3P121
ከᴟᑠࠊゎ㞳ᆺ࣏ࢸࣥࢩࣕࣝࢆᣢࡘศᏊࡢ⢭ᐦ᣺ືゎᯒ㸦㤳㒔኱㝔࣭⌮ᕤ㸧‫ۑ‬㛫ᐑ ṇ㍤㸪ᒾ℩ 㡪㸪໭ᒣ Ύ❶㸪ᶫᮏ ೺ᮁ
Precise vibrational analysis of multi-minima and dissociative systems(Tokyo Metropolitan Univ.) ‫ۑ‬Masaki Mamiya, Hibiki Iwase, Kiyoaki Kitayama,
Kenro Hashimoto
࠙ᗎࠚVan der Waals 㘒యࠊࢡࣛࢫࢱ࣮ࡸ᣺ື࡛άᛶ໬ࡍࡿศᏊࡣࠊศᏊ⛉Ꮫࡢ㔜せ࡞◊✲ᑐ㇟࡛࠶ࡿࠋ㟁Ꮚ࣭᣺ືࢫ࣌ࢡࢺࣝࡢᵓ㐀࠿ࡽศᏊᵓ㐀ࡸ཯ᛂࡢ▱ぢࡀᚓࡽࢀࡿࡀࠊ⮬⏤ᗘᩘࡢከࡉ
ࡸࠊከᴟᑠࠊ๓ᮇゎ㞳࡞࡝」㞧࡞࣏ࢸࣥࢩ࢚ࣕࣝࢿࣝࢠ࣮㠃(PES)ࡀ୺࡞ཎᅉ࡛ࠊ㧗⢭ᗘ࡞᣺ືゎᯒࡸண ࡣ㞴ࡋ࠸ࠋࡑࡇ࡛ࠊ᣺ື SCF ἲ(VSCF)࡜ࠊFourier- Grid-Hamiltonian㸦FGH㸧ἲ࠶ࡿ࠸ࡣ FGH-Hartree ἲࢆ⤌ࡳྜࢃࡏࡓศ๭⤫἞ᆺ᣺ືィ⟬ἲ࡟ࡼࡿၥ㢟ゎỴࢆヨࡳ࡚࠸ࡿࠋ
࠙᪉ἲࠚVSCF ࡛ࡣࠊ඲᣺ືἼື㛵ᩘࢆ༢࣮ࣔࢻ㛵ᩘࡢ Hartree ✚㸦ᘧ 1㸧࡛㏆ఝࡋࠊ࣮ࣔࢻࡈ
࡜ࡢࢩ࣮ࣗࣞࢹ࢕࣮ࣥ࢞᪉⛬ᘧ㸦ᘧ 2㸧࡟ศࡅ࡚ゎࡃࠋྛ࣮ࣔࢻࡢ Hamiltonian ࡟௚࣮ࣔࢻࡢἼ
ື㛵ᩘ࠿ࡽồࡲࡿᐇຠ࣏ࢸࣥࢩࣕࣝࡀ⌧ࢀࡿࡢ࡛ࠊSCF ࢆ⾜࠺ࠋCI, MPn ࡞࡝࡟ࡶᒎ㛤࡛ࡁࡿࠋNΨξ 1 ,..., ξ N    φ nI ξ I 

䠄ᘧ 1䠅

I 1

T̂( I )  V̂1 ( I ) 

N

N

K 1
KI

J 1
JI

 ( K ) V̂2 (1  N )  ( J )  ( I )  ε I ( I )䚷 䠄ᘧ 2䠅

㏻ᖖ༢࣮ࣔࢻ㛵ᩘࡣࠊ኱ᇦⓗ㛵ᩘ࡛࠶ࡿㄪ࿴᣺ືᏊࡢἼື㛵ᩘ(HOB)࡛ᒎ㛤ࡍࡿࠋἼື㛵ᩘࡢᡂศࡀゎࡿࡢ࡛ᐇ㦂ࢫ࣌ࢡࢺࣝࡢゎ㔘ࡀࡋࡸࡍ࠸཯㠃ࠊከᴟᑠ PES ࡸ㧗᣺ືບ㉳≧ែࡢၥ㢟࡬ࡢ㐺⏝ࡣ㞴ࡋ࠸ࠋFGH ࡣࠊ᱁ᏊⅬࡸᑠ㡿ᇦ࡟ᒁᅾ໬ࡋࡓᇶᗏ㛵ᩘࢆ⨨࠸࡚ᩘ್ⓗ࡟ࢩ࣮ࣗࣞࢹ࢕ࣥ
࣮࢞᪉⛬ᘧࢆゎࡃ᪉ἲࡢ୍ࡘ࡛ࠊᇶᗏ࡟ Dirac ࡢ Delta 㛵ᩘ(DDF)ࢆ⏝࠸ࡿࠋከᴟᑠࡸ㧗᣺ື‽఩ࡶゎࡅࡿࡀࠊ㧗⢭ᗘ໬࡟ࡣ᱁ᏊⅬᩘࢆከࡃ࡜ࡿᚲせࡀ࠶ࡿࠋ༢⣧ἲ࡛ࡣ 3 ḟඖࡀᐇ⏝ⓗ࡞㝈⏺
࡜ᛮࢃࢀࡿࡀࠊHartree ✚ࡢ㏆ఝࢆ౑࠼ࡤ FGH ࡛ᢅ࠼ࡿ⮬⏤ᗘࢆ኱ࡁࡃ࡛ࡁࡿࠋ ࡑࡇ࡛ࠊPES ࢆᇶ‽ᗙᶆࡢከ㡯ᘧ࡛㏆ఝࡋࠊ௚࣮ࣔࢻ࡜ࡢ⤖ྜࡸ㠀ㄪ࿴ᛶࡀᑠࡉ࠸࣮ࣔࢻ࡟ࡣ
VSCF/HOBࠊ࣏ࢸࣥࢩࣕࣝ᭤㠃ࡀ」㞧࡞࣮ࣔࢻ࡟ࡣ FGH-Hartree ἲࢆ⏝࠸ࡓࠋVSCF/HOB ἲ࡛ࠊࣁ࣑ࣝࢺࢽ࢔ࣥ⾜ิせ⣲ィ⟬ࡣࠊHermite ከ㡯ᘧࡢ₞໬ᘧࢆ⏝࠸࡚⢭ᐦ໬࡜㧗㏿໬ࢆᅗࡗࡓࠋ
༢⣧࡞ Nf(⮬⏤ᗘᩘ)ḟඖࡢ FGH ࡛ࡣࠊ㸯⮬⏤ᗘ࠶ࡓࡾ᱁Ꮚᩘ(NG)ࡢ Nf ஌ಶ(NGNf)ࡢ PES ࢹ
࣮ࢱࢆせࡋࠊ㸲ḟඖ௨ୖ࡛ࡣࡇࡢᅇᩘ㟁Ꮚ≧ែィ⟬ࢆ⾜࠺ࡇ࡜ࡍࡽ⌧ᐇⓗ࡛࡞࠸ࠋࡓ࡜࠼ NGNf ಶࡢࢹ࣮ࢱࡀ⏝ព࡛ࡁ࡚ࡶᐇຠ࣏ࢸࣥࢩࣕࣝࡢィ⟬࡟せࡍࡿࢥࢫࢺࡣ O(Nf NGNf)࡜࡞ࡾࠊ
NH3(Nf=6)࡛ NG ࡀࢃࡎ࠿ 31 ࡛ࡶ 6316 ࡟㐩ࡍࡿࠋࡇࢀ࡟ᑐࡋணࡵ PES ࡀ㡯ᩘ Nt ಶࡢᘧ࡛⾲ࡉࢀ࡚࠸ࡿ࡜ࠊᑐᛂࡍࡿࢥࢫࢺࡣ O(NfNtNG)࡜࡛ࡁࡿࡇ࡜ࢆぢฟࡋ࡚ࠊ㧗㏿ィ⟬࡟ά࠿ࡋࡓࠋ
࠙⤖ᯝࠚึࡵ࡟ H2O ࡛ Hatree ✚࡟ࡼࡿ㏆ఝࡢຠᯝࠊVSCF ࡜ FGH-Hartree ࡢ⢭ᗘࢆ᳨ウࡋࡓ⤖ᯝࢆ♧ࡍࠋPES ࡣ MP4/aug-cc-pVTZ ࡢ࢚ࢿࣝࢠ࣮ࢆࠊᏳᐃᵓ㐀ࢆཎⅬ࡜ࡋᇶ‽ᗙᶆ࡛ 3 ࣮ࣔ⾲ 1. H2O ࡢᇶᮏ᣺ືᩘ(cm-1)ࡢィ⟬್. ᑐ⛠ఙ⦰(1)ࠊኚゅ(2)ࠊ㠀ᑐ⛠ఙ⦰(3)ㄪ࿴

VSCF0a

VSCF

VSCF

FGH-H㹠

FGH-CIc

3DFGHd

ᐇ㦂್

1

3794

3711

3688

3677

3695

3623

3628

3657

2

1638

1625

1581

1577

1581

1574

1573

1595

3

3910

4003

3856

3745

3889

3740

3755

3756

 a ྛ࣮ࣔࢻࡢ㧗ḟ㡯ࡢࡳ⪃៖. bFGH-Hartree ἲ. c 㓄⨨ᩘࡣ 103. d3 ḟඖ FGH ἲࢻ஺ᕪࡲ࡛⪃៖ࡋ 6 ḟࡢ㛵ᩘ࡛㏆ఝࡋࡓࠋ⾲㸯࡟ᇶᮏ᣺ືᩘࡢィ⟬⤖ᯝࢆ♧ࡋࡓࠋ3DFGH ࡣࠊ
313 ಶࡢ᱁ᏊⅬࢆ౑ࡗ࡚㸱ḟඖ FGH ἲ࡛ࡲ࡜ࡶ࡟ゎ࠸ࡓ⤖ᯝ࡛ࠊᐇ㦂್࡜ࡼࡃ୍⮴ࡋ࡚࠸ࡿࠋ
VSCF ࡛ࡣࠊྛ࣮ࣔࢻ 10 ಶࡢ HOB ᇶᗏࢆ⏝࠸ࡓࠋVSCF0 ࡣ࣮ࣔࢻࡈ࡜࡟㧗ḟ㡯㸦㠀ㄪ࿴ᛶ㸧ࡢࡳ⪃៖ࡋ㸯ᅇࡢᑐゅ໬࡛ィ⟬ࡋࡓ⤖ᯝ࡛࠶ࡿࠋVSCF0 ࠿ࡽ VSCF ࡬ࡢኚ໬ࡀࠊ஺ᕪ㡯ࡢຠᯝ࡟ࡼࡿࡶࡢ࡛࠶ࡿࠋ㠀ᑐ⛠ఙ⦰ࡢ᣺ືᩘࡀ VSCF0 ࡛ㄪ࿴ࡼࡾ㧗ࡃ࡞ࡾࠊVSCF ࡛ୗࡀࡿࠋᑐ⛠ఙ⦰࡜ኚゅ᣺ືࡢ㠀ㄪ࿴ᛶࡢࡓࡵ OH ㊥㞳ࡢᮇᚅ್ࡣ PES ᴟᑠࡢ್ࡼࡾ㛗ࡃࠊఙࡧࡓ఩⨨࡛ࡢ㠀ᑐ⛠ఙ⦰ࡢ PES ࡢ᭤⋡ࡀᑠࡉࡃ࡞ࡿࡇ࡜ࡀࠊᐇຠ࣏ࢸࣥࢩࣕࣝࢆ㏻ࡌ࡚⌧ࢀ࡚࠸ࡿࠋVSCF
ࡣບ㉳‽఩࡛᭱㐺໬ࡋࡓ࢚ࢿࣝࢠ࣮ࢆ⏝࠸࡚ィ⟬ࡋࡓ᣺ືᩘ࡛ࠊᐇ㦂್࡜⣙ 1%ࡢㄗᕪ࡟཰ࡲࡗ
࡚࠸ࡿࠋ
FGH-Hartree ࡛ࡣྛ࣮ࣔࢻ࡟ 125 Ⅼࡢ᱁ᏊⅬࢆྲྀࡗࡓࠋVSCF ࡜ FGH-Hartree ࡣ࡯ࡰྠࡌ⤖ᯝࢆ୚࠼ࡿࠋCI ࡛㠀ᑐ⛠ఙ⦰ࡢ᣺ືᩘࡀ኱ᖜ࡟ᨵၿࡉࢀࠊ3D-FGH ࡸᐇ㦂್࡜ࡼࡃ୍⮴ࡋࡓࠋḟ࡟ NH3 ࡢച཯㌿ࢆ⪃៖ࡋ࡚ࠊ஧ᴟᑠၥ㢟࡟ྲྀࡾ⤌ࢇࡔࠋPES ࡣ㑄⛣≧ែࢆཎⅬ࡜ࡋ࡚ࠊ
MP2/aug-cc-pVDZ ࡢ࢚ࢿࣝࢠ࣮ࢆᇶ‽ᗙᶆࡢ᭱኱ 14 ḟࡢ㛵ᩘ࡛⾲ࡋࡓࠋ2 ࣮ࣔࢻࡢ஺ᕪ㡯ࡣྲྀࡾ㎸ࢇࡔࡀࠊ3 ࣮ࣔࢻ௨ୖࡢ஺ᕪࡣ඲࡚↓どࡋࡓࠋ⾲  ࡟ച཯㌿࣮ࣔࢻࡢ㸦2㸧ࡢ᣺ືᩘࢆಸ㡢ࡲ࡛ྵࡵ࡚ࠊࡲࡓ௚ࡢ࣮ࣔࢻࡣᇶᮏ᣺ືᩘࢆ♧ࡋࡓࠋFGH-Hartree ࡜ CI ࡣྛ࣮ࣔࢻ 125 Ⅼࡢ᱁Ꮚ
Ⅼࢆ⏝࠸ࡓࠋࡲࡓ CI ࡛⪃៖ࡋࡓ㓄⨨ࡣച཯㌿࡟ 9ࠊṧࡾࡣྛ࣮ࣔࢻ 3 ࡢྜィ 935 ࡛࠶ࡿࠋPESࡢ⢭ᗘ࠿ࡽ 1cm-1 ௨ୗࢆ㆟ㄽ࡛ࡁ࡞࠸ࡀࠊFGH-Hartree ࡛ࡶ2 ࡢࢺࣥࢿࣝศ⿣ࢆฟࡍࡇ࡜ࡀ࡛ࡁ
ࡿࠋFGH-CI ್࡛ࡶ኱ᖜ࡟ᨵၿࡉࢀࡿࠋ௚ࡢ࣮ࣔࢻࡢᇶᮏ᣺ືᩘࡶྵࡵ࡚⤯ᑐ್ࡢᐇ㦂࡜ࡢ୍⮴ࡣ‶㊊࡛ࡁࡿࡶࡢ࡛ࡣ࡞࠸ࡀࠊ୺࡞ཎᅉࡣ PES ࡟࠶ࡿࡢ࡛ࠊ⌧ᅾᨵⰋ࡟ྲྀࡾ⤌ࢇ࡛࠸ࡿࠋ⾲ 2 ࡢ
Hybrid ࡣࠊཎⅬ࡛ PES ࡀᴟ኱࡟࡞ࡗ࡚࠸ࡿച཯㌿ࡢ 1 ࣮ࣔࢻࡢࡳࢆ FGH ࡛ᢅ࠸ࠊ௚ࡢ࣮ࣔࢻ
࡟ࡣ HOB ࢆ⏝࠸ࡓ VSCF ࡢ⤖ᯝ࡛࠶ࡿࠋHOB ࡣᏳᐃᵓ㐀࡛ࡣࡃࠊ㑄⛣≧ែ࡛ࡢㄪ࿴᣺ືᏊࡢἼ
ື㛵ᩘࢆ⏝࠸࡚࠸ࡿࠋẚ㍑ᑐ㇟ࡣ FGH-Hartree ࡛ࠊ஫࠸࡟ఝࡓ⤖ᯝ࡜࡞ࡗ࡚࠾ࡾࠊࡉࡽ࡟ CI ࡛ẚ㍑ࡍࡿࡓࡵࣉࣟࢢ࣒ࣛ㛤Ⓨࢆ㐍ࡵ࡚࠸ࡿࠋ
⾲ 2. NH3 ࡢച཯㌿࣮ࣔࢻ㸦2㸧ࡢᇶ㡢ࠊಸ㡢࡜௚ࡢ࣮ࣔࢻࡢᇶᮏ᣺ືᩘ(cm-1)
2

ᐇ㦂್

FGH-

FGH-

H

CI

ᐇ㦂್

Hybrid

FGH-H

FGH-

Hybrid

CI

0-

0.66

1.24

1.98

1.20

1+

932.24

1355

983

1360

1-

968.08

1365

1049

1366

2+

1597.4

2496

1730

2501

2-

1910

2617

2289

2571

1

3336

3283

3216

3280

4

3444

3709

3625

3640

5

1628

1454

1430

1453

3P122ࣂࢵ࣒࣏࢟ࣥ࢞ࢸࣥࢩࣕࣝࢆ⏝࠸ࡓከ⎔ⰾ㤶᪘Ⅳ໬Ỉ⣲ࡢ⤖ᬗᵓ㐀᥈⣴
㸦㟁㏻኱㝔᝟⌮ᕤ㸧‫ۑ‬ఀ⸨㑈ࠊᒣ໭ెᏹ
Buckingham potential imposed crystal structure search of polycyclic aromatic hydrocarbons
㸦University of Electro-Communications㸧‫ۑ‬Ryo Ito and Yoshihiro Yamakita࠙ᗎࠚከ⎔ⰾ㤶᪘Ⅳ໬Ỉ⣲(PAH)࡟ࡣ㧗࠸㟁Ꮚࡢ⛣ືᗘࡀ࠶ࡿࡇ࡜ࡀሗ࿌ࡉࢀ࡚࠾ࡾࠊ᭷ᶵࢹࣂ࢖ࢫ࡬
ࡢ฼⏝ࡸᇶ♏◊✲ࡀ࡞ࡉࢀ࡚࠸ࡿࠋඃࢀࡓᑟ㟁ᛶࡣ࣌ࣥࢱࢭࣥࠊࢸࢺࣛࢭࣥࠊ࣌ࣜࣞࣥࠊࣝࣈࣞ
ࣥ࡞࡝ࡢ PAH ࡛☜ㄆࡉࢀ࡚࠸ࡿࠋ⤖ᬗᵓ㐀ࡣ≀ᛶ࡟኱ࡁࡃᙳ㡪ࢆཬࡰࡍࡓࡵࠊᐇ㦂࡛ᚓࡽࢀࡓ⤖ᬗᵓ㐀ࢆ⌮ㄽⓗ࡟⿬௜ࡅࡿࡇ࡜ࡀᚲせ୙ྍḞ࡛࠶ࡿࠋࡋ࠿ࡋࠊィ⟬ᑐ㇟࡜ࡍࡿཎᏊᩘࡀከ࠸ࡓࡵ
➨୍ཎ⌮ィ⟬࡛ࡣ㛗࠸ィ⟬᫬㛫ࡀᚲせ࡜࡞ࡿࠋࡲࡓࠊ᱁Ꮚᐃᩘࡔࡅ࡛࡞ࡃศᏊ㓄ྥࡢ⮬⏤ᗘࡶ⪃៖ࡍࡿࡍࡿᚲせࡀ࠶ࡾࠊ↓ᶵ⤖ᬗ࡜ẚ㍑ࡋ࡚」㞧࡞ィ⟬ࢆせࡍࡿࠋࡇࡢࡼ࠺࡞ၥ㢟ࡀ࠶ࡾࠊ⤖ᬗᵓ㐀ࢆ⮬ື᥈⣴࡛ࡁࡿ࢔ࣝࢦࣜࢬ࣒ࡣᮍ㛤Ⓨ࡛࠶ࡿࠋࡇࢀࡲ࡛ᡃࠎࡣࠊཎᏊ㛫㊥㞳ࡢࡳ࡟౫Ꮡࡋ
ࡓ⤒㦂ⓗ࡞࣏ࢸࣥࢩ࡛ࣕࣝ࠶ࡿࣂࢵ࣒࣏࢟ࣥ࢞ࢸࣥࢩࣕࣝࢆ⏝࠸ࠊ᱁Ꮚᐃᩘ࡜✵㛫⩌ࢆᐇ㦂್࡟ᅛᐃࡋ࡚ࣔࣥࢸ࢝ࣝࣟἲ࡟ࡼࡿศᏊ㓄ྥࡢ᭱㐺໬ィ⟬ࢆ⾜࠸ࠊᐇ㦂ࢆⰋዲ࡟෌⌧ࡍࡿࡇ࡜ࢆ♧ࡋ࡚ࡁࡓࠋࡇࡢᵝ࡞⤖ᯝ࠿ࡽࠊࣂࢵ࣒࣏࢟ࣥ࢞ࢸࣥࢩࣕࣝࢆ⏝࠸࡚ PAH ศᏊࡢ⤖ᬗከᙧࢆᚓࡽࢀࡿ
࡜⪃࠼ࡽࢀࡿࠋࡋ࠿ࡋࠊ᱁Ꮚᐃᩘࡢ⮬⏤ᗘࡣ 6ࠊศᏊ㓄ྥࡢ⮬⏤ᗘࡣ 1 ศᏊ࡟ࡘࡁ 3 ࡛࠶ࡿࡢ࡛ࠊ
㓄ྥࢆ᭱㐺໬ࡍࡿศᏊᩘࡀ N ࡢ࡜ࡁࠊ᭱㐺໬ࡍࡿ⮬⏤ᗘࡣ඲㒊࡛ 3N+6 ࡜࡞ࡾࠊࣔࣥࢸ࢝ࣝࣟἲ
ࡼࡾࡶຠ⋡ⓗ࡞ィ⟬ࢆ⾜࠺ᚲせࡀ࠶ࡿࠋࡑࡇ࡛ᮏ◊✲࡛ࡣࠊࣔࣥࢸ࢝ࣝࣟἲ࡛ศᏊ㓄ྥࢆ᭱㐺໬ࡋࡓᚋ࡟᭱ᛴ໙㓄ἲࢆ⏝࠸࡚⤖ᬗᵓ㐀඲యࡢ᭱㐺໬ィ⟬ࢆ⾜ࡗࡓࠋࣔࣥࢸ࢝ࣝࣟἲ࡛ࡣ᭱Ᏻᐃ࡞
ศᏊ㓄ྥࡋ࠿᥈⣴࡛ࡁ࡞࠿ࡗࡓࡀࠊࡇࢀ࡟ࡼࡾ᱁Ꮚᐃᩘࡢ᭱㐺໬ࡀᐇ⾜ྍ⬟࡟࡞ࡗࡓࡇ࡜࡟ຍ࠼ࠊ
‽Ᏻᐃᵓ㐀ࡶᚓࡽࢀࡿࡼ࠺࡟࡞ࡗࡓࠋ࠙ィ⟬ࠚศᏊ㛫┦஫స⏝ࡢィ⟬ࡣࠊᘧ(1)࡛୚࠼ࡽࢀࡿࣂࢵ࣒࣏࢟ࣥ࢞ࢸࣥࢩ࡛ࣕࣝ⾜ࡗࡓࠋAij, Bij, Cij ࡢ⤌ࡣ CC, CH, HH 㛫࡟ࡘ࠸࡚࡜ࡗࡓᐃᩘ࡛ࠊᩥ⊩[1]ࡢϫࢆ⏝࠸ࡓࠋ᭱ᛴ໙㓄ἲࡢィ⟬ࡣࠊ᱁Ꮚ࢚
ࢿࣝࢠ࣮U ࡢゎᯒⓗ୍ḟᑟ㛵ᩘ∂U/∂a~∂U/∂c, ∂U/∂α~∂U/∂γ, ∂U/∂θA1~∂U/∂θCN(N ࡣ༢఩᱁Ꮚ୰ࡢศᏊᩘ)ࢆ⏝࠸ࠊศᏊࡢ㔜ᚰࡢ Wyckoff position ࢆᅛᐃࡋ࡚ᐇ᪋ࡋࡓࠋࡇࡇ࡛ࠊa~γ ࡣ᱁Ꮚᐃᩘ㸪θA~θC
ࡣ័ᛶ୺㍈࿘ࡾࡢᅇ㌿ゅ࡛࠶ࡿࠋศᏊ㦵᱁ࡣணࡵ Gaussian 03 ࡛ᵓ㐀᭱㐺໬ࡋࡓᵓ㐀࡟ᅛᐃࡋ࡚⏝࠸ࠊ➨ 3 ㏆᥋᱁Ꮚࡲ࡛ࡢ┦஫స⏝ࢆィ⟬ࡋࡓࠋࡇࢀ௨ୖ⠊ᅖࢆ኱ࡁࡃࡋ࡚ࡶࠊィ⟬᫬㛫ࡣ኱ᖜ࡟ቑ࠼ࡿࡀࠊU ࡢኚ໬ࡣ 3 %ᮍ‶࡛࠶ࡿࡇ࡜ࢆ☜ㄆࡋࡓࠋࣔࣥࢸ࢝ࣝࣟィ⟬࡛ࡣࠊX ⥺⤖ᬗᵓ㐀ゎᯒ࡟ࡼࡾỴᐃࡉࢀ࡚࠸ࡿ᱁Ꮚᐃᩘ[2]࡟ᅛᐃࡋࡓࡲࡲศᏊ㓄ྥࡢࡳᏳᐃᵓ㐀᥈⣴ࢆ⾜࠸ࠊࡑࡇ࠿ࡽ
᭱ᛴ໙㓄ἲ࡛᱁Ꮚᐃᩘ࡜ศᏊ㓄ྥࢆ୍ᗘ࡟᭱㐺໬ࡋࡓࠋ
Eij (r) = Aij r-6 + Bij exp(-Cij r) ; i, j = C, H

(1)࠙⤖ᯝ࡜⪃ᐹࠚᅗ㸯࡟᭱ᛴ໙㓄ἲ࡟ࡼࡾ᭱㐺໬ࡉࢀࡓ࣌ࣥࢱࢭࣥࡢ⤖ᬗከᙧࢆ♧ࡋࡓࠋᵓ㐀ղࡣᐇ㦂ⓗ࡟☜ㄆࡉࢀ࡚࠸ࡿᵓ㐀[3]ࢆⰋዲ࡟෌⌧ࡋ࡚࠸ࡿࠋ࣌ࣥࢱࢭࣥࡢ᱁Ꮚ࢚ࢿࣝࢠ࣮U ࡣ-158.1 kJ/mol ࡜ᐇࡉࢀ࡚࠾ࡾ[4]ࠊㄗᕪ 3 kJ/mol ௨ෆࡢ⢭ᗘ࡛෌⌧ࡍࡿࡇ࡜ࡀ࡛ࡁࡓࠋ⾲㸯ࡣ᭱ᛴ໙㓄ἲ࡛᭱㐺໬ᚋࡢ᱁Ꮚ࢚ࢿࣝࢠ࣮U ࠾ࡼࡧ᭱ᛴ໙㓄ἲ࡛ࡢࣔࣥࢸ࢝ࣝࣟἲ࠿ࡽࡢ U ࡜᱁Ꮚᐃᩘࡢኚ໬㔞ࢆ♧ࡋ࡚࠸ࡿࠋศᏊ㓄ྥࡣ࠶ࡽ࠿ࡌࡵࣔࣥࢸ࢝ࣝࣟἲ࡛Ᏻᐃᵓ㐀᥈⣴ࢆ⾜ࡗࡓࡓࡵࠊ∆U ࡣ୺࡟᱁Ꮚᐃᩘࡢ
ኚ໬࡟ࡼࡿᐤ୚࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿࠋ|∆U|ࡣᵓ㐀ղ࡛᭱ᑠ࡜࡞ࡾࠊ᱁Ꮚᐃᩘࡢኚ໬ࡣࠊ኱ࡁࡃ࡚
ࡶ᱁Ꮚ㍈࡟㛵ࡋ࡚⣙ 0.2 Å㸪㍈ゅ࡟㛵ࡋ࡚⣙ 0.01°࡛࠶ࡗࡓࠋࡇࢀࡣࠊ᭱ᛴ໙㓄ἲ࡟ࡼࡿィ⟬ࡢ๓ᚋ࡛⤖ᬗᵓ㐀ࡀ࡯࡜ࢇ࡝ኚ໬ࡏࡎࠊᐇ㦂ⓗ࡟ᚓࡽࢀࡓ᱁ᏊᐃᩘࢆⰋዲ࡟෌⌧ࡋ࡚࠸ࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿࠋࡘࡲࡾࣔࣥࢸ࢝ࣝࣟἲ࡜᭱ᛴ໙㓄ἲࢆ⤌ࡳྜࢃࡏࡿ࡜ࠊ᱁Ꮚᐃᩘࢆࡇࡢ⛬ᗘࡢ⢭ᗘ࡛ᐇ㦂ࢆ෌⌧࡛ࡁࡿ࡜⪃࠼ࡽࢀࡿࠋ
ᮏ◊✲ࡢィ⟬࡛ࡣᵓ㐀ձࡀ᭱Ᏻᐃ࡛ࠊᐇ㦂ࢆ෌⌧ࡋ࡚࠸ࡿᵓ㐀ղࡣ 2 ␒┠࡟Ᏻᐃ࡜ィ⟬ࡉࢀࡓࠋᵓ㐀ձࡣᵓ㐀ղࡢศᏊࡢ㔜ᚰ㛫㊥㞳ࢆẚ㍑ࡍࡿ࡜ࡑࡢᕪࡣ 0.85 Å ࡛࠶ࡿࠋᵓ㐀ղ࡜௚ࡢᵓ㐀ࢆẚ
㍑ࡍࡿ࡜ࠊࡇࡢᕪࡣ 1.52~4.35 Å ࡛ࠊᵓ㐀ղ࡜ศᏊࡢ㔜ᚰ㛫㊥㞳ࡀ㏆࠸್ࡢ࡜ࡁ࡟Ᏻᐃ࡟࡞ࡿഴྥ
ࡀ☜ㄆࡉࢀࡓࠋ
ձ

ճ

ղ

ն

յ

մ

շ

ᅗ㸯㸬ᮏ◊✲࡛ィ⟬ࡉࢀࡓ࣌ࣥࢱࢭࣥࡢ⤖ᬗከᙧ⾲㸯㸬᭱ᛴ໙㓄ἲ࡟ࡼࡿ᱁Ꮚ࢚ࢿࣝࢠ࣮࡜᱁Ꮚᐃᩘࡢኚ໬᱁ࢿ ࢠ᱁ ᐃᩘ ኚ 
Wyckoff
positionU / kJmol-1∆U / kJmol-1∆a / Å

∆b / Å

∆c / Å ∆α / deg ∆β / deg ∆γ / degձ-164.6-9.3-0.176-1.016

0.085

0.021

0.010

0.021

c

ղ

-161.5-0.5-0.225-0.216-0.1570.008-0.001-0.001eճ

-155.3-5.7-0.175-0.483-0.391

0.059

0.003

0.016

b

մ

-154.6

-31.5

0.596

-0.981-0.699

0.040

0.040

0.090

d

յ

-149.6-3.1-0.330-0.247-0.1700.005-0.011

0.002

f

ն

-147.4-2.4-0.239-0.348-0.0910.011-0.012

0.000

g

շ

-145.6-4.0-0.320-0.333-0.1920.007-0.011

0.000

h

࠙ᘬ⏝ࠚ
[1] D. E. Williams, J. Chem. Phys., 45, 3770 (1966).
[2] R. B. Campbell, J. M. Robertson, and J. Trotter, Acta Cryst., 15, 289 (1962).
[3] H. Yoshida and N. Sato, Phys. Rev. B, 77, 235205 (2008).
[4] N. Wakayama and H. Inokuchi, Bull. Chem. Soc. Jpn., 40, 2267 (1967).

3P123㍍㔠ᒓࢆ⏝࠸ࡓ୰㛫ⓗ࡞྾╔ຊࢆࡶࡘỈ⣲྾╔ศᏊࡢ⌮ㄽⓗ᥈⣴(ᮾᾏ኱⌮) ‫ۑ‬ᆏᮏ ❶ࠊ▼ᕝ ⁠Theoretical search of the adsorbent molecules for hydrogenwith a middle adsorption force using light metals(Tokai Univ.) ‫ۑ‬Akira Sakamoto, Shigeru Ishikawa
࠙ᗎࠚ୍⯡࡟ศᏊ㛫ຊࡣࠊ㸦㸯㸧㐲㊥㞳࠿ࡽാࡃྂ඾ⓗ࡞ࢡ࣮ࣟࣥຊ࡟⏤᮶ࡍࡿᘬຊࠊ㸦㸰㸧㏆㊥㞳࡛ാࡁࡣࡌࡵࡿ㔞Ꮚㄽ࠿ࡽᑟ࠿ࢀࡿ໬Ꮫ⤖ྜ࡟࠶ࡎ࠿ࡿᘬຊࠊ
㸦㸱㸧ࡈࡃ㏆㊥㞳࡛ാࡃࣃ࢘ࣜࡢ
ཎ⌮࡟ᇶ࡙ࡃ᩺ຊࡢ୕ࡘ࡟ศ㢮ࡉࢀࡿࠋ㸦㸯㸧ࡢຊ࡟ࡣ㓄ྥຊࠊㄏ㉳ຊࠊศᩓຊ࡞࡝ࡀ࠶ࡾࠊ
㸦㸰㸧ࡢຊ࡟ࡣ㟁Ⲵ⛣ືຊ࡜஺᥮ຊࡀ࠶ࡿࠋ
㸦㸱㸧ࡢຊࡣ஺᥮᩺ຊ࡜࿧ࡤࢀࠊ㛢ࡌࡓ㟁ᏊẆྠኈࡀ᥋㏆ࡍࡿ࡟ᚑࡗ࡚ⴭࡋࡃቑ኱ࡍࡿࠋศᏊࡢᅛయ⾲㠃࡬ࡢ྾╔࡟ࡣࠊ㸦㸯㸧࡜㸦㸰㸧ࡢຊ࡟ᇶ࡙ࡃ஧ࡘࡢᶵ
ᵓࡀ࠶ࡾࠊࡑࢀࡒࢀ≀⌮྾╔࡞ࡽࡧ࡟໬Ꮫ྾╔࡜࿧ࡤࢀ࡚࠸ࡿࠋࡇࢀࡽࡢ྾╔࢚ࢿࣝࢠ࣮ࡢ඾ᆺ
ⓗ࡞኱ࡁࡉࡣࠊ≀⌮྾╔࡛ 0.2 eVࠊ໬Ꮫ྾╔࡛ 2 eV ࡯࡝࡛࠶ࡿࠋ㏆ᖺࠊ⇞ᩱ㟁ụ㥑ື㌴ࡢᐇ⏝໬࡟ྥࡅ࡚ࠊ㍍㔞࡛㧗ᐦᗘࡢỈ⣲㈓ⶶᮦᩱࡀồࡵࡽࢀ࡚࠸ࡿࠋ≀⌮྾╔ᮦᩱ࡛ࡣࠊỈ⣲ศᏊࡢ྾╔ຊࡀ 0.050.1 eV ࡜ᑠࡉ࠸ࡓࡵࠊ኱ᐜ㔞㈓ⶶࡢࡓࡵ࡟ࡣ㧗ᅽ࠿ࡘᴟపࡀᚲせ࡛࠶ࡾࠊ୍᪉ࠊ

໬Ꮫ྾╔ᮦᩱ࡛ࡣࠊ኱ࡁ࡞໬Ꮫ⤖ྜ࢚ࢿࣝࢠ࣮ࡸάᛶ໬࢚ࢿࣝࢠ࣮࡟⏤᮶ࡍࡿ⇕໬Ꮫୖ࡞ࡽࡧ࡟
㏿ᗘㄽୖࡢㄢ㢟ࡀ࠶ࡿࠋࡑࡇ࡛ᮏ◊✲࡛ࡣࠊ㸦㸯㸧࡜㸦㸰㸧ࡢຊࢆ⤌ࡳྜࢃࡏ࡚ࠊࡑࢀࡽࡢ୰㛫ࡢຊ࡛Ỉ⣲ศᏊࢆ྾╔ࡍࡿ⣔ࡢᐇ⌧ᛶࢆ⌮ㄽⓗ࡟᳨ウࡋࡓࠋ㑅ࢇࡔ┦஫స⏝⣔ࡣ࢝ࢳ࢜ࣥ̿㛢ẆศᏊ࡛࠶ࡿࠋࡇࡢ⣔ࡢศᏊ㛫ຊࡣࠊ㐲㊥㞳࡛ࡣ࢝ࢳ࢜ࣥࡀศᏊ࡟ཬࡰࡍㄏ㉳ຊࡀᨭ㓄ⓗ࡛ࠊ㏆㊥㞳࡛ࡣศᏊ࠿ࡽ࢝ࢳ࢜ࣥ࡬㟁Ꮚࡀ⛣ືࡍࡿࡇ࡜࡛㟁Ⲵ⛣ືຊࡀാࡃࠋ㟁Ⲵ⛣ືࡢࡋ᫆ࡉࡣࠊ࢝ࢳ࢜
ࣥࡢ㟁Ꮚぶ࿴ຊ࡜ศᏊࡢ࢖࢜ࣥ໬࢚ࢿࣝࢠ࣮࡟౫Ꮡࡍࡿࠋᡭጞࡵ࡟⡆༢࡞⣔ࢆ㑅ࢇ࡛ࠊࡑࡢศᏊ
㛫ຊࡢᡂศࢆศᏊ㌶㐨ἲ࡛ゎᯒࡋࡓࠋ࢝ࢳ࢜ࣥ࡟ࡣ Li+࡜ Be2+ࠊศᏊ࡟ࡣ He ࡜ H2 ࢆ㑅ࢇࡔࠋ࠙⌮ㄽࠚ㔠ᒓ࢝ࢳ࢜ࣥ࡜㸰㟁Ꮚ㛢Ẇ⣔ศᏊࡢ┦஫స⏝࢚ࢿࣝࢠ࣮ࢆࠊ༢⣧ࣄࣗࢵࢣࣝἲ࡛ồࡵࡓࠋ࢝ࢳ࢜ࣥࡢ LUAO ࡜ศᏊࡢ HOMO ࡢ࢚ࢿࣝࢠ࣮ᕪࢆ߂ߙࠊඹ㬆✚ศࢆߚ࡜ࡍࡿ࡜ࠊ┦஫స⏝࢚ࢿࣝࢠ࣮ࡣࠊ߂ߙ ‫ ب‬െߚࡢ࡜ࡁࠊߚࡢ 2 ḟࡲ࡛࡜ࡿ࡜߂‫ ܧ‬ൌ ʹ ቈെߚଶߚଶെ ቆͳ െ ଶ ቇ ߛ቉              ሺͳሻ߂ߙ߂ߙ࡜⾲ࡉࢀࡿࠋࡇࡇ࡛െߛࡣ 1 㟁Ꮚ࠶ࡓࡾࡢㄏ㉳ຊ࡛࠶ࡿࠋᘧ(1)ࡢ➨ 1 㡯ࡣ㟁Ⲵ⛣ືຊࢆ⾲ࡋࠊ➨ 2㡯ࡣㄏ㉳ຊࢆ⾲ࡋ࡚࠸ࡿࠋ࢝ࢳ࢜ࣥࡢ LUAO ࡟ࡣࠊ㟁Ꮚᐦᗘ࡛ʹߚଶ Ȁ߂ߙ ଶ ࡔࡅࡢ㟁Ⲵ⛣ືࡀ࠶ࡿࡢ
࡛ࠊࡑࡢศ࢝ࢳ࢜ࣥࡢṇ㟁Ⲵࡣῶᑡࡋㄏ㉳ຊࡣᙅࡵࡽࢀࡿࡀࠊ┦஫స⏝࢚ࢿࣝࢠ࣮඲యࡢ኱ࡁࡉ
ࡣߚࡢቑຍ࡜࡜ࡶ࡟ቑຍࡍࡿࠋࡇࡢࡇ࡜ࢆ⾲⌧ࡍࡿࡓࡵ࡟ࠊ㟁Ⲵ⛣ື࡟ࡼࡗ࡚⏕ࡌࡓඹ᭷⤖ྜࡢᙉ
ࡉࢆ Mayer ࡢ⤖ྜḟᩘࢆࡘ࠿ࡗ࡚ࡣ࠿ࡿࡇ࡜࡟ࡍࡿࠋ⤖ྜḟᩘ B ࡣࠊߚࡢ 2 ḟࡲ࡛࡜ࡿ࡜

‫ܤ‬ൌ

Ͷߚଶ
                     ሺʹሻ߂ߙ ଶ࡜࡞ࡿࠋࡇࢀࢆᘧ(1)࡟௦ධࡋ࡚ࠊ߂‫ ܧ‬ൌ െȟߙ‫ ܤ‬െ ʹߛ             ሺ͵ሻʹࢆᚓࡿࠋࡇࡇ࡛ࠊ߂ߙ െ ɀ ൎ ߂ߙ࡜ࡋࡓࠋ┦஫స⏝࢚ࢿࣝࢠ࣮ࡢ኱ࡁࡉࡣࠊ࢝ࢳ࢜ࣥ࡜ศᏊࡢ᥋㏆࡟ࡼࡗ࡚ㄏ㉳ຊ࡜㟁Ⲵ⛣ືຊ࡟ࡼࡗ࡚ቑຍࡍࡿࡇ࡜ࡀࢃ࠿ࡿࠋ
࠙⤖ᯝࠚMP2/cc-pVTZ ィ⟬࡟ࡼࡗ࡚߂‫ྜ⤖࡜ܧ‬ḟᩘࢆồࡵࡓࠋㄏ㉳ຊ┦஫స⏝㸦െʹߛ㸧ࡣࠊ㊥㞳ࡀR ࡔࡅ㞳ࢀࡓ㟁Ⲵ q ࡢ࢝ࢳ࢜ࣥ࡜ศᴟ⋡DࡢศᏊ࡜ࡢ㛫ࡢ┦஫స⏝െ‫ݍ‬ଶ ߙȀʹܴସ ࡟ࡼࡗ࡚ồࡵࠊⅬ㟁Ⲵィ⟬࡜ẚ㍑ࡋࡓࠋ߂‫ࢆࢀࡇࡽ࠿ܧ‬ᕪᘬ࠸࡚ࠊඹ᭷⤖ྜᛶࡢ┦஫స⏝߂‫ ܧ‬൅ ʹߛࢆồࡵࡓࠋᅗ㸯࡟
Li+He ⣔ࡢ߂‫࡜ܧ‬െʹߛࢆ R ࡢ㛵ᩘ࡜ࡋ࡚♧ࡍࠋ߂‫ ࡣܧ‬R ࡀ 3.65Bohr㸦1.93Å㸧ࡢ࡜ࡁ᭱ᑠ್70 meVࢆ࡜ࡿࠋㄏ㉳ຊࡣⅬ㟁Ⲵィ⟬࠿ࡽồࡵࡓ್࡜ࡼࡃ୍⮴ࡋࠊ߂‫ࡢܧ‬⣙༙ศࢆ༨ࡵ࡚࠸ࡿࡇ࡜ࡀࢃ࠿ࡿࠋ
ᅗ㸰࡟െሺ߂‫ ܧ‬൅ ʹߛሻࢆ⤖ྜḟᩘ࡟ᑐࡋ࡚ࣉࣟࢵࢺࡋ࡚♧ࡍࠋᴟᑠ್㏆ࡃ࡛ࡣ஺᥮᩺ຊࡢᐤ୚ࡀ኱ࡁ
ࡃ࡞ࡿࡢ࡛ࠊR ࡢ⠊ᅖࡣ 9.44 Bohr (5.0 Å)࠿ࡽ 4.72 Bohr (2.5 Å)ࡲ࡛࡜ࡋࡓࠋࡇࡢ⠊ᅖ࡛⤖ྜḟ
ᩘࡣ R ࡢῶᑡ࡟కࡗ࡚ 0.002 ࠿ࡽ 0.042 ࡲ࡛ቑຍࡋࠊᴟᑠ್࡛ࡣ 0.10 ࡜࡞ࡗࡓࠋࡇࡢ⤖ྜḟᩘࡢ
್ࡣ 1 ࡼࡾ࠿࡞ࡾᑠࡉ࠸ࡢ࡛ࠊ㟁Ⲵ⛣ື࡟ࡼࡿㄏ㉳ຊࡢῶᑡࡣ↓ど࡛ࡁࡿࠋᅗ㸰࠿ࡽࠊെሺ߂‫ ܧ‬൅ ʹߛሻࡣ⤖ྜḟᩘ࡟ẚ౛ࡋ࡚ቑຍࡍࡿࡇ࡜ࡀࢃ࠿ࡿࠋ┤⥺ࡢഴࡁ࠿ࡽ߂ߙࢆồࡵࡿ࡜ࠊ0.88 eV ࡜࡞ࡗࡓࠋ
ࡇࡢ್ࡣ߂‫ ࡢܧ‬10 ಸ௨ୖ࡛࠶ࡾࠊ߂ߙ ‫ ب‬െߚǡ ߛ࡜ࡳ࡞ࡏࡿࠋ௨ୖࡢࡇ࡜࠿ࡽࠊ⤖ྜḟᩘࡢᑠࡉ࠸ሙ
ྜ࡟ࠊᘧ(3)ࡢ㏆ఝࡀࡼࡃ࠶࡚ࡣࡲࡿ࡜⤖ㄽ࡛ࡁࡿࠋ ㄏ㉳ຊ࡜㟁Ⲵ⛣ືຊࡢ⤌ࡳྜࢃࡏ࡟ࡼࡾࠊ≀⌮྾╔࡜໬Ꮫ྾╔࡜ࡢ୰㛫ࡢศᏊ㛫ຊࡀᚓࡽࢀࡿ
⣔ࡀ࠶ࡿࡇ࡜ࡀศ࠿ࡗࡓࠋ㟁Ⲵ⛣ືຊࡣศᏊ㛫ຊࢆᙉࡵࡿࡔࡅ࡛ࡣ࡞ࡃࠊࣇࣟࣥࢸ࢖࢔㌶㐨┦஫స⏝ࢆ㏻ࡌ࡚ศᏊ྾╔ࡢ㑅ᢥᛶࢆ୚࠼ࡿࠋᚑࡗ࡚ࠊࡇࡇ࡛ᢅࡗࡓศᏊ㛫┦஫స⏝ࡣࠊỈ⣲㈓ⶶࡢ

10

20

0

18

10

16

20

14

30

12

 'E+2J meV

'E/meVၥ㢟ࡔࡅ࡛ࡣ࡞ࡃࠊゐ፹ࡸ㓝⣲཯ᛂࠊศᏊㄆ㆑࡞࡝࡟῝࠸㛵ࢃࡾࢆࡶࡘࠋ

MP2/ccpVTZ

40

Induction

50

PointCharge1e
60

10
8
6
4

70

2

80

0
2

4

6
R/Bohr8

10

ᅗ䠍 Li+  He┦஫స⏝䜶䝛䝹䜼䞊

0

0.01

0.02
0.03
BondOrder0.04ᅗ䠎 ('E+2J)vsBondOrder0.05

3P124➨୍ཎ⌮ศᏊືຊᏛィ⟬࡟ࡼࡿࣇ࢙ࣟࢭࣥ⮬ᕫ⤌⧊໬༢ศᏊ⭷ࡢ㓟໬㑏ඖ㟁఩ࡢホ౯(㜰኱㝔࣭ᇶ♏ᕤ 1, 㜰኱㝔࣭ᕤ 2)‫⛅ۑ‬ᒣ ⣧ே 1, ව⏣ ᭷ᕼኸ 1, ᶓ⏣ Ὀஅ 1, ✄ᇉ ⪔ྖ 2,
᳃ᕝ Ⰻᛅ 2, ⚟஭ ㈼୍ 1

First-Principles Molecular Dynamics Study on Redox Potential
Evaluation of Ferrocene-Terminated Self-Assembled Monolayer(Graduate School of Engineering Science, Osaka Univ.1,
Graduate School of Engineering, Osaka Univ.2)‫ۑ‬Sumito Akiyama1, Yukio Kaneda1, Yasuyuki Yokota1, Koji Inagaki2,
Yoshitada Morikawa2, Ken-ichi Fukui1࠙ᗎࠚࠚ ≉ᐃࡢᒁᡤ⎔ቃ࡟࠾࠿ࢀࡓ≀㉁ࡢ㓟໬㑏ඖ㟁఩ࢆồࡵࡿࡇ࡜ࡣࠊᇶ♏◊✲ࡢࡳ࡞ࡽࡎࠊ
⵳㟁ࢹࣂ࢖ࢫࡢᛶ⬟ྥୖ࡟࠾࠸࡚ࡶ㔜せ࡛࠶ࡿࠋ⁐ᾮ୰ࡢ࢖࢜ࣥࡢ㓟໬㑏ඖ㟁఩ࡣ⁐፹ࡢ㓄఩ᩘࡸ㟁Ⲵ≧ែࡢኚ໬࡟ࡼࡿ෌㓄ྥ࡟ᙉࡃᙳ㡪ࢆཷࡅࡿࡇ࡜ࡀ▱ࡽࢀ࡚࠾ࡾࠊMarcus ࡟ࡼࡗ࡚ࡑࡢᙳ
㡪ࡀ⌮ㄽⓗ࡟ᑟ࠿ࢀ࡚࠸ࡿ[1]ࠋ
0 ౯↔+1 ౯ࡢ㓟໬㑏ඖ཯ᛂࢆ㉳ࡇࡍࣇ࢙ࣟࢭࣥ(Fc)ࡢㄏᑟయࢆ௚ࡢࢳ࣮࢜ࣝࡢ⮬ᕫ⤌⧊໬༢ศᏊ⭷(SAM)୰࡟ศᩓࡋ࡚྾╔ࡉࡏࡓ㟁ᴟࢆ⏝࠸ࡿ࡜㺂࿘ᅖࢆྲྀࡾᅖࡴศᏊ㙐ࡢ㛗ࡉࡸᐁ⬟ᇶࡢ✀㢮࡟ᛂࡌ࡚㓟໬㑏ඖ㟁఩ࡀኚ໬ࡍࡿࡇ࡜ࡀ▱ࡽࢀ࡚࠾ࡾ[2]ࠊᮏ◊✲࡛ࡣ➨୍ཎ⌮ศᏊືຊᏛィ⟬࡜ Marcus ⌮ㄽࢆ⏝࠸࡚ࠊࡇࡢ౫Ꮡ㛵ಀ࡟ࡘ࠸࡚⌮ㄽⓗ࡟ホ౯ࡍࡿࡇ࡜ࢆ┠ⓗ࡜ࡋࡓࠋ࠙ィ⟬᪉ἲ࡜⌮ㄽࠚࠚ ィ⟬ࣔࢹࣝ࡜ࡋ࡚ࠊFc ࡛⤊➃ࡋࡓࣈࢱࣥ(Fc-SAM)ࡢ࿘ࡾ࡟ࡑࢀࡒࢀ┤㙐ࣈࢱࣥ(Fc_C4)ࠊ┤㙐࣊ࣉࢱࣥ(Fc_C7)ࠊඛ➃࡟ࣄࢻࣟ࢟ࢩࣝᇶࢆ᭷ࡍࡿࣈࢱࣀ࣮ࣝ(Fc_OH)ࢆ㓄ࡋࡓ
3 ✀㢮ࡢ SAM ࡟ᑐᛂࡍࡿࣘࢽࢵࢺࢭ
ࣝ࡟ᑐࡋࠊ㡰࡟ 50, 46, 50 ಶࡢỈศᏊࢆຍ࠼ࡓ⣔ࢆ‽ഛࡋࡓ(Fig. 1)ࠋ඲࡚ࡢ
ศᏊືຊᏛ(MD)ィ⟬ࡣ࿘ᮇቃ⏺᮲௳ࡢୗࠊᖹ㠃Ἴᇶᗏ㛵ᩘࠊᨃ࣏ࢸࣥࢩࣕ
ࣝἲ࡟ᇶ࡙࠸ࡓ DFT ィ⟬ࢥ࣮ࢻ
STATE-Senri ࢆ⏝࠸࡚⾜࠸( ᗘ 300
K)ࠊ஺᥮┦㛵࢚ࢿࣝࢠ࣮࡟ࡣ୍⯡໬໙㓄㏆ఝ(GGA)ࢆ⏝࠸ࡓࠋ ࣘࢽࢵࢺࢭࣝ඲యࡀ㑏ඖ⣔(R)࠿ࡽ
㓟໬⣔(O)࡟ኚ໬ࡍࡿ୍㟁Ꮚ㓟໬ࡢ༙཯ᛂࢆ

Fig. 1. ྛ⣔ࡢᵓ㐀ࡢ MD ୰ࡢࢫࢼࢵࣉࢩࣙࢵࢺ㸦ᕥ࠿ࡽ
Fc_C4, Fc_C7, Fc_OH㸧ࠋⓑࡣỈ⣲ࠊ㉥ࡣ㓟⣲ࠊ⥳ࡣⅣ⣲ࠊ⣸ࡣ㕲ཎᏊࢆ⾲ࡋ࡚࠸ࡿࠋ ՜  ൅ ି ሺͳሻ
࡜⾲ࡍࠋࡇࡇ࡛ N ཎᏊ⣔ࡢཎᏊᗙᶆࢆ RN ࡜ࡋ࡚ࠊᆶ┤࢚ࢿࣝࢠ࣮ࢆ௨ୗࡢࡼ࠺࡟ᐃ⩏ࡍࡿࠋȟ‫ܧ‬ሺࡾே ሻ ൌ ‫ܧ‬ை ሺࡾே ሻ െ ‫ܧ‬ோ ሺࡾே ሻሺʹሻ
ᘧ(2)ࡢ EO ࡜ ER ࡣࡑࢀࡒࢀ㓟໬⣔࡜㑏ඖ⣔࡟࠾ࡅࡿ㟁Ꮚᇶᗏ≧ែࡢ඲࢚ࢿࣝࢠ࣮࡛࠶ࡿࠋMarcus⌮ㄽࢆ⏝࠸ࡿ࡜ḟࡢ㛵ಀᘧࡀᚓࡽࢀࡿ(Fig. 2) [3]ࠋȟ‫ ܣ‬ൌ ሺ‫ۃ‬ȟோ ‫ ۄ‬൅ ‫ۃ‬ȟை ‫ۄ‬ሻΤʹ ሺ͵ሻߣ ൌ ሺ‫ۃ‬ȟோ ‫ ۄ‬െ ‫ۃ‬ȟை ‫ۄ‬ሻΤʹ ሺͶሻࡇࡇ࡛‫ۃ‬ȣ‫⌮≀ࡣۄ‬㔞ȣࡢ࢔ࣥࢧࣥࣈࣝᖹᆒࠊȟ‫ࡣ ܣ‬ᘧ(1)ࡢ
⮬⏤࢚ࢿࣝࢠ࣮ᕪࠊߣ ࡣ෌㓄ྥ࢚ࢿࣝࢠ࣮࡛࠶ࡿࠋ
ලయⓗ࡟ࡣࠊMD ࠿ࡽᚓࡽࢀࡓཎᏊᗙᶆࡢࡶ࡜㟁Ⲵࡢࡳኚ໬ࡉࡏ࡚㟁Ꮚ≧ែィ⟬ࢆ⾜࠸ࠊᆶ┤࢚ࢿࣝࢠ࣮㺂 ȟ‫ܣ‬㺂ߣࢆồࡵࡓࠋ
࠙⤖ᯝ࡜⪃ᐹࠚࠚ ྛ⣔࡛ 2 ps ௨ୖࡢ MD ࢆ⾜࠸ࠊỈࡢືᚄศᕸ㛵ᩘࡸ⾲㠃ᆶ┤᪉ྥࡢཎᏊᐦᗘゎᯒ࠿ࡽ MD ࡀ㐺

Fig. 2. Franck-Condon ཎ⌮࡟ᇶ࡙ࡃ㓟໬㑏ඖ༙཯ᛂࡢ࢚ࢿࣝࢠ࣮ࢲ࢖࢔ࢢ࣒ࣛ

ษ࡞᮲௳ୗ࡛⾜ࢃࢀ࡚࠸ࡿ࠿ࢆ᳨ウࡋࡓࠋFc ࡀ࢔ࣝ࢟ࣝ㙐࡟ᅖࡲࢀࡓ Fc_C7 ࡟࠾࠸࡚㓟໬⣔࡜㑏ඖ⣔࡟࠾ࡅࡿ୰ᚰ㕲ཎᏊ-ỈศᏊ㛫㊥㞳ࡢኚ໬ࡀ᭱ࡶᑠࡉࡃࠊFc ࡀỈ࡟ᅖࡲࢀࡓࡑࡢ௚ࡢ 2 ࡘࡢ⣔࡛ࡼࡾ኱ࡁ࡞ኚ໬ࡀぢࡽࢀࡓ(Table 1)ࠋᑐᛂࡍࡿࡼ࠺࡟ࠊFc ࿘ࡾ࡛ㄏ㟁⋡ࡢప࠸ᵓ㐀ࢆࡶࡘ Fc_C7
ࡢ෌㓄ྥ࢚ࢿࣝࢠ࣮Ȣࡀ᭱ࡶᑠࡉ࡞್࡜࡞ࡗ࡚࠾ࡾ(Table 2)ࠊ෌㓄ྥ࡟ࡼࡿᏳᐃ໬ࡀ㉳ࡇࡾ࡟ࡃ࠸
ࡇ࡜ࢆ⾲ࡋ࡚࠸ࡿࠋ୍᪉ࠊȟ‫ࣝ࢟ࣝ࢔ࡣ್ࡢܣ‬㙐ࡀ㛗ࡃࡼࡾ␯Ỉⓗ࡞ Fc_C7 ࡀ Fc_C4 ࡼࡾࡶᑠࡉࡃ
࡞ࡾࠊᐇ㦂஦ᐇ࡜␗࡞ࡿ⤖ᯝ࡜࡞ࡗࡓࠋFc_C7 ࡛ࡣ෌㓄ྥ࡟ࡼࡿᏳᐃ໬ࡀ㉳ࡇࡾ࡟ࡃ࠸ࡇ࡜࡜ Fc
࿘ࡾ࡛ࡢỈࡀᑡ࡞࠸ࡓࡵ࡟ᆶ┤࢚ࢿࣝࢠ࣮ࡀᑠࡉࡃ࡞ࡾࠊᘧ(3)ࡼࡾȟࡶᑠࡉࡃ࡞ࡿഴྥࡀぢࡽࢀࡓࠋ୍᪉ࠊࡼࡾ␯Ỉⓗ࡞⎔ቃ࡛ࡣ Fc ࡢ㓟໬㑏ඖ㟁఩ࡀᑐ࢔ࢽ࢜ࣥ࡟ࡼࡗ࡚኱ࡁࡃᙳ㡪ࢆཷࡅࡿࡇ
࡜ࡀሗ࿌ࡉࢀ࡚࠾ࡾ[4]ࠊࡼࡗ࡚௒ᅇࡢ⣔࡛ࡣᮏ᮶ࡢ㟁Ẽ໬Ꮫ ᐃ࡟࠾ࡅࡿ᭱Ᏻᐃ≧ែࢆ෌⌧࡛ࡁ࡚࠸࡞࠸ྍ⬟ᛶࡀ⪃࠼ࡽࢀࡿࠋ
ࡉࡽ࡟୍㐃ࡢィ⟬࡛ࡣ඲⣔ࡢ ᗘࡣ 300 K ࡟タᐃࡋ࡚࠸ࡿࡶࡢࡢࠊỈศᏊ࡜ SAM 㒊ศࢆᵓᡂࡍ
ࡿ஧ࡘࡢཎᏊ⩌࡟ࢃࡅ࡚ྛ⣔࡛ ᗘศᕸࡢ᫬㛫ኚ໬ࢆぢ࡚ࡳࡿ࡜ࠊFc_C4 ࡜ Fc_OH ࡛Ỉ㒊ศࡢᗘࡀ㧗ࡃࠊ㏫࡟ SAM 㒊ศࡢ ᗘࡀపࡃ࡞ࡗ࡚࠸ࡿࡇ࡜ࡀࢃ࠿ࡗࡓࠋࡇࢀ࡟ࡼࡗ࡚ࠊMarcus ⌮ㄽࡢ๓ᥦ࡜࡞ࡿᇶᗏ≧ែ௜㏆ࡢ㐺ษ࡞ᗙᶆ఩⨨࡛ࡢ࢚ࢿࣝࢠ࣮࡜ࡣ␗࡞ࡿྍ⬟ᛶࡀ࠶ࡾࠊࡑࢀࡀᐇ
㦂࡜ࡢ┦㐪࡜࡞ࡗࡓ࡜ࡶ⪃࠼ࡽࢀࡿࠋFc_C4 ࡢ⣔࡛ỈࠊSAM 㒊ศࡑࢀࡒࢀࢆタᐃ ᗘ࡛࢔ࢽ࣮ࣝ
ࡍࡿ࡜ Fc-SAM ࡢഴࡁゅࡢኚ໬ࡀぢࡽࢀࡓࠋ⌧ᅾࡇࢀ࡛ᚓࡽࢀࡓᵓ㐀ࢆึᮇᵓ㐀࡜ࡋ࡚෌ࡧ⮬⏤࢚ࢿࣝࢠ࣮ィ⟬ࢆ⾜࡞ࡗ࡚࠾ࡾࠊTable 2 ࡢ್࡜ẚ㍑ࡋ࡚⪃ᐹࡍࡿணᐃ࡛࠶ࡿࠋ
Table 2. ⮬⏤࢚ࢿࣝࢠ࣮ᕪ(ઢ‫࡜)ۯ‬෌㓄ྥ࢚ࢿࣝࢠ࣮ሺૃሻ(eV)

Table 1. Fe ཎᏊ࡜ O ཎᏊཬࡧ H ཎᏊࡢ᭱㏆᥋㊥㞳(Å)

Red state

Ox stateR(Fe-O)

R(Fe-H)R(Fe-O)

R(Fe-H)

Fc_C4

4.78

4.18

4.49

4.34

Fc_C7

4.99

4.50

4.94

4.75

Fc_OH

4.42

3.80

4.27

4.13

ΔA
ΔA vs.FcC4
ΔA vs.FcC4 Exp
λ

[2]

Fc_C4

Fc_C7

Fc_OH

1.86

1.74

1.54

-

-0.13

-0.32

-

0.25

-0.13

0.72

0.64

0.74

࠙ཧ⪃ᩥ⊩ࠚ
[1]. R. A. Marcus, J. Chem. Phys. 24, 966 (1956).
[2]. S. E. Creager, G. K. Rowe, J. Electroanal. Chem. 291, 420 (1997).
[3]. Y. Tateyama, J. Blumberger, M. Sprik and I. Tavernell, J. Chem. Phys. 122, 234505 (2005).
[4]. G. K. Rowe, S.E. Creager, J. Phys. Chem. 98, 5500 (1994).

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3P126㊄ዻ⴫㕙ߦ߅ߌࠆ㘻๺὇ൻ᳓⚛ߩ‛ℂๆ⌕ߦ㑐ߔࠆℂ⺰⊛⎇ⓥ(ᣧᄢవㅴℂᎿ 1, ᣧᄢℂᎿ⎇ 2, JST-CREST3, ੩ᄢ ESICB4)
Ⴆᧄ␭੺ 1㧘੖චᐈᐽᒄ 1㧘ਛ੗ᶈᏈ 1,2,3,4
Theoretical study on the physical adsorption of saturated hydrocarbons on the metal surface(Waseda Univ.1, Waseda Univ. RISE2, JST-CREST3, ESICB4)
Yusuke Tsukamoto1, Yasuhiro Ikabata1, Hiromi Nakai1,2,3,4‫ޤ⸒✜ޣ‬㊄ዻ⴫㕙ߦ߅ߌࠆ㘻๺὇ൻ᳓⚛ߩ⣕᳓⚛෻ᔕ߿↢ᚑ෻ᔕߥߤߩ㊄ዻ⸅ᇦ෻ᔕߪ㧘᭽‫᦭ߥޘ‬ᯏൻว‛ߩᎿᬺ⊛⵾ᴺߣߥߞߡ޿ࠆ‫ߥ߁ࠃߩߎޕ‬㊄ዻ⸅ᇦ෻ᔕࡔࠞ࠾࠭ࡓࠍℂ⺰⊛ߦℂ⸃ߔࠆߚ߼
ߦߪ㧘╙৻Ბ㓏ߢ޽ࠆ㘻๺὇ൻ᳓⚛ߩ㊄ዻ⴫㕙߳ߩ‛ℂๆ⌕ㆊ⒟ࠍᝒ߃ࠆߎߣ߇㊀ⷐߢ޽ࠆ‫‛ޕ‬ℂๆ⌕ߢߪ㧘ๆ⌕቟ቯൻߩਥⷐ࿃߇ಽᢔജߢ޽ࠆߣ⠨߃ࠄࠇࠆ‫ޕ‬ᐔ㕙ᵄၮᐩߦኻߔࠆኒᐲ᳢㑐ᢙ
ℂ⺰(DFT)⸘▚ߢㅢᏱ↪޿ࠄࠇࠆ੤឵⋧㑐᳢㑐ᢙߢߪ㧘ಽᢔജࠍ⸥ㅀߔࠆߎߣ߇࿎㔍ߢ޽ࠆ‫ޕ‬ᧄ⎇ⓥቶߢߪ㧘ಽᢔജࠍ⵬ᱜߔࠆᚻᴺߣߒߡዪᚲᔕ╵ಽᢔജ(LRD)ᴺ[1,2]ࠍ㐿⊒࡮᜛ᒛߒ㧘ࠟ࠙ࠬၮᐩࠍ↪޿ߚ DFT ⸘▚ߢߘߩ᦭ലᕈࠍ⏕߆߼ߡ߈ߚ[3,4]‫⎇ᧄޕ‬ⓥߢߪ㧘ߎߩ LRD ᴺࠍᐔ㕙ᵄၮ
ᐩߩ DFT ⸘▚ߦ᜛ᒛߒ㧘㊄ዻ⴫㕙ߦ߅ߌࠆ㘻๺὇ൻ᳓⚛ߩ‛ℂๆ⌕ㆊ⒟ߦᔕ↪ߔࠆ‫ߦ․ޕ‬㧘ๆ⌕᭴ㅧࠍ⸘▚ߔࠆߚ߼ߦ㧘ᐔ㕙ᵄၮᐩ DFT ⸘▚ࡄ࠶ࠤ࡯ࠫߢ޽ࠆ Quantum ESPRESSO ߦ LRD ᴺߦ
ኻߔࠆ᭴ㅧᦨㆡൻ⸘▚ࠍታⵝߒߚ‫ޕ‬‫ޣ‬ℂ⺰ߣታⵝ‫ޤ‬  ๟ᦼ♽ߦ߅ߌࠆ LRD ᴺߦࠃࠆಽᢔജࠛࡀ࡞ࠡ࡯ߪએਅߩࠃ߁ߦ⸘▚ߐࠇࠆ‫ޕ‬

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ᢙߩᰴᢙࠍ⴫ߒ㧘ታ㓙ߩ⸘▚ߢߪ 6㧘8㧘10 ߹ߢߢᛂߜಾࠆ‫ߚ߹ޕ‬㧘 Τ  n1p  n2q  n3r ( n i ߪᢛᢙ㧘p, q, r ߪᩰሶࡌࠢ࠻࡞)ߢ޽ࠅ㧘ᵈ⋡ߔࠆන૏ᩰሶ߆ࠄ⠨ᘦߔࠆ๟ࠅߩන૏ᩰሶ߹ߢߩࡌࠢ࠻࡞ߢ
޽ࠆ‫ޕ‬ේሶ a ߪᵈ⋡ߔࠆන૏ᩰሶౝߩේሶߢ޽ࠅ㧘ේሶ b ߪ Τ ߦࠃߞߡਗㅴᠲ૞ࠍᣉߒ㧘⋧੕૞↪〒㔌߇ 20 bohr ߹ߢߩන૏ᩰሶࠍ⠨ᘦߔࠆ‫ ߪ)ࡓࠗ࡜ࡊ(  ޕ‬Τ  0 ߩߣ߈ߦ a  b ࠍ㒰ߊߎߣࠍ⴫
ߒߡ޿ࠆ‫ ޕ‬R ߪේሶ㑆ߩ〒㔌ߢ޽ࠅ㧘 R  0 ߢಽᢔജࠛࡀ࡞ࠡ࡯߇⊒ᢔߔࠆߩࠍ㒐ߋߚ߼ߦ㧘࠳ࡦࡇࡦࠣ㑐ᢙ f dam p ߇ਸ਼ߓࠄࠇࠆ‫ޕ‬‫ޣ‬㊄ዻ⴫㕙ߦ߅ߌࠆ n-ࡉ࠲ࡦߩ‛ℂๆ⌕‫ޤ‬n-ࡉ࠲ࡦ߇ Cu(111) 㧘Au(111)㧘Pt(111)ߦๆ⌕ߔࠆ♽ߦኻߒߡ㧘᭴ㅧᦨㆡൻ⸘▚ࠍⴕߞߚ‫⴫ޕ‬㕙ߩࡕ࠺࡞ߪ㧘⌀ⓨጀࠍ 20Å㧘㊄ዻࠍ 4 ጀߣߒߚࠬ࡜ࡉࡕ࠺࡞ߣߒ㧘n-ࡉ࠲ࡦߩๆ⌕᭴ㅧߪ㧘ታ㛎ߢᓧࠄࠇߡ޿ࠆ Pt(111) ߩ⚿ᨐ[5]ࠍઁߩ㊄ዻߦኻߒߡ߽ㆡ↪ߒߚ(Fig. 1(a)ߩන૏ᩰሶ)‫ޕ‬᭴ㅧᦨㆡൻ
ߪ n-ࡉ࠲ࡦߩߺߣߒ㧘ᐔ㕙ᵄၮᐩߩᵄേ㑐ᢙߣ㔚ሶኒᐲߩࠞ࠶࠻ࠝࡈߪߘࠇߙࠇ 36 Ry ߣ 400 Ryߣߒߚ‫ޕ‬k ὐߪ Monkhorst- Pack ᴺߦࠃߞߡ 4×6×1 ߢࠨࡦࡊ࡝ࡦࠣߒ㧘࠙࡞࠻࡜࠰ࡈ࠻ᡆࡐ࠹ࡦࠪ
ࡖ࡞ߣ revPBE ᳢㑐ᢙࠍ↪޿ߚ‫ߚ߹ޕ‬㧘Ყセߣߒߡవⴕ⎇ⓥߩ⚿ᨐ(PBE ᳢㑐ᢙߢ᭴ㅧᦨㆡൻߒ㧘
vdW-DF2 ᳢㑐ᢙߢ⴫㕙-ๆ⌕ሶ㑆〒㔌ࠍ᳿ቯ)[6]߽วࠊߖߡ Table 1 ߦ␜ߔ‫ޕ‬ᧄ⎇ⓥ(revPBE+LRD)ߦࠃࠆๆ⌕ࠛࡀ࡞ࠡ࡯ߪ㧘ߤߩ㊄ዻ⴫㕙ߦ߅޿ߡ߽ታ㛎୯߆ࠄ 0.05 eV એౝߢ৻⥌ߒߚ‫ߒޕ‬(a)߆ߒ㧘Cu(111)ߦ㑐ߒߡߪ᭴ㅧᦨㆡൻߦࠃߞߡಽሶ㕙ߣ⴫㕙߇ਗⴕߦߥࠄߥ޿ߣ޿߁⚿ᨐ߇ᓧࠄࠇߚ‫ߪࠇߎޕ‬㧘ๆ⌕ሶ㑆〒㔌߇ㄭ޿ߚ߼ߦ↢ߓߚᱡߺߢ޽ࠆߣ⠨߃ࠄࠇࠆ‫ޕ‬ߘߎߢ㧘ߎߩᱡߺ߇↢ߓߥ޿ߣ⠨߃ࠄࠇࠆ 7  3 ߩන૏ᩰሶ(Fig. 1(b))ߦߟ޿ߡ߽⸘▚ߒ㧘⚿ᨐࠍ᜝ᒐౝߦ␜ߒߚ‫ޕ‬(b)ߘߩ⚿ᨐ㧘ੱὑ⊛ߥᱡߺ߽↢ߓߕ㧘ታ㛎୯ߣห᭽ߦ
Cu  Pt  Au ߣ޿߁ๆ⌕ࠛࡀ࡞ࠡ࡯ߩ㑐ଥࠍౣ⃻ߔࠆߎߣ߇ߢ߈ߚ‫৻ޕ‬ᣇ㧘వⴕ⎇ⓥ [6] ߩๆ⌕ࠛࡀ࡞ࠡ࡯ߪ㧘Cu(111)ߦ㑐ߒߡߪๆ⌕ሶ㑆⋧੕૞↪ߦࠃࠆਇ቟ቯൻߦࠃ
ߞߡㆊዊ⹏ଔߒߡ߅ࠅ㧘߹ߚઁߩ㊄ዻ⴫㕙ߦ㑐ߒߡߪㆊᄢ⹏ଔߔࠆ௑ะ߇⷗ࠄࠇࠆ‫⚿ޕ‬ᨐߣߒߡᄢዊ㑐ଥ ߪ
Pt  Au  Cu ߣታ㛎ߣ⇣ߥࠆ⚿ᨐࠍਈ߃ߚ‫ޕ‬

Fig. 1. Absorbed unit cell structure of(a) 7  3 and (b) 7  3 .

⴫㕙-ๆ⌕ሶ㑆〒㔌ߦ㑐ߒߡߪ㧘ᧄ⎇ⓥߩๆ⌕〒㔌ߪ
[6]
Au  Cu  Pt ߣߥߞߡ߅ࠅ㧘⋧੕૞↪߇ᒝ޿ᣇ߇〒㔌߇⍴޿ߎߣ߇ࠊ߆ࠆ‫৻ޕ‬ᣇ㧘వⴕ⎇ⓥ ߢߪ㊄ዻߩ⒳㘃ߦࠃࠄߕ߶߷৻ቯߩ〒㔌ࠍਈ߃ࠆ‫ޕ‬એ਄ߩ⚿ᨐ߆ࠄ㧘ᧄ⎇ⓥߢ㐿⊒ߒߚ revPBE ᳢㑐ᢙߣ LRD ᴺࠍ⚵ߺวࠊߖߚᣇᴺߦࠃࠅ㧘‛ℂๆ⌕ࠛࡀ࡞ࠡ࡯߅ࠃ߮ๆ⌕〒㔌߇ㆡಾߦ⸥ㅀน⢻ߢ޽ࠆߣ⏕⹺ߐࠇߚ‫ޕ‬

Table 1. Adsorption energies and distances of n -butane on metal surface. (Calculated adsorption
distance is defined as an average of distances from metal surface to each carbon atom in n -butane.)
Adsorption energy (eV)revPBE+LRD
Cu(111)
Au(111)0.47(0.53 )0.45

Ref. 6
0.37
0.52

Pt(111)

0.52

0.61

a

a

Adsorption distance (Å)
Expt.

0.51
0.42[8]3.76(3.52 )3.79

Ref. 6
3.76
3.78

0.53[9]

3.54

3.74

[7]

revPBE+LRDa

7  3 unit cell is used.

[1] T. Sato, H. Nakai, J. Chem. Phys. 131, 244104 (2009).
[2] T. Sato, H. Nakai, J. Chem. Phys. 133, 194101 (2010).
[3] Y. Ikabata, H. Nakai, Chem. Phys. Lett. 556, 386 (2013).
[4] Y. Ikabata, H. Nakai, J. Chem. Phys. 137, 124106 (2012).
[5] L. E. Firment, G. A. Somorjai, J. Chem. Phys. 66, 2901 (1977).
[6] K. Lee, Y. Morikawa, D. C. Langreth, Phys. Rev. B 82, 155461 (2010).
[7] R. Z. Lei, A. J. Gellman, B. E. Koel, Surf. Sci. 554, 125 (2004).
[8] S. M. Wetterer, D. J. Lavrich, T. Cummings, S. L. Bernasek, G. Scoles, J. Phys. Chem. B 102, 9266 (1998).
[9] S. L. Tait, Z. Dohnálek, C. T. Campbell, B. D. Kay, J. Chem. Phys. 125, 234308 (2006).

3 P127eÙĺà&

5>VW9:<[(čê&ĵ5îğôùþ

(ÄyĪî¦ 1, ÊĶ¦ 2, i ESICB3, Äî¦ù 4, JST-CREST5)ĢÅ× 1, ¥ñĒĠ 2,3, ¥ñç 2,3, bgå§ 1,3-5

Theoretical Study on De-Solvation Properties ofCareer-Ions in Secondary Batteries(Grad. Sch. of Adv. Sci. and Eng., Waseda Univ.1, Grad. Sch. of Eng., Univ. of Tokyo2,
ESICB, Kyoto Univ.3, Res. Inst. for Sci. and Eng., Waseda Univ.4, JST-CREST5)
Masaki Okoshi1, Yuki Yamada2,3, Atsuo Yamada2,3, Hiromi Nakai1,3-5
ĉĘ Li :<[eÙĺà(LIB))¾¨GM:C(ĺé#!«q76! 5Çħ")
ĺÝĎģ0CR]H@WEI%$(ACFS& 5äð/ãõ8ĸ.! 5(2%ĖÕ%ACFS(.( LIB &)ł;KX?]­"%łNZ]­/ĔÞ
65%7·Ĩ%x¿ĺ¶µĔ" 5
 LIB (ĺà¶& 5²ĨÛķ)êæ3ÐË+( Li :<[(»z" 4Ł&2
4´365¶(ä¸;KX?]#­ßĵÁîğ(DFT)ęā&24´365ê;KX?]&)ď ÷ĵ 5#ø36! 5 1,2%3«ß%ê& 5ê;KX?](Ăćô%ĞÎ)6! % ,Çħ") LIB (kÆ#! Na :<[eÙĺà0 Mg :<[eÙĺà/ãõ6! 4Na :<[0 Mg :<[&ĵ5Č
/µĔ" 5 Éùþ")DFT ęā8ð ! Li, Na, Mg (:<[( 27 ýŀ(ÈØê& 5ê;KX?]8ā};KX?]~â&2!ėÌ,ê(c\ ÐU]
T[H\ĻĺQF[AVX(ESP)\ôû­& 5r¸8ÏĚĻĺQF[AVX*ôû­ê;KX?]#ď ÷ĵ8ü#8ĕ}
ęāÂâ ê#!ïí carbonate 5 ýöĳ carbonate 2 ýïí ether 3 ýsulfolaneĝ¡o 2 ýöĳ nitrile 5 ýamide 4 ýöĳ nitro 2 ý#γ-valero lactone (GVL)ethylene sulfite(ES)DMSOtrimethyl phosphate (TMP)(ę 27 ý8ÏĚ>VW9:<[#!Li+,
Na+, Mg2+8ÏĚę 81 ýŀ(êÒĩ8 B3LYP/cc-pVDZ YOX"Çĭê
;KX?])Ù®&³!ċ(1)
ΔE = E[Li+ ]+ E[solvent]− E[complex]
E[Li+], E[solvent], E[complex])66ÿ Li :<[*ê#êÒĩ& 
5ĹëēÚ6;KX?]" 5"ĺ;KX?]) B3LYP/aug-cc-pVTZ YOX"ęā
 ,ê:<[(÷fpð;KX?]8£¹~ĤĬ;KX?]~(LMO-EDA)â 3
8ð !ėÌêÒĩ&!Ĳ¤=D<[#ê~866ULR]#ċULR]Ĵ÷fpð;KX?]8Ù®(2 &Ļĺ÷fpðh½ó~Ð~À(a&~

Eint. = EES + EX + Erep. + Epol. + Edisp.

(2)

ESP )ê~& !ĺ­ 0.04 ≤ ρ ≤ 0.05 " 52 %ë&!Ç/%v
8¼ðôû­)Ù®&³!ê(b¸"(Òĩ& !ā}"b¸"(ĺÁ8 N #
η = ( E(N +1) + E(N −1) − 2E(N )) / 2(3)

Energy components (kJ/mol)

Interaction energy (kJ/mol)

Interaction energy (Calcd.)(kJ/mol)

ĆÍ#Č  1 & PC ~((a)Āĺ­(ρ =0.05)Ľ_( ESP #(b) Li #(êÒĩ8ü
ESP Ç/%=XPJX(İă" Li #Ć5#7Ó(ĆÍ)j({!
(ê\:<[(ą-7& !´36  2 & Li :<[& 5ä¸;KX?](Łv 1,2 #ÉÏĚ"ā}ê;KX?](ęFig. 1 (a) ESP and (b) solvating structure of PC.
āv8üĈ v)ò%5w 1.15
300átÁ 0.97 #ļ©&ď ÷ĵ´36  3 & Li :<[(ê;KX?]& 5200
y = 1.15x + 155.3
Na :<[* Mg :<[(ê;KX?](÷R2 = 0.97ĵ8üLi :<[(úĊ)#ÜĦ!Na :<[100
")X:Cİ¸¯ .&ê;KX?]) 40 – 70 kJ/mol ¢ ^Â"Mg :<[")
0
100
0
50
B=D<[&ġ! 340 – 560 kJ/mol  ,
Activation energy (Exptl.) (kJ/mol)
Mg :<[")átÁ Na ( 0.96 &  Fig. 2 Correlation between activation energy and0.83 &n`6)^Į(ê"Òĩ1- solvation energy.
800
Mg: y = 2.55x + 45.58l 2 įmÒĩ8#." 5
R2 = 0.83
  4 & LMO-EDA &25 Li :<[(êÒĩ
600
& 5÷fpð;KX?](~ĆÍ8üÖĥ)ê;KX?]" 5h½÷fpð#400
óľ)8#4h½óľ#!üĻĺ
÷fpð#~Ð÷fpðê;KX?]#Ċ
200
Na: y = 0.78x + 14.0±(÷ĵ8ü3&ê;KX?](
R2 = 0.96¢)ê(c&2!Ñ'îė"5#
0200 400 600 800
0
7ªv") nitro < ether < ES < nitrile <Interaction energy (kJ/mol)
öĳ carbonate < ïí carbonate < GVL < sulfolane < Fig. 3 Correlation between interaction energies
amide < DMSO < TMP < di-nitrile (Ŀ#% of Li, Na, and Mg ions.
u(ê")Ŀ¬(z6Æ74/ĕ36
3&ïí carbonate 5 ý& !ôºÔ& ĜĄ%ÏĚ8Đđ 1 &
63(~(ê;KX?]#ESP *ôû­ ÐU]T[H#(÷ĵ8ü
vinylene carbonate (VC)"~|(eıĆ&25ôû­(īěsĕ36 
6/ď ÷ĵ8üÉøĕ)ê(ì¸(-3ê;KX?]8dè"5#
8ü! 5°Ã)j(êý(ĜĄ%ėÌ& !/5
300
200
100
0
-100
0

Table 1. Correlation between properties of solvents and solvation energies.
Li
Na
Mg
ESP
Gradient
0.68
0.55
0.93
(kJ/mol)Intercept
145.8598.47
418.54
0.96
0.96
0.93
R2

ES
y = 0.95x – 17.5
R2 = 0.92
Pol.
y = 0.41x + 12.9
R2 = 0.60

Chemical hardness GradientIntercept(eV)R2
w/o VC

X-Rep.
y = -0.24x – 19.1
R2 = 0.51

300 Dipole moment(Debye)Solvation energy of Li-ion complex (kJ/mol)
100

200

Fig. 4 Correlation between solvation energy
and energy components.

Gradient
Intercept
R2-67.68591.180.99-55.02460.700.99-141.64
1352.20
1.00

28.75
57.33
0.91

23.49
26.06
0.91

61.84
225.450.92[1] T. Abe, F. Sagane, M. Ohtsuka, Y. Iriyama, and Z. Ogumi, J. Electrochem. Soc. 152, A2151 (2005).
[2] Y. Yamada, F. Sagane, Y. Iriyama, T. Abe, and Z. Ogumi, J. Phys. Chem. C 113, 14528 (2009).
[3] P. Su and H. Li, J. Chem. Phys. 131, 014102 (2009).

3P128ィ⟬໬Ꮫ࡟ࡼࡿ᭷ᶵ㟁ゎᾮࡢ≉ᛶண(ኴ㝧ㄏ㟁ᰴᘧ఍♫,1 ᪩኱ඛ㐍⌮ᕤ,2 ᪩኱⌮ᕤ◊,3 ி኱ ESICB,4 JST-CREST5)۵῿⨾↷ኵ,1 ⧰ᮌṊ⏨,1 ᒾᓮ㄃ᚿ⣖,1 ▼⏣ඞⱥ,1 ኱㉺ᫀᶞ,2 ᾏᑌ୔ᙲ,2 ୰஭ᾈᕭ 2,3,4,5

Predictions of the properties of organic electrolytes solution using computational chemistry(TAIYO YUDEN CO., LTD.,1 Advanced Science and Engineering, Waseda Univ.,2 RISE, Waseda Univ.,3 ESICB,
Kyoto Univ.,4 CREST, JST Agency5)
۵Teruo Atsumi,1 Takeo Tsuzuki,1 Yoshiki Iwazaki,1 Katsuei Ishida,1 Masaki Okoshi,2 Takeaki Kaiho,2 Hiromi
Nakai2,3,4,5[⥴ゝ]ࣜࢳ࣒࢘࢖࢜ࣥ㟁ụࡸ㟁Ẽ஧㔜ᒙ࢟ࣕࣃࢩࢱ࡜࠸ࡗࡓ㟁Ꮚࢹࣂ࢖ࢫ࡟⏝࠸ࡽࢀࡿ᭷ᶵ㟁ゎᾮ࡟ࡣࠊ㧗࠸ᶵ⬟ᛶ࡜Ᏻᐃᛶࢆేࡏᣢࡘࡇ࡜ࡀồࡵࡽࢀࡿࠋලయⓗ࡟ࡣࠊ㟁Ꮚࢹࣂ࢖ࢫࡢప
᢬ᢠ໬ࡢࡓࡵ࡟ప⢓ᗘ࡛࠶ࡾࠊ㧗ᐜ㔞໬ࡢࡓࡵ࡟㧗ㄏ㟁⋡࡛⁐㉁ࢆ⁐࠿ࡋࡸࡍࡃࠊࡉࡽ࡟Ỉࡸ㟁Ẽ࡟ᑐࡋ࡚Ᏻᐃࠊࡍ࡞ࢃࡕຍỈศゎࠊ㟁Ẽศゎࡋ࡟ࡃ࠸࡜࠸࠺≉ᛶࡀᚲせ࡜࡞ࡿࠋࡇ࠺
࠸ࡗࡓ᮲௳ࢆ‶ࡓࡍ᭷ᶵศᏊࢆィ⟬໬Ꮫ࡟ࡼࡾண

ࡋࠊྜᡂ࣭ᐇ㦂๓࡟ೃ⿵ࢫࢡ࣮ࣜࢽࣥࢢ

ࡀฟ᮶ࢀࡤࠊ኱ᖜ࡟㛤Ⓨຠ⋡ࢆྥୖࡍࡿࡇ࡜ࡀྍ⬟࡟࡞ࡿࠋᮏ◊✲ࡣࠊྂ඾ศᏊືຊᏛࢩ࣑࣮ࣗࣞࢩࣙࣥ(ྂ඾ MD)࠾ࡼࡧ㔞Ꮚ໬Ꮫィ⟬࡟ࡼࡾࠊ᭷ᶵ⁐፹ࡢᐦᗘ࣭⢓ᗘ࣭ㄏ㟁⋡࣭⪏ຍỈศゎᛶ࣭⪏㟁Ẽศゎᛶࢆணࡍࡿࡇ࡜ࢆ┠ⓗࡋࡓࠋ[ィ⟬⤖ᯝ]
㟁Ꮚࢹࣂ࢖ࢫ࡛ࡼࡃ⏝࠸ࡽࢀ࡚࠸ࡿᅗ 1 ࡟♧ࡍ᭷ᶵศᏊࢆィ⟬ᑐ㇟࡜ࡋࠊྛ≀ᛶ್ࢆồࡵࡓࠋ
1. ᐦᗘ࣭⢓ᗘ

Ethylene Carbonate(EC)

Propylene Carbonate(PC)%-butyrolactone(GBL)

Dimethyl Carbonate(DMC)

Ethylmethyl Carbonate(EMC)

Acetonitrile(AN)ྂ඾ MD ࡟ࡼࡾᐦᗘ࠾ࡼࡧ⢓ᗘ[1]ࢆồࡵࡓࠋࣉࣟࢢࣛ
࣒ࡣ Gromacs 4.5.5 ࢆࠊ࣏ࢸࣥࢩࣕࣝࡣ GAFF[2]ࢆ⏝࠸ࠊ
NPT ࢔ࣥࢧࣥࣈࣝ(T=300K)ࡢ᮲௳࡛ࢩ࣑࣮ࣗࣞࢩࣙࣥࢆ

Figure 1. Structures of organic solution.

ᐇ⾜ࡋࡓࠋᚓࡽࢀࡓィ⟬⤖ᯝ࡜ᐇ㦂್ࢆ⾲ 1 ࡟♧ࡍࠋࡇࢀ࠿ࡽᐇ㦂್࡟ᑐࡋ࡚ᐦᗘࠊ⢓ᗘࡀࠊࡑࢀࡒࢀ

Table 1. Density  (g/L) and viscosity (cP).

1.5~6%, 1~12%ࡢㄗᕪ࡛ồࡵࡽࢀࡿࡇ࡜ࡀศ࠿ࡗࡓࠋ
2. ㄏ㟁⋡
ḟ࡟ࠊ⁐፹ࡢẚㄏ㟁⋡ ࢆࠊOnsagar ࡢᘧ(1)࡟ࡼࡾ
ồࡵࡿࡇ࡜ࢆヨࡳࡓࠋ  n 2  n  M  N ! n  2  9 k T
2

2

2

A

2

2

(1)""

EC
PC
GBL
DMC
EMC
AN

Density
calc.
1301
1180
1063
1042
980
742

expl.
1320
1200
1129
1070
1010
786

Viscosity
calc.
expl.
2.09
1.9
2.69
2.5
1.37
1.5
0.61
0.6
0.72
0.7
0.39
0.35

0 B

#!$཮ᴟᏊ࣮࣓ࣔࣥࢺ, n:ᒅᢡ⋡, M:ศᏊ㔞]ࡣྂ඾ MD ࡢ⤖ᯝ(⾲ 1)ࢆ⏝࠸ࠊT ࡣ 300K ࡜ࡋࡓࠋ!ࡣࠊ┿✵୰ࡢ 1 ศᏊࡢ㔞Ꮚ໬Ꮫィ⟬

(Gaussian 09, B3LYP/aug-cc-pVTZ)ࡼࡾồࡵࡓࠋn ࡣࠊྠᵝࡢ㔞Ꮚ໬Ꮫィ⟬࡛ồࡵࡓศᴟ⋡&ࢆ Lorentz-Lorenz ࡢᘧ(2)࡟௦ධࡋỴᐃࡋࡓࠋn 2  1 M N A&
3 0
n2  2 

Table 2. Dielectric constant .

calc.
73.0
60.9
45.9
2.1
2.3
43.2

EC
PC
GBL
DMC
EMC
AN

(2)

⾲ 2 ࡟ ࡢィ⟬⤖ᯝ࡜ᐇ㦂್ࢆ♧ࡍࠋEC ࡣィ⟬࡟ࡼࡾ㐣ᑠ࡟ぢ✚ࡶࡽࢀ࡚࠸ࡿࡀࠊࡇࢀࡣศᏊ㓄ྥ࡟ࡼࡿᙳ㡪ࢆྲྀࡾ㎸ࡵ࡚࠸࡞࠸ࡓࡵ
ࡔ࡜ᛮࢃࢀࡿࠋEC ௨እࡢ⁐፹࡟ࡘ࠸࡚ࡣࠊᐇ㦂್ࢆᴫࡡ෌⌧ࡍࡿࡇ

expl.
90
65
42
2.8
2.9
37.5

࡜ࡀ࡛ࡁࡓࠋ
3. ⪏ຍỈศゎᛶ࣭⪏㟁Ẽศゎᛶ ศゎᛶࢆண

ࡍࡿࡓࡵ࡟ࠊ㟁ẼศゎࠊຍỈศゎࡢ཯ᛂ⤒㊰ࢆᵓ⠏ࡋࠊࡑࡢ࢚ࢿࣝࢠ࣮ࢆ㔞Ꮚ໬Ꮫィ⟬(Gaussian 09, B3LYP/aug-cc-pVTZ, ⁐፹ຠᯝࡣ Polarizable Continuum Model ἲ࡟ࡼࡾ⪃៖)࡟ࡼࡾồࡵࡓࠋ౛࡜ࡋ࡚ࠊPC ࡢ㟁Ẽศゎ࡜ຍỈศゎࡢ࢚ࢿࣝࢠ࣮ࢲ࢖࢔ࢢ࣒ࣛࢆࡑ
ࢀࡒࢀᅗ 2, 3 ࡟♧ࡍࠋ㟁ẼศゎࡣࠊPC ࡀⅣ⣲㟁ᴟ࠿ࡽ㟁Ꮚࢆཷࡅྲྀࡿ㐣⛬ࢆึᮇ཯ᛂ࡜ࡋࠊⅣ⣲㟁ᴟࡢ໬Ꮫ࣏ࢸ
ࣥࢩࣕࣝࢆ 115.3kcal/mol(=5eV)ࠊ㟁ᴟ࡬ࡢ༳ຍ㟁ᅽࢆ 0, -1.5, -3V ࡜ࡋࡓࠋ࠸ࡎࢀࡢ㟁ᅽ᮲௳࡛ࡶࠊึᮇࡢ㟁Ꮚᤵཷࡀ㞀ቨ࡜࡞ࡾࠊࡑࡢᚋࡣ CO2 Ⓨ⏕ࡲ࡛ศゎࡀ㐍⾜ࡍࡿࠋࡲࡓࠊ༳ຍ㟁ᅽࡀప࠸࡯࡝㞀ቨࡢ㧗ࡉࡶపࡃ࡞ࡾࠊศゎࡣಁ㐍ࡉࢀࡿࠋຍỈศゎࡣࠊỈࡢ㟁㞳࡛⏕ࡌ

100

Energy (kcal/mol)ࡿ H+, OH- ࡜ࡢ཯ᛂ࡛㐍⾜ࡋ
CO2 ࡀⓎ⏕ࡍࡿ⤒㊰ࢆᵓ⠏ࡋࡓࠋࡲࡓࠊỈࡢึᮇ≧ែࢆ H2O,
H2O+H+, H2O+OH-ࡢ 3 ✀㢮࡜

50
0

0V
-50

-1.5V

-100
-150

-3V

-200

ࡋࠊࡑࢀࡒࢀࠊ୰ᛶ᮲௳(N), 㓟

+e-

+H+

+e-

+H+

+

+

+
H2O
+
CO2

ᛶ᮲௳(A), ሷᇶᛶ᮲௳(B)࡟ᑐ
ᛂࡍࡿ࡜ࡋࡓࠋ཯ᛂ⤒㊰ࡣࠊ୰ࡔࡀࠊሷᇶᛶ᮲௳࡛ࡣูࡢ
⤒㊰ࡀ᭷฼࡜ぢ✚ࡶࡽࢀࡓࠋࡲࡓࠊ୰ᛶ᮲௳ࠊ㓟ᛶ

Energy (kcal/mol)ᛶ᮲௳࡜㓟ᛶ᮲௳ࡣྠࡌ

Figure 2. Energy diagrams of electrolysis reaction of PC with applied voltage of 0, -1.5, and -3V.
50
40
30
20
10
0
-10
-20
-30
-40

᮲௳ࠊሷᇶᛶ᮲௳ࡢ㡰࡟ࠊ
N and A

N

N

N

N
N,A

N, A

B

A
A

A
B

+H+

A

B

B

+OH-

B

+OH-

+H+

+H+

+

+H+

+
H2O
+
CO2

⤒㊰ࡢ࢚ࢿࣝࢠ࣮ࡀᏳᐃ
໬ࡋ࡚࠾ࡾࠊPC ࡢຍỈศゎࡣࠊ㓟࣭ሷᇶඹ࡟ಁ㐍ࡍ

+OH-

+OH-

B

+

+H+

+

ࡿࡀࠊࡑࡢຠᯝࡣሷᇶࡢ᪉
ࡀᙉ࠸࡜ண᝿ࡉࢀࡓࠋ

+H+

+
H2O
+
CO2

Figure 3. Energy diagrams of hydrolysis reaction of PC in neutral (N), acid (A), and basic (B) condition.

Ⓨ⾲ᙜ᪥ࡣࠊ௚⁐፹࡟ࡘ࠸࡚ศゎᛶࡢ᳨ウࢆ⾜࠸ẚ㍑ࡋࡓ⤖ᯝࢆ♧ࡍࠋ
[1] Palmer, Phys. Rev. E 49 (1994) pp 359-366. [2] Wang, J., Wolf, R. M., Caldwell, J. W., Kollman,
P. A. and Case, D. A., J. Comput. Chem., Vol. 25, 1157 (2004).

3P129㛝ள㖄㖔ᆺ GaN ࡢග྾཰≉ᛶ࡟࠾ࡅࡿ㟁Ꮚ̿ࣇ࢛ࣀࣥ┦஫స⏝ࡢᙳ㡪㸦ᮾ኱㝔࣭ᕤ 1㸪Institut Laue Langevin2㸪Istituto di Struttura della Materia of the National
Research Council3㸪European Theoretical Spectroscopy Facilities (ETSF)4㸧‫ۑ‬Ἑྜ ᏹᶞ 1㸪ᒣୗ ᫭୍ 1㸪Cannuccia Elena2㸪Marini Andrea3, 4The effect of electron-phonon interaction on the optical properties of zinc-blende GaN
㸦School of Engineering, The University of Tokyo1㸪Institut Laue Langevin2㸪Istituto di
Struttura della Materia of the National Research Council3㸪European Theoretical
Spectroscopy Facilities (ETSF)4㸧
‫ۑ‬Hiroki Kawai1㸪Koichi Yamashita1㸪Elena Cannuccia 2㸪Andrea Marini 3, 4࠙ᗎࠚ༙ᑟయࢹࣂ࢖ࢫᮦᩱ࡜ࡋ࡚ᗈࡃ౑ࢃࢀ࡚࠸ࡿ❅໬࣒࢞ࣜ࢘ GaN ࡣࠊ᭱Ᏻᐃᵓ㐀ࡢ࢘ࣝࢶ㖔ᆺࡢ௚ࠊ‽Ᏻᐃᵓ㐀࡜ࡋ࡚㛝ள㖄㖔ᆺࢆ࡜ࡿࠋ㛝ள㖄㖔ᆺ GaN㸦zb-GaN㸧ࡣࠊ࢘ࣝࢶ㖔ᆺ࡜ࡣ␗࡞ࡾෆ㒊㟁ሙࢆᣢࡓ࡞࠸ࡇ࡜࠿ࡽࠊ࣊ࢸࣟᵓ㐀ࡸ㉸᱁Ꮚࡢタィ࡟࠾࠸࡚ࡼࡾᮃࡲࡋ࠸ᮦᩱ࡛࠶
ࡿ࡜ࡉࢀ࡚࠸ࡿ[1]ࠋ㏆ᖺࠊ᱁Ꮚ୙ᩚྜࡀᑠࡉࡃ㧗⣧ᗘ࡞ zb-GaN ࡢྜᡂࡀྍ⬟࡟࡞ࡿ࡟క࠸ࠊࡑ
ࡢ≀ᛶࡢヲ⣽࡞⌮ゎ࡟ὀ┠ࡀ㞟ࡲࡗ࡚࠸ࡿࠋ ᐇ㦂ⓗ࡟ zb-GaN ࡢㄏ㟁㛵ᩘཬࡧࣂࣥࢻࢠࣕࢵࣉࡀㄪ࡭ࡽࢀ࡚࠸ࡿ୍᪉࡛ࠊ➨୍ཎ⌮ィ⟬࡟ࡼࡿ⌮ㄽⓗ࡞ゎᯒ࡟ࡣࠊ⢭ᗘࡢ㠃࡛ᮍࡔၥ㢟ࡀṧࡉࢀ࡚࠸ࡿࠋCarvalho ࡽࡣࠊLDA ࡸ GGA ࡼࡾࡶ⢭☜࡞᱁Ꮚᐃᩘࢆ୚࠼ࡿ AM05 ஺᥮┦㛵ỗ㛵ᩘࢆ⏝࠸ࡓ DFT ィ⟬࡟ࡼࡗ࡚ᵓ㐀᭱㐺໬ࢆ⾜࠸ࠊࡑࡢᵓ㐀࡟ࡘ࠸࡚ࠊHSE ỗ㛵ᩘ࡟ࡼࡿ DFT ィ⟬ཬࡧ GW ㏆ఝࢆ⏝࠸࡚ࣂࣥࢻࢠࣕࢵࣉࢆィ⟬ࡋࡓ[2]ࠋࡋ࠿ࡋࠊࡑࡢ⤖ᯝࡣ 3.427 eV ࡜ࠊᐇ㦂್ࡢ 3.295 eV㸦T = 10 K㸧[3]࡟ẚ࡭࡚ࡸࡸ㐣኱ホ౯ࡉࢀ࡚࠾ࡾࠊࡇࡢࡼ࠺࡞ᕪࡀ⏕ࡌࡿཎᅉ࡟ࡘ࠸࡚ࡣᮍࡔ㆟ㄽࡢవᆅࡀṧࡉࢀ࡚࠸ࡿࠋ
 ㏻ᖖࠊࣂࣥࢻᵓ㐀ࡢィ⟬ࡣ Born-Oppenheimer ㏆ఝࠊࡍ࡞ࢃࡕཎᏊ᰾ࡣᅛᐃࡉࢀ࡚࠸ࡿ࡜࠸࠺
ᥥീࡢࡶ࡜࡛⾜ࢃࢀࡿࠋࡋ࠿ࡋࠊከయᦤືㄽ࡟ᇶ࡙ࡁ㟁Ꮚ̿ࣇ࢛ࣀࣥ┦஫స⏝࡟ࡼࡿࣂࣥࢻ࢚ࢿ
ࣝࢠ࣮ࡢ⿵ṇࢆ⪃៖ࡋࡓሙྜࠊ౛࠼⤯ᑐ㞽ᗘ࡛࠶ࢁ࠺࡜ࠊࡑࡢ㞽Ⅼ᣺ືࡀࣂࣥࢻᵓ㐀࡟ࡶࡓࡽࡍᙳ㡪ࡣ↓ど࡛ࡁ࡞࠸ࡇ࡜ࡀࠊࢲ࢖ࣖࣔࣥࢻࡸ࣏ࣜ࢔ࢭࢳࣞࣥ࡞࡝ࡢ⣔࡟࠾࠸࡚ሗ࿌ࡉࢀ࡚࠸ࡿ[4]ࠋ
ࡑࡇ࡛ࠊᮏ◊✲࡛ࡣ zb-GaN ࡟࠾ࡅࡿ㟁Ꮚ̿ࣇ࢛ࣀࣥ┦஫స⏝ࡢᙳ㡪ࢆㄪ࡭ࠊᐇ㦂⤖ᯝ࡜ࡢヲ⣽࡞ẚ㍑ࢆ⾜࠺ࡇ࡜࡜ࡋࡓࠋ
࠙⌮ㄽࠚ㟁Ꮚ̿ࣇ࢛ࣀࣥ┦஫స⏝ࢆ⪃៖ࡍࡿࡓࡵࠊBorn-Oppenheimer ㏆ఝ࡟࠾ࡅࡿ㟁Ꮚࡢࣁ࣑ࣝࢺࢽ࢔ࣥࢆཎᏊ᰾ᗙᶆ࡟ࡘ࠸࡚ Taylor ᒎ㛤ࡋࡓࠊ௨ୗࡢࣁ࣑ࣝࢺࢽ࢔ࣥࢆ⪃࠼ࡿࠋൌ଴ ൅ ଵ ൅ 
ଶ 


ሺͳሻ

଴ ࡣࠊཎᏊ᰾ࡀ᭱ᏳᐃⅬ࡟࠶ࡿ࡜ࡁࡢࣁ࣑ࣝࢺࢽ࢔࡛ࣥ࠶ࡾࠊଵ ཬࡧ ଶ ࡣࠊࡑࢀࡒࢀཎᏊ᰾
ଵ ཬࡧଶ ࡢࡑࢀࡒࢀ࡟ᑐࡍࡿ᭱పḟࡢ⮬ᕫ࢚ࢿࣝࢠ
ᗙᶆ࡟ᑐࡍࡿ୍ḟཬࡧ஧ḟᚤศࡢ㡯࡛࠶ࡿࠋ
࣮ࡣࠊFan term ཬࡧ Debye-Waller (DW) term ࡜࿧ࡤࢀࡿࡶࡢ࡛ࠊࡑࢀࡒࢀ௨ୗࡢࡼ࠺࡟᭩ࡁୗ
ࡉࢀࡿࠋ



ࢗఒ ଶ
௡௡ᇱ࢑

ி௔௡
ǡ  ൌ
ȭ௡࢑
௡ᇱࢗఒ



ࢗ

ࢗఒ  ൅ ͳ െ ௡ᇲ ࢑ିࢗࢗఒ  ൅ ௡ᇲ ࢑ିࢗ൅ା െ ௡ᇲ ࢑ିࢗ െ ࢗࣅ െ Ͳ െ ௡ᇲ ࢑ିࢗ ൅ ࢗࣅ െ Ͳା

஽ௐ
 ൌ
ȭ௡࢑

ͳ

ࢗఒǡࢗିఒ

ࢗ

Ȧ ௡௡࢑

ሺʹሻ
ሺ͵ሻ

ʹ ࢗఒ  ൅ ͳࢗఒࢗఒࢗఒǡࢗିఒ

ࠊࡣࡑࢀࡒࢀࣇ࢛ࣀࣥࡢ㐠ື㔞ࠊ࣮ࣔࢻ␒ྕࢆ⾲ࡋࠊ ௡௡ᇱ࢑ ཬࡧ Ȧ ௡௡࢑ࡣ୍ḟཬࡧ஧ḟࡢ㟁Ꮚ̿ࣇ࢛ࣀࣥ࢝ࢵࣉࣜࣥࢢ⾜ิ࡛࠶ࡿࠋ ࢗఒ  ࡣ Bose-Einstein ศᕸ㛵ᩘ࡛࠶ࡾࠊࡇࡢ㡯࡟ࡼࡗ࡚ᗘ౫Ꮡᛶࡀᑟධࡉࢀࡿࠋ

‽⢏Ꮚⓗᥥീ࡟ᇶ࡙ࡅࡤࠊ↓ᦤືࡢࣂࣥࢻ࢚ࢿࣝࢠ࣮ ௡࢑ ࡣ Dyson ᪉⛬ᘧࢆ㏻ࡋ࡚௨ୗࡢࡼ࠺
࡟⿵ṇࡉࢀࡿࠋ
ி௔௡஽ௐ௡࢑ ǡ  ൅ ȭ௡࢑ ௡࢑  ൌ ௡࢑ ൅ ௡࢑  ȭ௡࢑ࡇࡇ࡛ࠊ௡࢑  ൌ ͳ െିଵడୖୣஊಷೌ೙೙࢑ ሺఠǡ்ሻ
డఠ

ሺͶሻ

ఠୀఌ೙࢑

 ࡣ renormalization factor ࡜࿧ࡤࢀࠊ⮬ᕫ࢚ࢿࣝࢠ࣮

ࡀືⓗ࡛࠶ࡿࡇ࡜࡟⏤᮶ࡍࡿ㡯࡛࠶ࡿࠋ⮬ᕫ࢚ࢿࣝࢠ࣮ࢆ㟼ⓗ࡛࠶ࡿ࡜ࡍࡿ㏆ఝ ௡࢑  ൌ ͳ ࡣࠊ
On Mass Shell㸦OMS㸧㏆ఝ࡜࿧ࡤࢀࡿࠋᘧ(2)࡟♧ࡋࡓ Fan term ࡣ」⣲ᩘ࡛࠶ࡿࡇ࡜࠿ࡽࠊࡇ
ࡢ⿵ṇࡣᐇ㒊ࡀࣂࣥࢻࡢ࢚ࢿࣝࢠ࣮ࢩࣇࢺࢆ୚࠼ࡿࡢࡳ࡛ࡣ࡞ࡃࠊ⹫㒊࡜ࡋ࡚ࣂࣥࢻࡢᑑ࿨ࡢ㏫
ᩘࢆ୚࠼ࡿࠋࡇࡢᑑ࿨ࡣࠊ྾཰ࢫ࣌ࢡࢺࣝィ⟬ࡢ⤖ᯝ࡟኱ࡁ࡞ᐤ୚ࢆࡶࡓࡽࡍࡶࡢ࡛࠶ࡿࠋ
࠙⤖ᯝࠚィ⟬ཬࡧᐇ㦂࡟ࡼࡿࠊzb-GaN ࡟࠾ࡅࡿᑐ⛠ᛶࡢ㧗࠸ k Ⅼ㸦ȞࠊLࠊX㸧࡟࠾ࡅࡿ࢚ࢿࣝ
ࢠ࣮ࢠࣕࢵࣉࢆ⾲㸯࡟♧ࡍࠋィ⟬⤖ᯝࡣࠊLDAࠊLDA+G0W0ࠊHSE+G0W0ࠊཬࡧ HSE+G0W0 ࡢ⤖ᯝ࡟ OMS ㏆ఝ࡟ࡼࡿ㟁Ꮚ̿ࣇ࢛ࣀࣥ┦஫స⏝ࡢ⿵ṇ㡯ࢆຍ࠼ࡓࡶࡢࢆ♧ࡍࠋLDA ཬࡧLDA+G0W0 ࡣࠊ඲࡚ࡢ k Ⅼ࡟࠾࠸࡚ࢠࣕࢵࣉࢆ㐣ᑠホ౯ࡋ࡚࠸ࡿ୍᪉࡛ࠊHSE+G0W0 ࡣඛ㏙ࡢ㏻ࡾ㐣኱ホ౯ࡋ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿࠋࡋ࠿ࡋࠊ㟁Ꮚ̿ࣇ࢛ࣀࣥ┦஫స⏝࡟ࡼࡿ⿵ṇࢆ HSE+G0W0
ࡢ⤖ᯝ࡟ຍ࠼ࡿࡇ࡜࡛ࠊᐇ㦂್࡜ࡢ୍⮴ࡣ኱ࡁࡃᨵၿࡉࢀ࡚࠸ࡿࠋ㞽Ⅼ᣺ື࡟ࡼࡿࢠࣕࢵࣉࡢ⿵
ṇࡣ 0.1 eV ௨ୖ࡛࠶ࡾࠊᐇ㦂್࡜ࡢཝᐦ࡞ẚ㍑ࢆ⾜࠺ࡓࡵ࡟ࡣ↓ど࡛ࡁ࡞࠸ࡶࡢ࡛࠶ࡿࡇ࡜ࡀศ
࠿ࡿࠋᙜ᪥ࡢⓎ⾲࡟࠾࠸࡚ࡣࠊ㟁Ꮚ̿ࣇ࢛ࣀࣥ┦஫స⏝ࡢຠᯝࢆྵ

⾲㸯 zb-GaN ࡢ࢚ࢿࣝࢠ࣮ࢠࣕࢵࣉ(eV)ࡵࡓࣂࣥࢻᵓ㐀࡟ᑐࡋ࡚

Ȟ

L

X

Bethe-Salpeter equation (BSE)ࢆ

LDA

2.231

5.952

6.034

ゎ࠸࡚ồࡵࡓ」⣲ㄏ㟁㛵ᩘ࠿ࡽࠊLDA+G0W0

3.239

7.117

7.105

㟁Ꮚ̿ࣇ࢛ࣀࣥ┦஫స⏝ࡀ྾཰ࢫ

HSE+G0W0[2]

3.427

7.707

7.755

࣌ࢡࢺࣝ࡟ࡶࡓࡽࡍᙳ㡪࡟ࡘ࠸࡚

HSE+G0W0+OMS

3.300

7.517

7.624

♧ࡍࠋࡲࡓࠊࡑࡢ ᗘ౫Ꮡᛶ࡟ࡘ

Exp (T = 10K)[3]

3.295

7.33

7.62

࠸࡚ࡶ㆟ㄽࡍࡿணᐃ࡛࠶ࡿࠋ
࠙ཧ⪃ᩥ⊩ࠚ[1] C. Mietze et al. Phys. Rev. B 83, 195301 (2011) [2] L.C.de Carvalho et al. Phys.
Rev. B 84, 195105 (2011) [3] M. Feneberg et al. Phys. Rev. B 85, 155207 (2012) [4] E.

Cannuccia and A. Marini, Phys. Rev. Lett 107, 255501 (2011)

3P130ࢪࢩ࢔ࣀ࣓ࢳࣞࣥ໬ྜ≀࡜ TiO2 ࡀࡘࡃࡿ⏺㠃㘒య࡟㛵ࡍࡿ⌮ㄽⓗ◊✲(ᮾ኱㝔࣭ᕤ*ࠊᮾ኱࣭ඛ➃◊**) ࠐୗ⏣ ⿱ᖹ*ࠊᇛ㔝 ுኴ*ࠊỌ⏣ ⾫⏨**ࠊ⸨ἑ ₶୍**ࠊ℩ᕝ ᾈྖ**ࠊᒣୗ ᫭୍*

Theoretical study of the surface complex of dicyanomethylene
compounds and TiO2(The University of Tokyo*, The University of Tokyo (RCAST) **)ࠐYuhei Shimoda*, Ryota Jono*, Morio Nagata**,
Jun-ichi Fujisawa**, Hiroshi Segawa**, Koichi Yamashita*࠙◊✲⫼ᬒࠚ
Ⰽ⣲ቑឤኴ㝧㟁ụ࡜ࡣࠊ㏱᫂࡞ᑟ㟁ᛶ࢞ࣛࢫᯈ࡟஧㓟໬ࢳࢱࣥ⢊ᮎࢆ↝௜ࡅࠊⰍ⣲ࢆ྾╔ࡉࡏࡓ㟁ᴟ࡜ᑟ㟁ᛶ࢞ࣛࢫࡢᑐᴟ࠿ࡽᵓᡂࡉࢀࠊ㟁ゎ㉁⁐ᾮࡢ㓟໬㑏ඖ཯ᛂࢆక࠺㟁Ꮚࡢ⛣ື࠿ࡽ㟁ຊࢆᚓࡿኴ
㝧㟁ụࡢ୍✀࡛࠶ࡿࠋග㟁ᴟഃ࡛ࡣࠊኴ㝧ග࡟ࡼࡗ࡚ගບ㉳ࡋࡓⰍ⣲ศᏊࡢ㟁Ꮚࡀ㓟໬ࢳࢱࣥࡢఏᑟ
ᖏ(CB)࡬⛣ືࡍࡿࡇ࡜࡛ࠊⰍ⣲ࡣ㓟໬≧ែࠊ㓟໬ࢳࢱࣥࡣ㑏ඖ≧ែࡢ㟁Ⲵศ㞳≧ែ࡜࡞ࡿࠋ≉࡟ࠊ㓟໬ࢳࢱࣥ࡜Ⰽ⣲ศᏊࡢ⏺㠃࡟࠾࠸࡚ࡣࠊග࢚ࢿࣝࢠ࣮࡟ࡼࡗ࡚㟁ᏊࡀⰍ⣲ศᏊ࡬┤᥋㑄⛣ࡍࡿ࡜ࠊ㓟໬ࢳࢱࣥ CB ࡬㟁Ꮚࡀ༶ᗙ࡟ὶࢀࡿࡇ࡜࡛㟁Ⲵศ㞳≧ែ࡜࡞ࡿࡓࡵࠊගບ㉳࠿ࡽ㟁Ⲵศ㞳≧ែ࡬୍ẁ㝵࡛ኚ໬ࡍࡿࠋࡇࢀࡣⰍ⣲࠿ࡽ㓟໬ࢳࢱࣥ࡬ࡢ㟁Ꮚ⛣ື཯ᛂࡢάᛶ໬࢚ࢿࣝࢠ࣮࡟⏤᮶ࡍࡿ࢚ࢿࣝࢠ
࣮ᦆኻࢆῶࡽࡏࡿࡓࡵࠊග࢚ࢿࣝࢠ࣮࠿ࡽ㟁Ẽ࢚ࢿࣝࢠ࣮࡬ࡢኚ᥮ຠ⋡ྥୖ࡟ྥࡅ࡚ࠊ᭷ᮃ࡞ග㟁ụ࡜ࡋ࡚ὀ┠࡟್ࡍࡿࠋ ᙜ◊✲ᐊ࡛ࡣࠊ㓟໬ࢳࢱࣥ⾲㠃ୖ࡛ࡢ྾╔≧ែ࡟࠾࠸࡚ࠊୖグࡢ୍ẁ㝵ࡢ㟁Ꮚ⛣ືࡢᶵᵓࡀ㉳ࡇࡿ࡜⪃࠼ࡽࢀࡿ᭷ᶵศᏊࢆᑐ㇟࡜ࡋ࡚ࠊ㔞Ꮚ໬Ꮫィ⟬ࡢ⌮ㄽⓗᡭἲࢆ⏝࠸࡚ࠊศᏊࣞ࣋ࣝ࠿ࡽ≀ᛶゎᯒࢆ⾜ࡗ࡚ࡁࡓࠋ7,7,8,8-tetracyano-p-quinodimethane (TCNQ)࡜㓟໬ࢳࢱࣥ࡜ࡢ⏺㠃㘒యᵓ㐀࡛ࡣࠊ
TCNQ ࡢ HOMO-LUMO 㑄⛣ࢆ௓ࡉࡎࠊTCNQ ࡢ LUMO ࡼࡾࡶప࠸࢚ࢿࣝࢠ࣮‽఩ࡢ㓟໬ࢳࢱࣥࡢ
CB ࡬┤᥋ⓗ࡟㑄⛣ࡍࡿ┤᥋ⓗ㟁Ⲵ⛣ື㑄⛣࡟ࡼࡗ࡚ࠊྍど-㏆㉥እ㡿ᇦ(400-1000 nm)ࡢᗈ⠊ᅖ࡟྾཰ᖏࢆࡶࡘࡇ࡜ࢆ☜ㄆࡋࡓ 1ࠋᮏ◊✲࡛ࡣ㓟໬ࢳࢱࣥ⾲㠃ୖ࡛ࡢ྾╔≧ែ࡟࠾࠸࡚ࠊ┤᥋ⓗ㟁Ⲵ⛣ື㑄⛣ࡀ㉳ࡇࡿ࡜⪃࠼ࡽࢀࡿࠊࢪࢩ࢔ࣀ࣓ࢳࣞࣥ໬ྜ≀ࡢ≀ᛶゎᯒࢆ⾜࠺ࡇ࡜ࢆ┠ⓗ࡜ࡍࡿࠋᑐ㇟ศᏊࡣࠊ
5,5,6,6-tetracyanothiophenequinodimethane (TCNTQ) (Fig. 1-a)ࠊ࠾ࡼࡧ
2,5-bis(dicyanomethylene)-2,5-dihydrothieno[3,2-b]thiophene (TCNTTQ) (Fig. 1-b)࡜ࡋࡓࠋ
ᮏ◊✲࡛ࡣ TCNTQࠊTCNTTQ ࡜ࠊᙜ◊✲ᐊ࡛㛤Ⓨࡋࡓ࢔ࢼࢱ࣮ࢮᆺࡢ㓟໬ࢳࢱࣥ(101)㠃ࡢࢼࣀࢡ
ࣛࢫࢱ࣮Ti14O28H2(OH)(H2O)2-OH (Ti14-OH)࡜ࡢ⏺㠃㘒యࣔࢹࣝ[Ti14O28H2(OH)(H2O)2-O-C(CN)2C4H2SC(CN)2]− ([Ti14-O-TCNTQ]−)ࠊ
[Ti14O28H2(OH)(H2O)2-O-C(CN)2C6H2S2C(CN)2]− ([Ti14-O-TCNTTQ]−)࡟ࡘ࠸࡚ィ⟬ࡋࡓࠋ࠙ィ⟬᮲௳ࠚ
ィ⟬ࣃࢵࢣ࣮ࢪࡣ㔞Ꮚ໬Ꮫィ⟬ࣉࣟࢢ࣒ࣛ Gaussian09 ࢆ⏝࠸ࡓࠋᵓ㐀᭱㐺໬ࠊ᣺ືᩘィ⟬࡟ࡣ DFTࠊບ㉳≧ែィ⟬࡟ࡣ Time-Dependent DFT ࡢᡭἲࢆ⏝࠸࡚ࠊLC-'PBE/6-31G(d)࡛ࣞ࣋ࣝ⾜ࡗࡓࠋ(a) TCNTQ(b) TCNTTQ

Fig. 1 (a) TCNTQࠊ(b) TCNTTQ ࡢ᭱㐺໬ᵓ㐀(a) * = 0r(b) * = 90r(c) * = 180r(d) * = 0r(e) * = 90r(f)* = 180r

Fig. 2 [Ti14-O-TCNTQ]− (a-c)ࠊ[Ti14-O-TCNTTQ]− (d-f)ࡢ᭱㐺໬ᵓ㐀࠙⤖ᯝ࡜⪃ᐹࠚ
Fig. 2 ࡟ O-C-C(thiophene)-S(thiophene)ࡢ஧㠃ゅ(*)ࢆᅛᐃࡋࡓ㝿ࡢ[Ti14-O-TCNTQ]− (a-c)ࠊ
[Ti14-O-TCNTQ]− (d-f)ࡢ᭱㐺໬ᵓ㐀ࢆ♧ࡍࠋ* = 0rࠊ90rࠊ180r࡛ᅛᐃࡋࡓᵓ㐀᭱㐺໬ィ⟬࡛ࡣࠊ
TCNTQ ࡛ࡣ(a) * = 0rࠊTCNTTQ ࡛ࡣ(e) * = 90rࡀ᭱ࡶప࠸࢚ࢿࣝࢠ್࣮ࢆ♧ࡋࡓࠋTCNQ ࡛ࡣ㓟໬ࢳࢱࣥ⾲㠃ୖ࡟྾╔ࡋࡓỈศᏊࡀ⬺Ỉ⣲໬ࡋࡓ㓟⣲࢔ࢽ࢜ࣥ࠿ࡽ TCNQ ࡢࢪࢩ࢔ࣀ࣓ࢳࣞࣥᇶ࡬ࡢ
ồ᰾௜ຍ཯ᛂ࡟ࡼࡿ໬Ꮫ྾╔≧ែ࡜ࡋ࡚ࠊO-C-C(benzene)-C(benzene)ࡢ஧㠃ゅࡀ 90rࡢ᭱Ᏻᐃᵓ㐀ࢆᚓ࡚࠾ࡾࠊ[Ti14-O-TCNTQ]−ࡢࡳ␗࡞ࡿ⤖ᯝ࡜࡞ࡗࡓࠋࡇࢀࡣ TCNTQ ࡢ㠀྾╔ഃࡢࢪࢩ࢔ࣀ࣓ࢳ
ࣞࣥᇶࡢ୍᪉ࡢࢩ࢔ࣀᇶࡀࠊ㓟໬ࢳࢱࣥ⾲㠃࡟ᏑᅾࡍࡿỈศᏊ࡜Ỉ⣲⤖ྜࡍࡿࡇ࡜࡟ࡼࡿᏳᐃ໬ࡀཎ
ᅉ࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿࠋᙜ᪥ࡣ[Ti14-O-TCNTQ]−ࠊ[Ti14-O-TCNTTQ]−ࡢ᣺ືᩘࢫ࣌ࢡࢺࣝࠊ྾཰ࢫ
࣌ࢡࢺࣝࡢ⤖ᯝࢆሗ࿌ࡍࡿࠋ
࠙ཧ⪃ᩥ⊩ࠚ
1. R. Jono, J. Fujisawa, H. Segawa, K. Yamashita, J. Phys. Chem. Lett. 2, 1167 (2011)

3P131ప ࡟࠾ࡅࡿ༢ᒙ࣮࢝࣎ࣥࢼࣀࢳ࣮ࣗࣈࡢ⇕ࢥࣥࢲࢡࢱࣥࢫ࡟ࡘ࠸࡚ࡢ⌮ㄽⓗ◊✲㻔ᮾ኱㝔䞉ᕤ㻕㻌 䕿⏿㻌 ᬛ⾜䠈Ἑྜ㻌 ᏹᶞ䠈኱ᡞ㻌 㐩ᙪ䠈ᒣୗ㻌 ᫭୍㻌

Chirality Dependence of Quantum Thermal Transport in Carbon
Nanotubes at Low Temperatures: A First-Principles Study(Graduate School of Engineering, the University of Tokyo)
Tomoyuki Hata, Hiroki Kawai, Tatsuhiko Ohto, and Koichi Yamashita࠙◊✲⫼ᬒࠚ
༢ᒙ࣮࢝࣎ࣥࢼࣀࢳ࣮ࣗࣈ(SWCNT)ࡣᐊ ௜㏆࡛ࡶࠊ1 ੇ࡜࠸࠺㛗࠸ᖹᆒ⮬⏤⾜⛬ࢆᣢࡘࡇ࡜࠿ࡽࠊࢼࣀࢫࢣ࣮ࣝࡢ⇕㟁⣲Ꮚ࡜ࡋ࡚ࡢ฼⏝ࡀὀ┠ࡉࢀ࡚࠸ࡿࠋSWCNT ࢆ⇕㟁⣲Ꮚ࡜ࡋ࡚฼⏝ࡍࡿୖ࡛ࡣࠊࡑࡢࢼࣀᵓ㐀ࡀ⇕ఏᑟ≉ᛶ࡟࡝ࡢࡼ࠺࡞ᙳ㡪ࢆ୚࠼ࡿࡢ࠿ࢆ⢭ᰝࡍࡿᚲせࡀ࠶ࡾࠊᐇ㦂ࠊ⌮ㄽࡢ୧㠃࠿ࡽ◊✲ࡀ࡞ࡉࢀ࡚ࡁࡓࠋ
㏆ᖺࠊᴟప࡟࠾࠸࡚ࠊSWCNT ࡢ⇕ࢥࣥࢲࢡࢱࣥࢫࡀ୍ᐃ࡜࡞ࡿ

Ꮚ໬ࣉࣛࢺ࣮ࡀほᗘ㡿ᇦ(0~40K)ࠊ㔞ࡉࢀࡓ[1]ࠋLandauer බᘧ࡜ zone-folding model ࠿ࡽసᡂࡋࡓ phononband ࢆ⏝࠸ࡓィ⟬࡟ࡼࡾࠊ⌮ㄽⓗ࡟ࡶ㔞Ꮚ໬ࣉࣛࢺ࣮ࡣ☜ㄆ࡛ࡁࡓ[2]ࡀࠊࡑࡢ ᗘᖜࡣ᭱኱࡛ࡶ 20K ࡯࡝࡛ࠊᐇ㦂⤖ᯝ࡜ࡢ஋㞳ࡀၥ㢟どࡉࢀ࡚࠸ࡿࠋ
ࡲࡓࠊࣔࢹࣝ࡟ࡼࡿ phonon ࣂࣥࢻィ⟬࡞࡝࠿ࡽ SWCNT ࡢ㙐㛗౫Ꮡᛶࡸ༙ᚄ౫Ꮡᛶࡀホ౯ࡉࢀ࡚࠸ࡿࡀࠊ࢝࢖ࣛࣜࢸ࢕౫ᏑᛶࡣᏑᅾࡋ࡞࠸࡜ࡉࢀ࡚ࡁࡓࠋࡋ࠿ࡋࠊgraphene ࢩ࣮ࢺࡢ⇕ఏᑟᗘࡀࢩ࣮ࢺࡢ᪉ྥ࡟ࡼࡾ኱ࡁࡃᙳ㡪ࢆཷࡅࡿࡇ࡜ࡀࠊ➨୍ཎ⌮ィ⟬࡟ࡼࡾⓎぢࡉࢀࡓࡇ࡜࠿ࡽ[3]ࠊSWCNT ࡢ࢝࢖ࣛࣜࢸ࢕౫Ꮡᛶ࡟ࡘ࠸࡚ࡶࠊࡼࡾཝᐦ࡞ᡭἲ࡟ࡼࡿホ౯ࡀᚲせ࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿࠋ
࠙┠ⓗࠚୖ㏙ࡢ◊✲⫼ᬒࢆཷࡅ࡚ࠊᮏ◊✲࡛ࡣ➨୍ཎ⌮ⓗ࡟ SWCNT ࡢ⇕ࢥࣥࢲࢡࢱࣥࢫࢆィ⟬ࡋࠊప࡛ࡢ㔞Ꮚ໬ࣉࣛࢺ࣮ࡢ

ᗘᖜࡢ෌⌧ࢆᅗࡿ࡜࡜ࡶ࡟ࠊᐇ㦂࡜ࡢ஋㞳ࡢཎᅉࢆ⪃ᐹࡍࡿࠋࡲࡓࠊ࢝࢖ࣛࣜࢸ࢕౫Ꮡᛶ࡟ࡘ࠸࡚ࡶࠊ➨୍ཎ⌮ィ⟬࡟ᇶ࡙࠸ࡓࠊࡼࡾཝᐦ࡞ホ౯ࢆ⾜࠺ࠋ࢝࢖ࣛࣜࢸ࢕࡟ࡣ༙ᚄ౫Ꮡᛶࡢᙳ㡪ࢆྍ⬟࡞㝈ࡾ᤼㝖ࡍ࡭ࡃࠊ༙ᚄࡢ㏆࠸(3, 3)ࠊ(5, 0)ࠊ(4, 2)ࢆ᥇⏝ࡋࡓ㸦⾲ 1㸧ࠋ⾲ 1 : SWCNT ࡢᵓ㐀᝟ሗ࡜➨୍ගᏛ࣮ࣔࢻࡢẚ㍑┤ᚄ࿘ᮇ㛗➨୍ගᏛ࣮ࣔࢻ

࢝ࢵࣉࣜࣥࢢ

(Bohr)(Bohr)

(meV)

(meV)

(3, 3)

7.97

70.21

19.96

2.36

(5, 0)

7.75

72.38

16.74

4.70

(4, 2)

8.04

64.33

15.75

6.24

࠙ᡭἲࠚ
ᮏ◊✲࡛ࡣᐦᗘỗ㛵ᩘἲ࡜㠀ᖹ⾮ Green 㛵ᩘἲ(NEGF)ࢆ⏝࠸࡚ࠊ⇕ࢥࣥࢲࢡࢱࣥࢫࡢィ⟬ࢆ⾜ࡗࡓࠋࡲࡎࠊSWCNT ࡢ force constant matrix ࢆ᪤Ꮡࡢᐦᗘỗ㛵ᩘἲࣃࢵࢣ࣮ࢪࢆ⏝࠸࡚ィ⟬ࡋࡓࠋḟ࡟ࠊNEGF ࡟ᇶ࡙࠸ࡓ phonon transpot ࣉࣟࢢ࣒ࣛࢆ㛤Ⓨࡋࠊࡑࢀࢆ⏝࠸
࡚ force constant ࠿ࡽ㏱㐣ಀᩘࠊཬࡧ⇕ࢥࣥࢲࢡࢱࣥࢫࢆィ⟬ࡋࡓ[4]ࠋ
࠙⤖ᯝ࡜⪃ᐹࠚϨ ࢝࢖ࣛࣜࢸ࢕౫Ꮡᛶ
⇕ࢥࣥࢲࢡࢱࣥࢫࡢィ⟬⤖ᯝࢆࠊඛ⾜ࡢ⤖ᯝ[5,6]࡜ඹ࡟ᅗ 1 ࡟ࡲ࡜ࡵࡓࠋᐊ௨ୖ࡛

SWCNT(3, 3)࡜(4, 2)ࡀࡼࡃ୍⮴ࡋ࡚࠸ࡿ୍᪉࡛ࠊ(3, 3)ࡢప 㒊ศ࡛ࡢ஧ḟ᭤⥺ⓗ࡞❧ࡕୖࡀࡾࡸ(5, 0)ࡢ 150K ௨ୖ࡛ࡢᢚไࡉࢀࡓᣲື࡞࡝ࠊ࢝࢖ࣛࣜࢸ࢕౫ᏑᛶࡀᏑᅾࡍࡿࡇ࡜ࡀศ
࠿ࡗࡓࠋ㏱㐣ಀᩘ࠿ࡽ(3, 3)ࡀప 㒊ศ࡛᭤⋡ࢆᣢࡘࡢࡣࠊప ࡛ࡢගᏛ࣮ࣔࢻࡀఏᑟ࡟ᐤ୚
ࡋጞࡵࡿ ᗘࡀࠊ௚ࡢ஧ࡘ࡜ẚ㍑ࡋ࡚㐜࠸ࡇ࡜࡟㉳ᅉࡋ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡗࡓࠋࡇࢀࡣࠊ(3,3)ࡢ➨୍ගᏛ࣮ࣔࢻࡢບ㉳࢚ࢿࣝࢠ࣮ࡀ㧗࠸ࡇ࡜࡟㉳ᅉࡋ࡚࠸ࡿ࡜⪃࠼ࡽࢀࡿ㸦⾲ 1㸧ࠋࡲࡓࠊ(5, 0)࡟࠾ࡅࡿ⇕ࢥࣥࢲࢡࢱࣥࢫࡢ 150K
௜㏆࠿ࡽࡢᢚไࡣࠊ㏱㐣ಀᩘࡀ 50-70meV ௜㏆࡛኱ࡁࡃῶᑡࡍࡿࡇ࡜࡟㉳ᅉࡍࡿࡇ࡜ࡀศ࠿ࡗࡓࠋϩ 㔞Ꮚ໬ࣉࣛࢺ࣮ࡢ ᗘᖜ㔞Ꮚ໬ࣉࣛࢺ࣮ࡢ

ᗘᖜࢆࠊᐇ㦂⤖ᯝ[1]ཬ

ࡧࣔࢹࣝィ⟬ࡢ⤖ᯝ࡜ẚ㍑ࡋࡓ㸦ᅗ 2㸧ࠋ➨୍ཎ⌮࡟ࡼࡿ⤖ᯝࡣࠊࣔࢹࣝィ⟬࡜ẚ㍑ࡋ࡚
ᗘᖜࡀ㛗ࡃ࡞ࡾࠊᐇ㦂⤖ᯝ࡜ẚ㍑ࡋ࡚ࡶᩚྜᛶࡢ㧗࠸ࡶࡢ࡜࡞ࡗࡓࠋࡲࡓࠊ࢝࢖ࣛࣜࢸ
࢕࡟౫Ꮡࡋ࡚ࣉࣛࢺ࣮ࡢ ᗘᖜࡀ኱ࡁࡃ␗࡞ࡿࡇ࡜ࢆⓎぢࡋࡓࠋᐇ㦂࡜ྠᵝࡢ༙ᚄࢆᣢࡕࠊ
㐺ษ࡞࢝࢖ࣛࣜࢸ࢕ࡢ SWCNT ࢆ㑅ࡪࡇ࡜࡛ࠊ
ᐇ㦂ࢆ෌⌧࡛ࡁࡿྍ⬟ᛶࢆ♧၀࡛ࡁࡓࠋ
࠙ཧ⪃ᩥ⊩ࠚ
[1]J. Hone, M. C. Llaguno, M. J. Biercuk, A. T. Johnson, B. Batlogg, Z. Benes, J. E. Fischer, Appl. Phys. A 74
339 (2002).
[2]T. Yamamoto, K. Watanabe, Phys. Rev. Lett. 96 255503 (2006).
[3]Z. W. Tan, J.-S. Wang, C. K. Gan, Nano Lett. 11 214 (2011)[4]T. Hata, H. Kawai, T.Ohto, K. Yamashita, J. Chem. Phys. 139 044711 (2013)[5]N. Mingo, D. A. Stewart, D. A. Broido, and D. Srivastava, Phys. Rev. B 77 033418 (2008)[6]T. Yamamoto, S. Konabe, J. Shiomi, S. Maruyama, Appl. Phys. Express 2 095003 (2009)

3P132ሷ⣲྾╔㔠ࢡࣛࢫࢱ࣮࠿ࡽࡢỈ⣲࡟ࡼࡿሷ⣲㝖ཤ࡟㛵ࡍࡿ⌮ㄽⓗ◊✲㸦㜰኱㝔࣭⌮㸧ከ⏣ ᖾᖹ㸪 ᳜⏣ Ὧ⏕㸪 ᯘ ⚈⏕㸪 ᆏ⏣ ᫭ᖹ㸪 ᒣ୰ ⚽௓㸪 ໭Ἑ ᗣ㝯㸪 ᕝୖ ㈗㈨㸪 ዟᮧ ග㝯࠙ᗎࠚ㔠ࢆ⢏ᚄ 5nm ௨ୗ࡛㔠ᒓṧ໬≀࡟ᢸᣢࡋࡓࡶࡢࡣ㔠ᢸᣢゐ፹࡜࿧ࡤࢀࡿࠋ㔠ᢸᣢゐ፹࡟ࡣࠊ౛࠼ࡤ-70Υࡢప ࡛ࡶ୍㓟໬Ⅳ⣲ࡢ㓟໬཯ᛂ࡟ᑐࡋ࡚άᛶࢆ♧ࡍ࡜࠸ࡗࡓࠊ௚ࡢ㈗㔠
ᒓᢸᣢゐ፹࡟ࡣぢࡽࢀ࡞࠸≉␗࡞ゐ፹άᛶࡀぢฟࡉࢀ࡚࠸ࡿࠋ㔠ࢆ⢏ᚄ 5nm ௨ୗ࡛㔠ᒓ㓟໬≀࡟ᢸᣢࡍࡿ࡟ࡣࠊ୰࿴ࡸỈ⣲࢞ࢫ࡟ࡼࡿ㑏ඖ࡟ࡼࡾሷ⣲ࢆ㝖ཤࡍࡿ࠿๓㥑య࡜ࡋ࡚ሷ⣲ࢆྵࡲ࡞࠸㔠໬ྜ≀ࢆ⏝࠸࡞ࡃ࡚ࡣ࡞ࡽ࡞࠸ࠋࡇࡢࡼ࠺࡞ࠊ㔠ᢸᣢゐ፹ㄪ〇᫬࡟࠾ࡅࡿሷ⣲࡟ࡼࡿ㔠⢏Ꮚࡢจ㞟ಁ㐍ࡣࡼࡃ▱ࡽࢀࡓࡇ࡜࡛࠶ࡿࡀࠊࡑࡢヲ⣽࡞ᶵᵓ࡟ࡘ࠸࡚ࡢ᫂ᛌ࡞ㄝ᫂
ࡣᮍࡔ࡞ࡉࢀ࡚࠸࡞࠸ࠋࡑࡋ࡚ࠊሷ⣲࡟ࡼࡿ㔠ᚤ⢏Ꮚจ㞟ᶵᵓࢆṇࡋࡃ⌮ゎࡍࡿࡓࡵ࡟ࡣࠊ
ሷ⣲ࡀ㝖ཤࡉࢀࡿࡇ࡜࡟ࡼࡾจ㞟ࡀ࠾ࡇࡽ࡞ࡃ࡞ࡿࡇ࡜ࠊሷ⣲ࡀ⬺㞳ࡋ࡚࠸ࡃᶵᵓࡶㄪ࡭ࡿᚲせࡀ࠶ࡿࠋࡑࡇ࡛ᮏ◊✲࡛ࡣࠊỈ⣲࡟ࡼࡿሷ⣲㝖ཤᶵᵓ࡟╔┠ࡋࠊ཯ᛂࡢึᮇẁ㝵࡛⏕ᡂࡍࡿ࡜⪃࠼ࡽࢀࡿ HAunCl ࣔࢹࣝࢡࣛࢫࢱ࣮࠿ࡽࡢ HCl ศᏊ⬺㞳ࢆᐦᗘỗ㛵ᩘ⌮ㄽ㸦DFT㸧࡟ᇶ࡙ࡃ㔞Ꮚ໬Ꮫィ⟬࡛ྲྀࡾᢅࡗࡓࠋ

࠙ィ⟬ᡭἲࠚ
ィ⟬ࣉࣟࢢ࣒ࣛ࡟ࡣ Gaussian09 ࢆ⏝࠸ࡓࠋ㔠ࡢᇶᗏ㛵ᩘ࡟ࡣ SDD ࢆ౑⏝ࡋࡓࠋሷ⣲࡜Ỉ⣲ࡢᇶᗏ㛵ᩘ࡟ࡣࠊ6-31+G**ࢆ⏝࠸ࡓࠋ஺᥮࣭┦㛵ỗ㛵ᩘ࡟ࡣ PBE0 ࢆ⏝࠸ࡓࠋ࠙⤖ᯝ࡜⪃ᐹࠚHAunCl㸦n=1~6㸧ࣔࢹࣝࢡࣛࢫࢱ࣮࠿ࡽࡢࠊHCl ⬺㞳ࡢ཯ᛂࣃࢫࢆᅗ 1 ࡟♧ࡋࡓࠋ࠸ࡎࢀࡢࣔࢹࣝ཯ᛂ࡟࠾࠸࡚ࡶࠊ᭱ࡶ㞀ቨࡢ㧗࠸㑄⛣≧ែࡣࠊ᭱ᚋࡢ㑄⛣≧ែࠊࡘࡲ
ࡾࠊH-Cl 㛫ࡢ⤖ྜࢆᙧᡂࡍࡿ㑄⛣≧ែ࡛࠶ࡗࡓࠋࡑࡢࠊT=598.15 K ࡟࠾ࡅࡿάᛶ໬⮬⏤࢚ࢿࣝࢠ࣮ࡢ್ࡣࠊ16.16 kcal/mol; n=1, 26.15 kcal/mol; n=2, 17.52 kcal/mol; n=3, 28.16
kcal/mol; n=4, 20.70 kcal/mol; n=5, 33.93 kcal/mol; n=6 ࡜ồࡲࡗࡓࠋࡇࡢࡼ࠺࡟ࠊάᛶ໬㞀ቨ࡟ࡣഅወᛶࡀ࠶ࡾࠊ㔠ཎᏊᩘࡀወᩘಶ࡛࠶ࡿࣔࢹࣝࢡࣛࢫࢱ࣮࠿ࡽࡢ᪉ࡀࠊHCl ࡀᢤࡅࡸࡍ࠸ࡇ࡜ࡀࢃ࠿ࡿࠋࡇࡢഅወᛶࡣࠊ᭱ࡶᏳᐃ࡞྾╔ᵓ㐀㸦ᅗ 1 ୰ࡢ Ini㸧ࡢᏳᐃᛶࢆ཯ᫎࡋࡓ
ࡶࡢ࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿࠋࡑࡋ࡚ࠊn ࡀ኱ࡁࡃ࡞ࡿ࡟ࡘࢀ࡚άᛶ໬㞀ቨࡣ㧗ࡃ࡞ࡗ࡚࠾ࡾࠊ
ࡇࢀࡣࠊỈ⣲࡟ࡼࡿሷ⣲㝖ཤࡣ㔠ゐ፹ࡢㄪ〇ࡢึᮇẁ㝵࡛⾜࠺࡭ࡁ࡛࠶ࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿࠋ
ࡲࡓࠊᅗ 1 ࡟♧ࡋࡓ཯ᛂࡣ࠸ࡎࢀࡶ྾⇕཯ᛂ࡛࠶ࡾࠊࡑࡢάᛶ໬㞀ቨࡀᐊ㧗ࡉ࡛࠶ࡿࡇ࡜࠿ࡽࠊỈ⣲ࢆ⏝࠸࡚ሷ⣲ࢆ㝖ཤࡍࡿ࡟ࡣࠊ᪼
♧ࡉࢀࡓࠋ࡛ࡣ㉸࠼࡟ࡃ࠸ࡀᚲせ࡛࠶ࡿࡇ࡜ࡀ⌮ㄽⓗ࡟

(a)
(b)

(c)

(d)

(e)

(f)

ᅗ 1 HAunCl㸦n=1~6㸧ࣔࢹࣝࢡࣛࢫࢱ࣮࠿ࡽࡢࠊHCl ⬺㞳ᶵᵓࡢ཯ᛂࣃࢫࠋ(a) n=1, (b)n=2, (c) n=3, (d) n=4, (e) n=5, (f) n=6ࠋ

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#Õ£GÃ?Æ¿(*^ªÃ©¿)ÅÒÔ-ÈáºÅÕÑÜÅâÚÑÔ_Üo{ùÆâÐÄËÖwÑÛÐ%QÆâË7~Ñ¾á
[Mn12O12(CH3COO)16(H2O)4] Ñ ¾ á º . û Ô  È.û [Mn12O12(CH 3COO)16(H2O)4][Mn12O12(CH3COO)16(H2O)4]Ö¹N¥Õ Mn4+(S =3/2)ÂßÓá¥Ò)¡¥Õ Mn3+(S =2)Âß
Óá¥Ã#JPzÔØÎ¿ÐÁà¹7ÑÖ S =10 Ò¿À5ÄÓjóúòøìä`ÇÐ¿áºµ,Ö¹7~[Mn12O12(CH3COO)16(H2O)4]ÔÎ¿Ð¹ê÷3:X D äuÔÞàÈáÅÒÑÊÕjxZPäÜà¹ÊÕ7~sPÔÎ¿Ð>äÍËÕÑ¹2(ÈáºÚË¹ÉÐx§@ÒÇÐ Cr3+(S =3/2)Ý Fe3+(S =5/2)Ñ Mn3+äVÇËÔÎ¿ÐÜuÔÞá D Õä¿¹7~ÕhfÝÊÕ7ÕS¨Ô«Èá>ÜÍËÕÑ¹ÅâÜÉÐ2(Èáº¼u½µ ê÷3ÖÕïñöìíåøÔÞà¢Æâáºµ3 P133
ÅÅÑ D¹E ÃZ'¹D²Z'Õê÷3:XÑ¾áºê÷3ÖiÕW³Ñ¾

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Ö¹7Õéðø#Õ¯Õæîöçú°4Ô}KÈá·E =¶D ¶S 2 äv¿ËºdÕÖKµ[yÈáº¼!Yt½[1] R. McWeeny, Y. Mizuno, Proc. R. Soc. London, 1 961, 259, 554[2] M. Shoji, et al, Polyhedron, 2 005, 24, 2708
[3] M. R. Pederson, S. N. Khanna, Phys. Rev. B, 1 999, 60, 9566
[4] R. Takeda, et al, Polyhedron, 2 005, 24, 2238

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Analysis of electronic structure of chlorine adsorbed gold clusters
based on linear response function(Osaka Univ1, TOYOTA Research Institute2) Koki Ueda1, Kohei Tada1, Kyohei Komi1,
Shusuke Yamanaka1, Takashi Kawakami1, Yasutaka Kitagawa1, Haruki Nakamura1,
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spin density and bond-order versions of linear response functions(Osaka Univ.*, NEC**) Shusuke Yamanaka*, Kazuto Nakata**, Yasutaka Kitagawa*,
Takashi Kawakami*, Kizashi Yamaguchi, Mitsutaka Okumura *,Haruki Nakamura*µ Ļ§¨~¨(QM/MM)éç)ĺĐĎ(¨À4

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δPij = ∫ dr′ δPij δv(r′) δv(r′)(2)

pÂû&Ā δv m (r′) '¬8GRa«¶Ì δρm (r)δρm (r) = ∫ dr′(δρm (r) δv m (r′))δv m (r′)(3):ĢÛė$ĤĊv$"Y>B`Qa(f¿=>a Fe(III)'Í:e(«¶5+GRa«¶Ì:
Figure 1 'āÌ)´X^S<]aô
d'Ņ®
 X^S<(a)Fig. 1.

]aļ=>(b)

Fe(III)'Í:e((a)«¶, (b)GRa«¶Ìľx) 0.01.

+GRa(¢'¬8ĔĞň'&"8a(ńĚ5$õîìá¨#ęþ69hª:Ô"8ÌqÎ(Ņ¬ăÁ)Y>B`Qa( pdb ÞĴ(2cmm)(Ņ¬ăÁ'į"
8
Fig. 2 ')§ğā#(ĝ»¸(ē»ÀĉĽÐ {δρ (i) /δv( j)}i, j =1~ 37 (U`KN((a)«¶5+(b)GRa«¶):ā(a)Fig. 2.

(b)

D=N#((a)«¶5+(b)GRa«¶ē»ÀĉĽÐU`KN

index27 oŀäĐ#
7GRa(Ò)äĐd

,(qÎ(Ģy¶$./&(³)GRaÌļ=>a( d İķ$X^S<]a(İķ( d-ýjuö'į-ýjuö#)qÎ­h8ĒâÐ'Ľ8ĒÜ4Ĩđm(õtĽĵ§Ď'¬8ĒÜ)ºÓùğ8g©#8ĖÑñ
1. S. Yamanaka, et al. AIP Conf Proc 1504 (2012) 916; K. Ueda, S. Yamanaka, K. Nakata, M. Ehara,
M. Okumura, K. Yamaguchi, H. Nakamura, Int J Quantum Chem. 113 (2013) 336; S. Yamanaka et al.
J. Phys. Conf. Proc. submitted.
2. S. Yamanaka, et al. J. Phys. Soc. Jpn. sup. submitted.

3P136(/* ἲ࡟ࡼࡿᨃ୍ḟඖ㔠ᒓ㘒యࡢ㧗ᅽୗ ,㸫0㸫, 㑄⛣ࡢ㉸ຠ⋡ⓗᐃ㔞ゎᯒ㸦஑኱㝔࣭⥲⌮ᕤ 㸪-67&5(67㸧‫ۑ‬/LX.DL㸪ᢡᮏ⿱୍ 㸪㟷ᮌⓒྜᏊ 

Highly efficient analyses of I-M-I transition in quasi-1D metal
complexes by elongation method(Kyushu Univ.1㸪JST-CREST2) ○Liu Kai1㸪Yuuichi Orimoto1㸪Yuriko Aoki1, 2

The one-dimensional (1D) d8 transition metals systems, [M(dmg)2, M=Ni, Pd and Pt,
dmg=Bis(dimethylglyoximato)] have attracted a lot of attentions for their interesting electricaland optical properties. For example, the Pt(dmg)2 system (structure shown in Fig. 1(a)) basedon molecular stacking units exhibits insulator-to-metal-to-insulator (IMI) transition [1] at highpressure with potential applications of pressure switch devices. For the further development of
this kind of metals, we carefully examined the nature of this transition from the stand point ofelectronic structures .
The structure of Pt(dmg)2, is a d8-square-planar complex with Pt-Pt distance of 3.26 Å inthe direction of stack at normal pressure (shown in Fig. 1(b)). However, the distance of thismetal bond (Pt-Pt) between two units will decrease when the pressure increases.
Considering the stacking behaviors of the Pt(dmg)2 system, we deveploed the elongation(ELG) method [2] including the relativistic effectsby third order Douglas-Kroll (DK3) totheoretically simulate the chain stacking process for heavy metal included systems andexamine the orbital energy gaps changes along with the increasing of unit size at different
distance of metal bond. The different distance of metal bond represents the situation ofPt(dmg)2 system at different pressure.
(a)

(b)

Fig. 1 The structure of Pt(dmg)2. (a). For one Unit, (b) For the stacking structure.

The orbital energy gaps of 16 units of Pt(dmg)2 system, calculated by ELG with DK3correction at mini basis set of HF level, become narrow as the chain elongates (shown in Fig.
2). Meanwhile, the orbital gap also decreases, if the distance of metal bond decreases. In otherwords, when the pressure increases, the electrical conductivity of Pt(dmg)2 system isenhanced because of the narrowing orbital energy gaps.
In order to more accurately investigate the details of this gap changes, 8 units of Pt(dmg)2
are calculated by mPW1PW91 method with large basis set. The LanL2DZ basis set isemployed to include the relativistic effect for metal atoms, and 6-31G(d,p) for the rest atoms.
The orbital energy gap of 8 units of Pt(dmg)2 will
decrease as the pressure increases. However, when the
distance is less than 2.6 Å, the energy gap becomes large
again (shown in Fig. 3). This energy gaps changes arevery similar to the experiment data. When the pressure of
the system increases, the Pt(dmg)2 system indicates the
IMI transition. The orbital shape of the HOMO andLUMO is also compared as the metal bond changes forthe distance of metal bond is equal to 2.3 Å, 2.6 Å, and3.2 Å. The result shows that at normal pressure (3.2 Å)
the transition is attributed to dz2 to dpz. While when thepressure increases, the transition is changed to dpz to dz2,
at the same time, because of the small energy gap, thematerial shows the metallic properties. When thepressure is increasing, the transition changes back again.
However, the orbitals involving the transition becomeless. This change of orbital transition clearly explains theexperiment phenomenon. Under the pressures, the orbitaltransition arises the IMI transition of Pt(dmg)2 systems.
This findings will also guide us for the further material
design and properties improvement.

Fig. 2 The orbital energy gap

changes by ELG method with DK3approximation.

Fig. 4 The orbital shape of
Fig. 3 The orbital energy gaps of 8 units of Pt(dmg)2 system.

HOMO and LUMO.

[1] Takeda, K.; Shirotani, I.; Yakushi, K. Chem. Mater. 2000, 12, 912.
[2] Imamura, A.; Aoki, Y.; Maekawa, K. J. Chem. Phys. 1991, 95, 5419.

3P137
ELG ἲ࡟ࡼࡿྵ㔠ᒓ BN/C ࣊ࢸࣟࢼࣀࢳ࣮ࣗࣈࡢ㟁Ꮚ≧ែ࡜ᶵ⬟ゎᯒ㸦஑኱㝔࣭⥲⌮ᕤ 1, ஑኱᝟ᇶࢭ 2, JST-CREST3㸧‫⟄ۑ‬஭ுኴ 1, Liu Kai1, ᢡᮏ⿱୍ 1, ᮏ⏣ᏹ᫂ 2, 㟷ᮌⓒྜᏊ 1,3

Functional properties and electronic states of metal included BN/C
heteronanotubes by Elongation method(Kyushu Univ1., RIIT, Kyushu Univ2., JST-CREST3)‫ۑ‬Ryota Tsutsui1, Liu Kai1, Yuuichi Orimoto1, Hiroaki Honda2, Yuriko Aoki1,3࠙ᗎࠚ࣮࢝࣎ࣥࢼࣀࢳ࣮ࣗࣈ(Carbon NanoTubes: CNTs)ࡸ❅໬࣍࢘⣲ࢼࣀࢳ࣮ࣗࣈ(Boron
Nitride NanoTubes: BNNTs)࡞࡝ࡢࢼࣀࢳ࣮ࣗࣈࡣࢼࣀ࢜ࣉࢸ࢕ࢡࢫࡸࢼࣀ㟁Ꮚࢹࣂ࢖ࢫ࡞࡝ࡢ
ᵝࠎ࡞ศ㔝࠿ࡽὀ┠ࡉࢀ࡚࠸ࡿᮦᩱ࡛࠶ࡾ[1]ࠊࡑࡢ㟁Ꮚ≧ែ࡟ᇶ࡙ࡃᶵ⬟ゎᯒࡀ┒ࢇ࡟⾜ࢃࢀ࡚ࡁࡓࠋࡋ࠿ࡋࠊࡑࡢከࡃࡣࢳ࣮ࣗࣈࡢ୍㒊ࢆษࡾฟࡋࡓࢡࣛࢫࢱ࣮ィ⟬ࡸ࿘ᮇቃ⏺᮲௳ࢆㄢࡋࡓ
ࣂࣥࢻィ⟬࡛࠶ࡾࠊࢳ࣮ࣗࣈ࡬ࡢ୙つ๎࡞ࢻ࣮ࣆࣥࢢࡸ㔠ᒓࡢ」㞧࡞㓄఩ࣃࢱ࣮ࣥࡢຠᯝ࡞࡝ࢆ᳨ドࡍࡿ஦ࡣᅔ㞴࡛࠶ࡗࡓࠋ୍᪉࡛ࢼࣀࢳ࣮ࣗࣈࡣ㛗ࡉࡀ!m ࣮࢜ࢲ࣮࡟ࡶ㐩ࡍࡿᕧ኱⣔࡛࠶ࡾࠊ඲㟁Ꮚࢆ࠶ࡽࢃ࡟ྲྀࡾᢅ࠺ࡼ࠺࡞㔞Ꮚ໬Ꮫࡢᡭἲࡣィ⟬㈨※ࡢ㠃࡛ၥ㢟ࡀ࠶ࡿࠋᡃࠎࡢ◊✲ࢢ࣮ࣝࣉࡀ㛤Ⓨࡋ࡚ࡁࡓ Elongation(ELG)ἲ[2]ࡣࡇࡢࡼ࠺࡞ၥ㢟ࢆゎỴࡋᕧ኱⣔ࢆィ⟬ࡍࡿࡓࡵࡢᡭ
ἲ࡛࠶ࡿࠋᮏᡭἲ࡛ࡣ㐺ᙜ࡞ࢧ࢖ࢬࡢฟⓎࢡࣛࢫࢱ࣮ࢆ⏝ពࡋࠊࡇࢀ࡟ࣔࣀ࣐࣮ࣘࢽࢵࢺࢆḟࠎ࡜௜ຍࡋ࡚࠸ࡃ(Fig.1)ࠋྛࠎࡢࢫࢸࢵࣉ࡟࠾࠸࡚ࠊṇ‽ศᏊ㌶㐨(Canonical Molecular Orbitals:
CMOs)ࡢࣘࢽࢱ࣮ࣜኚ᥮ࢆ⾜࠸ࠊ௜ຍࣘࢽࢵࢺ࡟㏆࠸ Active 㡿ᇦ࡜௜ຍࣘࢽࢵࢺ࠿ࡽ㞳ࢀࡓ
Frozen 㡿ᇦ࡟㌶㐨ࢆᒁᅾ໬ࡉࡏ࡚㡿ᇦᒁᅾ໬㌶㐨(Region Localized Molecular Orbitals:
RLMOs)ࢆసࡿࠋ௜ຍࣘࢽࢵࢺࡣ Active 㒊ศ࡜ࡋ࠿┦஫స⏝ࡋ࡞࠸ࡓࡵᖖ࡟୍ᐃࡢ㡿ᇦࡢ HF ᪉⛬ᘧࢆゎࡅࡤࡼࡃࠊᚑ᮶ἲ࡛ࡣ฿㐩୙ྍ⬟࡞ᕧ኱⣔ࡢィ⟬ࡀྍ⬟࡟࡞ࡿࠋࡲࡓ ELG ἲࡣศᏊ㸦㉸㸧ศᴟ⋡ࢆィ⟬ࡍࡿ᪉ἲࡢ୍ࡘ࡛࠶ࡿ
Finite-Field ἲ࡜⤖ྜࡉࢀ࡚࠾ࡾ㸦ELG-FF
ἲ[3]㸧ࠊᑐ⛠࡞ 5 Ⅼࡢ㟁ሙࡢୗ࡛࢚ࢿࣝࢠ࣮ィ⟬ࢆ⾜࠺஦࡟ࡼࡗ࡚㠀⥺ᙧගᏛ(Non-Linear
Optics: NLO)≉ᛶࢆぢ✚ࡶࡿ஦ࡀ࡛ࡁࡿࠋᮏ
◊✲࡛ࡣ ELG-FF ἲࢆ⏝࠸࡚ࠊ㠀࿘ᮇⓗ࡟㔠ᒓࢆෆໟࡋࡓ࣊ࢸࣟࢼࣀࢳ࣮ࣗࣈࡢ㸦㉸㸧ศᴟ⋡࡟㛵ࡍࡿ⪃ᐹࢆ⾜࠺ࠋ࠙ィ⟬ࠚLi2 ࢆෆໟࡋࡓ(6,0)-BNNT ࢆィ⟬ᑐ㇟࡜ࡋ࡚ ELG-FF ィ⟬ࢆ⾜ࡗࡓࠋ௜ຍࣘࢽࢵ
ࢺࡣഅᩘ␒┠ࢆ B12N12ࠊወᩘ␒┠ࢆ B12N12Li2࡜ࡋ࡚஺஫࡟௜ຍࡉࡏࡓࠋFF ἲ࡟࠾ࡅࡿ㟁ሙࡢ้ࡳᖜࡣEz=0.001 a.u.࡜タᐃࡋࠊ-0.002

Fig.1 Elongation ἲࡢᡭ⥆ࡁ㸦ศᏊ㸸(6,0)-BNNT-Li2㸧

a.u.࠿ࡽ 0.002 a.u.ࡲ࡛ࡢ 5 Ⅼࡢ㟁ሙࡢୗ࡛
RHF/STO-3G ࡛࢚ࣞ࣋ࣝࢿࣝࢠ࣮ィ⟬ࢆ⾜ࡗࡓࠋᚓࡽࢀࡓ㟁ሙࡢୗ࡛ࡢ࢚ࢿࣝࢠ࣮࠿ࡽ௨ୗ
ࡢᘧࢆ⏝࠸࡚ఙ㛗᪉ྥ㸦z ᪉ྥ㸧࡟࠾ࡅࡿ஧ḟࡢ㉸ศᴟ⋡%zzzz ࢆ⟬ฟࡋࡓࠋ% zzzz  {6W (0)  4#W ( E z )  W (E z )1
 #W (2E z )  W (2E z )1} / E z

4

(1)

ࡇࡇ࡛ W(E)ࡣ㟁ሙ E ࡟࠾ࡅࡿ඲࢚ࢿࣝࢠ࣮ࠊ
Ez ࡣ㟁ሙ้ࡳᖜ࡛࠶ࡿࠋ
࠙⤖ᯝࠚFig.2 ࡟ྛࠎࡢ㟁ሙ࡟࠾ࡅࡿ ELG ἲ࡜ᚑ᮶㸦CONV㸧ἲࡢㄗᕪࢆ♧ࡋࡓࠋㄗᕪ

Fig.2 ྛ㟁ሙ࡛ࡢ ELG ἲ࡜ CONV ἲࡢㄗᕪ

E/atom ࡣఙ㛗࡟ᚑࡗ࡚ഹ࠿࡟ቑຍࡍࡿࡶࡢࡢᚎࠎ࡟୍ᐃ್࡟཰᮰ࡍࡿഴྥࡀぢࡽࢀࡓࠋࡲࡓ 10ࣘࢽࢵࢺ┠ࡲ࡛ࡢఙ㛗࡛ㄗᕪࡣ᭱኱ 4.510-7a.u./atom ࡛࠶ࡾࠊELG ἲࡣ CONV ἲࡢ㟁Ꮚ≧ែࢆ㧗࠸⢭ᗘ࡛෌⌧ࡋ࡚࠸ࡿ࡜ゝ࠼ࡿࠋFig.3 ࡟ᘧ(1)࡟ࡼࡗ࡚ồࡵࡽࢀࡓ஧ḟࡢ㉸ศᴟ⋡%zzzz ࡢẚ㍑ࢆ♧ࡋࡓࠋELG ἲ࡜ CONV ἲࡢㄗᕪࡣ᭱኱࡛-5.1%࡛࠶ࡾࠊ㉸ศᴟ⋡ࡢほⅬ࡛ࡶ㧗࠸⢭ᗘࢆ♧ࡋ࡚࠸ࡿ஦࠿ࡽ ELG ἲࡣ NLO ≉ᛶࡢゎᯒ࡟࠾࠸࡚᭷ຠ࡞ᡭἲ࡛࠶ࡿ࡜ゝ࠼ࡿࠋ%zzzz ࡢഴྥࢆぢࡿ࡜඲య࡜ࡋ࡚ࢳ࣮ࣗࣈࡢఙ㛗࡟ᚑࡗ࡚ቑຍࡍࡿഴྥࡀ࠶ࡿࠋࡲࡓࠊወᩘ␒┠ࡢࣘࢽࢵࢺ㸦Li2
ෆໟ㸧ࡀ௜ຍࡍࡿሙྜ࡜അᩘ␒┠ࡢࣘࢽࢵࢺ㸦ࢳ࣮ࣗࣈࡢࡳ㸧ࡀ௜ຍࡍࡿሙྜ࡛ഴྥ࡟ኚ໬ࡀ⌧ࢀ࡚࠸ࡿࠋࡇࡢኚ໬ࢆゎᯒࡍࡿࡓࡵ࡟ࣘࢽࢵࢺ௜ຍ࡟క࠺%zzzz ࡢኚ໬㔞%zzzz ࢆࣉࣟࢵࢺࡋ Fig.4
࡟♧ࡋࡓࠋLi2 ࢆෆໟࡋࡓࣘࢽࢵࢺࡀ௜ຍࡍࡿ࡜ࡁ㸦ᅗ୰㉥ࡢ㡿ᇦ㸧%zzzz ࡣ኱ࡁࡃṇ࡟ኚ໬ࡋࠊࢳ
࣮ࣗࣈࡢࡳࡀ௜ຍࡍࡿ࡜ࡁ㸦ᅗ୰㟷ࡢ㡿ᇦ㸧%zzzz ࡣ࡯࡜ࢇ࡝ኚ໬ࡋ࡚࠸࡞࠸஦ࡀࢃ࠿ࡿࠋࡲࡓ࡝
ࡕࡽࡢሙྜ࡛ࡶࢳ࣮ࣗࣈࡢఙ㛗࡟ᚑࡗ࡚ࡑࡢຠᯝࡣᚎࠎ࡟୍ᐃ್࡟཰᮰ࡍࡿഴྥࡀぢࡽࢀ࡚࠸ࡿࠋ
ᙜ᪥ࡣ㐪ࡗࡓ࢝࢖ࣛࣜࢸ࢕ࡢࢳ࣮ࣗࣈࡸ୍ḟࡢ㉸ศᴟ⋡0zzz ࡟ࡘ࠸࡚ࡶ⪃ᐹࢆ⾜࠺ࠋFig.3 ㉸ศᴟ⋡%zzzz ࡢィ⟬⤖ᯝ

Fig.4 ㉸ศᴟ⋡%zzzz ࡢኚ໬㔞(ELG ἲ)࠙ཧ⪃ᩥ⊩ࠚ
[1] D. Golberg, Y. Bando, C. Tang, and C. Zhi, Adv. Mater., 19, 2413-2432 (2007)[2] A. Imamura, Y. Aoki, and K. Maekawa, J. Chem. Phys. 95, 5419-5431 (1991).
[3] F. L. Gu, Y. Aoki, A. Imamura, D. M. Bishop, and B. Kirtman, Mol. Phys., 101(10),1487-1494 (2003)

3P138
1RGPUJGNN'.) ᴺߩ㐿⊒ߣᣂⷙ⏛ᕈ᧚ᢱ⸳⸘߳ߩᔕ↪㧔਻ᄢ㒮࡮✚ℂᎿ 㧘,56%4'56㧕٤<JW:WP㧘.KW-CK㧘᛬ᧄ⵨৻ 㧘㕍ᧁ⊖วሶ 

Development of open-shell elongation method and its application to
ferromagnetic material design(Kyushu Univ.1㧘JST-CREST2) Zhu Xun1㧘Liu Kai1㧘Yuuichi Orimoto1㧘Yuriko Aoki1, 2

1. Introduction
Conventional (CONV) ab initio method has problem in treating huge systems as big timescale. Many linear scaling schemes including elongation (ELG) method1 have been proposed
during the last decades. Most linear scaling methods are still limited to closed-shell systems.
It is very desired to extend the initial closed-shell ELG method to be able to treat open-shell
systems such as organic molecule-based ferromagnets, which have many advantages andapplications.2, 3 We investigated the accuracy and efficiency of the developed open-shellelongation method for high-spin nonbonding butadiene radicals at the level of restricted
open-shell Hartree-Fock (ROHF). Furthermore, we investigated the organic ferromagnetism
using high-spin stability index Lijmin based on the nonbonding molecular orbitals (NBMOs)
obtained by ELG at the level of ROHF.
2. Method
2.1. Open-shell elongation method
A target system is divided into N units
and each unit is assumed to have an
unpaired electron with up spin (see Fig. 1).
The eigenvalue problem of a starting
cluster consisting of A and B parts issolved to initiate the elongation method.
Canonical MOs of the starting cluster islocalized into A1 part and B part. Next, an
attacking monomer M is added, and the eigenvalue problem of B and M is solved. After that,the B+M part is localized into A2 part and B part. The procedure is repeated until the desired
system size is reached. Cutoff technique can be included to speed up the calculations. As the
eigenvalue problem is only solved for the B+M part, if the coupling between A1 and B + M
part is below threshold, A1 part can be ignored during the self-consistent-field process without
introducing big error in the next step. Finally, the total energy is calculated including thecutoff part.
2.2. High-spin stability index Lijmin
As it is still a challenging problem to obtain the exact energy difference between thelowest spin state and the highest spin state for a system with degenerate NBMOs, a high-spinstability index Lijmin was proposed for quick design of organic ferromagnets.4 Based on the

NBMOs obtained by ELG method at the level of ROHF, we can obtain Lijmin as following:(1) Perform unitary transformation on NBMOs in iterative way as(1)
where ࣂ is the transformation parameter and the optimized ࣂ generates the Lijmin value that is
the minimum overlap of coefficients of NBMOs. As Lijmin varies with ࣂ, ࣂ should be
optimized in iterative way, and the detailed process of obtaining ࣂ can be seen in Ref. 4.
(2) Calculate the Lijmin value4, 5 as(2)
where Lijmin corresponds to the minimum energy difference between the lowest spin (L) state
and the highest spin (H) state, that is, E(L-H) = E(L) – E(H).
3. Results and discussion
We have performed calculations for model 1 in Fig. 2 at
the ROHF/6-31G level of theory. The distance between twounits is 6
for the test. The number of units in the starting
cluster is 10, and 5 units are added each time. The first
cutoff calculation started from 25 units. The threshold of

N
1

N
2

Figure 2. Selected models. Black arrows
are unpaired electrons with up spin

density matrix is 10-8. The deviation of energy (per atom) from theconventional calculation is shown in Fig. 3a. The largest deviationis 1.90 u 10-8 a.u. per atom. As shown in Fig. 3b, the CPU time ofelongation method is faster than that of conventional method when
the system is big enough. We have also performed ELG
calculations at the level of ROHF/6-31G(d) for model 2 in Fig. 2
to obtain Lijmin, the number of units in the starting cluster is 6, and1 unit is added each time. E(L-H) obtained by conventional
method at the ROHF/6-31G(d) level can indicate the level offerromagnetism. As shown in Fig. 4, E(L-H) increases with Lijmin,which means Lijmin can indicate the degree of high-spin stability.
It indicates that the combination between open-shellelongation method and Lijmin index is promising for huge systems
and quick design of organic ferromagnet.
[1] Imamura, A.; Aoki, Y.; Maekawa, K. J. Chem. Phys. 1991, 95,

Figure 3. Comparison of energy
and CPU time between ELG andconventional methods at thelevel of ROHF/6-31G for model 1

5419-5431.
[2] Crayston, J. A.; Devine, J. N.; Walton, J. C. Tetrahedron 2000, 56,
7829-7857.
[3] Barone, V.; Boilleau, C.; Cacelli, I.; Ferretti, A.; Monti, S.; Prampolini, G.
J. Chem. Theory Comput. 2013, 9, 300-307.
[4] Aoki, Y.; Imamura, A. Int. J. Quantum. Chem. 1999, 74, 491-502.
[5] Zhu, X.; Aoki, Y. Curr. Phys. Chem. 2013, 3, 99-112.

Figure 4. Variation of
E(L-H) with Lijmin
for model 2

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Through-space/bond interaction analysis on NLO properties
enhancement of molecular switches(Kyushu Univ.1 㸪JST-CREST2) ○Jiang Lizhi1㸪Yuuichi Orimoto1㸪Yuriko Aoki1, 

Recently, the nonlinear optical materials with controlled switching properties draw a lotof interests, because such kinds of materials are good candidates for optical information
storage devices, and photoresponsive materials, as well as biosensors. A good NLO switch
should exhibit an enough large difference of the response between the two states. To date, avariety of the NLO switches have been designed and investigated experimentally andtheoretically [1-2]. There are several kinds of the molecular switches, of which, thetransformation can be caused by the acidochromes or photochromes, and so on. In this work,
we focus on the acidochromic induced tunable NLO switches, closed form (CF) and open
form (OF) of (10-ethenyl-indolino[2,1-b]oxazolidines), as shown in Fig. 1. When the pHs ofthe environments change, the structures of the acidochromic compounds are tuned. The
transformation of the structures can be detected by comparing the absorption spectra.
Although the designs and investigations of the mechanisms are increasing, the further deep
investigations of the mechanism are still on the way.

Fig. 1 The switching procedures of target molecules (10-ethenyl-indolino[2,1-b]oxazolidines).
This mechanism of the switchable properties can be examined through orbital interaction
perspective. The concept of through space/bond (TS/TB) orbital interaction which was
originally proposed by R. Hoffmann, et al.[3], is very useful in demonstrating the mechanismof the stereoelectronic effects and charge transfer. Our group developed the TS/TB orbital
interaction analysis in ab initio level[4], in this analysis, the interactions between orbitals areestimated quantitatively. The procedure of the
TS/TB orbital interaction analysis in ab initio
level is by modifying the exponent α of theGaussian-type orbitals (exp(-αr2)) in the basis-sets.
In the procedure, the estimation of the interaction
between hydrogen-like atoms A and B was
considered as an example (Fig. 2(a)). AOs r and s
belong to atoms A and B, respectively. The
absolute magnitude of the exponents in theGaussian-type functions related to the interaction
between r and s should be increased gradually until
orbital overlap is completely eliminated. And theFig. 2 The procedure of TS/TB orbital
deletion.

π-π interaction is deleted as shown in Fig. 2(b). The finite-field(FF) method has been applied
for the (hyper)polarizabilities calculations. All the molecules are optimized at HF/6-31G(d),and the polarizability and first hyperpolarizabilities are also calculated at HF/6-31G(d) in
GAUSSIAN 09.
For the OF system as shown in Fig. 3, the first hyperpolarizability β is 6300.49 au. The βof the CF is 712.99 au. The ratio of the β between OF and CF is 8.84 (OF/CF). The big ratiosof the hyperpolarizabilities between CF and OF suggest that these kinds of molecules will bea good candidate for the molecular switches.
There are two assumptions of theeffects that cause the big difference ofthe hyperpolarizabilities between CF
and OF. One of the factors causing thelarge hyperpolarizability of OF may befrom the electron transfer (seeFig.3(a)) , another one may be comefrom the interaction between the cation
and anion formed after the ring is open
Fig. 3 (a) The electron transfer along the backbone(see Fig.3(b)).
of OF, (b) electron interaction between the anion
The mechanism of the enhancement
and cation in the OF.
of the hyperpolarizabilities of OF
molecules is analyzed by evaluating the TS/TB orbital interactions. The investigations are stillon the way.
[1] Nenon, S.; Champagne, B. J. Chem. Phys. 2013, 138, 204107.
[2] Sanguinet, L.; Pozzo, J. L.; Rodriguez, V.; Adamietz, F.; Castet, F.; Ducasse, L.; Champagne, B. J. Phys.
Chem. B 2005, 109, 11139.
[3]Hoffmann, R.; Imamura, A.; Hehre, W. J. J. Am. Chem. Soc. 1968, 90, 1499.
[4]Orimoto, Y.; Aoki, Y. Int. J. Quantum Chem. 2003, 92, 355.