙǶĹĔ·ŭǦǎǗǭǶǏ –  ĴǝǋæǹD4ǦĺŒǢǑǶǏ 48B(.E3> =/ (.E33N- A<5D"*1 -0%)3 7?%)F ŴĞŹú4lŌŚÚ CCSD(T)/QZP +C9 < ~2 kcal/mol KN 7 5 K 6 MP2/DZP $+C9 KN 5 K 10 B3LYP(DFT)/DZP $+C9 KN 3K4 K 102K HF/SZ +19 KN 4 K 102K EĞŹú4lŌŚÚ PM5,AM1,PM4,MNDO +19 KN 3 K 10 MOZYME8 +19 KN 1.38 K 104 17 @ŊèȼŢĥȽ° cŮ°ęǧiǑǗ

³óǤǨǥź]k¦Đ§ĨĿŁ§ĩ ńŢŧťţřŨŘŧŞţŢħŧţħĿŚŢŦŞŧŬħŁŨŢŘŧŞţŢŖŠħŏŝŚţťŬ 18 ņţŝŢĬŎŝŖšħĨņŎĩħÅm •  ŒĭħņţŝŢƚŇĭħŅĭħŎŝŖšƝƩƬěV]kρĨrĩƝĐƏ ƬÅmħħ"RĈǒǃǠƽǗǝő œľ Ɲ]k¦ĐħδE [ρǤrǥ]/δρǤrǥƅ²ƭƬ
•  ñä¨0ĐƯěVnƝ^ƍƘ3nƯƧƗ ΨǧǸǵǦǅ3Î+ǹǱǟρȼrȽǹǞǡǱǳǋŵ "ŃţŝŚŢŗŚťŜĬņţŝŢƞZ³ 19 ˆ H = − 1 2 ∇i 2 i ∑ + Z A r iA i ∑ A ∑ + 1 r ij j>i ∑ i ∑ = − 1 2 ∇i 2 i ∑ + ˆ V + ˆ G → − 1 2 ∇i 2 + ˆ V i ∑ + ρ( ! r ) r − " r d ! r ∫ + ˆ V XC (r) ŃţŝŚŢŗŚťŜĬņţŝŢƞZ³ •  ÊZ³ǪĝÚĊNj¯yƞěV]kƚRĈ ǒǃǠƽǗǝǤZĈ'ƯēƇǥƞďƝƟ^ƞ ĐƅſƬż •  ÊZ³ǪſƬRĈǒǃǠƽǗǝƝ^ƍƘŻñä ěV]kƞƶǈǝƹǢ¦ĐǤƶǈǝƹǢǥƟŻ Nj¯yƞƶǈǝƹǢƩƫgƝĥƀƄſƬƀƟñ äěV]kƚNj¯yƞěV]kƅàƍƔƚ ƆƝĒƫËƍƀż •  "ųƯ!ÇďƙÆ'ƏƬƚěVƝƜƫŻom »ƝŻƶǈǝƹǢƯěV]kƞ¦ĐƚƍƘƈƬŵ E = E[ρǤrǥ] ½ĐǒǃǠƽǗǝǪ œľħ ĻħδE [ρǤrǥ]/δρǤrǥ 20 ƙƠÚǢǧƚƑƏƜŐǅƠƑƔĹĔ • GlŌŚ(AO)ǧĢğR(Linear Combination) GlŌŚχǧĢğRǢ4lŌŚǹıǸǙɃLCAO ȁȜȴȅȺ¼)ǹÖǰǶǝǰǦLCAOǧ4lč4ǹķǒ ķǒǬǑÕ³ČǨHartree-Fock-Roothaan³ČǣŸ Ǆİ5F,S,cǐĂÿǐäǒǥǶǭǢĹĔǹĤǵőǙ →Īä«āǥeǄself-consistent field(SCF)ĹĔ 1 m i ri r r c φ χ = = ∑ ˆ E H d Ψ Ψ τ ∗ = ∫ ( ) 0 i i i − = F S c e xŬǙǶcŮ°ǧŠ f4ÚǦǳǶȁȜȴȅȺ¹vC .ųlȁȜȴȅȺȼ¨þŮȁȜȴȅȺȽǨǝ4lŌŚǹǱǣ Ǧ8'ǦķǋǡLÀ7rǙǶǄ→ǄKSŌŚǅ4læ SCFǹķǒ³ÚŁǧŠ 21

ŋŚťřŚŪƞǘƼǎƞƟƍƋ •  ĿŁŏîÍƟ ¿ƜƞƄǬ – ŅţŝŢħŋŚťřŚŪħŅŖŘţŗŴŦħŇŖřřŚť – UGƣƙƞĴƗƞŽǤƊǥžǤōŨŢŜǥ 22 ƘƂŻƝƂŻƝƪƵƩƪƹŻƦƲƩŻƙƂŻƠƨƭƱƮƩƷƀŻǀƘƦƨƳƧƿƶŻưƦƩƩƪƵŻƳƫŻƩƪƲƶƮƷƻŻƫƸƲƨƷƮƳƲƦư ƦƴƴƵƳƺƮƱƦƷƮƳƲƶŻƫƳƵŻƷƭƪŻƪƺƨƭƦƲƬƪƁƨƳƵƵƪưƦƷƮƳƲŻƪƲƪƵƬƻǁƂŻƗƲŻƒƪƲƶƮƷƻŻ ƔƸƲƨƷƮƳƲƦưŻơƭƪƳƵƻŻƦƲƩŻƗƷƶŻƏƴƴưƮƨƦƷƮƳƲŻƷƳŻƛƦƷƪƵƮƦưƶƎŻƣƂŻƣƦƲŻƒƳƵƪƲƀŻƑƂŻƣƦƲŻ
ƏưƶƪƲƳƻƀŻƦƲƩŻƝƂŻƕƪƪƵưƮƲƬƶƀŻƓƩƶƂƀŻ ŻżƅƃƃƄŽŻƄƾƅƃƂ VWN PW91 PBE LYP VS98 TPSS B3LYP PBE0 EĞŹúƍŻƐƌƊƀŻƐƌƊƁƒƀŻƛƺężǝǣǍǩ ƛƃƉǨǅƝƐƓǹĲÏǘǝƛƃƈǣƐƌƊþŮǣ ƣƠƌƋ¨þŮǣƖƦƵƷƵƪƪƁƔƳƨƯ¨ǧ ȞǾȤȳȔșȽƀŻƛƃƉƁƅƤǥǤ ƩƇƮƭƬ½Đ¦Đ •  ŇĿļĹħŎŠŖŧŚťƞœűīħőţŦşĬŒŞŠşĬŉŨŦŖŞťĨőŒŉĩ½Đ •  łłļĹħĽŚŘşŚķķīħŋŚťřŚŪĬŒŖŢŜİĸĸİĨŋŒĸİĩīħ ŋŚťřŚŪĬĽŨťşŚĬŀťŢŭŚťŝţśĨŋĽŀĩīħťŚũŋĽŀǡǡǡīħ ŋŒĸİ½ĐīħŋĽŀ½ĐīħŇŚŚĬŔŖŢŜĬŋŖťťǤŇŔŋǥ½Đīħǧ QǏǟƻǞǂƽǎǤŊŋǥ½ĐƜƛ •  ǕǀłłļĹħũŖŢħőţţťŝŞŦĬŎŘŨŦŚťŞŖİĸĸķǤőŎĸķǥǕǀ½ ĐīħŏŖţĬŋŚťřŚŪĬŎŧŖťţũŚťţũĬŎŘŨŦŚťŞŖǤŏŋŎŎǥǕǀ ½ĐħƜƛ •  ǉƳǎǜǂǆĹħĽĲŇŔŋīħŋĽŀįħƊƞWƟǊǛǕǢǀ •  2ÖĤ»ĹħĽĸĶīħĽĸĶĬĿīħňūÑĨƔƚƂƠňįĵƟŻŋĽŀƯæ ƍƔňįĴƚĽĸĶ½ĐƚőŎĸķ½ĐƚŃŖťŧťŚŚĬŁţŘş ƞǉƳǎǜǂǆǥīħňįĵĬıœƜƛź'Vď-ƝnƤ 24 NjĐÑƞć} ŎŚŠŚŘŧŞţŢħţśħŗŖŦŞŦħŦŚŧ 30 aNjĐÑźŦŞŢŜŠŚħŭŚŧŖħŎŕ •  N»ƜÝƂĹħİƗƞħļŊħƯİƗƞNjĐƙ ûƏƬżħ – åħŎŏŊĬłħĨħĻıĵĩīħňńŉńĬİ – FǪİīıīĲīĴħƞłŖŨŦŦLøĂĨłŏŊĩƞÚÒƞăƀ 32

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•  'Vď-ǤŇţŢřţŢƞ'-ǥƞÝz – òö5VǖǢǕǠǅƝ¶ƏƬ –  ňŋıƞěV½ĐƞÝzŻ'æ Ĩ2ÖĤ»ĿŁŏƜƛĩ 46 ěV/ö •  ǍǛǠƺǫƼǠǆǠƞK¼/öźũŚťŧŞŘŖŠħŚūŘŞŧŖŧŞţŢ – âŻøĂƶǈǝƹǢ©ƞďƞěVĆÄ •  $ČLeźŘţŢŞŘŖŠħŞŢŧŚťŦŚŘŧŞţŢ – 1X6vƝéƪƭƬ •  ĠďeźŞŢŧŚťŦŬŦŧŚšħŘťţŦŦŞŢŜ – N»ƝƟÂ*ĆÄźǥĊĠĬĊĠĆÄ – ƾǌǠĬøĂ½µħŦŤŞŢĬţťŗŞŧħŘţŨŤŠŞŢŜħƞÝz •  ƳƷǠ1ǒǃǠƽǗǝħńŋħƚěVëA-ħŀļ – ňŊƙƟÎ»ƝƟŻŃŊňŊƞøĂƶǈǝƹǢƞýÉ9ƚŵ ŇŐňŊƞøĂƶǈǝƹǢƞýÉ9ǤņţţŤšŖŢŦƞZ³ǥ – ĿŁƙƟŅŖŢŖşƞZ³ǤņŎøĂƖƘƩƀƞƄǬǥ 51 ƒƞƞƾǑƺǅǝ •  õR>7'ħŞŢśťŖťŚřĺħńō – ǓƳƺǟ¨ġMŻ'V0ǖǢǆƝ¶ •  DùƾǑƺǅǝ – ǓƳƺǟ¨ġMŻDùǖǢǆƝ¶ RPƝ^ƏƬvÌw •  À£"ĦƾǑƺǅǝħŢŨŘŠŚŖťħšŖŜŢŚŧŞŘħ ťŚŦţŢŖŢŘŚĺħŉňō •  ěVƾǌǠ"ĦƾǑƺǅǝħŚŠŚŘŧťţŢħŦŤŞŢħ ĨŤŖťŖšŖŜŢŚŧŞŘĩħťŚŦţŢŖŢŘŚĺħŀŎōħƣƔƟħŀŋō 57 łļŐŎŎńļŉµƞ[Ė 'VǖǄǜǠƻƞǁǙǢǅǜƱǝǪłŖŨŦŦŞŖŢįĸǡłŖŨŦŦőŞŚŪƯƝ 61

62 GaussView νϡʔτϦΞϧ •  4lÌǧÊė •  File> New> Create MolGroup
²ǘǋBuilderǿǽȸșǿ •  Element fragment ǹȆȳȔȆǘǡX¼ıǹıć •  Builderǿǽȸșǿ1ǢȆȳȔȆǙǶǣŠ ǘǝȣȲȇȭȸȘÊŖǐëǷ Ƕǆ ȼȕȺȴȹȟȺǧÍĩȽ Inquire: 4lǧÊŖȠȲȭȺȒĹá Element Fragment: X¼ıǧıć Modeify Bond/Angle/Dihedral: Ring Fragment: íèÊŖ4lȖȸȥȵȺȘ ğRũȹğRĶȹ ŵĶǧȠȲȭȺȒģŲ R-group Fragment: qĩcȖȸȥȵȺȘ Add Valence: ÔěǣǘǡGl!ǹœ? Biological Fragment: ǼȫȝţȹDNAȖȸȥȵȺȘ Atom delete: ĳǥGlǧÞH ԋश1)m-ΞϛϊϑΣϊʔϧ(Ϟσϧ)ͷߏங •  File> New> Create MolGroup •  Ring Fragment ǹȆȳȔȆǘŻȖȸȥȵȺȘǏǴbenzeneǹŠ •  Builderǿǽȸșǿ1ǢȆȳȔȆǘbenzeneíǹıćǗǛǶ •  Element Fragment ǹȆȳȔȆǘǅNǏǴNitrogen Tetravalent(sp3) ǼǾȉȸǅOǏǴOxygen Tetravalent(sp3)ǼǾȉȸǹŠ $  Builderǿǽȸșǿ1ǢǅbenzeneíǧÔě ǧǢȆȳȔȆǙǶǣqĩcǦĥǑ¨ǸǶ $  File> Save ǏǴŻǀtest.gjfǁǣǘǡ$n $  File> Save Image ǭǝǨ Edit> Image Capture Ǣó*ǹȣǻǾȴǦ $nǙǶǖǣǐǢǑǶ(tiff, jpg, ps, bmp, png) ȼBuilderǢǧ"9ǥ¬³ÚȽ ~ȆȳȔȆ:Īñ^ō Ctrl+Z: ǲǵýǘ QȆȳȔȆ:ȏȺȬȹŵ^ō Ctrl+Y: ǲǵýǘǧǲǵýǘ ȆȳȔȆ(~ȹQT·) ǭǝǨ Ctrl+~ȆȳȔȆ: İċB 63 ԋश2)ਫ෼ࢠͷߏங, Ұ఺ܭࢉ •  File> New> Create MolGroup •  Element Fragment ǹȆȳȔȆǘŻȖȸȥȵȺȘǏǴOǹŠ •  File> Save> ǀh2o.gjfǁŻǾȸȥȔȘȣǻǾȴǧ$n •  Calculate> Gaussian ĹĔÁǧĻr •  Edit ǹȆȳȔȆǘinputȣǻǾȴǹý¦ģŲ(Vi, XEmacsĒ)* %chk=h2o.chk ȓȀȔȆȩǾȸȘ(chk)ȣǻǾȴ¢r %mem=64MB ȭȮȳ %nproc=1 CPU° #P HF/STO-3G Pop=full ǄǄȴȺȘȐȆȌȱȸ SCF=(Conver=8) test ȼďİȽ H2O single-point ǄǄȍȱȤȒǾȘȴ ȼďİȽ 0 1 ǄǄǄųĬ(0:)ǅȎȢȸhŤ(1:ŤŶ) O H 1 B1 ǄǄǄǄǄǄǄǄZ-matrix(1šÌ) H 1 B2 2 A1 ȼďİȽ B1 0.96 B2 0.96 ǄǄǄǄǄǄǄŻÊŖȠȲȭȺȒ A1 109.5 ȼďİȽ 2 1 3 4 bond angle dihedral 64 O1 H3 H2 B2 A1 B1 ȼGJFȣǻǾȴǧçȽ ȹ#İ(ȴȺȘȐȆȌȱȸ)Ǩ°İǦǸǝǞǡǱÊ Ǹǥǋǆ ȹi±m/v±mǧßaP ȹȄȺȷȺșŭǧďùǨǋǒǟǢǱÊǸǥǋ ȹďİǨŷ *additional keyword ǏǴǧĻrǱPĩ ݁Ռ2)OutputͷදࣔͱՄࢹԽ –  GlųĬǣȊȪȳǧıć •  File> Open> ǀh2o.logǁ •  Results> Charges •  Displayǿǽȸșǿǧ Show Charge NumberǦȓȀȔȆ •  Results> Summary ȊȪȳǧıć $  MOǅ.ųltǧıć $  File> Open> ǀh2o.fchkǁ $  Edit> MOs> Visualize ıćǗǛǝǋMOǹŠ updateǹȆȳȔȆǙǶǣ§óǢǑǶ $  Results> Surfaces $  Cube Actions> New Cube> Total density Surface Actions> New Surface ȼMOǧËǇǥıć³ÚȽ BuilderǿǽȸșǿǢQȆȳȔȆ > Display Format > Surface Mesh(ȭȔȌȰıć)ǅSolid(ȑȳȔș)ǅTransparent(EŔ¶ıć) 65 $  ĹĔǧsİ+fchkȣǻǾȴǫǧf¨ $  prompt> g09 h2o.gjf prompt> formchk h2o.chk

ԋश3)ਫ෼ࢠͷߏ଄࠷దԽ –  InputȣǻǾȴǧ%Ï •  File> Open> ǀh2o.gjfǁ •  File> Save>
ǀh2o_opt.gjfǁ 8UǢ$nǙǶ •  Calculate> Gaussian •  Edit> ǧ4ēǹ%Ï ȼlogȣǻǾȴǣchk(fchk)ȣǻǾȴǧŜǋȽ logȣǻǾȴǦǨǅĹĔřČǣ4lÊŖǅȁȜȴȅȺǅMO#°ǅGlųĬǅJÈlȮȺȭȸȘǥǤǧĹ ĔğÄǐ3>ǗǷǶǆǖǧeR(OPTȄȺȷȺș)ǦǨǅÊŖ¹ŝCǧŕǧÊŖǱ3>ǦVǭǷǶǆ chk(fchk)ȣǻǾȴǦǨMOǦŮǙǶdǱVǭǷǶǧǢǅ¹ĝÊŖǧMOǹıćǗǛǝǋǣǑǦïǋǶǆ %chk=h2o_opt.chkȓȀȔȆȩǾȸȘȣǻǾȴ¢r %mem=64MB ȭȮȳ %nproc=1 CPU° #P OPT HF/STO-3G Pop=full SCF=(Conver=10) test ȼďİȽ H2O optimization ȍȱȤȒǾȘȴ ȼďİȽ ȹȹȹȹȹȹ ȹȹȹȹȹȹ $  ¹ŝCÊŖǧıć $  File> Open> ǀh2o_opt.logǁ ǿǽȸșǿšǦǊǶRead Intermediate geometriesǦȓȀȔȆ $  Results> Optimization $  Results> Summary 66 ԋश4)ਫ෼ࢠͷج४ৼಈղੳ –  ¹ŝCÊŖǏǴǧInputǧ •  File> Open> ǀh2o_opt.logǁ =^ǧ¹ĝÊŖǹĿǮŏǯ •  File> Save> ǀh2o_freq.gjfǁ •  Calculate> Gaussian •  Edit> ǧ3ēǹ%Ï ȼprÊŖǏǤǌǏǧȓȀȔȆȽ cã£BķÃǏǴǨǅŉgWL(IR)ǎǳǪȲȪȸȎȧȆȘȴǧWLÛũǣǐÖǰǴǷǶǆ ȁȜȴȅȺǐprǥÊŖǹïǋǥǔǷǩĹĔğÄǦYǨǥǋǆǭǝǅÊŖ¹ŝCǢïǋǝĹĔÚ/ cŮ°ǣöǥǶĹĔȵȦȴǹïǋǡǱǋǔǥǋǆǱǘņȼįȽǧ£B°ǐğÄǦëǷǷǩǅǜǧÊŖ ǐprŭȼşċèȽǢǊǶǖǣǹćǙ→prǥcèǧÊŖǢǨǥǋȻȻ %chk=h2o_freq.chkȓȀȔȆȩǾȸȘȣǻǾȴ¢r %mem=64MB ȭȮȳ %nproc=1 CPU° #P FREQ HF/STO-3G Pop=full SCF=(Conver=10) test ȼďİȽ H2O frequency ȍȱȤȒǾȘȴ ȼďİȽ ȹȹȹȹȹȹ ȹȹȹȹȹȹ $  cã£BȮȺșǅIRȎȧȆȘȴǧıć $  File> Open> ǀh2o_freq.logǁ ğÄǧĿǮŏǮ $  Results> Vibrations 67 ԋश5)ਫ෼ࢠͷ࣓֩ؾःṭఆ਺ 68 –  InputȣǻǾȴǧ%Ï •  File> Open> ǀh2o_opt.logǁ ¹ŝCÊŖǹĿǮŏǯ •  File> Save> ǀh2o_nmr.gjfǁ •  Calculate> Gaussian •  Edit> ǧ3ēǹ%Ï %chk=h2o_nmr.chkȓȀȔȆȩǾȸȘȣǻǾȴ¢r %mem=256MB ȭȮȳ %nproc=1 CPU° #P NMR=GIAO HF/6-31G(d) Pop=full SCF=(Conver=8) test ȼďİȽ H2O NMR tensor ȍȱȤȒǾȘȴ ȼďİȽ ȹȹȹȹȹȹ ȹȹȹȹȹȹ $  NMRȎȧȆȘȴıćǅcãæňǧ¢r $  File> Open> ǀh2o_nmr.logǁ ğÄǧĿǮŏǮ $  Results> NMR Element> H Reference> TMS HF/6-31G(d) ȼĹĔĘǅcãæňǣǧÒŎǦǟǋǡȽ ÆąÓŞĮr°ǨǅīǦcãæňǣǧǣǘǡǴǷǶ(ɅCoȌȣȘǅppmF)ǆGaussViewǦ ǨTMS(ȖȘȲȭȓȴȌȲȸ)ǧĹĔ)ǐ ǰïǗǷǡǋǡǅHF/6-31G(d) ǣ B3LYP/6-311+G(2d,p) ǧĹĔȵȦȴǢǧCoȌȣȘǹĴčǱǶǖǣǐǢǑǶǆąe nǧæǹÖǰǶcŮ°ȹ³ÚŁǦǟ ǋǡǨ°hǒǧńŁǐǊǶǆD4ǥȵȦȴǢ¹ŝCǗǷǝÊŖǏsŹÊŖǹïǋǶǖǣǹǎkǰǙǶǆ ǪƿǍǅƴƵƱƞć}Ż²[ÑƢ ƞąµƚĒ· 69

◦ਿ৿ެҰ1ɼ઒ล߂೭1ɼ௕ඌल࣮2ɼ੢઒ਗ਼2  ʢ1ۚ৓େֶࣾձ෱ࢱֶ෦ɾ2ۚ୔େֶେֶӃࣗવՊֶݚڀՊʣ Ϧϯࢷ࣭εϑΟϯΰϛΤϦϯ෼ࢠͷߏ଄ ͱIRεϖΫτϧʹؔ͢Δཧ࿦తݚڀ Fig.1: Chemical structure of sphingomyelin and
the truncated model. head group interface hydrophobic group truncated model (Sphingomyelin) (acyl chain) (sphingosine) (phosphocholine) head group interface hydrophobic group truncated model (Dihydrosphingomyelin) (acyl chain) (sphingosine) (phosphocholine) Fig.2: Truncated model of sphingomyelin and Ca2+ starting positions of geometry optimization. (II) (I) 1-(II)Ca2+ 2-(II)Ca2+ ഑࠲ؒͷΤωϧΪʔࠩ͸ ྵ఺ΤωϧΪʔิਖ਼ޙͷ શΤωϧΪʔͷࠩ ΔEtot+ZPE (E1 – E2 ) Fig.3: Optimized structures by using B3LYP/6-31G(d,p); (1,2) sphingomyelin, and (1’,2’) dihydrosphingomyelin. 1 2 2’ ΔE = –4.070 kcal/mol 1’ ΔE = –7.4536 kcal/mol

Fig.4: Calculated IR spectrum of (a)1 and (b)1-(II)Ca2+ by B3LYP/6-31G(d,p),
without scaling. O—H !@ a) 3699 cm-1 b) 3744 cm-1 C=O !@ a) 1717 cm-1 b) 1752 cm-1 H-:!@ a) 1572 cm-1 b) 1522 cm-1 Fig.5: Calculated IR spectrum of (a)2 and (b)2-(II)Ca2+ by B3LYP/6-31G(d,p), without scaling. O—H !@ a) 3544 cm-1 b) 3683 cm-1 C=O !@ a) 1763 cm-1 b) 1641 cm-1 H-:!@ a) 1541 cm-1 b) 1609 cm-1 +dǖǄǝƙƞ'Vď-ǐǠǁǓǢƺ 92 .1( E Q źħdLDBMNPM

ǭǣǰǦǍǡ Ǆ Őǅź4lăĎǧ4ťǦǎǋǡǱĹĔÍȌȫȰȵȺȌȱȸǧÝ ïǐǒĽǮǴǷǡǎǵǅȉȸȢȰȺȒȞȺșǿȀǼǧŗÐǣ0Ǧǅ hËǥȑȣȘǿȀǼǐ/ŬǗǷǡǋǭǙǆǘǏǘǅź4lǹuŅǣǙ ǶǣĸǢĸǞǡǱǅKǅÊŖǅÍĩǥǤuŅǨŴǦh{ǦǸ ǝǵǅMǶǬǑȌȫȰȵȺȌȱȸÚǅïǋǶǬǑȑȣȘǿȀǼǧú ĄǥŠ ǐĳǣǥǵǅǏǴǹǔǡǋǋǧǏǸǏǴǥǋǣǋ ǌ³ǇǱhǋǣǋǭǙǆȹȹȹ
ǃŻ️ĹĔĉoȹȌȫȰȵȺȌȱȸĉoǫǧĩȹ¼ ǃŻìŁǧ;ĚǣǅĘǧůôǅřiǥĹĔȉȎȘȹȹȹ ǮǥǗǭǧǅĹĔĉoǫǧ¼ǣ÷\Ǧǂ ǙǖǘǢǱǍǶǖǣǐǢǑǡǋǝǴǋǢǙ IĦ±ê cĆúǥìķǧǝǰǦ •  ĭØ%ɃcĆŦlCoǅ»&¸ȼ1997Ƚ •  ȋȨȹȃȎȘȲȸșǅiť/òǴļɃ²ǘǋŦlCoŻȹǅÂi o3åȼ1982Ʌ1987Ƚ ÒŎú¹ŐǧǱǧ •  ´¾CoɃđɂåsŹCoŃȾȿǄĹĔCoǅ ]ȼ2004Ƚ •  w/ǴɃǙǓǢǑǶŦlCoĹĔȡȅȚȺȏȪțȰǼȴǅŃŀ ĈȊǾȁȸȖǽȣǽȆȼ2006Ƚ •  Åð®űǴɃĹĔĉoɁǄĹĔǣî[ǅ}Û¸ȼ2012Ƚ •  ðŇjɃt×Ů°ÚǧcĆǅŃŀĈȊǾȁȸȖǽȣǽȆȼ2012Ƚ •  zO,ǴɃŧyŨǧŦlȹĹĔCoǅ03åȼ2014Ƚ •  ȌȱȺȴȹȎȖȔȈȴǅǇ½ÜŖǴļɃt×Ů°ìŁ-ŪǅS |¸ȼ2014Ƚ 100

Gaussianを用いた分子モデリングと量子化学計算

Gaussianを用いた分子モデリングと量子化学計算

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ǹïǋǝ4lȮȗȳȸȇǣ ŦlCoĹĔ ıįİĴĭĵĭıĵħİİĹįįĬİİĹĴį đıį^ź4lĹĔÍĉoăĎŃ ǈź4lȌȫȰȵȺȌȱȸǧǝǰǧȑȣȘǿȀǼ-Ūǉ ¿ÇŻ/ ŧÙioŻio¯ĨŬøȹ©ȐȸȒȺ ¯Ĩ©ȌȎȖȬăĎšŪǄ2¯¤

¾Ńǧüú ǄŦlCoĹĔȥȶȇȲȬ ǹïǋǅ4lŌŚÚ ǎǳǪt×Ů°ÚǦǳǶ4lȮȗȳȸȇǧcĆǅsŰ ǧĹĔǦǎǔǶȩǾȸȘǹķľǙǶ •  :śüÌɃ – ȄȺȷȺșǹǱǣǦ ĳǥÉǹǅǟǏǯ

ŎŠŖŧŚťä(m • ųlÛBŮ° →ųlǧ¨ǦǟǋǡKuĊǹâǝǙ →Ƞǿȳǧ¥<ǹâǝǙ •  m ƞ1, 2, …, 2nƟŻěVlr

'VøĂîÍĨŃŖťŧťŚŚĬŁţŘş§ĩƝƩƖƘsƪƭƬxO ź¤'Vƞ Ɩ Ɩ Ɯ ƖƜƛƜ ƚƢƛƜ ųlÑǣųlŌŚ ɈÑ

³óǤǨǥź]k¦Đ§ĨĿŁ§ĩ ńŢŧťţřŨŘŧŞţŢħŧţħĿŚŢŦŞŧŬħŁŨŢŘŧŞţŢŖŠħŏŝŚţťŬ 18 ņţŝŢĬŎŝŖšħĨņŎĩħÅm •  ŒĭħņţŝŢƚŇĭħŅĭħŎŝŖšƝƩƬěV]kρĨrĩƝĐƏ ƬÅmħħ"RĈǒǃǠƽǗǝő œľ Ɲ]k¦ĐħδE [ρǤrǥ]/δρǤrǥƅ²ƭƬ

ƒƞ •  ŋţŤŠŚħƞNjĐÑ – ÊĲ?đƞ4VƝƞƤ'ĐƯ` ƍƔƧƞħŮħŮħŮħ ĲĬıİłĨŷĩħīħĵĬĲİłĨŷĩħħƜƛħ'Đƚ'ĐƯ ` ƍƔƧƞħŮħŮħŮħĲĬıİĪłŷīħĵĬĲİĪĪłŷħħƜƛ •  ěV½ĐƯµƀƬĖƞNjĐÑ

'Vÿƚ1X6v •  YZÿ – N©0íƞ×Żôƞ0ƅƜƀ¯y •  «ŻĆÄ¯y – N©0íƞ×Żôƞ0ƯǧƗ~Ɨ •  b|YZÿƝĔƖƘƀƜƀƄǬ – ĉlíŻčďƞňĿƜƛƙÔƍƘ¿ƄƦƬ

62 GaussView νϡʔτϦΞϧ •  4lÌǧÊė •  File> New> Create MolGroup

ԋश3)ਫ෼ࢠͷߏ଄࠷దԽ –  InputȣǻǾȴǧ%Ï •  File> Open> ǀh2o.gjfǁ •  File> Save>

◦ਿ৿ެҰ1ɼ઒ล߂೭1ɼ௕ඌल࣮2ɼ੢઒ਗ਼2  ʢ1ۚ৓େֶࣾձ෱ࢱֶ෦ɾ2ۚ୔େֶେֶӃࣗવՊֶݚڀՊʣ Ϧϯࢷ࣭εϑΟϯΰϛΤϦϯ෼ࢠͷߏ଄ ͱIRεϖΫτϧʹؔ͢Δཧ࿦తݚڀ Fig.1: Chemical structure of sphingomyelin and

Fig.4: Calculated IR spectrum of (a)1 and (b)1-(II)Ca2+ by B3LYP/6-31G(d,p),