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TRANSCRIPT
+HšůņūŦűņ�´¨11=
«-ĥ#FÎÔéšůņūŧ
ŀœŗŰųŗŤşťű& (şůűŔľĽÎÔ�Ë)
1
w�+Hij��+HĄ��+HĨÂČĦ1ĩęĄQH#ÛĢıĄ#FÎÔÃ
©ĨZæħÔ ģĥğġđġċĶą
ŲQÙ®Åà ŲQ�6aÅÃ
Ų�pã�ĥĤħ�åĢħ2[ ŲD�+Hħ+H2[ŋŦũŮųŋŪű
Ų,¹;Þ� Ų#F]�¶]ypíw�öøïìw�UÈã�ïì-#F¡�ððî
ĥĤĄĆ#FćĐàĹĶ£Hd»#ÛħīĬ�ġĢĄ#FÎÔ�Đ�iŲßi�
Ħ�ĹķġċĶą
�¦ħ�AĢĨĄ��]ij2[]ĺĆ��ćĘĶ�ĦĄãFßħ2�ıµ`Ė
Ĝ¬Rħêċƨ�/�éćģ:ĩķĶéĐ�ĹķĶĐĄ�=ĄĔħh}Ģ
�ğġ�ČĄĆŝũœŇŭ�ćĥĤ«-ĥ#FÎÔéıĄDâeĥ#Fħ]Ìĺ
�ÁĘĶħĦ�Ģı�ċĵķġċĶą 2
#FÎÔ�
Ųw�#FħãF�_ĦMĘĶ(rßĦ�GĖĥċ)ŋũŮųŕľűŃųq¥SĺÁĒq�
Ų/FÎÔĺŢųōģĖġĄÎÔłřŭńųĺ>w�ģĘĶ>wào=#FÎÔĺ�İĶ
Ųw�#Fħ2[ij�](�N]ij�93Ų��)ĢĨĄ�®�ħpπÎÔŲpπãFĐ�XĥħĢĄěķĝēĺcČ(1sãFijĄ2pσ±6ħãFĨ�¿ĘĶ=π����)
C C
H
C
H
H
H H
C H
C C
C C
Ā�Ÿcis-ŠŐŌłű ā
C C
C C
Ă
C C
C C
ă
C C
C C
e-e- e-
e-
Ĥħ�®/F�ħpπÎÔĦãFĐċĶrħłřŭńųĺαģĘĶą
C C
C C
e-
ãFĨĊĶpπÎÔďĵáħpπÎÔĦĝē
èĪģĖĄěħŚŦŭŖŘĽűº$½®ĺβģĘĶą
ŜūŨųŐα,βĨé±{ĐLéĦ6ČĴČĦÕVĦ�İĶą3
ŝũœŇŭ(Hückel)�
α 0 0 00 α 0 00 0 α 00 0 0 α
α β 0 0β α β 00 β α β
0 0 β α
0 β 0 0β 0 β 00 β 0 β
0 0 β 0
+
ŝũœŇŭ�ħŚŦŭŖŘĽű
=
V(��³łřŭńų)
T(�Ó*łřŭńų)
H(��łřŭńų)
ÜF)Hħ� K]/�TV-VT≠0(�³ģÓ*Ĩ7rĦ KĖĥċ)→ HģVħº$Đä4m:HV-VH≠0ĥħĢĄłřŭńų�KħãFĨŶĠħ/F�ħπÎÔĦėğģĖġċĵķĥċą→ #F��ĦäP?+ĘĶą→ Ć#FÎÔćĐWaą #FÎÔĨ� K]/�ħb�!4
α β 0 0β α β 00 β α β
0 0 β α
C1C2C3C4
0 x 0 0x 0 x 00 x 0 x0 0 x 0
C1C2C3C4
€
E
€
=�čĩĄŠŐŌłűħA6Ÿ
�ÐαĢ(ğġβ/α=xģĘĶą
ĕĵĦ-�º$ĺTĒ
C1C2C3C4
E α −1( )
€
=
�Ð-xĢ(ğġĄ
1−E α( ) xĺnİġEģĎĒ
šůņūŧ+ĘĶ�Ħ>w�<çĺ«-+ĘĶ
C1C2C3C4
0 −1 0 0−1 0 −1 00 −1 0 −10 0 −1 0
C1C2C3C4
E
€
=C1C2C3C4
#FÎÔĺ�İĶĜİĦĨĔķĺÁēĩ·ċ
5
6
ĈÊç11.1ĉŵ«-ĥ#FÎÔšůņūŧ)
ʼnĿŖoí�®ħoîĐòñ�ĭĢħÿ�XĺcčĶ÷þùûúü�ħšůņūŧ
ĺ�ķą
ĜĝĖMÀØ#ĨĄĆNumerical Recipesin Fortran77ć(WilliamHPress�¸,
CambridgeUniversityPress,1992)ĦjÏħJacobi�ħsubroutine(CO
nBĖĜıħ)ĺ��Ėġ·ċą
7
/Foģ±6ħ^@ĺhuckel.inpďĵÉĮÑĮ
HückelŚŦŭŖŘĽűħ%x+
HückelŚŦŭŖŘĽűħ~ª
HückelŚŦŭŖŘĽűħŒŁœŅ
MÀ+ŭųŒűĺ:Ī
ÎÔłřŭńųħ±{ħŒŁœŅ
±{ħ")ŭųŒűĺ:Īe
end
e
8
(²đ)
±{ħ")
MÀ+ŭųŒű(diagonalize.f)ĺ°Į6ĹĚġJa
huckel.fĺtđ¯čĜĵĄ
şļĿŭhuckel.fĺ�GħYĄÝėġĄ
řœŖħŠūŀŊĢ�ÄʼnĿŖĦĽŅŎōŸhttp://www.chem.sci.osaka-u.ac.jp/lab/guchi/chemprog/diagonalize.f
(Numerical Recipesin Fortran77)
ĺőŀűůųŗą
cphuckel.f huckel.f.back (←\ħĜİĄhuckel.fĺśœŅĽœš)
ls diagonalize.f (←diagonalize.fĐ7ėŕľŮŅŖŬĦňŞųĕķġċĶď Ç)
catdiagonalize.f >>huckel.f ( catA>>BĢĄAĺBħYĸĦ ēĶ)
huckel.fĺıČ�RÞċġĄĞIJĻģsubroutinediagonalizeĐ ċġċĶĺ Çą
gfortran huckel.f -ohuckel (ňűŜĿŭ)9
21
12
ethylene.inp
(1)cp ethylene.inp huckel.inp
(2)./huckel
(3)cp huckel.out ethylene.out
òº�Ÿ�®/Foíóîģ±6oíòî
óº�Ÿ±6ĐĤħ�®ģĤħ�®ħßħ±6ďĺgK
C C
H
H H
HĀ ā
(1) �)şļĿŭ奚ůņūŧĐÉįşļĿŭ8(”huckel.inp”)ĦBs(2)šůņūŧĺLº(3)")şļĿŭĺBsą
4 3
12
23
34
butadiene.inp
òº�Ÿ�®/Foíõîģ±6oíôî
ó�õº�ŸôĠħ±6ĐĤħ�®ģĤħ�®ħßħ±6ďĺgK
C C
H
C
H
Ā
ā
H
H H
C H
Ă
ă
(1)cp butadiene.inp huckel.inp
(2)./huckel
(3)cp huckel.out butadiene.out
šůņūŧħLºŷĠħ#Fħé�ħ�)şļĿŭ(ethylene.inp,butadiene.inp)ħ��
10
11
é±{ħ¾q
�čĩĄ'ţųŌħbutadieneħ±{ĨĄCygwinħňťűŗ
$cp huckel.out butadiene.out ←")şļĿŭ8ħBs
$catbutadiene.out ←±{ħ¼¢
ģĘĶģ�ÄħĴČĦ¼¢ĕķĶ(Ĩę):
-- MolecularOrbitalenergiesandCoefficients--
12 3 4-1.618 -0.618 0.6181.618
1 0.372 0.6020.6020.372
2 0.602 0.372-0.372 -0.6023 0.602 -0.372-0.372 0.602
4 0.372 -0.6020.602 -0.372
Ĕħ±{ħ¾qĨ�ħţųŌ0�ą
C C
H
C
H
Ā
ā
H
H H
C H
Ă
ă
-- MolecularOrbitalenergiesandCoefficients--
1 2 3 4
-1.618-0.618 0.6181.618
Ā 0.3720.602 0.602 0.372ā 0.6020.372-0.372-0.602
Ă 0.602-0.372-0.3720.602
ă 0.372-0.6020.602-0.372
ÎÔłřŭńųí�ċqĐIKî
5�®/FħÎÔ�oíýıÚ½Ŵî
C C
C C
�Ÿ
HOMO=HighestOccupiedMolecularOrbital
ŵãFĐ.wĖĜÎÔĢuıłřŭńųħêċÎÔ)
HOMO
LUMO
+0.602 -0.602
-0.372+0.372
1
2
3
4
-1.618
1.618
0.618
-0.618
ÎÔłřŭńų#FÎÔĨĄ5πÎÔĺÎÔ�oĦ��ĖĜDđĕĄýĢ��(ë�)Đ�ĭĶą
�Ÿ
LUMO=LowestUnoccupiedMolecularOrbital
ŵãFЧħÎÔĢuıłřŭńųħ�ċÎÔ)
C C
C C
+0.602 +0.602
-0.372-0.372
12
#FÎÔéĺ�ğĜ#Fßħ2[��(#FÎÔĺ�ċĜWoodward-Hoffman&ħ|Æ)
łŒŮűßĨ�2[ĢĨ2[ĖĥċĐĄłŒŮűģŠŐŌłűĨ2[ĺÍĔĘą
C2H4 +C2H4 2[Ěę
�
C2H4 +cis-C4H6
C6H10
�
13
#FÎÔéĺ�ğĜ#Fßħ2[��(#FÎÔĺ�ċĜWoodward-Hoffman&ħ|Æ)
±6ĐWaĕķĶí+H2[ĐÍĔĶî
łŒŮűßĨ�2[ĢĨ2[ĖĥċĐĄłŒŮűģŠŐŌłűĨ�Äħ2[ĺÍĔĘą
HOMO
LUMOLUMO
HOMO
ŠŐŌłűłŒŮű
14
LºÊç11.1
MathematicaħÁznbĄWoodward-Hoffman-MOs.nbĺ
http://www.chem.sci.osaka-u.ac.jp/lab/guchi/chemprog/
ďĵőŀűůųŗŲLº(*1)ĖĄłŒŮűģŠŐŌłűħ±6Waĺ ďİĴą
(ĥĎĄĔħnb!Ģk�ĖġċĶłŒŮűģŠŐŌłűĄ2#Fħ~ÒĨĄığģê¬RĥÜF+HéĦĴğġ
�KĖĜĄłŒŮűģŠŐŌłűħ+H2[ħÖ¤�_~ÒĢĊĶ)
Elumo ! ! """; Bhomo !
""""
;
(*1) ŝũœŇŭéħ±{ħĄłŒŮűħLUMOħ#FÎÔ�oĄŠŐŌłűħ
HOMOħ#FÎÔ�oĺĄ�ÄMathematica nb!ħ
Ħ�ķĄLºĘĶ(�×f→shift+enter)ĝēĢ·ċą
15
��ĺl"ħĔģŸZæ
(1)Êç11.1šůņūŧħŏųōňųŗ(diagonalize.fħØ#Ĩ�½)
(2)LºÊç11.1ŸŠŐŌłűHOMO-łŒŮűLUMOħÎÔ�àĺ¼Ę
3DšůœŖ(*1)
1vu%ħh}ÞErĦl"ą
(*1)
16