1P097㛜Ṿᆵࡡ㐼⛛≟ឺࢅ⤊⏜ࡌࡾ⇍Ề୯ࡡ᭯ᶭཬᚺ࡞㛭ࡌࡾ㔖Ꮔ໩ᏕⓏ◂✪   㸝㜨ኬ㝌ᇱᕝ㸞 ‫ې‬ኬ㔕 ๭ࠉ㧏ᶣ ⱝ᪺*ࠉ⏛㎰ ᖶ㍔ࠉཿᕖ ಘୌࠉ୯㔕 㞖⏜࠘⥬ゕ࠙ ᴗᛮ⁈፳୯ࡡ㛜ṾฦᏄࡡ㞹Ꮔ≟ឺࡢࠉ㔖Ꮔ໩Ꮥゝ⟤ࡡᑊ㇗࡛ࡊ࡙⮾࿝῕࠷ࠊᮇ◂✪࡚ࡢ㛜Ṿᆵࡡ㐼⛛≟ឺࢅ⤊⏜ࡌࡾ࢓ࣜࢤ࣭ࣜࡡ⬲Ềཬᚺࢅཱིࡽ୕ࡅࡾࠊ㏳ᖏࠉ࢓ࣜࢤ࣭ࣜࡡ⬲Ềཬᚺࡢ㓗り፳ᶭᵋ࡞ࡻࡖ࡙㐅⾔ࡌࡾࠊࡆࡿ࡞ᑊࡊ Nagai ࡼࡢ㧏Ὼ㧏ᅸỀ࡞࠽࠷࡙ᐁ㥺ࢅ⾔࠷ࠉ1,4-ࣇࢰࣤࢩ࢛࣭ࣜ
(HO-(CH2)4-OH)ࡡ⬲Ềࡡ୹ࡒࡾཬᚺ⤊㊪࠿ࣈࣞࢹࣤり፳࡞ࡻࡼ࡝࠷ࡆ࡛ࢅ᪺ࡼ࠾࡞ࡊࡒ[1]ࠊᠻࠍࡢࡆ
ࡡ⬲Ềཬᚺ࠿ỀࡡỀ⣪⤎ྙ㙈࡞Ἒࡖࡒࣈࣞࢹࣤ⛛ິ࡞ࡻࡽり፳ࡈࡿࡾ࡛⩻࠻ࠉbiradical ࡝㐼⛛≟ឺࢅ⤊⏜ࡌࡾཬᚺᶭᵋࢅ௫ᏽࡊࡒ㸝ᅒ 1㸞ࠊࡆࡡ㐼⛛≟ឺࡢẴ┞୯࡚ࡢ୘Ꮽᏽ࡚࠵ࡾ࠿ࠉᴗᛮ⁈፳୯࡚ࡢ
zwitterion ࡛ࡊ࡙Ꮽᏽ໩ࡌࡾࠊࡱࡒࠉ㧏Ὼ㧏ᅸỀ୯࡚ࡢἴິ㛭ᩐࡡ᥺ࡼࡁ࡞ࡻࡖ࡙࢙ࣤࢹࣞࣅ࣭࠿ቌ
ຊࡊࠉࡈࡼ࡞Ꮽᏽ໩ࡌࡾࡆ࡛࠿஢᝷ࡈࡿࡾࠊᮇ◂✪࡚ࡢ QM/MM Ἢ࡛࢙ࢾ࣭ࣜ࢟⾪♟ࡡ⌦ㄵ[2]ࢅ࢜ࢴ
ࣈࣜࡈࡎࡒ᩺ぞ࡝ᡥἪ㸝QM/MM-ER Ἢ㸞[3]ࢅ⏕࠷࡙ࠉ᥺ࡼࡁࡡຝᯕࢅྱࡴࡒ⁈፳࿰⮤⏜࢙ࢾ࣭ࣜ࢟ࢅゝ⟤ࡌࡾࠊཬᚺ∸ࠉ㐼⛛≟ឺࡡ⁈፳࿰⮤⏜࢙ࢾ࣭ࣜ࢟࠾ࡼࠉࡆࡡཬᚺ⤊㊪࡞ఔ࠹⮤⏜࢙ࢾ࣭ࣜ࢟ን໩ࢅゝ⟤ࡊࠉ௫ᏽࡊࡒཬᚺᶭᵋࡡጂᙔᛮࢅ᳠ッࡌࡾࠊ+ 3H2Oཬᚺ∸(1,4-butanediol)ᅒ㸦㐼⛛≟ឺ(biradical)⏍ᠺ∸(THF)ࣈࣞࢹࣤ⛛ິᶭᵋ࡞ࡻࡾ 1,4-ࣇࢰࣤࢩ࢛࣭ࣜࡡ⬲Ềཬᚺ࠘⌦ㄵ࠙ QM/MM Ἢ࡚ࡢࠉධ࢙ࢾ࣭ࣜ࢟ࡢ QM ⣌ࡡ࢙ࢾ࣭ࣜ࢟ࠉMM ⣌ࡡ࢙ࢾ࣭ࣜ࢟ࠉཀྵࡦ QM ⣌࡛ MM ⣌࡛ࡡ┞பష⏕࢙ࢾ࣭ࣜ࢟ࡡ࿰࡚ᵋᠺࡈࡿࡾࠊQM ⣌ࡡ㞹Ꮔ≟ឺࡡゝ⟤࡞ࡢ Kohn-Sham ࡡᐠᗐỏ㛭ᩐἪࢅ⏕࠷ࠉἴິ㛭ᩐࡢᐁ✭㛣ࢡࣛࢴࢺ࡞ࡻࡖ࡙オ㏑ࡊࡒࠊᐁ✭㛣ࢡࣛࢴࢺἪ࡚ࡢࠉ㸦㞹Ꮔ㌮
㐠 " (r) ࡞ᑊࡌࡾ㐘ິ࢙ࢾ࣭ࣜ࢟ Tˆ ࡡⁿ⟤ࡢࠉࢡࣛࢴࢺⅤ࡞࠽ࡄࡾೋ " (x , y ,z ) ࡡᕣฦ࡞ࡻࡖ࡙ࠉi!

ijkl

N
N(1 % NTˆ" i (r) = # 2 ' $ Cn1 " i (x j + n1h, y k ,zl ) + $ Cn 2 " i (x j , y k + n 2 h,zl ) + $ Cn 3 " i (x j , y k ,zl + n 3 h)*
2h '&n1 =#N*)
n 2 =#Nn 3 =#N(1)!
!
࡛⾪ࡈࡿࡾ[4]ࠊࡆࡆ࡚ Cn ࡢᒈ㛜౿ᩐࠉh ࡢࢡࣛࢴࢺࡡᖕࠉN ࡢᕣฦࡡḗᩐ࡚࠵ࡾࠊ౮㞹Ꮔ࠿វࡋࡾ᭯ຝࢤ࢓࣎ࢷࣤࢨࣔࣜࡢ Kleinman-Bylander ᆵࡡ᧻࣎ࢷࣤࢨ࡚ࣔࣜオ㏑ࡊࡒࠊ௧ୖ࡞ᐁ✭㛣 QM/MM!

Ἢ࡛࢙ࢾ࣭ࣜ࢟⾪♟ࡡ⌦ㄵࢅ࢜ࢴࣈࣜࡈࡎࡒ᪁Ἢࢅㄕ᪺ࡌࡾࠊ
 ㏳ᖏࡡ⁈ᾦࡡ⌦ㄵࡢࠉ⁈㈻ࡡఴ๨໩Ꮥ࣎ࢷࣤࢨࣔࣜ "µ ࢅ⁈㈻ࡱࢂࡽࡡ⁈፳ࡡ✭㛣Ⓩ࡝ฦᕱ㛭ᩐ࡞ࡻࡖ࡙オ㏑ࡌࡾࠊ࢙ࢾ࣭ࣜ࢟⾪♟ࡡ⌦ㄵ࡚ࡢࠉ"µ ࡢ✭㛣Ⓩ࡝ฦᕱ㛭ᩐࡡ௥ࢂࡽ࡞⁈㈻-⁈፳㛣ࡡ┞பష⏕࢙ࢾ࣭ࣜ࢟ࡡฦᕱ㛭ᩐ࡞ࡻࡖ࡙⾪ࡈࡿࡾࠊన⨠࡛㒼ྡྷࡡ 6 ḗඔࡡንᩐࢅᣚࡗ✭㛣Ⓩ࡝ฦᕱ㛭ᩐࡢࠉ㏳!
ᖏࠉ┞பష⏕Ⅴ㛣ࡡฦᕱ㛭ᩐࡡ⤄࡞ࡻࡖ࡙⾪⌟ࡈࡿࡾࠊࡆࡿ࡞ᑊࡊ࢙ࢾ࣭ࣜ࢟ฦᕱ㛭ᩐࡢࠉ࠷࠾࡝ࡾ
!
⁈㈻-⁈፳ࡡ⤄ࡲྙࢂࡎ࡞ࡗ࠷࡙ࡵ 1 ḗඔࡡᗑᵾࡡࡲ࡚オ㏑࡚ࡀࡾࠊࡊࡒ࠿ࡖ࡙ࠉ࢙ࢾ࣭ࣜ࢟⾪♟ࡡ⌦ㄵࡢࠉ┞பష⏕Ⅴ࡛࠷࠹ᴣᛍࢅᚪさ࡛ࡊ࡝࠷ࡡ࡚ QM/MM Ἢࡡࡻ࠹࡝➠ୌཋ⌦Ⓩ࡝ᡥἪ࡛ࡡ⼝ྙ࠿ᐖ᪾࡚࠵ࡾࠊࡊ࠾ࡊ࢙ࢾ࣭ࣜ࢟⾪♟ࡡ⌦ㄵࡢ┞பష⏕࠿஦మⓏ࡚࠵ࡾࡆ࡛ࢅ๑ᥞ࡛ࡊ࡙࠷ࡾࡡ࡚ࠉ㔖Ꮔ
໩ᏕⓏ࡝⣌࡫㐲⏕ࡌࡾࡒࡴ࡞ࡢᕝኰ࠿ᚪさ࡚࠵ࡾࠊᮇ◂✪࡚ࡢࠉ⁈㈻ࡡ㞹Ꮔᐠᗐࢅᖲᆍࡡ㞹Ꮔᐠᗐ n˜ (r)࡚ᅖᏽࡌࡾࡆ࡛࡞ࡻࡽࠉ⁈㈻-⁈፳㛣┞பష⏕ࢅኣమ࡝㒂ฦ࡛஦మⓏ࡝㒂ฦ࡞ฦ๪ࡌࡾࠊ㞹Ꮔᐠᗐ n˜ (r) ࢅ!
!ᣚࡗ⁈㈻ࡡ⁈፳࿰⮤⏜࢙ࢾ࣭ࣜ࢟ "µ ࡢ㎾జ࡝ࡊ࡞   "#$µ = & d%*,'(%) " ' 0 (%) + #( (%)' (%) " # & d)( (%; )) ( '(%) " ' 0 (%))-/

(+10)

 .

 (2)!
࡛オ㏑࡚ࡀࡾࠊࡆࡆ࡚ ρ(ε), ρ0(ε)ࡢࡐࡿࡑࡿ⁈ᾦ⣌ࠉ⣟⁈፳⣌ࡡ࢙ࢾ࣭ࣜ࢟ฦᕱ㛭ᩐ࡚࠵ࡽࠉω(ε)ࡢ⁈
㈻-⁈፳㛣ࡡᖲᆍງ࣎ࢷࣤࢨࣔࣜࡡ㛣᥃㒂ฦࠉλ ࡢ⤎ྙࣂ࣒࣭ࣚࢰ࡚࠵ࡾࠊࡱࡒࠉβ ࡢ࣍ࣜࢵ࣏ࣤᏽᩐ!

kB ࡛Ὼᗐ T ࡛ࡡ✒ࡡ㏣ᩐ࡚࠵ࡾࠊᖲᆍฦᕱ n˜ (r) ࡱࢂࡽࡡ㞹Ꮔᐠᗐ n(r) ࡡ᥺ࡼࡁࡢ⁈㈻⁈፳㛣┞பష⏕ࡡ ኣ మ Ⓩ ࡝ ຝ ᯕ ࢅ ྱ ࡲ ࠉ ࡆ ࡿ ࡞ ఔ ࠹ ⮤ ⏜ ࢙ ࢾ ࣜ ࢟ ࣭ ን ໩ "µ ࡢ ࠉ ᩺ ࡒ ࡞ ࢙ ࢾ ࣜ ࢟ ࣭ ᗑ ᵾ ࢅ"i = v(n,x i ) # v( n˜ ,x i ) ࡛ࡊ࡙ᑙථࡌࡾࡆ࡛࡚ᘟ  ࡛㢦జࡡᘟ࠾ࡼゝ⟤࡚ࡀࡾࠊఢࡊࠉ] L ࡢ L ␊┘ࡡ⁈፳!
!

ฦᏄࡡᗑᵾ࡚࠵ࡾࠊ!
࠘ゝ⟤᮪௲࠙ 1,4-butanediol ࡛ཬᚺ࡞㛭୙ࡌࡾ஦಴ࡡỀฦᏄࢅ QM ฦᏄ࡛ࡊ࡙᡽࠷ࠉஹᥦ┞㛭ỏ㛭!

ᩐ࡞ࡢ BLYP ࢅ⏕࠷ࡒࠊMM ⣌ࡢ 252 ಴ࡡ TIP4P ࣓ࢸࣜࡡỀฦᏄ࡚オ㏑ࡊࠉῺᗐࡢ 575 ࠽ࡻࡦ 690 Kࠉ⁈፳ᐠᗐࡢ 0.6 g/cm3 ࡛ࡊࡒࠊࢰ࢕࣑ࢪࢷࢴࣈࡢ 1 fs ࡛ࡊࠉᖲᆍࡡ㞹Ꮔᐠᗐ n˜ (r) ࡢ 5 ps ࡡᖲ⾦໩ᚃࠉ
50 ps ࡡ࢓ࣤࢦࣤࣇࣜᖲᆍ࡞ࡻࡽỬᏽࡊࡒࠊࡱࡒ࢙ࢾ࣭ࣜ࢟ฦᕱ㛭ᩐࡢࠉ⁈ᾦ⣌࡚ࡢ 50 psࠉ⣟⁈፳⣌
࡚ࡢ 100 ps ࡡ࢓ࣤࢦࣤࣇࣜᖲᆍ࡞ࡻࡽᵋᠺࡊࡒࠊ!
࠘⤎ᯕ࠙ Ὼᗐ 690 K ࡚ࡡཬᚺ∸ࠉཀྵࡦ㐼⛛≟ឺࡡ⁈፳࿰⮤⏜࢙ࢾ࣭࡛ࣜ࢟ࡐࡡฦよ㡧ࢅ⾪ 1 ࡞♟ࡌࠊE ࡢ⁈ᾦ࡞࠽ࡄࡾἴິ㛭ᩐࡡᖲᆍࡡṅࡲࡡ࢙ࢾ࣭࡚ࣜ࢟࠵ࡽࠉ"µ ࡢᖲᆍࡡ㞹Ꮔᐠᗐ n˜ (r) ࢅᣚࡗ⁈㈻ࡡ
⁈፳࿰⮤⏜࢙ࢾ࣭࡚ࣜ࢟࠵ࡾࠊࡱࡒࠉδµ ࡢἴິ㛭ᩐࡡ᥺ࡼࡁ࡞ఔ࠹⮤⏜࢙ࢾ࣭ࣜ࢟ን໩࡚࠵ࡾࠊ㐼⛛≟ឺࡡཫᴗᏄ࣓࣭࣒ࣤࢹࡢ 14.1 Debye ࡛ኬࡀࡂࠉṅࡲࡡ࢙ࢾ࣭ࣜ࢟ E (=12.7 kcal/mol)ࡵ࠾࡝ࡽኬࡀ
!
!
࠷ࠊࡆࡡࡆ࡛࠾ࡼ⁈ᾦ୯࡚ࡢ biradical ࡡ㞹Ꮔ≟ឺ࠿ኬࡀࡂን໩ࡊࠉ
㐼⛛≟ឺ࠿ zwitterion ࡛ࡊ࡙⁈፳

!

࿰ࡈࡿ࡙࠷ࡾࡆ࡛࠿ฦ࠾ࡾࠊࡆࡡ㞹Ꮔ≟ឺࡡን໩ࡢࠉ㐼⛛≟ឺࡡධ⁈፳࿰⮤⏜࢙ࢾ࣭ࣜ࢟Δµ ࠿ཬᚺ∸!

ࡡࡐࡿ࡞Ẓ࡬ኬࡀࡂ΅ᑛࡌࡾࡆ࡛࡞ᐞ୙ࡊ࡙࠷ࡾࠊ᥺ࡼࡁࡡᐞ୙ δµ ࡢࠉཬᚺ∸ࠉ㐼⛛≟ឺ࡞࠽࠷࡙ࡐ
ࡿࡑࡿ-4.0ࠉ-5.4 kcal/mol ࡚࠵ࡽࠉᴗᛮ⁈፳୯࡚ࡢἴິ㛭ᩐࡡ᥺ࡼࡁ࡞ࡻࡾᐞ୙ࡢ↋っ࡚ࡀ࡝࠷ࡆ࡛
࠿ฦ࠾ࡖࡒࠊ⁈፳࿰⮤⏜࢙ࢾ࣭ࣜ࢟࠾ࡼゝ⟤ࡈࡿࡾὩᛮ໩⮤⏜࢙ࢾ࣭ࣜ࢟ࡢ 575ࠉ690 K ࡚ࡐࡿࡑࡿ
49.7ࠉ54.7 kcal/mol ࡚࠵ࡽࠉNagai ࡼࡡᐁ㥺ೋ 50.0 kcal/mol(658 K, 0.6 g/cm3)࡛ࡻࡂୌ⮬ࡊࡒࠊࡆࡿࡼࡡࡆ࡛࠾ࡼࠉᴗᛮ⁈፳୯࡚㛜Ṿᆵࡡ㞹Ꮔᵋ㏸࠿ zwitterion ࡞ን໩ࡌࡾࡆ࡛࡞ࡻࡽ㐼⛛≟ឺ࠿Ꮽᏽ໩ࡊࠉࣈࣞࢹࣤ⛛ິᶭᵋ࡞ࡻࡽ 1,4-ࣇࢰࣤࢩ࢛࣭ࣜࡡ⬲Ề࠿ಀ㐅ࡈࡿࡾࡆ࡛࠿ࢂ࠾ࡖࡒࠊ
࠘ཤ⩻ᩝ⊡࠙
[1] Y. Nagai, N. Matubayasi, M. Nakahara, Bull. Chem. Soc. Jpn, 77 . 691 (2003).
[2] N. Matubayasi, M. Nakahara, J. Chem. Phys, 113 . 6070 (2000).
[3] H. Takahashi, N. Matubayasi, J. Chem. Phys, 1 21 . 3989 (2004).
[4] J. R. Chelikowsky, N. Troullier, K. Wu, Y. Saad, Phys. Rev. B , 5 0, 11355 (1994).
⾪l⮤⏜࢙ࢾ࣭ࣜ࢟ࡡฦよ㡧࡛ཫᴗᏄ࣓࣭࣒ࣤࢹ㸝690 K㸞㸝༟న㸯kcal/mol, Debye㸞

ΔµΔµdipole

-0.2

-1.9

4.2

-1.5

-10.1

14.1

E

"µnonpol"µpolδµδµonsager

ཬᚺ∸

3.7

-1.8

0.4-4.0

㐼⛛≟ឺ

12.7

-4.5

-11.4-5.4!

!

!

"µnonpol ࡢẴ┞୯ࡡ㞹Ꮔᐠᗐࢅᣚࡗ⁈㈻ࡡ⁈፳࿰⮤⏜࢙ࢾ࣭࡚ࣜ࢟࠵ࡽࠉ "µpol ࡢ⁈㈻࠿ฦ
ᴗࡌࡾࡆ࡛࡞ࡻࡾ⮤⏜࢙ࢾ࣭ࣜ࢟ን໩࡚࠵ࡾࠊᚉࡖ࡙ "µ = "µnonpol + "µpol ࡚࠵ࡾࠊ!

!

!