1E17!"#$%&'()*+,-./0123: 456+789:;<+=.>?(@ABCD(EFGH 1IEFJKLMN?2) OPQD R 1ISTD UV 1IWQD XY 1IZD [\ 1,2D]^_` !"#$%&'()*A>?(abcId5efgbhijkAlmnopqr-.stut
vwxyIz{p|y}~A 1 + Heller A6 (&x. [1]zAcIijkA
lmno+&'()*pIeflm>?(abp<+-.lmnocIijkAu+ .no¡:¢£1¤¥¦§¨wAno¡A 2 +d©
ª{I«¬c>?(A@p­®Ik¬c>?(Aeflmp-.ª¯+IHeller cIijkAu+ .no¡A°+±²³ (&p´µ. [2]zAcI&'()*Aeflm+,c|y}~z:w¶uI>?(A·ap¸¹1uº»w¼yI½+I&'()*A>?(@ijkA456+789:¾¿+,À-.z:pÁ.Âw½Ã1:_Ä.IHeller A³ (&cI>?(A;<ÅÆÇp|y}ÈuÉ23wcI
Heller A³ (&pÊËI;<ÅÆÇp!"#$%&'()*A>?(·apÌ8»pÍÎª¯+IÍÎ»pijÏÐÑÒA!"&'()*+ÓÔI>?(@AFÕ+,I456+789:;<A 2 AÖÂ¯×Ø]` ij«Abh j :ijkAbh f p 1 ÙÚAÛoÜÝMÞß*w

Ef

-. (Scheme 1)àbhAÜÝMÞß*áâ*ã?äå+IæçlmAèép q0 j êë q0 f I9A®ºp kj êë kfIìíîïp mj êë mf :Ièé q0 j + .bhAáâ*ã?ðp !ω 0 :-. (! chω 0φftjφitPlanck ®º)q!"#$%Añ¶.òp t = 0 :-.Heller A³ (&w

q0 j q0 fcIzAòwA6φ j t = 0 êëφ f t = 0 pbh j + .óÂefAef

Scheme 1

f,ºw-.
!#φ jt =0 = φ ft =0 = N 0 exp $−#&mjk j"#q−q ) %(2!
20j(N0 côõö®º)

(1)

#'

Ù+Iz{¯A6pÅÆ Schrödinger ÷»+øÈ$ùªúIû,,º ct = <φ jt = 0|φ f t = 0 >püý-.þÿ1u6wcIt = 0 ¯ !

wAû,,ºpüý-.I³ (&wcIò t AÕª§¨wAû,,ºp!. [2]"IzAû,,ºp Fourier #$-.z:w!"#$%&'()*Aab,º I (ω) pÍÎ-.³ (&¯%¯{.ab,º I (ω) cIÙA=~uefºω +,-. Gauss &,º+u.
"!# ! m j k j(ω − ω 0 )2 #%I (ω ) = N exp$−
2
Ff#'
#&(2)

zzwIN côõö®ºwxyIFf cijkA456+789I-u'(Ièé q0 j + .bh f A
energy gradient wx.
É23wcI³ (&+;<ÅÆÇp|y)* +Ibh j +,I;< T + .

æçlmpS,:-1lm.¯/Ad0 Dj (T,q) p1Ä.z{cIeff,ºχjν (q) (ν cefAï5º) : Boltzmann d0¯%¯{.àefbhA2ì3 Pjν (T ) pÔÙA=~+4 .
222D j (T , q ) = Pj 0 (T ) χ j 0 (q ) + Pj1 (T ) χ j1 (q ) + Pj 2 (T ) χ j 2 (q ) + …

(3);< T  0 ¯ 300 K ÷<A56IóÂefA2ì3c Pj 0 (T ) cef7ñbhA2ì3 Pj 1 (T ),Pj 2 (T ),… :¢89:+F¶u;p:.ª¯+IóÂefAf,ºχj 0(q) c Gauss &,ºwx.
Ilm.¯/Ad0 Dj (T,q) cI<=A=~u Gauss &,º gj (T,q) A 2 >w?@1+¼-z:w¶. ( gj (T,q) AÍÎ¦÷c$¼w8.)
!
"##mjk j2
2##
D j (T , q ) ≈ g j (T , q ) = N 0 exp $−q − q0 ) %2 ()# 2! (#* . (2ν + 1) Pjν (T ) +##0
ν=,&'2(4)zA gj (T,q) pò t = 0 A6φ j t = 0 êëφ f t = 0 :®AI³ (&:BCADE¶pF~:I;<+ÅÆab,º I (T,ω) %¯{.!
"##! mjk j
2##ωωI (T , ω ) = N exp $ −−0) %2 ()# F2 (#2ν + 1 Pjν (T ) +# f *, ν.
#=0&'(5)zA»cI;< T 56Ix.cIijkA456+789 Ff G56+I!"#$%&'()*A>?(@H8u.z:pÁ.
]&'()*A×Ø` IJKæL&ÑÒ [PtCl4]2− + ,   1A1g M

1Table 1. [PtCl4]2− A 1A1g M 1A2g !"&'()*A>?(ab(d−d) ijA!"&'()*p×Ø;< (K)üýXY

A1g NOPQRS?Tp Scheme 1 Aè15298

0.99
1.20

0.360.45

é q :I» 5 Aab,º I (T,ω) +U;@A¢ (15 K Z)

U;@ (eV)

A2g4

üý

XY 4

1.00
1.211.00
1.25

>?(AU;@p! (Table 1)üý+=.U;@cI15 K A56+ 0.99 eVI298 K A56+
1.20 eV wxyIHeller A³ (&Á-þÿ1uVW [3] :BC+XY; (0.36 êë 0.45
eV; ref 4) =y¦FBCª{I15 K pZ:U;@A¢+[²-.:Iüýwc 1.21 :B
Cª{IXY;wx. 1.25 :=8þ\z{cI» 5 Aab,º I (T,ω) >?(@A;<ÅÆÇpÓ]+|y)^w.z:pÁ.zA_`¯I>?(@A;<ÅÆÇcI-1lm.¯/ Dj (T,q)(» 3) A;<ÅÆÇp"Aqr-.¡:_Ä.

» 5 ¯a¯u=~+I>?(@AFÕcijkA456+789 Ff +ÅÆ-.zAb:I
É23wcIcJKdLÒ&ÑÒ [Co(NH3)6]3+ êë [Rh(NH3)6]3+ A d−d !"&'()*p|y}È_`e+c$¼w8.
[1] Heller, E. J. Acc. Chem. Res. 1981, 14, 368. [2] Heller, E. J.; Sundberg, R. L.; Tannor, D. J. Phys. Chem. 1982,86, 1822. [3] Neese, F.; Petrenko, T.; Ganyushin, D.; Olbrich, G. Coord. Chem. Rev. 2007, 251, 288. [4] Martin, D.
S. Jr.; Tucker, M. A.; Kassman, A. J. Inorg. Chem. 1965, 4, 1682.