ᅛ య 㧗 ศ ゎ ⬟
NMR䜢⏝ 䛔䛯䝡䝇䝣䜵䝜䞊䝹
A䛾◊ ✲
High Resolution NMR Studies of Bisphenol-A Crystalsᮏ ከ 㻌 ᑦ
(
ᶓ ᕷ ❧ Ꮫ Ꮫ 㝔 ⏕ 䝘䝜䝅䝇䝔䝮⛉ Ꮫ ◊ ✲ ⛉
)[
ᗎ ㄽ
]㻌
NMR䛿㟁 Ꮚ ≧ ែ 䛻ᑐ ᛂ 䛧䛯ඹ 㬆 ࿘ Ἴ ᩘ 䜢ᣢ 䛴䛾䛷䚸ᵓ 㐀 ゎ ᯒ 䜔≀
ᛶ ◊ ✲ 䛺䛹䛷ᗈ 䛟⏝ 䛔䜙䜜䛶䛔䜛䚹ᵓ 㐀 ゎ ᯒ 䛾ሙ ྜ 䚸䛭䛾ከ 䛟䛿⁐ ፹ 䛻ヨ ᩱ 䜢
⁐ ゎ 䛥䛫䚸 ᐃ 䜢⾜ 䛳䛶䛔䜛䚹䛭䛾䛯䜑䚸ᚋ ㏙ 䛩䜛ཎ Ꮚ ᰾ 㛫 䛾 ᴟ Ꮚ 䠉 ᴟ Ꮚ
┦ స ⏝ 䜔 Ꮫ 䝅䝣䝖䛾␗ ᪉ ᛶ 䛺䛹⥺ ᖜ 䛾ཎ ᅉ 䛸䛺䜛┦ స ⏝ 䛿ศ Ꮚ 㐠 ື 䛻 䜘䜚ᖹ ᆒ 䛥䜜䜛䚹୍ ᪉ 䚸ᅛ య ヨ ᩱ 䛾ሙ ྜ 䚸┦ స ⏝ 䛜ᖹ ᆒ 䛥䜜䛺䛔䛯䜑䚸
⥺ ᖜ 䛾 䛝䛔䝇䝨䜽䝖䝹䛜ᚓ 䜙䜜䜛䚹≉ 䛻䚸
1H᰾ 䛿Ᏻ ᐃ ྠ య 䛾୰ 䛷᭱ 䜒᰾ ☢ Ẽ 䝰䞊䝯䞁䝖䛜 䛝䛔䠄ཝ ᐦ 䛻ゝ 䛖䛸☢ Ẽ ᅇ ㌿ ẚ 䛜 䛝䛔䠅䛯䜑䚸
1H-1H㛫 ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స ⏝ 䛜 䛝䛟䚸ᵓ 㐀 ゎ ᯒ 䜔≀ ᛶ ◊ ✲ 䛻⪏ 䛘䜙䜜䛺䛔䝇䝨䜽䝖 䝹䛧䛛ᚓ 䜙䜜䛺䛔䚹䛭䛾䛯䜑䚸ᅛ య ヨ ᩱ 䛷䜒㧗 ศ ゎ ⬟ 䛺
NMR䝇䝨䜽䝖䝹䜢ᚓ 䜛 䛯䜑䛾ᢏ ⾡ 㛤 Ⓨ 䛜⾜ 䜟䜜䚸㏆ ᖺ 䚸䜘䛖䜔䛟ᅛ య ヨ ᩱ 䛷䜒
1H NMR䝇䝨䜽䝖䝹䛜ᚓ 䜙 䜜 䜛 䜘 䛖 䛻 䛺 䛳 䛯 䚹 䝝 䞊 䝗 㠃 䛾 ᢏ ⾡ 㛤 Ⓨ 䛷 䛿 䚸 㧗 ㏿
MAS(Magic Angle Spinning)ἲ 䛜 ⏝ 䛷 䛝 䜛 䜘 䛖 䛻 䛺 䛳 䛯 Ⅼ 䜢 ᣲ 䛢 䜛 䛣 䛸 䛜 䛷 䛝 䜛 䚹 䝋 䝣 䝖 㠃 䛷 䛿
CRAMPSἲ 䛺䛹䛾䝟䝹䝇⣔ ิ 䛾㛤 Ⓨ 䛜㐍 䜣䛰䛣䛸䜢ᣲ 䛢䜛䛣䛸䛜䛷䛝䜛䚹䝋䝣䝖 㠃 䛾Ⓨ 㐩 䛻䜘䜚ከ 䛟䛾䝟䝹䝇䝥䝻䜾䝷䝮䛜Ⓨ ⾲ 䛥䜜䚸
2ḟ ඖ
NMRἲ 䛺䛹䜒ྍ ⬟ 䛸 䛺䛳䛯䚹䛭䛾䛯䜑䚸㏆ ᖺ 䛾
NMR䛷䛿䚸䛹䛾䝟䝹䝇䝥䝻䜾䝷䝮䜢㑅 䜆䛛䚸䛹䜣䛺 ᐃ ᮲ ௳ 䛻タ ᐃ 䛩䜛䛛䛺䛹䚸ᇶ ♏ ⌮ ㄽ 䛸 ᐃ ᢏ ⾡ 䜒ᚲ せ 䛸䛺䛳䛶䛝䛶䛔䜛䚹
NMR䛻㛵 䛩䜛ከ 䛟䛾᭩ ⡠ 䛜ฟ ∧ 䛥䜜䛶䛔䜛䛜䚸ᩘ ᘧ 䜢┬ ␎ 䛧䛶䛔䜛䜒䛾䛜ከ 䛔䛾䛷䚸 䛣䛣䛷䛿䚸NMR ᐃ 䛻ᙳ 㡪 䛩䜛┦ స ⏝ 䜔✀ 䚻䛾 ᐃ ἲ 䛺䛹䚸ᇶ ᮏ ཎ ⌮ 䜢グ 䛧䛯ᚋ 䚸ᐇ 㝿 䛻 ᐃ 䛧䛯⤖ ᯝ 䜢♧ 䛩䚹ල య ⓗ 䛻䛿䚸䝡䝇䝣䜵䝜䞊䝹
A⤖ ᬗ 䛾
1H HS-MAS NMR䛸
CRAMPSᐃ 䛾 ⤖ ᯝ 䛚 䜘 䜃 䚸
13C CP/MAS䚸
13C-1H FSLG-HETCORᐃ, COSY, HMQC ᐃ 䛾⤖ ᯝ 䜢♧ 䛩䚹
㻌 䝡䝇䝣䜵䝜䞊䝹
A (ᅗ
1)䛿䚸䜶䝫䜻䝅 ᶞ ⬡ 䜔䝫䝸䜹䞊䝪䝛䞊䝖䛾ཎ ᩱ 䛺䛹䚸 ᕤ ᴗ ⓗ 䛻ᗈ 䛟⏝ 䛔䜙䜜䛶䛔䜛䚹㻌 䜎䛯䚸 䛭䛾୍ ᪉ 䛷䝡䝇䝣䜵䝜䞊䝹
A䛿ෆ ศ Ἢ ᨩ ≀ ㉁
(⎔ ቃ 䝩䝹䝰䞁)䛾 䛔䛜䛒 䜚 䚸 ⏕ ែ 䛻 䛘 䜛 ᙳ 㡪 䛜 ㄪ 䜉 䜙 䜜 䛶䛔䜛䚹䝡䝇䝣䜵䝜䞊䝹
A䛿䚸✵ 㛫 ⩌
P21/n䜢䛸䜚䚸3 ✀ 㢮 䛾㠀 ➼ ౯ 䛺ศ Ꮚ 䛜 ⤖ ᬗ ୰ 䛷 Ỉ ⣲ ⤖ ྜ 䝛 䝑 䝖 䝽 䞊 䜽 䜢 ᙧ ᡂ 䛧䛶䛔䜛
(ᅗ
2)[1]䚹䛣䜜䜙
3✀ 㢮 䛾㐪 䛔䛿䚸2 䛴䛾䝣䜵䝜䞊䝹ᇶ 䛜స 䜛
ᵏᴾ ἥἋἧỹἠὊἽ ᵟ ỉನ ᡯ ᴾ ᵡᵆᵏᵇᴾ
ᵡᵆᵐᵇᴾ ᵡᵆᵑᵇᴾ
ᵡᵆᵒᵇᴾ ᵡᵆᵓᵇᴾ ᵡᵆᵔᵇᴾ
ᵡᵆᵕᵇᴾ ᵡᵆᵖᵇᴾ
ᵦᵆᵏᵇᴾ ᵦᵆᵐᵇᴾ
ᵦᵆᵑᵇᴾ
ᵦᵆᵒᵇᴾ ᵦᵆᵓᵇᴾ
ᵦᵆᵔᵇᴾ
2
㠃 ゅ 䛜䚸䛭䜜䛮䜜
86.9°䚸
83.6°䚸
79.7°䛸␗ 䛺䛳䛯್ 䜢ᣢ 䛳䛶䛔䜛Ⅼ 䛷䛒䜛䚹䛣 䜜䜙䛾ᵓ 㐀 䛾㐪 䛔䛜䚸ᅛ య
1H MAS NMRᐃ 䛷䛹䛣䜎䛷༊ ู 䛷䛝䜛䛾䛛♧ 䛧䚸
⌧ ᅾ 䛾ᅛ య
NMR䛾ศ ゎ ⬟ 䛻䛴䛔䛶䜒䛣䛣䛷䛿㏙ 䜉䛶䛔䛟䚹
[
⌮ ㄽ
]㻌 䛣䛣䛷䛿䚸
(1)NMR䛷ほ 䛥䜜䜛┦ స ⏝ 䚸
(2)ᐃ ἲ 䛻㛵 䛩䜛⌮ ㄽ ⓗ
⫼ ᬒ 䜢⡆ ༢ 䛻グ 䛩䚹䛺䛚䚸ᑟ ฟ ᪉ ἲ 䛜ཧ ⪃ ᩥ ⊩
[2-7]䛻ヲ ⣽ 䛻グ 䛥䜜䛶䛔䜛㒊 ศ 䛿⡆ ␎ 䛧䛯䚹
(1)NMR
䛷ほ 䛥䜜䜛┦ స ⏝
ᅇ 䛾ෆ ᐜ 䛻㛵 㐃 䛧䛶䛔䜛┦ స ⏝ 䛿䚸௨ ୗ 䛾
3䛴䛷䛒䜛䚹
㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌
H ൌHHୈୈ Hୌ ڮ (1)䛴䜎䜚䚸䝊䞊䝬䞁┦ స ⏝(H
Z )䚸 ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స ⏝(H DD)䚸 Ꮫ 䝅䝣䝖
(HCS)䛷䛒䜛䚹
䞉䝊䞊䝬䞁┦ స ⏝
H Z䝊䞊䝬䞁┦ స ⏝ 䛿☢ ሙ 䛸☢ Ẽ 䝰䞊䝯䞁䝖䛾┦ స ⏝ 䛷䛒䜛䚹㟼 ☢ ሙ
B0୰ 䛻
☢ Ẽ 䝰䞊䝯䞁䝖
ȝ䜢⨨ 䛟䛸䚸┦ స ⏝ 䛾䜶䝛䝹䜼䞊䛿௨ ୗ 䛾䜘䛖䛻᭩ 䛝⾲ 䛩䛣䛸 䛜䛷䛝䜛䚹
ܧ ൌ െࣆ ή (2)
a b
c
x yz
ᅗ 㻞㻌 䝡䝇䝣䜵䝜䞊
䝹 㻭 䛾⤖ ᬗ ᵓ 㐀 㻌 㼍 ㍈ ᢞ ᙳ ᅗ 䚹༢ ᱁ Ꮚ 㻠 ಶ ศ 䜢ᅗ ♧ 䛧䛶䛔䜛䚹㻟 ✀ 㢮 䛾 䝡䝇䝣䜵䝜䞊䝹 㻭 䛿 䜰䝹䝣䜯䝧䝑䝖䛷ศ 䛡䛶䛔䜛䚹䛺䛚䚸ᐇ
⥺ 䛿 Ỉ ⣲ ⤖ ྜ 䜢
⾲ 䛩䚹㻌
A
A
A A A
A A A
A A
A A
A A A A
B B
B B
B B
B B
B B
B B
B B
B B
C C
C C
C C
C C
C C
C C
C C
C C
䛣䛣䛷䚸☢ Ẽ 䝰䞊䝯䞁䝖䛿䚸᰾ 䝇䝢䞁㐠 ື 㔞
I䛻ẚ 䛩䜛䛾䛷䚸☢ Ẽ ᅇ ㌿ ẚ
Ȗ䜢 ẚ ᐃ ᩘ 䛸䛧䛯௨ ୗ 䛾ᘧ 䛷᭩ 䛝⾲ 䛩䛣䛸䛜䛷䛝䜛䚹
ࣆ ൌ ɀࡵ (3)
䛣䜜䜢㔞 Ꮚ 䛩䜛䛸䚸䝊䞊䝬䞁┦ స ⏝ 䛾䝝䝭䝹䝖䝙䜰䞁䛿䚸㟼 ☢ ሙ 䛾᪉ ྥ 䜢
z㍈ 䛻䛸䜛䛸௨ ୗ 䛾䜘䛖䛻䛺䜛䚹
H ൌ െɀܤI (4)
䛣䛣䛷䚸
1H᰾ 䛾䜘䛖䛻᰾ 䝇䝢䞁䛜
1/2䛾ሙ ྜ 䚸☢ Ẽ 㔞 Ꮚ ᩘ
m䠙
±1/2㛫 䛾㑄 ⛣ 䛾 䜶䝛䝹䜼䞊ǻE
Z䛿䚸௨ ୗ 䛾䜘䛖䛻䛺䜛䚹
ȟܧൌ ɀܤൌȦ (5)
ᅇ ⏝ 䛔䛯 ⨨ 䛷䛿䚸
1H᰾ 䛾
NMRඹ 㬆 ࿘ Ἴ ᩘ 䛜
600.13 MHz䛷䛒䛳䛯䛾䛷䚸
ǻEZ䠙 4.0㽢10
䠉25 J䛷䛒䜛䚹NMR 䛿䚸䛣䛾
䜘䛖䛻ᑠ 䛥䛺䜶䝛䝹䜼䞊䜢ほ 䛩䜛䛾䛷䚸 ᐃ 䛻䜘䜚ศ Ꮚ 䛾㐠 ື ≧ ែ 䜔 ື ≧ ែ 䜢䜋䛸 䜣䛹ኚ 䛥䛫䜛䛣䛸䛜䛺䛔䠄 ᗘ 䛻 ⟬ 䛩䜛 䛸
1 Kᮍ ‶ 䛷䛒䜛䠅䚹䜎䛯䚸௨ ୗ 䛻㏙ 䜉䜛┦ స ⏝ 䛿䚸䛣䛾䜶䝛䝹䜼䞊䛻ẚ 䜉䛥䜙䛻ᑠ 䛥䛔 䠄 ᴟ Ꮚ ┦ స ⏝ 䜔 Ꮫ 䝅䝣䝖䛿䚸䛭䜜䛮䜜
䝊䞊䝬䞁┦ స ⏝ 䛾
10-6䚸
10-6䡚
10-3⛬ ᗘ 䠅䛾䛷䚸䝊䞊䝬䞁┦ స ⏝ 䛾ᦤ ື 㡯 䛸䛧䛶ᢅ 䛖䛣䛸䛜䛷䛝䜛䚹
䞉 ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స ⏝
H DD䛣䛾┦ స ⏝ 䛿䚸䝇䝢䞁㛫 䛾┤ ᥋ ┦ స ⏝ 䛸㛫 ᥋ ┦ స ⏝ 䛜䛒䜛䚹㛫 ᥋ ┦ స ⏝ 䛿䝇䝢䞁䜹䝑䝥䝸䞁䜾┦ స ⏝ 䛷䛒䜛䚹ᅛ య ヨ ᩱ 䛷䛿䚸䛣䛾┦ స ⏝ 䛻䜘䜛
⥺ ᖜ 䜘䜚䜒┤ ᥋ ┦ స ⏝ 䛾᪉ 䛜 䛝䛺⥺ ᖜ 䜢 䛘䜛䛾䛷䚸䛣䛣䛷䛿┤ ᥋ ┦ స
⏝ 䛾䜏䜢ᢅ 䛖䚹┤ ᥋ ┦ స ⏝ 䛻䛿᰾ 䝇䝢䞁䠉᰾ 䝇䝢䞁㛫 䛸᰾ 䝇䝢䞁䠉㟁 Ꮚ 䝇䝢 䞁㛫 䛾┦ స ⏝ 䛜䛒䜛䛜䚸ᚋ ⪅ 䛿ᖖ ☢ ᛶ ≀ ㉁ 䛾䜘䛖䛻㟁 Ꮚ 䝇䝢䞁䜢ᣢ 䛴⣔ 䛷䛿 㔜 せ 䛺┦ స ⏝ 䛸䛺䜛䛜䚸䝡䝇䝣䜵䝜䞊䝹
A
䛾䜘䛖䛺 ☢ ᛶ ≀ ㉁ 䛷䛿↓ ど 䛷䛝䜛䚹䛭 䛣䛷䚸䛣䛣䛷䛿᰾ 䝇䝢䞁㛫 䛾 ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స ⏝ 䛻䛴䛔䛶グ 䛩䚹
㻌 ྑ ᅗ 䛾䜘䛖䛻᰾
i䛸᰾
j䛜㊥ 㞳
rij㞳 䜜䛶 Ꮡ ᅾ 䛩䜛ሙ ྜ 䚸᰾
i䛾 ⨨ 䛻᰾
j䛜స 䜛
☢ ሙ 䛿䚸᰾
j䛾☢ Ẽ 䝰䞊䝯䞁䝖䜢
ȝj䜢⏝ 䛔 䜛䛸௨ ୗ 䛾䜘䛖䛻䛺䜛䚹
ൌ સૄೕή࢘
ೕయ ൌ െૄೕ
ೕయଷ൫ૄೕή࢘൯࢘
ೕఱ (6)
䜘䛳䛶䚸ᘧ
(2)䜘䜚䚸┦ స ⏝ 䛾䜶䝛䝹䜼䞊䛿௨ ୗ 䛾䜘䛖䛻䛺䜛䚹
Eୈୈൌ െଵଶσ ࣆǡ ή ൌ െଵଶσ ൬ૄήૄೕೕయ െଷሺૄή࢘ሻ൫ૄ ೕή࢘൯
ೕఱ ൰
ǡ (7)
rij
B0
㸻
0B0 0
䛣䛣䛷䚸ᘧ
(7)䛿ྠ 䛨᰾ 䜢2ᅇ 䜹䜴䞁䝖䛧䛶䛔䜛䛾䛷
2䛷 䛳䛶䛔䜛䚹䛣䛾ᘧ
(7)䛿䚸ᘧ
(3)䛸
(4)䜢⏝ 䛔௨ ୗ 䛾䜘䛖䛻㔞 Ꮚ 䛩䜛䛣䛸䛜䛷䛝䜛䚹
Hୈୈൌଵଶσ ȖήȖೕ
ೕయ ଶሺA +B +C +D +E +F ሻ
ǡ (8)
䛣䛣䛷䚸ᴟ ᗙ ᶆ 䜢⏝ 䛔䜛䛸䚸ᘧ
(8)䛾
A䡚
F㡯 䛿௨ ୗ 䛾䜘䛖䛻䛺䜛䚹
A = ൫ͳ െ ͵ ଶș൯II㻌 㻌
B =െଵସ൫ͳ െ ͵ ଶș൯ൣIାIିIିIା൧C =െଷଶș șି୧மೕൣI௭IାIାI௭൧
㻌
D =െଷଶș ș୧மೕൣI௭IିIିI௭൧E =െଷସଶșିଶ୧மೕIାIା
㻌 㻌
F =െଷସଶșଶ୧மೕIିIି (9)䛣䛣䛷䚸ș
ij䛿䚸᰾
i䛸᰾
j䜢⤖ 䜆䝧䜽䝖䝹
rij䛸
㟼 ☢ ሙ
(z㍈
)᪉ ྥ 䛜䛺䛩ゅ 䛷䚸
ijij䛿
rij䜢
xyᖹ 㠃 䛻ᢞ ᙳ 䛧䛯䝧䜽䝖䝹䛸
x㍈ 䛜䛺䛩ゅ 䛷䛒 䜛䠄ྑ ᅗ 䠅䚹ᘧ
(9)䛻ྵ 䜎䜜䜛
I ±䛿᪼ 㝆 ₇ ⟬ Ꮚ 䛷䛒䜛䚹䛴䜎䜚䚸
C䡚
F䛾㡯 䛿䚸䜶䝛䝹䜼䞊
䛜క 䛖䚹 ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స ⏝ 䛿䝊䞊 䝬䞁┦ స ⏝ 䛾ᦤ ື 㡯 䛺䛾䛷䚸䝊䞊䝬䞁䝝 䝭䝹 䝖 䝙䜰 䞁 䛸 ྍ 䛺 㡯 ௨ እ 䛿 ↓ ど 䛩䜛 䛣 䛸 䛜䛷䛝䜛䚹䛣䛣䛷䚸H
Z䛿ᘧ
(4)䜘䜚䚸Iz䛾ᡂ ศ
䜢ᣢ 䛴䛾䛷䚸
A䡚
F䛾୰ 䛷䚸ྍ 䛺ᡂ ศ 䛿䚸
i䛸
j䛜␗ ✀ ᰾ 䛾ሙ ྜ 䚸
A㡯 䛾䜏䛷䚸
i䛸
j䛜ྠ ✀ ᰾ 䛾ሙ ྜ 䛿䚸A䠇B 㡯 䛷䛒䜛䚹䜘䛳䛶䚸NMR 䛷ほ 䛥䜜䜛 ᴟ Ꮚ 䠉
ᴟ Ꮚ ┦ స ⏝ 䛿௨ ୗ 䛾䜘䛖䛻᭩ 䛟䛣䛸䛜䛷䛝䜛䚹
Hୈୈൌଵଶσ ȖήȖೕೕయ ଶ൫ͳ െ ͵ ଶș൯II
ǡ
㻌
(10)Hୈୈൌଵସσ Ȗమ
ೕయଶ൫ͳ െ ͵ ଶș൯൫͵IIെIήI൯
ǡ
㻌
(11)䛣䛣䛷䚸ᘧ
(10)䛿␗ ✀ ᰾ 㛫 䛾 ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స ⏝ 䜢⾲ 䛧䚸ᘧ(11)䛿ྠ ✀᰾ 㛫 䛾┦ స ⏝ 䜢♧ 䛩䚹ᅛ య 䛾ሙ ྜ 䚸
ș䛻ศ ᕸ 䛜䛒䜛䛯䜑䚸⥺ ᖜ 䛜ᗈ 䛜䜛䚹䛣 䛾ᗈ 䛜䜚䛜䚸ᅛ య
NMRᐃ 䜢ప ศ ゎ ⬟ 䛺䜒䛾䛻䛧䛶䛔䜛䚹⁐ ᾮ 䛾ሙ ྜ 䚸ศ Ꮚ 㐠 ື 䛻䜘䜚䚸
(1-3cos2ș)䛜ᖹ ᆒ 䛥䜜䚸
0䛸䛺䜛䛯䜑䚸ඛ 㗦 䛺ಙ ྕ 䛜ᚓ 䜙䜜䜛䚹䛴 䜎䜚䚸ᅛ య 䛷䜒䛣䛾㡯 䛜
0䛻䛺䜜䜀䚸㧗 ศ ゎ ⬟
NMR䝇䝨䜽䝖䝹䛜ᚓ 䜙䜜䜛䚹
1-3cos2ș䠙0䛸䛺䜛
ș䛿⡆ ༢ 䛻ィ ⟬ 䛷䛝䚸54.7 °䛷䛒䜛䚹䛴䜎䜚䚸㟼 ☢ ሙ 䛻ᑐ 䛧䚸 䝇䝢䞁㛫 䜢⤖ 䜆䝧䜽䝖䝹䛜䛩䜉䛶
54.7 °䛻䛺䜜䜀䚸 ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స ⏝ 䛿
0䛸䛺䜛䚹䛭䛣䛷䚸ヨ ᩱ 䜢㟼 ☢ ሙ 䛻ᑐ 䛧䛶ゅ ᗘ
Įഴ 䛡䛶䚸䛭䛾㍈ ࿘ 䜚䛻
Ȧ䛷ᅇ ㌿ 䛥䛫䛯ሙ ྜ 䜢⪃ 䛘䜛䚹䛩䜛䛸䚸Legendre ከ 㡯 ᘧ 䛾ຍ ἲ ᐃ ⌮ 䜢⏝ 䛔䜛䛸
3cos2ș-1䛿௨ ୗ 䛾䜘䛖䛻䛺䜛䚹
͵ ଶɅ െ ͳ ൌଵଶሺ͵ ଶȽ െ ͳሻሺ͵ ଶȾ െ ͳሻ ଷଶʹȽʹȾ ɘݐ ଷଶଶȽଶȾ ʹɘݐ (12) B0
x
ȟ
y
ȭ
rij
䛣䛣䛷䚸ȕ 䛿
MAS䛾ᅇ ㌿ ㍈ 䛸
r䛾䛺䛩ゅ 䛷䛒䜛䚹ᘧ
(12)䛷䚸Į=54.7 °䛻䛩䜛䛸➨1㡯 䛜
0䛸䛺䜛䚹䜎䛯䚸Ȧ 䛜 ᴟ Ꮚ ┦ స ⏝ 䛾⥺ ᖜ 䜘䜚༑ ศ 䛝䛟䛺䜛䛸䚸➨
2㡯 䛸
➨
3㡯 䜒
0䛸䛺䜛䚹䛴䜎䜚䚸
MASἲ 䛷䛿䚸䛭䛾ᅇ ㌿ ㏿ ᗘ 䛜㔜 せ 䛸䛺䜛䚹
1H᰾ 䛾ሙ
ྜ 䚸
1H-1H㛫 䛾 ᴟ Ꮚ ┦ స ⏝ 䛻䜘䜛⥺ ᖜ 䛿
20䡚50 kHz䛷䛒䜛䛾䛷䚸100 kHz ௨ ୖ 䛾
MAS㏿ ᗘ 䛜ᚲ せ 䛸䛺䜛䚹 ᅇ ⏝ 䛔䛯 ⨨ 䛷䛿
35 kHz䛜㝈 ⏺ 䛺䛾䛷䚸
⁐ ᾮ 䛾䜘䛖䛺⥺ ᖜ 䛿ᮇ ᚅ 䛷䛝䛺䛔䛜䚸䛣䜜䜎䛷ከ 䛟䛾ᅛ య ⨨ 䛷⏝ 䛔䜙䜜䛶䛝䛯
MAS㏿ ᗘ 䛜
10 kHzᮍ ‶ 䛷䛒䛳䛯䛣䛸䜢⪃ 䛘䜛䛸䚸 䛝䛺
MASຠ ᯝ 䛜ᮇ ᚅ 䛷䛝 䜛䚹䜎䛯䚸ᘧ
(11)䛾䝖䝺䞊䝇䠄⾜ ิ 䛾ᑐ ゅ ᡂ ศ 䛾 䠅䛜
0䛷䛒䜛䛣䛸䛛䜙䚸 ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స ⏝ 䛿 䚸⥺ ᖜ 䛰䛡䛻 ᐤ 䛧 ࿘ Ἴ ᩘ 䝅䝣䝖䜢 䛘䛺䛔䛣䛸䛜ศ 䛛 䜛䚹
䞉 Ꮫ 䝅䝣䝖䛾␗ ᪉ ᛶ
H CS Ꮫ 䝅䝣䝖䛿䚸㟁 Ꮚ 䛻䜘䜛☢ ሙ 䛾㐽 ⶸ 䜢⾲ 䛩䚹㟁 Ꮚ 䛾㉁ 㔞 䜢
m䛸䛩䜛䛸䚸䛭䛾㐠
ື 㔞 䛿☢ ሙ ୰ 䛷௨ ୗ 䛾䜘䛖䛻䛺䜛䚹
ൌ ݉࢜ ݁ (13)
䛣䛣䛷䚸
A䛿䝧䜽䝖䝹䝫䝔䞁䝅䝱䝹䛷䚸
ൌ સ ൈ
㻌
(14)䛸䛔䛖㛵 ಀ 䛜ᡂ 䜚❧ 䛴䚹䝇䜹䝷䞊䝫䝔䞁䝅䝱䝹䜢
V䛸䛚䛟䛸䚸䝝䝭䝹䝖䝙䜰䞁䛿 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌
Hୌൌଶଵ ሺ െ ሻ ή ሺ െ ݁ሻ ܸ㻌
(15)䚹䛣䛣䛷䚸☢ ሙ 䛾㉳ ※ 䛸䛧䛶㟼 ☢ ሙ 䛸ཎ Ꮚ ᰾ 䛜⪃ 䛘䜙䜜䜛䚹䛭䛣䛷䚸䝧䜽䝖䝹䝫䝔䞁 䝅䝱䝹䜢
A0䛸
A1䛾 䛸䛧䚸䛭䜜䛮䜜㟼 ☢ ሙ 䚸ཎ Ꮚ ᰾ ㉳ ※ 䛸⨨ 䛟䚹ᘧ
(18)䜢ᒎ 㛤 䛧䚸 ᦤ ື ㄽ 䜢⏝ 䛔䜛䛸䚸௨ ୗ 䛾䜘䛖䛻䛺䜛䚹
㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌
Hୌ ൌ ߛI·ı㻌
(16)䛣䛣䛷䚸㐽 ⶸ 䝔䞁䝋䝹
ı䛾ྛ ᡂ ศ 䛿௨ ୗ 䛾䜘䛖䛻᭩ 䛟䛣䛸䛜䛷䛝䜛䚹
ɐ௭௭ൌ䠉
మଶۃͲ ቚ௫మȁȁା௬యమቚ Ͳۄ ଶమ σ ቄۃȁLா ȁۄ
ିாబ ۃ݊ ቚȁȁLయቚ Ͳۄ ۃͲ ቚȁȁLయቚ ݊ۄۃȁLா ȁۄ
ିாబቅ
㻌
ɐ௭୶ൌ
䠉
మଶۃͲ ቚȁȁ௭௫యቚ Ͳۄ మ
ଶσ ቄۃȁLா ȁۄ
ିாబ ۃ݊ ቚȁȁLೣయቚ Ͳۄ ۃͲ ቚL
ȁȁయቚ ݊ۄۃȁLೣȁۄ
ாିாబቅ
㻌
ɐ௭௬ ൌ
䠉
ଶమ ۃͲ ቚȁȁ௭௬యቚ Ͳۄ ଶమ σ ቄۃȁLா ȁۄିாబ ۃ݊ ቚȁȁLయቚ Ͳۄ ۃͲ ቚL
ȁȁయቚ ݊ۄۃȁLா ȁۄ
ିாబቅ
㻌
(17)䛣䛣䛷䚸
L䛿㟁 Ꮚ 䛻ᑐ 䛩䜛㌶ 㐨 ゅ 㐠 ື 㔞 ₇ ⟬ Ꮚ 䛷䚸
En䛸
E0䛿䚸䛭䜜䛮䜜ບ ㉳
≧ ែ 䛸ᇶ ᗏ ≧ ែ 䛾䜶䝛䝹䜼䞊‽ 䛷䛒䜛䚹䜎䛯䚸ı
xx䛸
ıyy䛿➨
1ᘧ 䛾➨
1㡯 䛾
x2+y2䜢
y2+z2䚸z
2+x2䛻䚸➨
2㡯 䛾
z䜢
x,y䛻䛛䛘䜛䛣䛸䛷ᚓ 䜙䜜䜛䚹䜎䛯䚸ı
zx䠙ı
xz䛷䛒䜚䚸
ıxy䛿䚸➨
3ᘧ 䛾
z䜢
x䛻䛩䜜䜀ᚓ 䜙䜜䜛䚹ᘧ
(17)䛛䜙䚸 Ꮫ 䝅䝣䝖䛿䚸㟁 Ꮚ ᐦ ᗘ 䛻㛵 ಀ 䛧䛶䛔䜛䛣䛸䛜ศ 䛛䜛䚹䜎䛯䚸ᇶ ᗏ ≧ ែ 䛾ᐤ 䠄 ☢ ᛶ 㡯 䠅䛸ບ ㉳
≧ ែ 䛾ᐤ 䠄ᖖ ☢ ᛶ 㡯 䠅䛾 䛷⾲ 䛥䜜䜛䛜䚸䛣䜜䜙䛾㡯 䛾➢ ྕ 䛜␗ 䛺䜛䛣䛸䛻ὀ
ព 䛩䜛ᚲ せ 䛜䛒䜛䚹 䛘䜀䚸Ỉ ⣲ 䛾ሙ ྜ 䚸ບ ㉳ ≧ ែ 䛸ᇶ ᗏ ≧ ែ 䛾䜶䝛䝹䜼䞊ᕪ
䛿Ⅳ ⣲ 䛺䛹䛻ẚ 䜉 䛝䛔䛾䛷䚸 ☢ ᛶ 㡯 䛾ᐤ 䛜 䛸䛺䜛䚹䛭䛾䛯䜑䚸⎔ 㟁 ὶ
䛺䛹䛾ᐤ 䜢㝖 䛟䛸䚸ඹ 㬆 ࿘ Ἴ ᩘ 䛿㟁 Ꮚ ᐦ ᗘ 䛜ᑠ 䛥䛔䜋䛹 䛝䛟䛺䜛䛣䛸䛜ศ 䛛 䜛䠄㈇ 䛾➢ ྕ 䛜䛴䛔䛶䛔䜛䛯䜑䠅䚹୍ ᪉ 䚸㔜 ཎ Ꮚ 䛻䛺䜛䛸ᖖ ☢ ᛶ 㡯 䛾ᐤ 䛜 䛝 䛟䛺䜛䛾䛷䚸Ỉ ⣲ 䛾ሙ ྜ 䛸ഴ ྥ 䛜㏫ ㌿ 䛩䜛ሙ ྜ 䜒䛒䜛䚹
㻌 ᘧ
(17)䛿㟼 ☢ ሙ 䜢z㍈ 䛻䛸䜛䛸䚸௨ ୗ 䛾䜘䛖䛻䛺䜛䚹
㻌 㻌 㻌 㻌 㻌 㻌
Hୌൌ ɀ൫I௫ǡ I௬ǡ I௭൯ ൮ɐ௫௫୪ୟୠ ɐ௫௬୪ୟୠ ɐ௫௭୪ୟୠ ɐ௬௫୪ୟୠ ɐ௬௬୪ୟୠ ɐ௬௭୪ୟୠ ɐ௭௫୪ୟୠ ɐ௭௬୪ୟୠ ɐ௭௭୪ୟୠ
൲ ൭ Ͳ Ͳ
ܤ൱ (18)
䛣䛣䛷䚸 Ꮫ 䝅䝣䝖䛾㡯 䜒䚸䝊䞊䝬䞁┦ స ⏝ 䛸ྍ 䛺㡯 䛾䜏⪃ 䛘䜜䜀䜘䛔䛾䛷䚸 ᘧ
(18)䛿䚸௨ ୗ 䛾䜘䛖䛻䛺䜛䚹㻌 㻌 㻌 㻌 㻌 㻌
Hୌൌ ɀɐ௭௭୪ୟୠܤ I௭㻌
(19)䛣䛣䛷䚸 Ꮫ 䝅䝣䝖䛾 ㍈ ⣔ 䜢⏝ 䛔䚸ᐇ 㦂 ᐊ ⣔ 䛾
ızz䜢⾲ 䛩䛸䚸௨ ୗ 䛾ᘧ 䛜ᚓ 䜙 䜜䜛䚹䛺䛚䚸ș 䛸
ij䛿㟼 ☢ ሙ 䛸 ㍈ ⣔ 䛾䛺䛩ゅ ᗘ 䛷䛒䜛䚹
㻌 㻌
Hୌൌ ɀ ቀɐ௫௫୮ୟଶɅ ଶԄ ɐ௬௬୮ୟଶɅଶԄ ɐ௭௭୮ୟ ଶɅቁ ܤ I௭ (20)䛣䛾ᘧ 䛷⾲ 䛥䜜䜛䜘䛖䛻䚸ᅛ య ヨ ᩱ 䛾ሙ ྜ 䚸 ㍈ ⣔ 䛾
ı䛾 䛝䛥䛻䜘䜚䚸䝇䝨䜽䝖 䝹䛾⥺ ᖜ 䜔⥺ ᙧ 䛜␗ 䛺䜛䛜䚸 ᅇ 䛾䜘䛖䛻
MASᐃ 䜢⾜ 䛖䛸䚸 Ꮫ 䝅䝣䝖䛾␗
᪉ ᛶ 䛻䜘䜛⥺ ᖜ 䛿ほ 䛥䜜䛺䛔䚹䛣䛣䛷䛿䚸䛭䛾
MAS䛾ຠ ᯝ 䜢グ 䛩䚹 㻌 㟼 ☢ ሙ
(z㍈
)䛛䜙
Įഴ 䛔䛯㍈ ࿘ 䜚䛷ヨ ᩱ 䜢ᅇ ㌿ 䛥䛫䜛䛸䚸
ij䛿ᖹ ᆒ 䛥䜜 㻌
തതതതതതതത ൌଶԄ ଶଵ ଶ ଶԄԄ ൌଵଶ㻌 㻌 㻌 㻌 㻌
Çതതതതതതത ൌଶԄ ଶଵ ଶ ଶԄԄ ൌଵଶ (21)䛸䛺䜛䚹䜘䛳䛶䚸ᘧ
(20)䛿䚸௨ ୗ 䛾䜘䛖䛻᭩ 䛟䛣䛸䛜䛷䛝䜛䚹
Hୌൌଵଷɀ ቀɐ௫௫୮ୟ ɐ௬௬୮ୟ ɐ௭௭୮ୟቁ ܤ I௭ଵɀሺͳ െ ͵ ଶɅሻ ቀɐ௫௫୮ୟ ɐ௬௬୮ୟെ ʹɐ௭௭୮ୟቁ ܤ I௭
㻌
(22)䛣䛣䛷䚸➨
1㡯 䛿䚸ゅ ᗘ
ș䛻౫ Ꮡ 䛧䛺䛔䛾䛷䚸➼ ᪉ ᛶ Ꮫ 䝅䝣䝖䛸 䜀䜜䜛䚹➨
2㡯 䛿
ș䛻౫ Ꮡ 䛩䜛䛾䛷⥺ ᖜ 䛾㡯 䜢ྵ 䜏䚸 Ꮫ 䝅䝣䝖䛾␗ ᪉ ᛶ 䛸 䜀䜜䛶䛔䜛䚹
⁐ ᾮ 䛾ሙ ྜ 䚸ศ Ꮚ 㐠 ື 䛻䜘䜚➨
2㡯 䛜ᖹ ᆒ 䛥䜜
0䛸䛺䜛䛾䛷䚸 Ꮫ 䝅䝣䝖䛾␗
᪉ ᛶ 䛻 䜘 䜛 ⥺ ᖜ 䛿 ほ 䛥 䜜 䛪 䚸 ➼ ᪉ ್ 䛾 䜏 䛜 ᚓ 䜙 䜜 䜛 䚹 ᅛ య ヨ ᩱ 䛾 ሙ ྜ 䚸
(1-3cos2ș)䛾㡯 䛿䚸 ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స ⏝ 䛾ᡤ 䛷グ 䛧䛯 MASἲ 䜢⏝ 䛔䜛䛣 䛸䛷
0䛸䛩䜛䛣䛸䛜䛷䛝䜛䚹 ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స ⏝ 䛾ሙ ྜ 䛸␗ 䛺䜛䛾䛿䚸
1H᰾ 䛾 Ꮫ 䝅䝣䝖䛾␗ ᪉ ᛶ 䛜ᑠ 䛥䛔䛣䛸䛷䛒䜛䚹䛣䜜䛿☢ ሙ 䛜䛺䛔ሙ ྜ 䚸s ㌶ 㐨 䛿㌶
㐨 ゅ 㐠 ື 㔞 䜢ᣢ 䛯䛺䛔䛣䛸䛛䜙⌮ ゎ 䛷䛝䜛䚹䛭䛾䛯䜑䚸 ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స
⏝ 䛸䛿␗ 䛺䜚䚸ᩘ
kHz䛾
MAS㏿ ᗘ 䛷 Ꮫ 䝅䝣䝖䛾␗ ᪉ ᛶ 䛻䜘䜛⥺ ᖜ 䛿
0䛻䛩䜛
䛣䛸䛜䛷䛝䜛䚹୍ ᪉ 䚸
13C᰾ 䛾ሙ ྜ 䚸p 㟁 Ꮚ 䜢ᣢ 䛴䛾䛷䚸␗ ᪉ ᛶ 䛾ᐤ 䛿 䛝䛔䚹
MAS䛾ᅇ ㌿ ᩘ 䛜⥺ ᖜ 䜘䜚䜒ᑠ 䛥䛔ሙ ྜ 䚸䝇䝢䝙䞁䜾䝃䜲䝗䝞䞁䝗䛸 䜀䜜䜛䝢䞊
䜽䛜ほ 䛥䜜䜛䛾䛷䚸
13C᰾ 䛾 ᐃ 䜢⾜ 䛖䛻䛿䚸MAS 䛾ᅇ ㌿ ㏿ ᗘ 䜢 䛝䛟䛩䜛ᚲ
せ 䛜䛒䜛䚹䛭䛾䛯䜑䚸 ᅇ 䛿
12 kHz䛾
MAS㏿ ᗘ 䛷
13C᰾ 䛾 ᐃ 䜢⾜ 䛳䛯䚹
(2) ᐃ ἲ
䞉 ᕪ ศ ᴟ
(CP)ἲ 䛸RAMP䝟䝹䝇
NMR
䛿ಙ ྕ ᙉ ᗘ 䛜ᙅ 䛔䛾䛷䚸䝟䝹䝇↷ ᑕ ᚋ 䛾⮬ ⏤ ㄏ ᑟ ῶ ⾶
(FID)ಙ ྕ 䜢ᩘ
༑ 䡚ᩘ ᅇ ᐃ 䛧䚸䛭䜜䜢✚ ⟬ 䛩䜛䛣䛸䛷䚸
S/Nẚ 䛾Ⰻ 䛔䝇䝨䜽䝖䝹䜢ᚓ 䜛䚹
1H᰾ 䛾䜘䛖䛻ኳ ↛ Ꮡ ᅾ ẚ 䛜
99 %䛾᰾ 䛿ಙ ྕ ᙉ ᗘ 䛜 䛝䛔䛾䛷䚸✚ ⟬ ᅇ ᩘ 䛜ᑡ 䛺 䛟䛶῭ 䜐䚹䛥䜙䛻䚸⦆ ຠ ⋡ 䛜Ⰻ 䛔䛾䛷䚸⦆ 㛫 䛜▷ 䛟䚸▷ 㛫 䛷
S/Nẚ 䛾 Ⰻ 䛔䝇䝨䜽䝖䝹䜢ᚓ 䜛䛣䛸䛜䛷䛝䜛䚹୍ ᪉ 䚸
13C᰾ 䛿ኳ ↛ Ꮡ ᅾ ẚ 䛜
1 %⛬ ᗘ 䛺䛾䛷䚸✚ ⟬ ᅇ ᩘ 䜢ከ 䛟䛸䜛ᚲ せ 䛜䛒䜛䚹䜎䛯䚸⦆ ຠ ⋡ 䛜ᝏ 䛔䛾䛷 ᐃ 䛻 㛫 䛜 䛛䛛䜛䚹
1H䛾☢ 䜢
13C䛻⛣ 䛩䛣䛸䛜䛷䛝䛯䜙䚸▷ 㛫 䛷
S/Nẚ 䛾Ⰻ 䛔
13C NMR䝇䝨䜽䝖䝹䜢ᚓ 䜛䛣䛸䛜䛷䛝䜛䛜䚸ᐇ 㦂 ᗙ ᶆ ⣔ 䛷䛿ᅔ 㞴 䛷䛒䜛䚹
1H䛸
13C㛫 䛷 䚸 ☢ 䜢 ⛣ ື 䛥 䛫 䜛 䛻 䛿 䚸 ୧
⪅ 䛾 䜶 䝛 䝹 䜼 䞊 ᕪ
(1/2ĺ䠉
1/2㑄 ⛣ 䛾䜶䝛䝹䜼䞊ᕪ
)䛜➼ 䛧䛟䛺 䛡䜜䜀䛺䜙䛺䛔䚹䛭䛣䛷䚸ඹ 㬆 ࿘ Ἴ ᩘ 䛸 ྠ 䛨 ㏿ ᗘ 䛷 ᅇ ㌿ 䛩 䜛 ᗙ ᶆ ⣔ 䛻⛣ 䜛䠄ᐇ 㝿 䛾 ⨨ 䛷䛿᳨
ฟ 䛻 ඹ 㬆 ࿘ Ἴ ᩘ ᡂ ศ 䜢 ᘬ 䛟 䛣䛸䛷ᐇ ⌧ 䛷䛝䜛䠅䚹䛣䛾ᅇ ㌿ ᗙ ᶆ ⣔ 䛷䛿䚸㟼 ☢ ሙ
B0䛿ᾘ 䛘䜛 䛾䛷䚸☢ 䜢ᢅ 䛔䜔䛩䛟䛺䜛䚹䛣 䛾ᗙ ᶆ ⣔ 䛷☢ 䜢
xyᖹ 㠃 䛻ಽ 䛧䚸ಽ 䜜䛯᪉ ྥ 䛻䝷䝆䜸Ἴ ☢ ሙ
B1H䜢䛛䛡䚸䝇䝢䞁䜢䝻䝑䜽䛩䜛䚹 ḟ 䛻
13C᰾ 䛻 䜒 ☢ ሙ
B13C䜢
Ȗ1HB1H䠙Ȗ
13CB13C䛾᮲ ௳ 䜢‶ 䛯 䛩 䜘 䛖 䛻 䛛 䛡 䜛 䚹 䛣 䛾 ᮲ ௳ 䛿
Hartmann-Hahn᮲ ௳ 䛸 䜀䜜䜛䚹 䛣 䛾 ᮲ ௳ 䜢 ‶ 䛯 䛩 䛸 䛝 䚸 ୧ ⪅ 䛾 䜶 䝛 䝹 䜼 䞊 ᕪ 䛜 ➼ 䛧 䛟 䛺 䜚 䚸
1H᰾ 䛾☢ 䛜
13C᰾ 䛻⛣ 䜛䚹䛣䜜 䜢 ᕪ ศ ᴟ
(CP)ἲ 䛸䛔䛔䚸MASἲ 䛸䛒䜟䛫䛶䚸
CP/MAS䛸グ 䛩䚹
CPἲ 䛿
1H᰾ 䛜⦆ 䛩䜜䜀䚸☢ 䜢
13C᰾ 䛻
⛣ 䛫䜛䛾䛷䚸 ᐃ 㛫 䛿䚸
1H᰾ 䛾⦆ 㛫 䛻౫ Ꮡ 䛩䜛䜘䛖䛻䛺䜛䚹䛥䜙䛻䚸CP ἲ 䛷䛿ಙ ྕ ᙉ ᗘ 䛜䝁䞁䝍䜽䝖䝟䝹䝇䛾 㛫 䛻౫ Ꮡ 䛩䜛䛾䛷䚸䝁䞁䝍䜽䝖䝍䜲䝮䜢㛗 䛟䛩䜛䛸䚸㐲 ᪉ 䛾
1H᰾ 䛛䜙☢ 䜢⛣ ື 䛥䛫䜛䛣䛸䛜䛷䛝䜛䚹䛴䜎䜚䚸䝁䞁䝍䜽䝖䝍䜲 䝮䜢ኚ ᩘ 䛸䛧ಙ ྕ ᙉ ᗘ 䜢 ᐃ 䛩䜛䛸
C-H㊥ 㞳 䛻㛵 䛩䜛 ሗ 䛜ᚓ 䜙䜜䜛䚹䛣䜜䛿䚸
2ḟ ඖ ᐃ 䛾ᇶ ♏ 䛸䛺䜛⪃ 䛘᪉ 䛷䛒䜛䚹
CPἲ 䛷䚸ୖ グ 䛾
Hartmann-Hahn䛾᮲
௳ 䛜ᡂ 䜚❧ 䛴䛾䛿䚸
MAS㏿ ᗘ 䛜ప ㏿ 䛾ሙ ྜ 䛷䛒䜛䚹
MAS㏿ ᗘ 䛜 䛝䛔ሙ ྜ 䚸 ᐇ 㦂 ᐊ ⣔ ᐇ 㦂 ᐊ ⣔
13C
᰾
1H
᰾
ᅇ ㌿ ᗙ ᶆ ⣔
1H
᰾
1H
᰾
13C
᰾
13C
᰾
CP DC
CP
CP DC
RAMP
CP
᮲ ௳ 䛿䚸Ȗ
1HB1H䠇nȦ
r䠙Ȗ
13CB13C䛸䛺䜛䚹䛣䛣䛷䚸
n䠙0, ±1, ±2,䡡䡡䡡䛷䛒䜚䚸Ȧ
r䛿
MAS䛾ᅇ ㌿ ㏿ ᗘ 䛷䛒䜛䚹
MAS㏿ ᗘ 䛜 䛝䛟䛺䜛䛸䚸
n䠙
±1, ±2䚸䛴䜎䜚䚸䝃䜲䝗 䝞䞁䝗䛸䝬䝑䝏䞁䜾䛩䜛䜘䛖䛻䛺䜛䚹CP 䛾᮲ ௳ 䛿䚸䝟䝹䝇䝟䝽䞊䛻ᩄ ឤ 䛺䛾䛷䚸䝁 䞁䝍䜽䝖䝟䝹䝇䛾䝟䝽䞊䜢 㛫 䛸ඹ 䛻ኚ 䛥䛫䜛
RAMP[8]ἲ 䛜㧗 ㏿
MASἲ 䛷䛿
᭷ ຠ 䛻䛺䜛䚹
RAMP䝟䝹䝇䛷䛿䚸䝟䝹䝇䝟䝽䞊䜢┤ ⥺ ⓗ 䛻ኚ 䛥䛫䚸ᩘ
kHz䛾
࿘ Ἴ ᩘ ᖜ 䜢䜹䝞䞊䛩䜛䛣䛸䛜䛷䛝䜛䚹䛣䛾䝟䝹䝇䜢⏝ 䛔䜛䛣䛸䛻䜘䜚䚸䝟䝹䝇୰ 䛾 䛒䜛Ⅼ 䛷䚸
CP᮲ ௳ 䛜‶ 䛯䛥䜜䚸ศ ᴟ ⛣ ື 䜢㉳ 䛣䛩䛣䛸䛜䛷䛝䜛䚹ᮏ ◊ ✲ 䛷䛿
12 kHz䛾
MAS㏿ ᗘ 䛷 ᐃ 䛩䜛䛸䛝䛿䚸RAMP 䝟䝹䝇䜢⏝ 䛔䛯䚹䛺䛚䚸ᅗ ୰ 䛾
DC䛿䝕䜹䝑䝥䝹䜢ព 䛧䛶䛔䜛䚹
㻌 䝕䜹䝑䝥䝹䛸䛿䚸
13C᰾ 䛾
FID䜢ྲྀ 䜚㎸ 䜐㝿 䚸
1H᰾ 䛛䜙䛾 ᴟ Ꮚ ┦ స ⏝ 䜢 ᢚ 䛘䜛䛯䜑䛻
1H᰾ 䛾☢ 䛻䝟䝹䝇䜢↷ ᑕ 䛧䛶䚸ᖹ ᆒ 䛩䜛䛣䛸䛷䛒䜛䚹䝕䜹䝑䝥 䝹䝟䝹䝇䛻䛿
cwἲ 䛸
tppmἲ 䛜䛒䜛䚹๓ ⪅ 䛿䚸
Continuous Wave䛾␎ 䛷䚸
2ʌ䝟 䝹䝇䜢ྠ ┦ 䛷㟼 ☢ ሙ 䛻ᆶ ┤ 䛺᪉ ྥ
(x㍈
)䛛䜙㐃 ⥆ ⓗ 䛻↷ ᑕ 䛩䜛᪉ ἲ 䛷䛒䜛䚹 䛣䜜䛻䜘䜚䚸㟼 ☢ ሙ ᪉ ྥ
(z㍈)䜢ྥ 䛔䛶䛔䜛
1H᰾ 䛾☢ 䜢
yzᖹ 㠃 䛷ᅇ ㌿ 䛥䛫䚸 䛭䛾ᖹ ᆒ ್ 䜢
0䛻䛩䜛᪉ ἲ 䛷䛒䜛䚹䛧䛛䛧䚸┦ స ⏝ 䛜䛒䜛ሙ ྜ 䛿䚸㟼 ☢ ሙ 䜢
䛻ᾘ 䛩ᅇ ㌿ ᗙ ᶆ ⣔ 䛻 䜛䛣䛸䛜ᅔ 㞴 䛺䛯䜑䚸䝷䝆䜸Ἴ 䜢↷ ᑕ 䛧䛯
x㍈ ࿘ 䜚 䛷䛿䛺䛟䚸
z㍈ 䛾ṧ ␃ ☢ ሙ 䛸
x㍈ 䛾䝷䝆䜸Ἴ 䛻䜘䜛☢ ሙ 䝧䜽䝖䝹䛾 䛾᪉ ྥ
(᭷ ຠ
☢ ሙ
)䜢୰ ᚰ 䛻☢ 䛜ᅇ ㌿ 䛩䜛䚹䛣䛾ሙ ྜ 䚸㟼 ☢ ሙ 䛸᭷ ຠ ☢ ሙ 䛾䛺䛩ゅ 䜢
ș䛸 䛩䜛䛸䚸cosș 䛻ẚ 䛧䛯☢ 䛜
z㍈ 䛻ṧ 䜛䛣䛸䛻䛺䜚䚸䝕䜹䝑䝥䝹䛜 ༑ ศ 䛸䛺䜛䚹 䛭䛣䛷䚸
1995ᖺ 䛻
tppmἲ 䛜ᥦ 䛥䜜䛯䚹
tppm䛿
Two Pulse Phase Modulation䛾␎ 䛷䚸
cwἲ 䛷㏙ 䜉䛯䚸᭷ ຠ ☢ ሙ ᪉ ྥ 䛾☢ 䜢䛥䜙䛻ᖹ ᆒ 䛩䜛᪉ ἲ 䛷䛒䜛䚹 䛴䜎䜚䚸᭷ ຠ ☢ ሙ 䛛䜙ഴ 䛔䛯᪉ ྥ 䛛䜙䝷䝆䜸Ἴ 䜢↷ ᑕ 䛧䚸☢ 䜢ᅇ ㌿ 䛥䛫䚸ᖹ ᆒ
䛩䜛䚹
tppmἲ 䛿䝕䜹䝑䝥䝹ຠ ⋡ 䛜Ⰻ 䛔䛾䛷ከ 䛟䛾 ᐃ 䛻⏝ 䛔䜙䜜䛶䛔䜛䚹ᮏ
◊ ✲ 䛷䜒
tppm15䝟䝹䝇䝅䞊䜿䞁䝇䜢⏝ 䛔䛯䚹
䞉
CRAMPSἲ
CRAMPS
䛿
Combined Rotation and Multiple-Pulse Spectroscopy䛾␎ 䛷䛒䜛䚹 䛴䜎䜚䚸
MAS䛸ከ 㔜 䝟䝹䝇䜢⏝ 䛔䛶䚸
1H-1H㛫 䛾 ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స ⏝ 䜢 ᑠ 䛥䛟䛩䜛ᡭ ἲ 䛷䛒䜛䚹ከ 㔜 䝟䝹䝇䛻䛿䚸
WAHUHA-4䜔
MREV-8䛺䛹䛾䝟䝹䝇
⣔ ิ 䜒䛒䜛䛜䚸ᮏ ◊ ✲ 䛷䛿
BR-24䜢⏝ 䛔䛯䚹䛣䜜䜙䛾䝟䝹䝇⣔ ิ 䛿䚸
MAS㏿ ᗘ 䛸䛾ᖸ ΅ 䜢㑊 䛡䜛䛯䜑䛻䚸ప ㏿
MAS䛷 ᐃ 䛩䜛䜘䛖䛻⤌ 䜏❧ 䛶䜙䜜䛶䛔䜛䚹䛣䜜 䜙䛾䝟䝹䝇⣔ ิ 䛾ᇶ ᮏ ⓗ 䛺⪃ 䛘᪉ 䛿䚸☢ 䜢▷ 䛔 㛫 䛾㛫 䛻
x,y,z㍈ 䛻ಽ 䛧䚸
☢ 䜢
3ḟ ඖ ᖹ ᆒ 䛩䜛᪉ ἲ 䛷䛒䜛䚹䛣䛣䛷䚸
BR-24䛜
ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స ⏝ 䜢 ᑠ 䛥 䛟 䛩 䜛 䛣 䛸 䜢 ௨ ୗ 䛻
♧ 䛩䚹䜎䛪䚸
(ʌ/2)x䝟䝹䝇䜢
X䛸⾲ 䛧䚸䝟䝹䝇┤ ๓ 䛾
้ 䜢
0䠉䠄⇕ ᖹ ⾮ ≧ ែ
t䠙
XYYXXYYXYXYYXYXXYYXXYX
BR-24
䝟䝹䝇⣔ ิ
X,Y
䛿ྛ ㍈ 䜈
ʌ/2䝟䝹䝇䜢༳ ྍ 䛧䚸
X,Y䛿
-x,-y㍈ ᪉ ྥ 䜈
ʌ/2䝟䝹䝇䜢༳ ྍ 䛩䜛䛣䛸䜢ព 䛩䜛䚹
0
䛻➼ 䛧䛔䠅䚸┤ ᚋ 䜢
0䠇䛸䛩䜛䚹Ἴ ື 㛵 ᩘ|ij(t)>䛿䝟䝹䝇
X䛻䜘䜚௨ ୗ 䛾䜘䛖䛻ኚ
䛩䜛䚹
|ij(0䠇)>
䠙 X|ij(0
䠉)>䠙 X|ij(0)>
(23)ḟ 䛾䝟䝹䝇䜢↷ ᑕ 䛩䜛䜎䛷䛾㛫 㝸
IJ䛾㛫 䚸☢ 䛿
U䛸䛔䛖┦ స ⏝ 䜢ཷ 䛡䜛䠄䛣 䛾୰ 䛻 ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స ⏝ 䛜ྵ 䜎䜜䛶䛔䜛䠅䛾䛷䚸
IJ 㛫 ᚋ 䛿
|ij(IJ)>
䠙 U|ij(0
䠇)>䠙 UX|ij(0)>
(24)䚹ḟ 䛻
IJ䠉䛷
Y䝟䝹䝇䜢↷ ᑕ 䛧䚸䛭䛾ᚋ 䛥䜙䛻
IJ 㛫 䠄䛴䜎䜚
2IJ䠅⤒ 㐣 䛧䛯ᚋ 䚸
3䛴
┠ 䛾
Y䝟䝹䝇䜢↷ ᑕ 䛩䜛䛸䚸
|ij(2IJ䠇)>
䠙 YUY|ij(IJ)> 䠙 YUYUX|
ij(0)> (25)䚹䛣䛣䛷䚸
ൌ ି୧ಘమ୍ೣ㻌 㻌 㻌 㻌 㻌 ൌ ୧ಘమ୍ೣ (26)
䛺䛾䛷䚸
XX䠙
XX䠙
1䛷䛒䜛䚹䜘䛳䛶䚸ᘧ
(25)䛿䚸௨ ୗ 䛾䜘䛖䛻᭩ 䛟䛣䛸䛜䛷䛝䜛䚹
|ij(2IJ䠇)>
䠙 YUYUX|ij(0)> 䠙 XXYUYXXUX|ij(0)> (27) 䛴䜎䜚䚸
XYUYX䛸
XUX䜢ྵ 䜐䛾䛷䚸䛭䜜䜙䜢ィ ⟬ 䛩䜜䜀䚸Ἴ ື 㛵 ᩘ 䛾ኚ 䜢 ண 䛩䜛䛣䛸䛜䛷䛝䜛䚹䛣䛣䛷䛿ᅇ ㌿ ᗙ ᶆ ⣔ 䛻䛝䛱䜣䛸 䛳䛯ሙ ྜ 䜢⪃ 䛘䚸U 䛸䛧 䛶 Ꮫ 䝅䝣䝖䛸 ᴟ Ꮚ 䠉 ᴟ Ꮚ ┦ స ⏝ 䜢⪃ 䛘䜛䚹䛴䜎䜚䚸
ൌ ି୧ሺHାHሻ௧
㻌
(28)䛷䛒䜛䚹䛣䛣䛷䚸ᣦ ᩘ 㛵 ᩘ 䜢ᒎ 㛤 䛧䚸
XX䠙1䜢⏝ 䛔䜛䛸௨ ୗ 䛾䜘䛖䛻䛺䜛䚹
㻌 㻌 㻌
ൌ ି୧ሺHାHሻ௧ ൌ ି୧ଡ଼ሺHାHሻଡ଼௧㻌 (29)䛴䜎䜚䚸ᘧ
(27)䛿
ȁɔሺͲሻ ൌ ି୧ଡ଼ଢ଼ሺHାHሻଢ଼ଡ଼௧ି୧ଡ଼ሺHାHሻଡ଼௧ȁɔሺͲሻ (30)
䛸䛺䜛䛾䛷䚸ᣦ ᩘ 㒊 ศ 䜢ィ ⟬ 䛧 䜢䛸䜛䛣䛸䛷䚸䝟䝹䝇䛾ຠ ᯝ 䜢⟬ ฟ 䛩䜛䛣䛸䛜䛷 䛝䜛䚹᭱ ⤊ ⓗ 䛻䚸<I
y>䜢ほ 䛩䜛䛾䛷䚸௨ ୗ 䛾ᮇ ᚅ ್ 䜢ィ ⟬ 䛩䜛䛣䛸䛻䛺䜛䚹 <Iy>䠙<ij(nIJ)| Iy |ij(nIJ)>䠙<ij(0)|XUX䡡䡡䡡Iy䡡䡡䡡XUX|ij(0)> (31)
BR-24䛾ሙ ྜ 䚸᭱ ึ 䛾
X䝟䝹䝇䜢
P1䛸䛩䜛䛸䚸ḟ 䝨䞊䝆䛻♧ 䛧䛯⾲ 䛾䜘䛖䛻ィ
⟬ 䛩䜛䛣䛸䛜䛷䛝䜛䚹䛣䜜䜙䛾 䜢䛸䜛䛸䚸I
z㡯 䛿䚸4IJ(I
z䠇I
x䠉I
y )䛸䛺䜚䚸I1zI2z㡯 䛿䚸
8IJ(I1xI2x䠇
I1yI2y䠇
I1zI2z)䛸䛺䜛䚹
Iz㡯 䛸
I1zI2z㡯 䜢ィ ⟬ 䛧䛯䛾䛿
H CS䛸
H DD䛿䚸 ᘧ
(22)䛸
(11)䛻♧ 䛧䛯䜘䛖䛻䚸䛣䜜䜙䛾㡯 䜢ྵ 䜣䛷䛔䜛䛛䜙䛷䛒䜛䚹ゝ 䛔 䛘䜜䜀䚸
Ꮫ 䝅䝣䝖㡯 䛸 ᴟ Ꮚ ┦ స ⏝ 㡯 䛸ゝ 䛔 䛘䜛䛣䛸䛜䛷䛝䜛䚹䝟䝹䝇ᖜ 䜢↓ ど 䛩 䜛䛸䚸䛣䛾䝟䝹䝇⣔ ิ 䜢↷ ᑕ 䛧䛶䛔䜛 㛫 䛿䚸
24IJ䛺䛾䛷䚸 ᴟ Ꮚ 㡯 䛾 㛫 ᖹ ᆒ 䜢䛸䜛䛸䚸(I
1xI2x䠇I
1yI2y䠇I
1zI2z )/3䛸䛺䜛䚹ᘧ
(11)䛛䜙䚸 ᴟ Ꮚ ┦ స ⏝ 䛿䚸䛣䛾⤖ ᯝ 䛛䜙ᖹ ᆒ 䛥䜜
0䛻䛺䜛䛣䛸䛜ศ 䛛䜛䚹䜘䛳䛶䚸ᘧ
(31)䛿௨ ୗ 䛾䜘䛖䛻䛺䜛䚹㻌
൏I࢟ൌ൏ ɔሺͲሻห୧Hి௧ I࢟ି୧Hి௧หɔሺͲሻ ൌ൏ ߮ሺͲሻห୧Hి௧ Iࢠି୧Hి௧หɔሺͲሻ (32)䛣䛣䛷䚸
Hୌן ሺI࢟െI࢟I࢟ሻ䛷䛒䜛䚹䛣䛾䜘䛖䛻ほ 䛥䜜䜛ಙ ྕ 䛻䛿 ᴟ Ꮚ 䠉
ᴟ Ꮚ ┦ స ⏝ 䛻䜘䜛⥺ ᖜ 䛜ྵ 䜎䜜䛶䛔䛺䛔䛜䚸 Ꮫ 䝅䝣䝖㡯 䛿ṧ 䜛䚹
㻌 䛺䛚䚸
CRAMPSἲ 䛿䚸⌧ ᅾ 䜒ᨵ Ⰻ 䛜ຍ 䛘䜙䜜䚸㧗 ㏿
MAS䛷䜒 ᐃ 䛷䛝䜛䝟䝹
䝇⣔ ิ 䛜㛤 Ⓨ 䛥䜜䛶䛔䜛䚹䛧䛛䛧䚸CRAMPS ἲ 䛾᭱ 䛾ၥ 㢟 Ⅼ 䛷䛒䜛䝇䜿䞊䝹
ᅉ Ꮚ 䛾ၥ 㢟 䛿ゎ Ỵ 䛷䛝䛺䛔䚹䛣䜜䛿䚸ከ 㔜 䝟䝹䝇䜢⏝ 䛔䜛䛸䚸ᚓ 䜙䜜䜛䝇䝨䜽䝖
䝹䛾ᶓ ㍈ 䛜⦰ ᑠ 䛧䛶䛧䜎䛖䛾䛷䚸䝇䜿䞊䝹ᅉ Ꮚ 䜢䛛䛡䛶䚸⿵ ṇ 䛧䛶䛔䜛䛾䛷䛒䜛䚹 䛣䛾ᅉ Ꮚ 䛿⌮ ㄽ ⓗ 䛻ồ 䜑䛯್ 䛷䛿䚸ᐇ 㦂 ್ 䜢 ⌧ 䛩䜛䛣䛸䛜㞴 䛧䛔䛾䛷䚸᪤ ▱ 䛾≀ ㉁ 䛾䝇䝨䜽䝖䝹 ᐃ 䜢⾜ 䛔䚸䝇䜿䞊䝹ᅉ Ꮚ 䜢Ỵ 䜑䛶䛔䜛䛣䛸䛜ከ 䛔䚹
⾲ 㻌
BR-24䝟䝹䝇⣔ ิ 䛸 Ꮫ 䝅䝣䝖㡯(I
z)䛸 ᴟ Ꮚ 㡯(I1zI2z)Pi ȆPi Iz I1zI2z Pi Ȇ Pi Iz I1zI2z
1 X X -Iy I1yI2y 13 Y Y - I x I 1xI 2x
2 Y XY I x I 1xI 2x 14 X YX - I y I 1yI 2y
3 Y X - I y I 1yI 2y 15 Y YXY Iz I 1zI 2z
4 X 1 Iz I 1zI 2z 16 X YXYX I x I 1xI 2x
5 X X I y I 1yI 2y 17 X YXY Iz I 1zI 2z
6 Y X Y I x I 1xI 2x 18 Y YX - I y I 1yI 2y
7 Y X I y I 1yI 2y 19 Y YXY - Iz I 1zI 2z
8 X 1 Iz I 1zI 2z 20 X YXYX I x I 1xI 2x
9 Y Y I x I 1xI 2x 21 X YXY - Iz I 1zI 2z
10 X YX - I y I 1yI 2y 22 Y YX - I y I 1yI 2y
11 X Y I x I 1xI 2x 23 X Y - I x I 1xI 2x
12 Y 1 Iz I 1zI 2z 24 Y 1 Iz I 1zI 2z
䞉
2ḟ ඖ ᐃ
2
ḟ ඖ ᐃ 䛾ᇶ ᮏ ⓗ 䛺䝟䝹䝇⣔ ิ 䛿䚸‽ ഛ ᮇ 䞉ᒎ 㛤 ᮇ 䞉ΰ ྜ ᮇ 䞉᳨ ฟ ᮇ 䛛䜙䛺 䜛䚹‽ ഛ ᮇ 䛷䛿䚸☢ 䜢ᅇ ㌿ ᗙ ᶆ ⣔ 䛾
xyᖹ 㠃 䛻ಽ 䛧䚸䛭䜜䜢ᒎ 㛤 ᮇ 䛷ᒎ 㛤 䛩 䜛䚹1 ḟ ඖ 䛾 ᐃ 䛷䛿䚸䛣䛾☢ 䜢
FID䛸䛧䛶᳨ ฟ 䛩䜛䛜䚸2 ḟ ඖ 䛷䛿䚸䛣䛾 㛫 䜢
t1䛸䛧䚸ḟ 䛾ΰ ྜ ᮇ 䛻㐍 䜐䚹ΰ ྜ ᮇ 䛷䚸᰾ 㛫 䛷ศ ᴟ ⛣ ື 䜢㉳ 䛣䛧䚸᳨ ฟ ᮇ 䛷䚸
FIDಙ ྕ 䜢ᚓ 䜛䚹᳨ ฟ ᮇ 䛷ᚓ 䜙䜜䜛
FID䛿
1ḟ ඖ ᐃ 䛸ྠ ᵝ 䛻 㛫
(t2)䛸ඹ 䛻ῶ ⾶ 䛩䜛䛜䚸t
1䛾㛵 ᩘ 䛻䜒䛺䛳䛶䛔䜛䚹䛴䜎䜚䚸t
1䛸
t2䛻ᑐ 䛧䛶䝣䞊䝸䜶ኚ 䛩䜛䛣 䛸䛷䚸
2ḟ ඖ 䝇䝨䜽䝖䝹䛜ᚓ 䜙䜜䜛䚹䛷䛿䚸䛺䛬᳨ ฟ ჾ 䛷ᚓ 䜙䜜䜛
FID䛜
t1䛾㛵
ᩘ 䛸䛺䜛䛾䛛䚸ḟ 䛻⡆ ༢ 䛻㏙ 䜉䜛䚹
㻌 ヰ 䜢⡆ ༢ 䛻䛩䜛䛯䜑䛻䚸䛣䛣䛷䛿᰾
I䛸
S䛜
J䜹䝑䝥䝸䞁䜾䛧䛯
2䝇䝢䞁⣔ 䛾᰾ 䜢
ᢅ 䛖䚹䜎䛪䚸‽ ഛ ᮇ 䛷
2䛴䛾᰾ 䛻
x㍈ ᪉ ྥ 䛛䜙
ʌ/2䝟䝹䝇䜢༳ ྍ 䛩䜛䚹䛩䜛䛸⇕
ᖹ ⾮ ≧ ែ
(ձ)䛻䛒䛳䛯☢ 䛿䚸-y㍈ 䛻ಽ 䜜䜛(ղ
)䚹ᒎ 㛤 ᮇ 䛾t1䛾㛫 䛻
I䛾☢ 䛿䝇䝢䞁䜹䝑䝥䝸䞁䜾䛻䜘䜚䚸䝷䞊䝰䜰࿘ Ἴ ᩘ
ȍI䜘䜚䜒㏿ 䛔ᡂ ศ 䛸㐜 䛔ᡂ ศ 䛜䛒䜛 䛾䛷䚸ճ 䛾䜘䛖䛻䚸䝕䜱䝣䜵䞊䝈䛩䜛䚹䛺䛚䚸ճ䛾䝧䜽䝖䝹䛿
xᡂ ศ 䛸
yᡂ ศ 䛾 䛷
⾲ 䛩䛣䛸䛜䛷䛝䜛䚹t
1 㛫 ᚋ 䛻
x㍈ ᪉ ྥ 䛛䜙
ʌ/2䝟䝹䝇䜢༳ ྍ 䛩䜛䛸䚸ճ 䛾
yᡂ
ศ 䛿䚸մ 䛾
zᡂ ศ 䛻䛺䜛䚹 մ䛿䚸☢ 䛜ศ ᴟ 䛧䛯≧ ែ 䛷䛒䜛䚹䛺䛚䚸մ䛾
zᡂ ศ 䛾 䛝䛥䛿䚸t
1䛾㛵 ᩘ 䛻䛺䛳䛶䛔䜛䚹䛣䛾
ʌ/2䝟䝹䝇䛜ΰ ྜ ᮇ ᚋ 䛾᳨ ฟ ᮇ 䛷
FID䛷ほ 䛥䜜䚸
t1䛸
t2䛾㛵 ᩘ 䛸䛺䜛䚹
ḟ 䛻䚸ᐦ ᗘ ₇ ⟬ Ꮚ 䜢⏝ 䛔䛶
COSYᐃ 䛜ྍ ⬟ 䛺䛣䛸䜢௨ ୗ 䛻ㄝ ᫂ 䛩䜛䛜䚸䛣䛣 䛷䛿⦆ 䛿↓ ど 䛩䜛䚹
NMR䛷ほ 䛩䜛᰾ 䛿
1ಶ 䜔
2ಶ 䛷䛿䛺䛟䚸
1018ಶ ⛬ ᗘ 䛷䛒䜛䛾䛷䚸≧ ែ 䜢ᐦ ᗘ 㛵 ᩘ
ȡ䛷⾲ 䛩䛣䛸䛜ከ 䛔䚹ほ ㍈ 䛿
xyᖹ 㠃 䛺䛾䛷䚸
I䠇䛾ᮇ ᚅ ್ 䜢ィ ⟬ 䛩䜛䚹ୖ グ 䛾 䛻䛺䜙䛔䚸2 䝇䝢䞁⣔ 䜢⪃ 䛘䜛䚹
<I䠇
䠇S
䠇>I䠙Tr{(I
䠇䠇S
䠇)ȡ(t)}䠙Tr{(I
䠇䠇S
䠇)U(t2)XU(t1)Xȡ(0)XU(t1)XU(t2)} (33)䛣䛣䛷䚸ᕥ ㎶ 䛾ῧ 䛘Ꮠ 䛿
I䝇䝢䞁䛻䛴䛔䛶ィ ⟬ 䛩䜛䛣䛸䜢♧ 䛧䛶䛔䜛䚹S 䝇䝢䞁䛿 ᚓ 䜙䜜䛯⤖ ᯝ 䛾
I䛸
S䜢ධ 䜜᭰ 䛘䜛䛣䛸䛷ᚓ 䜙䜜䜛䚹䜎䛯䚸
Tr䛿䝖䝺䞊䝇䛷⾜ ิ 䛾 ᑐ ゅ 㡯 䛾 䜢䛸䜛䛣䛸䜢ព 䛩䜛䚹ᘧ
(33)䛾 U(t )䛿䝇䝢䞁䜹䝑䝥䝸䞁䜾䛸 Ꮫ 䝅䝣䝖䛾㡯 䜢ྵ 䜐䚹
I䛸
S䛾 Ꮫ 䝅䝣䝖䛿䚸ᅇ ㌿ ᗙ ᶆ ⣔ 䛾㏿ ᗘ 䛸䛭䜜䛮䜜
ȍI䛸
ȍS␗ 䛺䜛࿘ Ἴ ᩘ 䛸䛩䜛䚹䛴䜎䜚䚸
୧ஐ௧୍୧ஐ௧ୗ (34)
䚹 䜎䛯䚸䝇䝢䞁 䜹䝑䝥䝸䞁䜾䛿䚸௨ ୗ 䛾䜘䛖䛻⾲ 䛩䚹
ିଶ୧୍ୗ௧ (35)
⇕ ᖹ ⾮ ≧ ែ
ȡ(0)䛿䚸Iz䛻ẚ 䛧䛯ᡂ ศ 䜢ᣢ 䛴䛸㏆ ఝ 䛷䛝䜛䛾䛷䚸ᘧ(33)䛿䚸௨
ୗ 䛾䜘䛖䛻䛺䜛䚹
<I䠇
䠇S
䠇>I䠙Tr{(I
䠇䠇S
䠇)U(t2)XU(t1)X IzXU(t1)XU(t2)} (36)䛣䛣䛷䚸
X IzX䛿⡆ ༢ 䛻ィ ⟬ 䛷䛝䚸
Iy䜢 䛘䜛䛾䛷䚸ḟ 䛻
U(t1) IyU(t1)䜢ィ ⟬ 䛩䜛 䛣䛸䛻䛺䜛䚹ᘧ
(34)䛸
(35)䛿䚸䛭䜜䛮䜜
Iy䛻ᑐ 䛧䛶௨ ୗ 䛾䜘䛖䛻 䜛⯙ 䛖䚹
㻌
ି୧ஐ௧ୗି୧ஐ௧୍௬୧ஐ௧୍୧ஐ௧ୗ ൌ ௬ ȳ୍ݐ ௫ ȳ୍ݐ㻌 㻌 㻌 㻌 (37)㻌
ିଶ୧୍ୗ௧௬ଶ୧୍ୗ௧ ൌ ௬ ሺɎܬݐሻ ʹ௫௭ሺɎܬݐሻ (38)䛣䛣䛷䚸ᘧ
(38)䛿᰾ 䝇䝢䞁1/2䛾ሙ ྜ 䛻ᡂ 䜚❧ 䛴䚹ᘧ(38)䛾ᑟ 䛝᪉ 䜢௨ ୗ 䛻♧ 䛩䚹 䜎䛪䚸௨ ୗ 䛾ᘧ 䛜ᡂ 䜚❧ 䛴䚹
㻌 㻌 㻌 㻌
ି୧୍௬୧୍ൌ ௬ Ʌ ௫ Ʌ㻌 㻌 㻌
(39)䛣䛣䛷䚸ș䠙2ʌJtS
z䛸䛩䜛䛸䚸
ିଶ୧୍ୗ௧௬ଶ୧୍ୗ௧ൌ ௬ ሺʹɎܬݐ௭ሻ ௫ሺʹɎܬݐ௭ሻ (40)䚹
䛣䛣䛷䚸
cos䛸
sin䜢ᒎ 㛤 䛩䜛䛸䚸
㻌
ሺʹɎܬݐ௭ሻ ൌ ͳ െሺଶ௧ሻమଶǨ ௭ଶሺଶ௧ሻସǨ ర௭ସെ ڮ
㻌
(41)x
y
