4P110ಽሶߩᝄേㆇേࠍ⠨ᘦߒߚశวᚑࠕࡦ࠹࠽♽ౝߦ߅ߌࠆ
ബ⿠ࠛࡀ࡞ࠡ࡯⒖േㅦᐲߩ╙৻ේℂ⸘▚㧔ᘮᄢ㒮ℂᎿ㧕٤ጊᧄ ᜏ⏴‫⮳ޔ‬ਅ ⡡[ᐨ] ᧁ᧛‫ޔ‬၂⼱ࠄߦࠃߞߡ⏕┙ߐࠇߚਛ㑆⚿วബ⿠⒖േߩℂ⺰ 1 ߪ‫ޔ‬ಽሶ㑆⋧੕૞↪ߩᄢ߈ߐ߇ਛ㑆⊛ߥᄢ߈ߐߩ႐วߦ߅ߌࠆബ⿠ࠛࡀ࡞ࠡ࡯⒖േ(EET)ࠍℂ⺰⊛ߦ⠨ኤߒߚℂ⺰ߢ޽ࠆ‫⎇ᧄޕ‬ⓥߢߪ‫ߩߎޔ‬ℂ⺰ࠍෳ⠨ߦ EET ㅦᐲࠍ╙৻ේℂ⊛ߦ᳞߼ࠆᣇᴺࠍ⏕┙ߒ‫ޔ‬శวᚑࠕࡦ࠹࠽♽ߦ߅
ߌࠆ B800→B850 ߩ EET ㅦᐲ▚಴߳ߩᔕ↪ࠍ⋡⊛ߣߔࠆ‫ޕ‬[ℂ⺰] ᧄ⎇ⓥߢߪ‫(ޔ‬1)ᑼߦ␜ߔ Liouville ᣇ⒟ᑼࠍၮ⋚ߦߒߡ EET ㅦᐲߩቯᑼൻࠍⴕߞߚ‫ޕ‬i!

&( (t )i ti t
$ [ H (t ), ( (t )] % ( (t ) $ exp ' [# ! dt "H (t ")]( (0) exp # [# ! dt ""H (t "")]
! 0! 0&t(1)ߚߛߒ‫ ޔ‬H (t ) ) H 0 ' V (t ) ߪో♽‫ ޔ‬H 0 , V (t ) ߪ㕖៨േ♽‫ޔ‬៨േ♽ߩࡂࡒ࡞࠻࠾ࠕࡦߢ޽ࠆ‫ޕ‬V (t )߇ᤨ㑆ߦ㕖ଐሽߥṶ▚ሶߣ⷗ߥߖࠆ႐ว‫ⴕޔ‬೉ H jk ) + j | H 0 ' V | k * ࠍቯ⟵ߒ‫ߩߘޔ‬࿕᦭୯⸃ᨆࠍⴕ߁ߎߣߢ(2)ᑼߢቯ⟵ߐࠇࠆࠃ߁ߥ‫ᤨޔ‬ೞ t ߦ߅ߌࠆ․ቯߩ㊂ሶ⁁ᘒ | l * ߩሽ࿷⏕₸ Pl (t ) ࠍ࿑␜ൻߔࠆߎߣ߇ߢ߈ࠆߩߢ‫ౕޔ‬૕⊛ߦ EET ㅦᐲࠍ⹏ଔߔࠆߎߣ߇ߢ߈ࠆ‫ޕ‬

iPl (t ) ) + l | ( (t ) | l * $ , [ ( (0)] jj" (Q jk t Qkl )(Q j"k " t Qk "l ) exp[ (- k "k " # - kk )t ]!
jj ",kk "(2)ߎߎߢ‫ ޔ‬Q ߪ QHQ $ ! 㧔ኻⷺⴕ೉㧕ࠍḩߚߔⴕ೉ߢ޽ࠆ‫(ޕ‬2)ᑼߪή㒢ᰴߩ៨േ߹ߢขࠅ౉ࠇtߚ⴫ᑼߢ޽ࠆߚ߼ࠦࡅ࡯࡟ࡦ࠻ߥ EET ࠍ⴫⃻ߔࠆࠃ߁ߥ⴫ᑼߣߥߞߡ߅ࠅ‫ޔ‬శวᚑࠕࡦ࠹࠽♽ߩࠃ߁ߦࠗࡦࠦࡅ࡯࡟ࡦ࠻ߥ EET ߩᝄࠆ⥰޿ࠍ฽߻ࠃ߁ߥ‛ℂឬ௝ࠍౣ⃻ߢ߈ࠆ⴫ᑼߣߪߥߞߡ޿ߥ޿‫ޔߡߞࠃޕ‬㊂ሶ⺰⊛ࡑࠬ࠲࡯ᣇ⒟ᑼߥߤߩℂ⺰ࠍᔕ↪ߔࠆߎߣߦࠃߞߡࠗࡦࠦࡅ࡯࡟ࡦ࠻ߥឬ௝ࠍขࠅ౉ࠇߚ⴫ᑼ߳ᡷ⦟ߔࠆᔅⷐ߇޽ࠆ߇‫੹ޔ‬࿁ߩ⊒⴫ߢߪ(2)ᑼࠍ↪޿ߡ EET ㅦᐲࠍ⹏ଔߔࠆߎߣࠍ੍ቯߒߡ޿ࠆ‫ޕ‬ (2)ᑼࠍ↪޿ߡౕ૕⊛ߦ EET ㅦᐲࠍ⹏ଔߔࠆ㓙ߦߪᩭᵄേ㑐ᢙߩ㊀ߥࠅⓍಽ‫ޔ‬හߜ FC ࿃ሶࠍ᳞߼ࠆᔅⷐ߇޽ࠆ‫ޕ‬Gaussian03 ࡊࡠࠣ࡜ࡓ╬ߦࠃߞߡ㔚ሶ⁁ᘒ⸃ᨆ߇ቢੌߒߡ޿ࠆߎߣࠍ೨ឭߣߒ‫ోޔ‬ේሶᩭߦ㑐ߔࠆࡂࡒ࡞࠻࠾ࠕࡦ H ߇⺞๺ᝄേሶㄭૃࠍណ↪ߒߡ

1 3N&2& 2V!2H / , (#V)''.
.
00, j k &.0 &.00
2 j ,k2M j &.0 j2
j $1jkt

3N." $ 0

1!2 & &
' V0 ' t qEq$#2 &q &q
2(3)ߩࠃ߁ߦ⸥ㅀߢ߈ࠆ߽ߩߣ઒ቯߔࠆ‫ޔߒߛߚޕ‬శวᚑࠕࡦ࠹࠽♽ߪⰮ⊕⾰ਛߦၒ߼ㄟ߹ࠇߚ♽ߢ޽ࠆߚ߼‫ޔ‬ಽሶ࿁ォߩലᨐߪ⠨ᘦߒߡ޿ߥ޿‫ޔ߈ߣߩߎޕ‬ၮḰᐳᮡߣᄌ឵೨ߩᐳᮡߣߩ㑐ଥ߇᣿⏕ߦዉ߆ࠇࠆߚ߼‫ޔ‬ฦ‫ߩޘ‬㔚ሶ⁁ᘒ㧔ၮᐩ‫ޔ‬ബ⿠㧕ߦኻᔕߔࠆၮḰᐳᮡߩ㑆ߦᚑ┙ߔࠆ㑐ଥࠍq g $ Sq e ' D  㧔߽ߒߊߪ q e $ S "q g ' D" 㧕(4)ߩᒻߢ⸥ㅀߔࠆߎߣ߇ߢ߈ࠆ 2‫ ޔߒߛߚޕ‬S ߪ Duschinsky ⴕ೉ߢ޽ࠆ‫ޕ‬ ߘࠇߙࠇߩ㔚ሶ⁁ᘒߦ߅޿ߡోᝄേḰ૏߇ၮᐩ⁁ᘒߦ޽ࠆ႐ว‫ޔ‬FC ࿃ሶߪ⸃ᨆ⊛ߦዉ಴ߔࠆߎߣ߇ߢ߈ࠆ‫ޕ‬㔚ሶ⁁ᘒ s ߦ߅ߌࠆ‫ޔ‬ᝄേࠛࡀ࡞ࠡ࡯ࠍ⸥ㅀߔࠆኻⷺⴕ೉ [# ] jk ) 2 jk 1 j ࠍቯ⟵ߒ‫ޔ‬sⴕ೉ # ' S# S ߩ࿕᦭୯⸃ᨆࠍⴕߞߡetgst

U (# e ' t S# g S)U $ $ $ diag (3 1 , 3 2 , 3 3 , ", 3 3 N #6 )(5)ߩ㑐ଥࠍᓧࠆߎߣ߇ߢ߈ࠇ߫‫ޔ‬ᝄേၮᐩ⁁ᘒ㑆ߩ FC ࿃ሶࠍ(6-A)ᑼߢ⹏ଔߔࠆߎߣ߇ߢ߈ࠆ 3,4‫ޕ‬
3 N #6

13 j # 12
61 91t) : exp[ # t D77 # g # # g S e t
S# g 44 D]
g2! 82# ' S# Sj $15

3 N #6

FC{0, 0,",0}g #{0, 0,", 0}e ) ; (1 gj 1 ej ) 4 : ; (j $1(6-A)(6-A)ᑼ߇⸘▚ߢ߈ࠇ߫‫ߩߘޔ‬୯ࠍ೑↪ߒߡૐᰴߩᝄേബ⿠⁁ᘒ㑆ߩ FC ࿃ሶ߽એਅߩࠃ߁ߥ⴫ᑼߢᓧࠆߎߣ߇ߢ߈ࠆ‫ޕ‬

FC{0, 0,",1 j ,", 0}g #{0, 0,",0 j ,", 0}e
FC{0,0,", 0}g #{0, 0,",0}e21 gj 9 3 N #66C$ (#)77 , [SU] jm m # D j 443m! 8 m$15

FC{0, 0,",0 j ,", 0}g #{0, 0,",1 j ,", 0}e
FC{0,0,", 0}g #{0,0,",0}e$ (#21 ej 9 3 N #6C 6)77 , U jm m 44
! 8 m$13m 5(6-B)(6-C)[⸘▚⚿ᨐ࡮⠨ኤ] ࿑㧝ߪ‫ޔ‬B800 ߇㔚ሶബ⿠⁁ᘒߣߥߞߡ޿ࠆሽ࿷⏕₸ߩᤨ㑆ᄌൻࠍ‫(ޔ‬2)ᑼࠍ↪
޿ߡౕ૕⊛ߦⷞⷡൻߒߚ߽ߩߢ޽ࠆ‫ޕ‬B800 ߣ B850 ߩ㑆ߩ⋧੕૞↪ߩᄢ߈ߐߪ╙৻ේℂ⸘▚ߦࠃࠅᓧࠄࠇߚ 2.5264 meV‫ޔ‬ബ⿠ࠛࡀ࡞ࠡ࡯Ꮕߪ 800nm,850nm ߩᵄ㐳߆ࠄᓧࠄࠇࠆ 735 cm #1 ࠍ↪
޿ߡ߅ࠅ‫ޔ‬ᝄേḰ૏ߪࡕ࠺࡞ߣߒߡ 50 Ḱ૏ࠍ㈩೉ߒߡ޿ࠆ‫ޕ‬࿑㧝ߢߪ FC ࿃ሶࠍ⠨ᘦߖߕߦ⸘▚ࠍߒߡ޿ࠆߚ߼‫ޔ‬EET ㅦᐲ߇⚂ 0.16ps㧔᷹ⷰ୯ 0.7ps㧕ߣ㕖Ᏹߦᣧ޿୯ߣߒߡ▚಴ߐࠇߡ޿ࠆ߇‫ޔ‬(6)ᑼߦࠃߞߡ⸘▚ߐࠇࠆ FC ࿃ሶ㧔࿑㧞ෳᾖ‫ޔ‬ᮮゲߪ㔚ሶၮᐩ࡮ബ⿠⁁ᘒߩᝄേࠛࡀ࡞ࠡ࡯Ꮕ .E#1

ߢ‫ޔ‬Förster ߩℂ⺰ߢߪ .E $ 735 cm ߣߥࠆᝄേḰ૏߇ EET ߦ㑐ਈߔࠆ㧕ࠍዉ౉ߔࠆߎߣߦࠃࠅ‫♽࠽࠹ࡦࠕޔ‬ౝߢߩ EET ㅦᐲࠍౣ⃻ߔࠆߎߣ߇ߢ߈ࠆน⢻ᕈ߇޽ࠆߣ⠨߃ࠄࠇࠆ‫৻╙ޕ‬ේℂ⸘▚ߦࠃߞߡ EET ㅦᐲࠍ⹏ଔߔࠆߚ߼ߦߪ‫ޔ‬FC ࿃ሶࠍ෩ኒߦ⹏ଔߔࠆᔅⷐ߇޽ࠅ‫ߚ߹ޔ‬⠨߃ࠄࠇࠆోߡߩᝄ㔚Ḱ૏ࠍ⠨ᘦߒߥߌࠇ߫ߥࠄߥ޿ߚ߼‫ߩࠄࠇߎޔ‬࿎㔍ࠍ࿁ㆱߔࠆߚ߼ߩᣇᴺࠍ⠨᩺ߒߥߌࠇ߫ߥࠄߕ‫⎇ᧄޔ‬ⓥߦ߅ߌࠆ੹ᓟߩ⺖㗴ߣߥࠆ‫ޕ‬
1.0

㪇㪅㪊㪌
㪇㪅㪊

0.8

㪝㪚㩷㪽㪸㪺㫋㫆㫉㪇㪅㪉㪌
0.6

㪇㪅㪉
㪇㪅㪈㪌
㪇㪅㪈

0.4

㪇㪅㪇㪌0.2㪇㪇
5. ! 10"14

1. ! 10"13 1.5 ! 10"13 2. ! 10"13 2.5 ! 10"13 3. ! 10"13 㪌㪇㪇㪈㪇㪇㪇ᝄേ䉣䊈䊦䉩䊷Ꮕ㪈㪌㪇㪇 2#1࿑㧝 ሽ࿷⏕₸ߩᤨ㑆⊒ዷ㧔❑㧦⏕₸‫ޔ‬ᮮ㧦ᤨ㑆 s㧕 ࿑㧞 FC ࿃ሶ㧔❑㧦 FC ‫ޔ‬ᮮ㧦 .E cm 㧕0ࠃࠅ⹦⚦ߥᖱႎ߿‫(ޔ‬2),(6)ᑼࠍ↪޿ߚታ㓙⸘▚߳ߩᔕ↪╬ߪ⊒⴫ᒰᣣߦ⚫੺ߔࠆ੍ቯߢ޽ࠆ‫ޕ‬[ෳ⠨ᢥ₂] [1] A.Kimura et al, J.Phys.Chem.B, 2000,104, 9276
[2] F. Duschinsky, Acta Physicochim. URSS, 1937, 7, 551[3] R. Islampour, M. Dehestani and S. H. Lin, J. Mol. Spectrosc., 1999, 194, 179[4] Jun Liang et al., Mol. Phys., 2007, 105, 1903