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ŀœŗŰųŗŤşťű& (şůűŔľĽÎÔ�Ë)

1

w�+Hij��+HĄ��+HĨÂČĦ1ĩęĄQH#ÛĢıĄ#FÎÔÃ

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ŲQÙ®Åà ŲQ�6a­ÅÃ

Ų�pã�ĥĤħ�åĢħ2[ ŲD�+Hħ+H2[ŋŦũŮųŋŪű

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ĥĤĄĆ#FćĐàĹĶ£Hd»#ÛħīĬ�ġĢĄ#FÎÔ�Đ�iŲßi�

Ħ�ĹķġċĶą

�¦ħ�AĢĨĄ��]ij2[]ĺĆ��ćĘĶ�ĦĄãFßħ2�ıµ`Ė

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�ğġ�ČĄĆŝũœŇŭ�ćĥĤ«-ĥ#FÎÔéıĄDâeĥ#Fħ]Ìĺ

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#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