59
［18］annulene dianion C isHls2 （D2h）
and C18Hl82−and electron transitions which mainly
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Figure 5． Coordinate axes of Cl8Hl8 and Cl8Hl82一
Table 4． Decomposition of the iH magnetic shielding constants into xx， yy and zz components（PPm）
dia para
totalCl8Hl8 H（out） σxx
σyy σzz 、 σiso
Cl8Hl8 H（m） σ，α
σyy σZZ σisO
29．36 −0．22 29．14 42．49 −17。73 24．76 17．30 −10．61 6．69 29．71 −9．52 20．19 35．23 −4．79 30．44 36．58 −19．13 17．45 45．15 37．29 82．44 38．99 4．46 43．45 C18H182−
@H（out） σxx
6yy 6zz 6iSO CI8Hl82−@H（in） σxx
σyy σZZ 6iSO
21．83 1452 36．35 31．94 −0．23 31．71 43．41 −13．41 30．00 32．39 0．29 32．68 35．07 −5．00 30．07 39．75 −19．29 20．46 37．05 −63．87 −26．82 37．29 −29．39 7．90
9
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3．4．3．【18］anulene analogues
Table 3 also shows the lH magnetic shielding constants of Cl6Hl8， the M6bius type molecules C l8H20 and the M6bius type molecules C18H20 inserted the methyl anion CH3 ． Figure 6 shows a molecular stmcture of C l 6Hl8． C i 6Hi8 is a molecule made by removing tWo c arbons from C18Hl8． As shown in Figure 7， C l8H20 was made by removing one C−C（s−bond from［18】annulene and adding two hydrogen atoms， and then it is distorted helically from a planar structure． Two te㎜inalπ一〇rbitals interact we akly with each other． We call this C i 8H20 a M6bius−typ e molecule． R
in Figure 7 is the horizontal distance between the terminal CH2 planes． We prepared three kinds of R（15，2．O and 3．O A）． Figure 8 shows the M6bius−type molecule C l8H20（R・ 3。O A）into which a
methyl anion CH3−is inserted． In C i 6H l 8， H（out）was close to H（in）（H（out）＝25。74 ppm， H（in）＝
22．63ppm）． The aromaticity of C i sHis completely vanished because of cutting the aromatic ring． In the M6bius type Cl8H20（R＝1．5 A）， the magnetic shielding contrary to that of C18H18 was generated． H（out）was 29．82 ppm and H（in）was 6．90 ppm． These results are illustrated in Figures g and 10． Cl8H18 is aromatic， while Cl8Hl82 and Cl8H20（R＝1．5 A）are anti−aromatic． HOMO of Cl8Hl8 and Cl8H20（R＝15 A）weζe shown in Figures l l and 12， respectively． The difference between these two systems is expressed by the 18×18 HUckel secular equations as
●
°．
求D
求D
求D
°．
求D
求D
求D
●
●
0
190
0
●0
1＝0
（8）and
一69一
りoo…
・
の
●
0
10 0
一θ
＝0
（9）fbr C l 8Hl8 and C l 8H20（R＝1．5 A）， re spectively． The HUckel resonance energy betWeen the terminal
p−orbitals is assumed to be 06（0＜θ＜1）where the normal HUckel resonanc e energy is 6． ln case ofθ＝1，Eq．（9）is equivalent to the Mebius−type HUckel secular equation． The resonance energy of
Cl8H18 was 5．04βand that of C18H20（Rニ15A）was 4．69βin case ofθ＝1． Cl8Hl8 is more stable than CisH20（Rニ15 A）． According to the IH magnetic shielding constants of H（out）and H（in），
Cl8H20（R＝1．5 A）seems to be anti−aromatic． As R increases， the difference betWeen H（out）and
且（in）was smaller． That is to say， the anti−aromaticity of the M6bius type C i 8H20 became smaller．
Table 3． iH magnetic shielding constants of C i 8Hi8， C l 8Hl82− C M6bius−type C l 8H20（R・1．5，
2．0，and 3．0）， M6bius−type C l 8H20＋．methyl anion（ppm）
H（out） H（in）
σ（dia）a σ（para）a σ（total） σ（dia）a σ（para）a σ（total）
Cl8Hl8
Cl8Hl82
Cl6Hl8
Cl8H20（R＝1．5 A）b
Cl8H20（Rニ2．OA）b Cl8H20（Rニ3．OA）b Cl8H20＋CH3口
29．71 31．32 23．44 22．69 29．38
2952
28．37
一952
0．18 2．30 7．13
−1．53
−3．13
−2．94
20．19 31．50 25．74 29．82 27．85 26．39 25．43
40．34 37．34 39．70 38．57 39．97 41．17 37．90
4．46
−27．70
−17．07
−31．67
−2452
−20．13
−7．13
44．80 9．64 22．63 6．90 15。45 21．04 30．77 aσ（dia）andσ（para）are Eq．（2）and（3）， respectively．
bRis shown in Figure 3．
一70一
H（out）
／
．．」『
轟歯
拶施 。瀕疑
一H（in）
．．fg
tt，。適縄
Figure 6． Molecular structure of C l 6Hl8
一71一
H（out）
Figure 7． MolecUlar structure of M6bius−type open−chain C l 8H20（IR＝15A）
Figure 8． Molecular structUre of M6bius−type C l 8H20． A methyl anion CH3 the ter血inalπ一〇rbitals．
−72一
9
is inserted between
［18］annulene C l 8Hl8
［1 8］ annulene dianion C 18Hl82
Cl6Hl8
Cl8H2。（R−1．5 A）
Cl8H20（R＝3．O A）＋CH3一
H（out） H（in）
H（in）
H（in） H（out）
H（out）
H（out）
10 20 30 40 50
1H magnetic shielding constant／ppm
Figure 9． The lH magnetic shielding constants of C18H18， C18Hl82−， open−chain Cl6Hl8 and mδ1）ius−type open−chain C 18H20（R＝15A）
一73一
撚綴β1
鍮 麹義畿塾晦
耳（in）
。、
@ 鼠塾糠
（a）C18H18
H（out）
H（out）
BI
BI
（b）Cl8Hls2
砿
⑩
I H
β一翻團圃團
（c）Cl8H2。（R・・＝ 1．5 A）
Figure 10． External magnetic field Bo and induced magnetic field Bi
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Figure 11． Schematic pictUre of the HOMO of［18］amulene（Cl8Hl8）
一75一
Figure l 2， Schematic picture ofthe HOMO of［18］anllulene（Cl8H20）（R＝1．5 A）
一76一
Next， we inserted the methyl anion CH3−into the M6bius type Cl8H20（R＝3．O A）． The difference between H（out）and H（in）became larger again． H（out）was 25．43 ppm and H（in）was 30．77ppm， i．e．， the aromaticity became larger． The HOMO of C i 8H20＋CH3− was shown in Figure 13．2pz orbitals（πorbitals）of carl）ons of the both ends of the cutting Part and sp30rbital of carbon of CH3−interacted． sp30rbital interacted with one in s ame phase， while sp30rbital interacted with
the other in reverse phase． The 19×19secular equations of C 18H20＋CH3−was shown beIow・
●
9
……ooり
o
AU（U（U
κ｛1（U
●
lXθ
り0・………0θぜ
＝0
（10）The definition ofθ（1＜θ＜1）is the same as that in Eq（9）， dζis added to express the sp30rbita1，
In case ofθ＝1andζ＝3， the resonance energy of C18H20＋CH3−was 10．86β． When we compare the resonance energy fbr Cl8H18， Cl8H20（Rニ1．5 A）， and Cl8H20＋CH3−， it seems that C18H20＋
CH3一has the largest stabilization byπelectrons．
Table 5 shows NICS values of C18H18， CI8H182 ， M6bius−type Cl8H20（R＝1．5，2．O and 3．0）
and M6bius−type Cl8H20 inserted methyl anion CH3−． The calculated points were Bq in Figures 2，6，
7and 8． The NICS values listed in Table 5 are illustrated in Figure l 4． A large negative sign of電he
NICS value represents the strong aromaticity， and a large positive sign of that represents the strong anti−aromaticity． As reference， a NICS value of benzene was shown in Figure l 4． A NICS value of benzene was−10．48 ppm． A NICS value of Cl8Hl8 was a large negative value（−15．26 ppm）， namely，
astrong aromaticity． On the other hand， a NICS value of Cl8Hl82−was a large positive value（1451
ppm）， namely， a strong anti−aromaticity． C16Hl8 resulted in a neutral value． That is to say， the aromaticity of Cl8Hl8 vanished． A NICS value of M6bius−type Cl8H20（R＝1．5 A）was a positive value（15．83 ppm）， namely， a strong anti−aromaticity． When a methyl anion CH3− was inserted into M6bius−type Cl8H20（、R＝3．O A）， a NICS value changed into a negative value． Afヒer all， Cl8H20（Rニ
ー77一
3．O A）＋CH3−showed the aromaticity． These results were c onsistent with above results of Table 3．
rbita1
Figure 13． Schematic picture of the HOMO of［18］annulene（Cl8H20）（R＝3．O A）＋CH3−一
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Table 5．NICS Values of Cl8H18， Cl8Hl82−C C16Hl8， M6bius・・type CisH20（R＝1．5，
2．0，and 3．0）， M6bius−type C 18H20＋CH3 （ppm）
σof the ring center
σ（dia） σ（para） σ（total） NI CS
Cl8Hl8
C18Hl82 − Cl6且18
M6bius−type C i sH20（R＝1．5 A）
M6bius−type Cl8H20（R＝2．O A）
M6bius−type CisH20（R＝3．O A）
M6bius−type Cl8H20＋CH3
7．42 4．69 6．45 7．64 6．97 8．93 6、26
7．84
−19．20
−9．21
−23．47
−15．76
−12．75
−1．62
15．26
−14．51
−2．76
−15．83
−8．79
−3．82
4．64
一15．26 14．51 2．76 15．83 8．79 3．82
−4．64
●C18H20（R＝15A）
●C18Hl82暉
●Cl8H20（R＝2．OA）
●C18H2。（R−3．OA）
●Cl6H18
●C18H20＋methyl anion
●1）enzene●CI8H18
20 15 10
ant1−arOmat1C
5 0 −20一5 −10 −15
aromatlC
Figure 14． Calculated NICS values（ppm）of C l 8H20 and its analogues and benzene（ppm）．
一79一
3．5．
Conclusion
We carried out a series of the ab inii io quantum−chemical calculations of Cl8Hl8 and its analogues and discussed the calculated nuclear magnetic shielding tensors and chemical shifts of these molecules． We also discussed the aromaticity ofthese molecules With the NICS values．
（1）The trend of the NMR chemical shi丘s of Cl8H18 and Cl8Hl82−was reproduced by the present calculations． The decomposition of the magnetic shielding tensors reasonably explained the difference betWeen aromatic and anti−aromatic molecules．
（2）The M6bius−type open−chain Cl8H20 generated from Cl8Hl8 and Cl8H20＋CH3−are an
alternative model of the Mebius−type systems． The conventional HUckel rule still worked well in these cases， when we considered the phase of the冗一electron system． The M6bius open−chain ClsH20 showed anti−aromaticity due to the weak interaction between the terminal 2pz−orbitals．
The C18H20＋CH3−complex is suggested to be an aromatic system， since it has the M6bius −type Connection in the x−electron system and（4n）π electrons．
By this study， we understood that these magnetic properties of simple electron systems can be repro duced by the ab in itio calculation． However， the predictioh of the magnetic property of the
complicated systems will not be easy， and the unexpected result may be produced． We think to perform the systematic ab・ initio calculatioris of the magnetic properties of complicated rt electrons
systems and to try discovering the law about n electrons systems．
9
3．6．Acknowleαg坦Ωpt
This work was supported by Japan S cience and Technology Agency（JST）．
一80一
3．7．References
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−81一
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勝
●
83
General Conclusion
In this thesis， we carried out the multi−nuclear NMR calculations of the various syste皿s，
We discussed the various cases， i．e．， halogen一㎜， metal−NMR，13C−NMR， and l H−NMR． We did
not aim at only the calculation precision and， by analytical techniques of the quantUm chemistry，
argued about the origin of the NMR chelnical shifしdeeply．
In chapter 1， the NMR calculations taking account into the relativisti c theory and the electron correlation were carried out The former was considered by DKH2 method， and the latter was considere d by MP2 method． We used the GUHF wave fUnction in order to describe better the SO interaction and the re spoIlse to the extemal magnetic field． The target molecules were X and
XO4一
ﾐ（＝F， C1， Br， and I）。 The resonance atom was X， The relativistic effects were larg er as the resonance atoms were heavier． In the other hand， the electron correlation effects were smaller as the halogen atoms were heavier． The Ferrni−contact term mainly contributed to the relativistic effect，while the paramagnetic te㎜mainly con励uted to the electron co∬elation effect． When the
relativistic theory and the electron correlation were considered at the same time， the effect c a not be
represented by the sum of the relativistic effect and the electron correlation effect． That is to say， the
coupl血g effe ct between the relativistic theory and the electron correlation exists．
In chapter 2， the calculation of NMR che血cal shi丘s of Mn（CO）5Xσ（ニH， F， Cl， BI， I and CH3）and M（CO）（NH3）3（M＝Cr2＋， Fe2＋， Cu＋and Zn2＋）were carried out． The㎞prove皿ent of
basis sets in the fbrmer of chapter 2 gave better results than the previous study． It was shown that the d−d transition c ontributed mainly to 55Mn chemical shift． These results supPorted the traditionaL
analysis． Our calculation values by RHF and DKH2 taking into account the relativi stic effect were
good agreement with the experimental values． In the latter of chapter 2， we reproduced t㎞e experimental results by using the models of the enzymes in a living body． We clarified that t㎞e origin of NMR che血cal shifts seems to be mainly the paramagnetic term． Moreover， With an expression of the pe血ぽbation theory， we analyzed why the paramagnetic term is dominant in the
−85一
NMR che血ical shifts． The origin of the che血cal shifts was due to the difference of the electron configuration ofthe metal of the center．
In chapter 3， the ab initio calculations of Cl8Hl8 and its derivatives were carried out．
Cl8Hl8 was aromatic， while Cl8Hl82 was anti−aromatic． The fbrmer is a（4n＋2）πelectrons system．
The latter is a（4n）πelectrons system The conventional・ HUckel rule was right． We explained the origin of these results by the electron configurations and Eq．（4）in chapter 3． C18H20 made by distorting C18Hl8 and connecting into the M6bius type was anti−aromatic． This is a new result．
Moreover， when Cl8H20 was inserted CH3凹
C the molecule changed into aromatic． These resUlts suggest that we can control the aromaticity， i．e．， the magnetic properties of cyclic compomds． When stUdies on the aromaticity advance mote， the concept of the aromaticity may change．Thiゴthesis includes froin the theoretical fbundation to the applied calculations and the analytical techniques as the su切ect in quantum chemistry about the NMR． We analyzed lH−NMR，
13C−NMR， and the multi−nuclear NMR． Moreover， we also discussed the aromaticity． The AO and
MO analyses are the original method of our laboratory． We clarified the NMR che血ical shifts by the concept of or1）ital which is easy fbr the experimentalists to understand． Our studies gave the important suggestions to the experimental studies。
Here we give tWo fUture research themes．
At first， we want to refer the dependency of the gauge origin betWeen the diamagnetic term
and the paramagnetic te㎜． Because of this dependency of the gauge origin， the values of each te㎜
change according to where the gauge origin is taken（The total value doesn曾t change）． It is necessary to advance the research on this problem in the future though we think that the influence which the present study receives l）y this dependency will be small．
Next， we mention the ring current which appeared in chapter 3． We want to decide whether the ring current exists or not． There were not results which let us doubt the existence of the ring current． However， there are some stUdies to let us doubt it［1，2］． It is necessary to get more experimental and calculated data． Studies on the quantum chernical treatment of the ring current are
−86一
progressing ［3−5］．
fUture．
The new acknowledgement ab out the ring current will be gotten in the
near
Finally， we describe our thought about science． There will not be the person putting in an
obj ection to having been a scientific century in the 20th centUry． Outlook on view of the world and the material changed completely by the quantUm mechanics and the relativistic theory in the first half in the 20th century， The first half in the 20th cen加ry can be said to have been，，an era of
the materials science ． On the other hand， by the elucidation of the double−helix structure of the DNA in the latter half in the 20th cen加ry， it was shown that life can be described by means of the
language of physics and chemistry． That is to say， it may be said that the latter half in the 20th
century was an era of the bio science Shifts ffom the materials science ， to the bio science are the big undulation in science． In the fUtUre， the approach to the life will be more imp ortant topics in
the quantum chemistry that we specialize． The molecules controlling the life are very enormous and
complicated． Various methodologies are studied fbr such a problem For example， the calculations of the molecule consisting of more than ten thousands of atoms can be carried out now by the improvement of the algorit㎞， the speedup of the computers， and the massively parallel computers．
In addition， the trials th漁re going to reproduce the且mctions and prope式ies of the eno㎜ous and complicated systems are performed by the modeling and simplification， We wamt to try the studies of the life． In the fUture， our views of the life and the concept of the life may change．
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［5］ P．1／azzerretti， Progre∬in 7＞MR勘εc 705c6ワ2：ソ；36，1（2000）
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Appendix A． The definition of Nuclear Magnetic Shieldi耳g Constant
（Ramsey，s Formula）
The interaction energy betwe en μ2＞ and Bo is
7＝一μ2ゾBo （1）
whereμN is the nuclear magnetic moment of nucleus Al and Bo is the external uniform magnetio 且eld． However，血molecules， Bo is shielded by electrons． When we assume this ratio the nuclear
magnetic shielding c onstantσ，we obtain
7＝一μパ（1一σ）Bo （2）
Since、Bo is the vector，σis the 3×3 tensor The molecular energy E≡．E（μN，Bo）is
E（μN，Bo）＝E。一μパ（レσ）B。
（3）
＝E。＋μパσβ。一μパB。．
Eo is the molecular energy withoutμN and、Bo．When the third term of the right hand side is
ignored，σis defined as fbllows．
∂2E
σNtu＝・PtNt・B。u＿（t， u＝x，ア，z） （4）
This is called Ramsey s fbrmula．
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Appendix B．
terms
The Derivation of Diamagnetic and Paramagnetic
When nucleus IV has the magnetic momentμ漏、（u＝x，ア，z）under the presence of the unifomi extemal magnetic field Bt（t＝x，ア，z），the vector potential 4（t＝κ，ア， z）is as fbllows・
A＝圭B×（r−R）＋讐
（1）We replace the m・men加m・perat・rρ， withρ，＋94．
C
P，→P，＋94（t−x，ア，z） （2）
C
The Ha血ltonian is expressed by
A一粧（．P ＋94）2＋v・ （3）
When we expand the total Ha血ltonian in powers ofμN and B，we obtain
A−A（°・°）＋Σ倉1 ・°）B，＋ΣΣ倉織）ILtN，u＋ΣΣB，・鶴：1 、 N，u＋… （4）
t＝x，ア，z Nu＝x，ア，z Nt，u＝x，ア，z where t， u denote x， y， z axes， and
A（°・°）一誰▽1＋v （5）
醇誰易 （6）
鶴 ）一誰鶏 （7）
珊1）−4羨lc・写幅讐 （8）
9
We use Pノー4▽ノ． Lプ， is the t c・mp・nent・fthe angularm・ment㎜・perat・r・f・electr・nブ・r／
z
is the c・・rd血ates・f elec廿・nノ．馬is the vect・r丘・m・nucleus N t・electr・nプ・a（°・°）is the
Hamilt・㎡an in the absence・fthe external magnetic field．窃1・°）is the Zeeman te㎜・felectr・nプ．
鶴1）includes the angular m・men加m・perat・r ar・u・・d the res・nance nuleus and is the interacti・n
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be餅een the nuclear magnetic m・ment and electr・nノ．珊 ）is・the・Lamb・f・miula・if・we・c。nsider
the atom system． IfΨis the variational wave fUnction， Hartree−Fock SCF wave fUnction in this s加dy， we c an use止e Hellmam−Feyuman theorem． We obtain
6Ntu−［話〈Ψ1乱1Ψ＞L （9）
一〈Ψ（・）1瑠）1Ψ（・）〉＋［話〈Ψ（B，）1鶴1）1Ψ（B，）＞L（ちu− Z）
HereΨ（0）is the㎜pe血lrbed wave fUnction andΨ（Bt）is the wave fUnction in the pre sence of
the component of extemal magnetic field． The first teml is the diamagnetic shielding tensor σ魏、＠のand the・second term is the paramagnetic shielding tensorσ酌、（parの． crNtu伽）and crNtu（parのin the pertUrbative f・rm can be expressed bシ
σNtu（dia）−4羨lc・〈・1「°黙一弓騙1・〉 （1・）
2〈・1L， lm＞〈磨1・〉
・ N・・（para）−i箒鶉層≒±均㌦ （11）
We mainly discuss the isotropic t．erms of the shielding c onstants， namelyσ＠α）N andσ（parのN．
We obtainσ（diのN andσ（、ρarのN by
σ（dia）N−1（σ（伽）一＋σ＠a）吻＋σ㈹Nzz） （13）
σ（鯛N−1（σ（卿）Nxx＋σ（卿）吻＋σ（卿）Nzz）・ （14）
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