2E05㻃㻃 㻃 㻃 㻃 㻃 㻃 㻃 ┞ᑊㄵⓏ䝦䝋䝯හṾ䝡䝊䝷䜻䝧䝯䛱䜎䜑㻃 㻃 㻃 㻃 㻃 ฦᏄᵋ㏸᭩㐲໩䝛䝱䜴䝭䝤䛴㛜Ⓠ䛮䛣䛴ᚺ⏕(ஐኬ㝌⥪⌦ᕝ1㸡࢓࢕࢛࣠ᕗ❟ኬᏕ2㸡CREST3)‫ې‬᲻ ᐰᨼ1,2㸡Mike Schmidt2㸡ሪᮇ ᫬ஒ1㸡ᓙ 㞖⣎1㸡୯ᓞ ஁ᶖ1㸡ኬሔ ᗀ᪺1㸡୔ይỄష1,3
E-mail: mori1@asem.kyushu-u.ac.jp, miyoshi@asem.kyushu-u.ac.jpi.ᗆ࣬┘Ⓩ 㔔ඔ⣪ࢅྱࢆࡓ ab initio ฦᏄ㌮㐠ゝ⟤࡚ࡢ㸡ゝ⟤ㇿⲬࢅ΅ࡼࡌࡒࡴ㸡ୌ⯙࡞㸡᭯ຝහṾ࣎ࢷࣤࢨࣔ
ࣜ㸝ECP㸞࠿౐ࢂࡿࡾ㸣ࡓ࠿㸡ECP Ἢ࡚ࡢ㸡౮㞹Ꮔ㌮㐠ࡡ⟿ᵋ㏸ࢅḿࡊࡂ්⌟࡚ࡀࡍ㞹Ꮔ┞㛭࠿㐛ኬフ౮ࡈࡿࡾࡒࡴ㸡⢥ᐠ࡝ฦᏄ∸ᛮೋࡡぜ✒ࡵࡽ࡞୘Ꮽ࠿ṟࡾ㸣ᠻࠍࡢ㸡ḿࡊ࠷౮㞹Ꮔ㌮㐠ᵋ㏸ࢅ්⌟ࡊ㸡ࡻࡽ⢥ᐠ࡞ฦᏄ∸ᛮೋࢅゝ⟤࡚ࡀࡾ᧻࣎ࢷࣤࢨࣔࣜἪࠔ࣓ࢸࣜහṾ࣎ࢷࣤࢨࣔࣜ㸝MCP㸞ࠕࢅᥞ၌ࡊ㸡㛜Ⓠࢅ⾔ࡖ࡙ࡀࡒ㸣௑ᅂ㸡┞ᑊㄵⓏ MCP ἪࢅኣཋᏄฦᏄ࡞ࡵ㐲⏕࡚ࡀࡾࡻ࠹࡞ฦᏄᵋ㏸᭩㐲໩ࣈࣞࢡ࣑ࣚࢅᏰᠺࡊ㸡㔘ྱ᭯ࢻࢿࢠࣚࢪࢰ࣭ [1]࣬࢜ࣜࢤࢣࣤ᪐ࢠࣚࢪࢰ࣭ [2]࣬ࣚࣤࢰࢼࢺり፳ཬᚺ➴ [3] ࡡᖼࡗ࠾ࡡ㔔ཋᏄ⣌࡞㛭ࡊ࡙㸡㞹Ꮔ┞㛭࣬┞ᑊㄵຝᯕࢅྜྷ᫤࡞ཱིࡽ᡽ࡖࡒᚺ⏕ゝ⟤ࢅ⾔ࡖࡒࡡ࡚ሒ࿈ࡌࡾ㸣i┞ᑊㄵⓏ࣓ࢸࣜහṾ࣎ࢷࣤࢨࣔࣜ㸝2(5㸞Ἢ [4] ┞ᑊㄵⓏ MCP Ἢࢅ⏕࠷ࡒ ab initio ฦᏄ㌮㐠ゝ⟤࡚౐⏕ࡌࡾฦᏄࣀ࣐ࣜࢹࢼ࢓ࣤࢅ௧ୖ࡞♟ࡌ㸣

(Hˆ 1,2,L,N!

Nvv) = #hi=1

Nv

MCPi

N atom1( Z " N L,Core )( Z M " N M ,Core )+# + # L
RLM
i> j rij
L>M%(1hiMCP = " # i + $'VKMCP ( ri ) + $ BK, core p core p core *2)
K &coreVKMCP ( ri ) = "!

33)
ZK " N K, core &2
21+Aexp"#r+Br
exp"%r( I iK ) $ J iK ( J iK )+( $ IriK'*IJ

(1)

(2)

(3)

ࡆࡆ࡚㸡N 㸯౮㞹Ꮔᩐ㸡N atom 㸯ฦᏄࢅᵋᠺࡌࡾཋᏄࡡᩐ㸡N L,Core 㸯ཋᏄ L ࡡහṾ㞹Ꮔᩐ㸡 p core 㸯v!

හṾ㌮㐠࡚࠵ࡽ㸣(3) 式中のỞ MCP ࣂ࣒࣭ࣚࢰ࣭ { AI , " I , BJ , " J , BK ,core } ࡢ㸡᧻┞ᑊㄵⓏ Hartree-Fockゝ⟤࡞ࡻࡽᚋࡼࡿࡾཋᏄ㌮㐠࠽ࡻࡦࡐࡡ㌮㐠࢙ࢾ࣭ࣜ࢟ࢅ්⌟ࡌࡾࡻ࠹࡞Ửࡴࡼࡿࡾ㸣┞ᑊㄵⓏ!
!
! (2) ᘟ࡞ぜࡼࡿࡾࡻ࠹࡞㸡ୌ㞹Ꮔⁿ⟤Ꮔ㒂ฦ࡫ࡡ
!MCP Ἢࢅ⏕࠷ࡒゝ⟤࡛㏳ᖏࡡධ㞹Ꮔゝ⟤ࡡ㐢࠷ࡢ㸡හṾ㌮㐠࢙ࢾ࣭ࣜ࢟ࢨࣆࢹⁿ⟤Ꮔ㸝ᑏᙫⁿ⟤Ꮔ㸞ࡡ㏛ຊ࡚࠵ࡾ㸣Phillips-Kelinman ㎾జ࡞ᇱࡘࡂ㏳ᖏ
! ! ! ! !
ࡡ ECP ࡛␏࡝ࡽ㸡ᠻࠍࡡ┞ᑊㄵⓏ MCP Ἢ࡚ࡢ (2) ᘟ࡞♟ࡌࡻ࠹࡞㸡හṾ㌮㐠ࡡ᝗ሒࢅᑏᙫⁿ⟤Ꮔࡡᙟᘟ࡚ḿࡊࡂよࡀࡗࡗහṾ㞹Ꮔࢅ᭯ຝ࣎ࢷࣤࢨࣔࣜ㡧࡚⨠ᥦࡌࡾࡒࡴ㸡㞹Ꮔ┞㛭㸝࠽ࡻࡦฦᏄ∸ᛮ㸞ࡡᏽ㔖Ⓩぜ✒ࡵࡽ࡞୘ྊḖ࡝౮㞹Ꮔ㌮㐠ࡡ⟿ᵋ㏸ࢅḿࡊࡂ්⌟࡚ࡀࡾ㸝ᅒ 1 ཤ↯㸞㸣ࡱࡒ㸡┞ᑊㄵⓏMCP Ἢ࡚ࡢ㸡(1) ᘟ࡞♟ࡈࡿ࡙࠷ࡾࡻ࠹࡞㸡஦㞹Ꮔⁿ⟤Ꮔ㒂ฦࡡ㞹ᏄᩐࡵහṾ㞹Ꮔᩐฦࡓࡄ΅ࡼࡊࡒゝ⟤ࢅᐁ⾔ࡌࡾࡆ࡛࡞࡝ࡾ㸣ᚉࡖ࡙㸡┞ᑊㄵⓏ MCP Ἢࢅ౐࠻ࡣ㸡ab initio 㔖Ꮔ໩Ꮥゝ⟤࡞࠽࠷࡙ࢾࢴࢠ࡛࡝ࡾ஦㞹Ꮔ✒ฦࡡ㔖ࢅ᭩ᑚ㝀࡞ᢒ࠻ࡗࡗ㸡ኬぞᶅ࡝┞ᑊㄵⓏ ab initio 㔖Ꮔ໩Ꮥゝ⟤ࢅ⾔࠹ࡆ࡛࠿ྊ⬗࡞࡝ࡾ㸣ᮇ◂✪࡚ࡢ㸡୕オ  ᘟࡡよᯊⓏୌḗ᚜ฦᙟᘟࢅᑙฝࡊ㸡㔖Ꮔ໩Ꮥゝ⟤ࣈࣞࢡ࣑ࣚ
ࣂࢴࢢ࣭ࢩ,&2*88@B࡫ࡡ࢕ࣤࣈ࣒ࣛࣤࢹࢅ⾔ࡖࡒ㸣ࡆࡿ࡞ࡻࡽ㸡┞ᑊㄵⓏ2(5࡞ࡻࡾฦᏄᵋ㏸᭩㐲໩ࢅᐁ⾔࡚ࡀ㸡┞ᑊㄵⓏ2(5Ἢࡡኬぞᶅ⣌࡫ࡡᚺ⏕࠿ྊ⬗࡞࡝ࡖࡒ㸣rR(r) / a.u.

┞ᑊㄵⓏධ㞹Ꮔゝ⟤
ECPMCP%(1hiMCP = " # i + $'VKMCP (ri ) + $ BK ,core pcore pcore *2)
K &core02!

46

810r / a.u.

ᅒ 1 ┞ᑊㄵⓏ MCP Ἢ࡛ᚉᮮࡡ ECP Ἢ࡛ࡡ㐢࠷㸯Tl ཋᏄࡡ 6s ㌮㐠ࡡౚ㸯㸝┞ᑊㄵⓏධ㞹Ꮔゝ⟤㸯Cowan-Griffin Hartree-Fock࣬ECP㸯SBKJC࣬MCP㸯MCP-dzp [6]㸞ECP ࡚ࡢ 6s ㌮㐠࠿ࡵࡗ⟿ᵋ㏸࠿ḿࡊࡂ්⌟ࡈࡿ࡙࠽ࡼࡍ㸡㞹Ꮔ┞㛭ࡡぜ✒ࡵࡽࡡ࢙࣭ࣚࡡ
ཋᅄ࡛࡝ࡾ㸣ୌ᪁㸡ᠻࠍࡡ 2(5ᇱᗇ࡚ࡢ  ᘟ୯ࡡහṾ㌮㐠࢙ࢾ࣭ࣜ࢟ࢨࣆࢹⁿ⟤Ꮔ㸝ᑏᙫⁿ⟤Ꮔ㸞ࡡ࠽࠾ࡅ࡚㸡හṾ㞹Ꮔࢅᾐཡࡊࡒࢤࣤࣂࢠࢹ࡝ゝ⟤࡞ࡵ㛭ࢂࡼࡍ㸡ධ㞹Ꮔゝ⟤࡞ࡻࡽᚋࡼࡿࡾ㌮㐠⟿ᵋ㏸ࢅᚽᐁ࡞්⌟ࡌࡾࡆ࡛࠿࡚ࡀࡾ㸣iᚺ⏕ゝ⟤࡛௑ᚃࡡᒈ㛜 ௧ୖ࡞♟ࡌ㔔ඔ⣪ྱ᭯⣌࡞ࡗ࠷࡙㸡┞ᑊㄵⓏ MCP ἪࡡよᯊⓏୌḗ᚜ฦᙟᘟࢅ⏕࠷ࡒฦᏄᵋ㏸᭩㐲໩㸡࠽ࡻࡦᩐೋⓏ஦ḗ᚜ฦ࡞ࡻࡾᣲິᩐよᯊࢅᐁ⾔ࡊࡒ㸣྘⣌ࡡゝ⟤⤎ᯕࡡレ⣵࡞ࡗ࠷࡙ࡢ㸡ࡐࡿࡑࡿ࣎ࢪࢰ࣭Ⓠ⾪࡞࡙⣺௒ࡌࡾ஢ᏽ࡚࠵ࡾࡡ࡚ࡐࡔࡼࡡさ᪠ࢅཤ↯ࡊ࡙㡤ࡀࡒ࠷ [1-3]㸣࠷ࡍࡿࡡ⣌࡞࠽࠷࡙ࡵ㸡㧏࠷⢥ᗐ࡚ᐁ㥺⤎ᯕࢅ්⌟ࡌࡾࡆ࡛࡞ᠺຉࡊ࡙࠷ࡾ㸣≁࡞ Auࢻࢿࢠࣚࢪࢰ࣭࡫ࡡᚺ⏕࡚ࡢ Au20 ࡞ࡗ࠷࡙㸡ᐠᗐỏ㛭ᩐἪ B3LYP/MCP-tzp ࣝ࣊ࣜࡡゝ⟤ࡡࡲ࡝ࡼࡍ㸡ab initio MP2/MCP-tzp ࡚ࣝ࣊ࣜࡡᵋ㏸᭩㐲໩ゝ⟤࡞ᠺຉࡊ࡙࠽ࡽ㸝㞹Ꮔᩐ㸯ධ㞹Ꮔゝ⟤ Ѝ 79
20 = 1580 elec.㸡┞ᑊㄵⓏ MCP Ѝ 17 20 = 340 elec.㸞
㸡┞ᑊㄵⓏ MCP Ἢࡡኬぞᶅ┞ᑊㄵⓏ㔖Ꮔ໩Ꮥゝ⟤࡫ࡡྊ⬗ᛮࢅぜฝࡌࡆ࡛࠿࡚ࡀࡒ㸣ࡱࡒ㸡⌟ᅹ㸡AB-INIT MP ࣈࣞࢡ࣑ࣚࣂࢴࢢ࣭ࢩ࡫ࡡ┞ᑊ
ㄵⓏ MCP ἪࡡよᯊⓏ᚜ฦࣈࣞࢡ࣑ࣚࡡ⛛᳔ࡵ㐅⾔୯࡚࠵ࡾ㸣AB-INIT MP ࡢ໪὾࡞ࡻࡽᥞ၌ࡈࡿࡒ
ࣆࣚࢡ࣒ࣤࢹฦᏄ㌮㐠Ἢࢅ࣭࣊ࢪ࡞ኬぞᶅ⣌ࡡ㔖Ꮔ໩Ꮥゝ⟤࡫ࡡ࢓ࣈ࣭ࣞࢲࢅ⾔ࡖ࡙࠷ࡾࣈࣞࢡ࣑ࣚ
࡚࠵ࡽ㸡ᠻࠍࡡ┞ᑊㄵⓏ MCP Ἢࡡ࢕ࣤࣈ࣒ࣛࣤࢹ࡞ࡻࡽ㔘ᒌࢰࣤࣂࢠ࣬㔔ඔ⣪ྱ᭯ࢻࢿ⾪㟻⣌࡫ࡡᒈ㛜࠿᭿ᙽࡈࡿࡾ㸣レ⣵ࡢᙔ᪝ሒ࿈ࡌࡾ㸣‫ڦ‬௑ᅂ⾔ࡖࡒ┞ᑊㄵⓏ MCP ࡡᚺ⏕ゝ⟤
1. Au, Ag, Cu ࢻࢿࢠࣚࢪࢰ࣭㸝܏ ࣎ࢪࢰ࣭Ⓠ⾪㸯5㸞[1]2. ࢜ࣜࢤࢣࣤ㸝S, Se, Te㸞ࢠࣚࢪࢰ࣭ࡡᖼరᵋ㏸࡛㨩Ἢᩐ࡞㛭ࡌࡾ⌦ㄵⓏ⩻ᐳ   㸝܏ ࣎ࢪࢰ࣭Ⓠ⾪㸯5㸞[2]3. ࣚࣤࢰࢼࢺୌ౮࢜ࢲ࢛ࣤ㸝Ce+࣬Gd+࣬Yb+㸞࡞ࡻࡾ C-F ⤎ྙว᩷り፳ཬᚺᶭᵋࡡよ᪺㸝܏ ࣎ࢪࢰ࣭Ⓠ⾪㸯5㸞[3]࠘ཤ⩻ᩝ⊡࠙ [1] ฦᏄᵋ㏸⥪ྙゞㄵఌ 2006, ୯ᓞ㸡2P040 㸡[2] ฦᏄᵋ㏸⥪ྙゞㄵఌ 2006, ኬሔ㸡2P041㸡
[3] ฦᏄᵋ㏸⥪ྙゞㄵఌ 2006, ᲻㸡2P042㸡[4] (a) Y. Sakai et al., J. Comput. Chem. 8, 264 (1987). (b) Y. Sakai et al.,J. Chem. Phys. 106, 8084 (1997). (c) E. Miyoshi et al., J. Mol. Struct.: THEOCHEM, 451, 73 (1998). (d) Y. Sakai et al.,J. Mol. Struct.: THEOCHEM, 451, 143 (1998). [5] M. W. Schmidt et al., J. Comput. Chem. 14, 1347 (1993). [6] (a)E. Miyoshi et al., J. Chem. Phys., 122, 074104-1-8 (2005)., (b) http://meg.cube.kyushu-u.ac.jp/sapporo3/index.jsp