蝿
難
化学
氏名
1381
Tanimura Hirotaka
〆
谷村景貴 1
Quan伽m−Chemical Analyses on
the Multi−Nuclear NMR Chemical Shifts of Metal Complexes andπ一Electron Systems
Hirotaka Tanimura
2010
首都大学東京 博士（理学）学位論文（課程博士）
論文名
金属錯体とπ電子系化合物における多核種NMR化学シフトの 量子化学的解析手法に関する研究（英文）
著 者 谷村景貴
審査担当者 主 査 委 員 委 員 委 員
；皮国雅％
鞠ヰィ蘇〕／
上記の論文を合格と判定する
平成？2年3．月2S日
首都大学東京大学院理学研究科教授会
研究科長
DISSERTATION FOR A DEGREE OF DOCTOR OF SCIENCE
TOKYO METROPOLITAN UNIVERSI TY
TITLE：
Quantum−Chemica1 Analyses on the Multi−Nuclear NMR C血emical S血ifts of Meta1 Complexes and z−Electron Systems
AUT且OR： Hirotaka Tanimura
EXAMINED BY
Examiner in chief
Examiner Examiner
み曜み砂な緬り
1（：＆−s／wh s ekr IL− ・tぺ
Examiner
QuAHFIED BY T且E GRADuATE ScHoOL oF ScIENCE TOKYO METROPOLITAN UNIVERSITY
Dean
Date
Akms OLcu4e−
iVN，，一，，L z薪z∂／・
Contents
Preface．．．．．．．．。．．．．＿．．＿．．．＿．．．．．．．．．．．．＿＿．．．．．，．，．．．．．．．，．．．．．．．＿．．．．＿．．．．．．．＿＿．＿．．．．．．．．．．．．．．．．＿．＿．．．．＿．．．．．．．＿＿＿．＿．＿9
Acknowledgments。．．．．．＿．＿．．．．．．．．．．＿＿。．．＿．．．。．．．＿．．．．．．．．．．．．．．．．．．．．．．．．＿．．．＿．．．．＿．．．．．。．．．＿＿．．．．．．．＿。．．．．＿．＿．＿＿13
List of Publications．．．．＿．．＿．．．．．．．．．＿．．．．＿．．．．。．．．．．．．．．．．．．．．．．．．＿．．．．．＿．．．．．．．．＿．．．．．．．．．．．＿．．．＿．．＿．．．．．＿＿．．．＿＿．．．，，14
Chapter 1． Nuclear Magnetic Shielding Constants of Halogens in X and XO4 （X＝F， Cl， Br，1）−
Relativistic and Electron・Correlation Effects−．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．。．．．．．．．．＿．．．．。．．．．．．．．．．．．．＿＿．．。．．．．．．．」7
1．1．Abstract．．＿．．．＿．＿．．．．．＿．．．．＿．．．．．．．＿．．．．．．．．．．．．＿．．．＿．．．．．．．．，．．．．．＿．．．．．．．．，．．．．．．．．．．．．．．＿．．．．．．．．＿＿＿．．．．．．．．．．．17
1．26 1ntroduction．＿．＿．＿．．．．．．＿．．＿．．＿．．。．．．．．＿．．．．．．．＿．．＿．．．．．．．．．．．．．．．．．．．．．．．．＿．．．．．．．．．．．．．＿．＿．．．．，．．．＿＿．．．．．．．18
1．3．Theory∴＿．．＿＿．．＿．＿＿＿＿＿．＿＿＿＿＿＿．．．＿＿＿＿＿＿．．．＿＿＿＿＿＿．＿＿．＿＿＿＿．．．．＿＿＿19
1．3．1．Relativistic且amitonian．．．．．．．＿．＿．．．．．＿．＿．．．＿．．．．＿．．．．一．．．．．．．．．＿．．．．．一＿．．∴．．＿．．．．＿．＿．．．．．．．．．．．．19
1．3．2．Nuclear Magnetic Shielding Constant．．．．．．．＿．＿．．．．．．．．．．＿．．．．．．．．．．．．＿．．．．．．．．．．．＿．＿．．，．。＿．．＿．＿21
1．3．3．Generalized UHF Method＿．．．．．．＿．．．．。．＿．．．．．．．．．．．．＿．．．．．．．．．．．．．．．．．＿．．．．．．＿．＿．．．．．．．＿．．．．．，．．一＿＿22
1．3．4． Basis sets＿＿＿＿．＿＿＿．＿＿＿．．＿＿＿＿．＿＿．．＿．＿．＿＿＿＿．＿＿＿＿．＿＿．．．＿＿．＿＿＿＿．＿．．22
1．4． Results and Discussions．．．．＿．．．．．．＿．＿．．．．．．．．．．．．＿．．．．．．．。．．．．＿．．．．．．．．．．．．．＿．．＿．．．．＿．．．．．．＿＿．．．．．，，，．．，＿＿23
1．4．1． Relativistic Effe ct．．＿．．．．．．．．．．＿．．．．．．＿．．．．．．．．．．．．．．＿．．．．．．．．＿．．＿．．．＿．．．＿．．。．．．．．．．．．．＿．．．．．．．．＿，，．＿．．．．23
1．42． Electron Correlation Effect，．．。．．＿．．．．＿．．，．＿．．．．．．＿．．．＿．．．．．．．．．．．．．．．＿．．．．．．．．．．．．＿．．．＿．＿．．．，．．，．．＿．．26
1．4．3． Coupling Effect of Electron Correlation and Relativistic Theory．．．．．．．．＿＿．＿．．．．．．．＿＿，，．28
1．5．Acknowledgments．．．＿．．．．．＿，．．．．．．，．一．一．．．．．．＿．＿＿．．．．．＿．．．．．．．．．．＿．．．．．．．．．．．．．．．．＿．．．．．．＿＿．．．．．．．．，＿，．，，，＿2g
1．6． Refbrences．．．．．．．＿＿．．．．．．＿．＿．．．．．．．．．．，．。一．．．＿．．．．．．の．．．．．．．．．．．．．．．．．．．．．．．．．．．。＿．．。．．．．．．＿．＿＿．．．．．．．．．＿．．，．．，．＿＿30
Chapter 2． Calculations and Electronic Analyses of 55Mn and 13C Nuclear Magnetic Sllieユding Constants for Mn（CO）5X（X＝且， F， Cl， Br，1， and CH3）and M（CO）（NH3）3（M＝Cr2＋， Fe2＋， Cu＋， and
Zn2＋）。．．．．．．．．＿．．＿．．．．．．．．．．．．．．．．．＿．＿．．＿＿．。＿．．．．．。．．＿．．．．．．．．＿＿．9．．．．．．．＿．＿．．．＿．＿＿．．＿．．＿．．．．．．．．．．．．，．．＿．＿．．．．＿，＿33
2．1．Abstract．．．．．．．．．．＿．．．．．．．．＿．．．．．＿．．．．．＿．．．．．．．．．．．．．．．．．．．．．．＿．．．．．．．一．．．＿．．．＿．＿．．．．＿．．．＿．．，．．．＿．．．．．．．．＿．．．．＿．，，33
22． Introduction．．．．．．．．．．．＿．＿．．．．．．＿．＿．．，．．，．．．．．．．．．．＿．．．．．．．．．．．．．．．，＿．．．．．．．．．．．．．＿．＿．＿．．．．＿．．．．．．．＿＿．．＿．．．．＿34
2．3．Computational D etails＿．．＿．．．．．＿＿．．．，．一＿．．．＿．．．．．．．．。．．．．．，．．＿＿．．．．．．．一＿．．．．＿．＿．．．．．，．＿．．．．．．．．．．＿．＿．35
2．4． Results and Discussion．＿＿＿＿＿．＿．＿．＿＿＿＿．＿．＿＿＿＿．．＿．．．＿＿．＿．＿＿．．．．．．．．．＿＿．．＿＿＿．．，37 2．4．1．55Mn Magnetic Shielding Constants for Mn（CO）5X．．．．．．．．．．．＿．＿．．．．．．．．．．．＿，＿．．．．＿．．＿．．．＿．．．37 2．4．2．13C Magnetic Shielding Constants fbr M（CO）（NH3）3．．。＿．．．．．．．，．．．．＿．．＿．．＿．＿．＿．＿．．．．＿＿44 2．5． Conclusion．．＿＿＿．．．．，，．．．．．＿．＿．＿＿＿＿．＿．＿＿＿．＿＿．＿＿＿＿＿．．．．．，．＿＿＿．＿＿．＿．．．．．＿＿＿．＿＿．5（〕
2．6．Acknowlegemen七s−＿．＿．＿．＿．＿．＿．＿．＿．＿．＿．．．．＿．＿．＿．＿．．．＿．＿．＿．．．＿．．．．＿＿。＿．．＿．＿．．．＿．＿＿50
2．7． References．．．．．．．．＿．．．，．．，．．．＿．．．．．．．．．．．．．＿．．．．．．．．．．＿．．．．．．．＿．＿＿＿．＿．．＿＿．．．．．．＿．．．．．．．．＿．．．＿．＿．＿＿．．．．．．i5丑
Chapter 3． Nuclear Magnetic Shielding and Aromaticity of［18］Annulene and its Derivatives＿．．55
3．1．Abstract．．．．．．＿．．＿．．＿．．．．．．＿．．．．．．．．．＿．．．．．．．．．．：．．．．．．．．．．．＿．．．．．．．．．．．＿．．．．．．＿．．．．．．＿．．．．．．．．．＿．．．．．．＿．．＿．．．＿．＿55
3．2． Introduction．．．．．．．＿．＿．．．．．．．＿．．．．．．．．．．＿．．．．．．．．．．．．．．。＿．．．．＿．．．．．．．．．．．．＿．．．．．．．．．．．．．＿．．．＿．．．．＿．＿．＿，＿．＿．．．56
−7一
3．3．Method．．．＿．．．．．．．．．．．＿．．＿．．．．．．＿．．．．．＿．＿＿＿．．．．．．．．．．．＿．．．．．．．＿．．．．．．＿．．＿．＿一．．．＿．．．＿．＿．．．。．．．，＿．．．．．．．＿59
3．4．Results and Discussion．．＿．．．＿．．．．．．．．．．．．．．．．，．＿．＿．．．。＿．．．．．．＿＿．．＿．．．．．．．＿．＿．．．．．．．＿．．．．＿．．．．．．．＿．＿．．．61
3．4．1．Accuracy Check．．．．．．．．．．＿．．．．．．．．＿．．．．．＿．．．．．＿＿．．＿．。．．．．．．．．．．．．＿，．．．．＿＿．．＿．．．．．．．．．．＿．．．＿．．．．．．．．．．．．．61
3．4．2．Neutral［18】annulene and its double anion．．．．．＿．．．．．＿．＿．．．．．．．．．．．．．．．．．＿．．．．．．．．．．．．．．．．。．．＿．．．＿．63
3．4．3． ［18】anulene analogues．．＿．．．．．．．．．．．．．．．．．．．．．．．．．．．．。．．．．＿．．．．．．．．．＿．＿．．＿．．．．．．．．．．．．．．＿．．．．．．．．＿．＿．．．＿．．69
3．5． Conclusion．＿．＿＿．＿＿．＿＿＿＿．．＿＿．＿＿＿．＿．．．＿．＿＿．．＿＿．．＿＿．．＿＿．．＿．．＿．＿＿＿＿＿．．＿＿＿．80
3．6．Acknowledgment．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．＿．．＿．．＿．＿．．．．．．＿．＿．．＿＿．．．．．。．．＿．．．．．．．．．．＿．＿＿80
3．7． References．．．．．．．．．．．．．．．。．．．．．．．＿．．．．．＿．．．．．．．．．．．．＿．．．．．．．．．．．．．．．．．．．＿＿．．．．．．．．．．．．．．．．．．。．．．．．．．．．＿．．．．．．．．．．．＿．＿．＿．81
General Conclusion＿．．．．．．．．．．．．．．．＿＿．．．．．．．．．．．．．．．．．．．．．．．＿．．．．．．．．＿．．．．．．＿．．．．．．．．．．．．．．．＿．．．．．．．．＿．．．．．＿．．．．．．．．．．．．．．．．．．．．85
Appendix A．
Appendix B．
Appendix C．
Appendix D．
Apperrdix E．
Appendix F．
Appendix G．
Appendix H．
Appendix 1．
The definition of Nuclear Magnetic Shielding Constant（Ramsey s Formula）．＿．＿＿89
The Derivation of Diamagnetic and Paramagnetic七erms．．．．．．．．．．．＿．．．．．．．．．．．．．．．．．．。．．＿．．．．90 The Deriva七ion of Fermi・Contact and Spin−Dipolar terms．．＿．．．．．＿．．．．．．。．．．．．．．．＿．．．．．．．．．．92 Gauge・lncluding Atomic Orbital（GIAO）method．．．．．．．．．．．．．．．。．．．．．．．．．．．．．．．．．．．＿．．．．．．．．．．．．．．．．．．94
The Derivation of DKH2 and DKH3且amiltonians．．．．．．．．＿．．．．．．一．．．．．．．．．．．．．．．．．．．．．．．．．．．．．＿．95
The Derivation of the MP2 theory．．。．＿．．．．．．．．．＿．．．．．．．．．．．．．．．．．．．．．．．．．．＿＿．．．．．．．．．．．．．．．．．．．．．．．．．．．．．98
Basis sets fbr F， Cl， Br，1， and O in Chapter 1．＿＿＿＿．＿＿＿＿．．＿＿．．＿．＿．＿＿．＿．．．．100 Basis sets for Cr， Fe， Cu， Zn， C， N，0， and H in Chapter 2＿＿＿．＿．．＿．＿＿．＿＿＿．＿106 The AO and MO contributions＿．＿．＿＿＿＿＿＿．＿＿＿＿．＿．＿．＿＿＿．＿．．．＿＿＿＿＿＿．116
ノ
一8一
Preface
Che血stry is a field of science to search the natUres of materials in our space． Concretely，
chemists stUdy the structUre， property， change， and energy of materials． Che血stry has been the empirical study mtil recently． However， the exact quantum chemical calculation（the ab initio calculation）was enabled by the rapid development of the computer． As a fesult， chemistry that was experiential science is varying to the non−empirical study． It is the most important goal fbr theoretical chemists to replace the empirica1㎞owledge with the non−empirical understanding．
Because theoretical che血sts have the wave f㎞ction of molecules， they can do analyses to be impossible fbr experimental chemists． A role of the theoretical che血stry in chemistry is more important in the fUtUre．
The history of nuclear magnetic resonance（NMR）started by the paper of C． J．一Gorter。 It was in 1936． More than half a century already passed since the technique of the NMR was introduced into the field of che血stry． Now， NMR is used in many fields of the experimental science such as organic che血stry， physical che血stry， and biochemistry． NMR is the most important and is wide as the powerfUI measurement means of the spectroscopy． Because the
／
necessary extemal energy on NMR is very small（radio wave degree）， we can draw information without almost disturbing the electronic structures of molecules． In addition， many nuclei are observable in NMR If the nuclear spin of a nucleus is not zero， we can observe it on NMR．
Therefbre， it may be said that quantity and the quality of the inforrnation that NMR brings excel others in every spectroscopy． It is one of the important problems in the theoretical chemistry to elucidate the mechanism of the NMR che血cal shift theoretically． On the theoretical chemistry，
NMR calculations are carried out based on the fbllowing equation（fbr details， see Appendix A）．
σNtu−［∂μ諺糺（t， u＝x，ア，z）
一9一
Nuclear magnetic shielding c・nstant is the sec・nd derivative ab・ut the t・tal energy E・PtNt is the
magnetic moment of the nucleus 2＞in the≠direction．β
is the extemal㎜ifb㎜magnetic O㍑
field in the初direction． This is called Ramsey s fbmlula． The relationship between the NMR chemical shi丘δwhich is observed in NMR experiment and nuclear magnetic shielding constant
σis defined as fbllows．
δ＝σ（ref）一σ
σ（ref）is the nuclear』magnetic shielding constant ofthe reference molecule．
We carried out the NMR calculations of various sy stems and various resonance atoms．
This thesis consists ofthe following contents．
μ
In chapter 1， we studied the importance of the relativistic theory and the electron correlation on NMR calclations． The theory that considered both of the relativistic theb ry and the electron correlation is essential to build the theory that can calculate electronic structures with uniform precision of all atoms in the periodic table． The nuclear magnetic shielding constant is a property that is sensitive to the electronic correlation． When the resonance atom is heavy， the relativistic effect is large． A series of calculations of halogen nuclear magnetic shielding constants and chemical shifts in X−and Xq4 （X＝F， Cl， Br，1）were carried out to discuss the relativistic and electron−correlation effects and， especially， the non−additivity of both effects． The relativistic theory
is introduced by the second order Douglas−Kroll−Hess（DKH2）method with the spin−orbit（SO）
interaction， and the electron correlation is introduced by the second order Moller−Plesset（MP2）
method． We used generalized UHF（GUHF）wave fimctions in order to describe correctly the spin−orbit interaction and the response to extemal magnetic fields．
In chapter 2， we aimed to elucidate the origin of NMR chemical shifts fbr the metal complexes． We calculated 55Mn magnetic shielding constants of Mn（CO）5X（XニH， F， Cl， Br， I and CH3）and l3C magnetic shielding constants of M（13CO）（NH3）3（M＝Cr2＋， Fe2＋， Cu＋and Zn2→）．
Mn（CO）5X are molecules important industrially． M（13CO）（NH3）3 are the model molecules of the
−10一
enzyme in a living body． In the former， we compared the calculated 55Mn che血cal shifts with the
experimental ones， and clarified the influence of the relativistic effects． The relativistic effect is considered by the DKH2 method， however， without the S O interaction．55Mn magnetic shielding
constants calculated by the．DKH2 metho d were good agreement with experimental ones． The origin of NMR chemical shift was elucidated by the ≠狽曙撃メ@orbitals（AO）contribution analysis． In the
latter， NMR chemical shifts were calculated by B 3 LYP which is a kind of density fUnctional theory
（DFT）．13C che血cal shifts showed the variety with e ach metal atom． When the metal atoms were Cr2＋or Fe2＋， the lower field shifts were seen． When the metal atoms were Cu＋or Zn2＋， the upper
field shifts were seen． These results were good agreement with experimental ones． We elucidated the origin of the NMR chemical shift according to the analysis of the contribution of the molecular orbitals（MO）and AO．
In chapter 3， we treated rt electrons systems． We canied out the ab in itio quantum che血cal
calculations（RHF／6−311G（d，p））of［18］amulene C l 8Hl8 and its M6bius type derivatives． We tried to decide the aromaticity or the anti−aromaticity by magnetic properties， namely， IH magnetic shielding constants， IH−NMR chemical shifts and the nucleus−independent chemical shift（NI C S）．
［18］㎜ulene of the，（4n＋2）πelectom system was aromatic． On the other hand，［18］a皿ulene dianion of the（4n）πelectom system was anti−aromatic． We elucidated the origin by the analyses of electronic co面gurations． In C l 8H20 made by distorting C l 8Hl8 and comecting into the M6bius type，
the magnetic shielding was reverse to［18］amulene． The outside proton was shielded and the inside proton was deshielded． C 18H20 was anti−aromatic． Moreover， when the methyl anion was inserted to Cl8H20， this system changed into aromatic． These results suggest that we can control the aromaticity，
i．e．， the magnetic properties ofπelectron systems．
In general conclusion， above results and discussions are surnmarized． Moreover， we refer to the fUtUre problems which we were not able to mention enough in this thesis． Finally， we describe the thought about science which we cultivated in writing this thesis．
There are nine appendixes in this thesis． Appendix A is the definition of nuclear magnetic shielding constant The detail of the derivation of Ramsey s fomlula is described． Appendix B is ．the
−11一
derivation of diamagnetic and paramagnetic terms． These terms are important in every chapter．
Appendix C is the derivation of Fermi−contact and spin−dipolar terms． These terms appears on Iy in chapter l which the SO interaction is considered． In appendix D， we describe gauge−including atomic orbital（GIAO）method． This method is used in every chapter． Appendix E is about the derivation of DKH2 under the absence of the external magnetic field． We also mention more highly order Hamiltonian， i．e．， DKH3 method． Appendix F is about the derivation of MP2 method．
Appendix G and H are basis sets fbr F， C1， Br，1，0 in chapter 1 and fbr Cr， Fe， Cu， Zn， C， N，0，且in
chapter 2， respectively． Appendix I are the AO and MO contributions．
一12一
Acknowledgments
1 would like to give heart血1 thanks to Profe ssor Masahiko Hada whose comments and suggestions were㎞umerably valuable throughout the course of my study， Special thanks also go to Associate Professor Kenro Hashimoto and Assistant Professor Yasushi Honda whose comments made enormous contribution to my work． The author is also grate制to all members in Theoretical and computational che血stry laboratory．
Iwould also like to express my gratitUde to my fa血ly fbr their moral support and warm
enCOUragementS．
IgratefUlly appreciate the financial support of Research Fellowships of the Japan Society fbr the Promotion of Science fbr Ybmg Scientists and Japan． Science and Technology Agency
（JST） that made it possible．to complete my thesis．
11ike to reading books about science． For example， E J， Dyson， C． R． Dawkins， P． W．
Atldns，1． Prigogine， T． Tachibana， E R． J． A． S chr6dinger， and so on． I was especially influenced by
Dyson s lnfinite in All Directions ， S chr6dinger s What is Life？ ， and Tachibana s Uchuu Karano Kikan ． Because I read these books in my high school days， I made up my mind to study science． I also thank these writers and books．
Iwant to thank fbr the next sentense． ℃hemistry has the original concept that we ca皿ot reduce to its elements in physics （L． Wblpert and A． Richards，1）a∬ionate Minds，1997）． I valued these words all the time when I was studying．
FinallY， the re sponsibility for the final． formulation， and any errors that it may c oncern， are
entirely mine． 、
February，2010 Hirotaka Tanimura
一13一
正ist of Publications
［1］Hirotaka Tanimura and Masahiko． Hada， Relativistic and Electron−Correlation Effects on Halogen Chemical Shifts in X巳and XO4−（X＝F， Cl， Br， and I） ，」． Comput． Che〃z． Jpn．， Vbl．3，
No．4， pp．153−158（2004）
［2］Hirotaka Tanimura， Ayu血Kitahori， Chie Kuzuoka， Yasushi Honda， and Masahiko Hada，
Calculations and Electronic Analyses of 55Mn and l3C Nuclear Magnetic Shielding Constants fbr Mn（CO）5X（X＝H， F， Cl， Br，1， and CH3）in M（CO）（NH3）3（M＝Cr2＋， Fe2＋， Cu＋， and Zn2†） ，
Bu11． Che〃z． Soc． Jpn．，in press．
［3］Hirotaka Tanimura and Masahiko Hada， Nuclear Magnetic Shielding and Aromaticity of
［18］Amulene and its Derivatives ， in preparation．
9
一14一
Chapter 1
Nuclear Magnetic Shielding Constants of Haloge皿s
in X and XO4 （X＝ECl， Br， 1）
−Relativistic and Electron−Correlation Effects 一一
一15一
Chapter 1． Nuclear Magnetic Shielding Constants of Halogens in X−
and XO4− iX＝F， C1， Br，1）−Relativistic and． Electron−Correlation
Effects 一一
1．1．A『bstract
Aseries of calculations of halogen nuclear magnetic shielding constants and chemical shifしs in X and XO4 iX＝F， C1， Br，1）were carried out to discuss the relativistic and electron−correlation effects and， especially， the non−additivity of both effects． The second−order Douglas−Kroll−Hess method was used as a relativistic method， and the M／11er−Plesset method was applied to the generalized UHF wave fUnction． The calculated chemical shifts in ClO4−and IO4 agree reasonably well with the observed ones， though there are no experimental values in F O4 and BrO4°． The relativistic effect was quite large especially in IO4 as reported previously， while the electron−gorrelation effect is significant in both F O4−and IO4 ． The non−additivity of the relativistic
and the electron−correlation effects in magnetic shielding c onstants is unexpectedly large in 104
C
and therefbre a relativistic electron−correlated method is crucial fbr describing accurate heavy−element nuclear magnetic shielding constants and che血qal shifts．
Keywords：Nuclear Magnetic Shielding， NMR， Chemical rhift， Relativistic effect， Electron Correlation Effect
一17一
1．2． Introduction
Nuclear magnetic shielding constants（σ）are sensitive to chemical envirouments around the resonance nuclei． Their variation can be observed by nuclear magnetic resonance（NMR）as the che血cal shi負δ， and the chemical shift of molecule A，δ（A）， is defined as
δ（A）＝σ（reference）一σ（A），
When we calculate nuclear magnetic shielding constants fbr heavy atoms， consideration of the relativistic effe ct is necessary to describe electronic distribution of the resonance nucleus neighborhood precisely． The 6 value often changes by several times through relativistic treatments．
Although this simple relativistid effe ct tends to be cancelled each other in the chemical shiftδ
which is given by difference of the twoσvalues， the relativistic correction is important also fbrδ when heavy atoms exist a（lj acent to the r．esonarice nucleus． For example， lH−NMR chemica1 shifts
of hydrogen halides， HX（X＝F， Cl， Br， a血d I）， are caused by spin−orbit interactions in the halogen
atoms［1−3］． The calculations of theσvalues were reported fbr HX using a semi−elhpirical third−order pe血rrbation theory［3】． However， the definite conclusions were not obtained because of the insuf且cient quantitative characteristics． On the other hand， in case that both of resonance and a（lj acent atoms are heavy， the spin−orbit interaction of the a（lj acent atoms and the relativistic effe ct
of the resonance nucleus synergistically have an influence on the nuclear magnetic shielding constant， and as a result， also on theδvalue［4，5］． This series of reports provided theoretical chemists the oppo血mity to strongly recognize that the relativistic effects are important in various chemical phenomena．
9
0n the other hand， electronic correlation changes the calculation values ofσ［7］and also affects the 6 value greatly［6］． In addition， to describe delicate chemical environmental difference among various molecules， the electronic correlation effects seems to be essential。
Thus， the nuclear magnetic shielding constants fbr heavy elements are sensitive to both relativistic and electron correlation effects and are suitable to examine their individual and coupling
−18一
effects． In this study， we used the second−order Douglas−Kroll−Hess method（DKH2）［8−10］as the relativistic Ha血ltonian， and considered electron correlation by the second−order Mσ11er−Plesset
（MP2）pe傭bation method伽details， see ApPendix F）． Generalized umestricted Hartree−Fock
（GUHF）wave fUnctions［10】were used to describe appropriately the spin−orbit interactions and tlle effects of external magnetic fields， We stUdied the effeCts of the relativistic and electron c orrelation
upon absolute values of nuclear maghetic shielding constantsσand upon the che血cal shi丘sδ which correspond to the difference of 6 b etWeen for tWo molecules． In addition， additivity of the tWo effects is also discussed． The target molecules are halide X−and perhalide ions XO4一 ﾐ（＝F， C1，
Br， and I）．
1．3． Theory
1．3．1．RelatiVistic H amiltonian
The relativistic Ha血ltonian in this stUdy is given by the second−order D ouglas−Kroll−Hess
（DKH2）method． The derivation of this ha血ltonian was described in the previous papers ［10，11】，
but we write it down also here in order to conclude tlle derivation within this article（also see Appendix E）。
To calculate the magnetic shielding constantσ， the hamiltonian must contain the vectcr
potential A． The vector potential is generated from the nuclear magnetic momentμ＞and the magnetic field B， namely，
． A・B×r−十ΣμN×▽G．， （1）
c N
where GN is a fUnction depending on the shape of the ato血c nucleus N． In this study， the point charge model was employed as the nuclear shape（G＞＝ rNhl）．
−19一
Di「ac equati°n c°「ttainin．9 A is given by
島＝cα・P＋fic2＋7＋cα・A， （2）
where p is the momentum operator Theαandβare termed Dirac matrices and are respectively given by
ai＝〔0σ iσiO〕（鴫β＝〔島〕・ （3）
where l and oi・are the 2×2 unit matrix and Pauli spin matrix， respectively． The Pauli matrices are given by
a・一〔96｝σ，一〔？6 〕・ら＝倒・ （4）
Using F oldy−Wouthuysen transformati on matrix乙幅we obtain the transformed Dirac Hamiltonian
Hl． It iS giVen by
バ ハ
uptiA．σ．．≡H1
（5）
＝μ㍗∬ 丑t（7）＋丑血t（A）＋0（7）＋0（A）
where
σF〃・＝1（＋1iRα・」ρ， （6）
E＋c2
K＝ P ， （7）
2Ep
R＝［2Ep（E。＋・・）］ i， （8）
E．−6》アア， （9）
丑血（v）＝KV・（＋R（c2pV・P）R＋Rレc2α・（pV×P）］R， （10）
9
脚）一β隈κ一Kた驚）K］・ （11）
0（v）一β［R（岬7）K−K（cVa・P）R］， （12）
and ・
−20一
・（の＝κ（a・A）κ＋R［62α・P（α・のα・P］R・ （ユ3）
To remove the o dd matrix parts Oのand O（IA），1五is fU曲er transfotmed by the s e c ond−order Douglas−Kloll transfbmlation matrix乙IDHm， The乙を）Kzn is given by
UDxa、−1＋［m（v）＋即）］2＋［m（V）＋叩）］， （14）
where〃7 is an integral operator in the momentum space and is defined so as to satisfシ
rv（x）一難1（x ・一〈牌〉） （15）
P P
The transformed hamiltonian ・i s written as
Uska、印＿一μ，＋丑 nt（7）＋H t（A）
＋圭［η7（7），0（V）］＋去［凧・（A）］ （16）
＋圭［rv（A），0（V）］＋圭陶・（A）］＋…
In this study， we employ the terms up to the second−order expansions of V and A in Eq。（16）as a
quasi−relativistic Ha血ltonian， and its left upper 2×2 component is called the second−order Douglas−Kroll−Hess Hamiltonian， Hl）K硯．
1．3．2．Nuclear Magnetic Shielding C onstant
The nuclear magnetic shielding constantσis a second derivative property of the to重al energy and is given by
∂2E
σNtu＝∂μ遇伽＝綱 （17）
To obtain an explicit expression of Eq．（17）， we assign Eq。（1）to Eq．（16）and expand it in te㎜s of
μ＞and B． In Eq．（16）， V and A are equally treated， and the magnetic field term is relativistically
described at a level of DKH2 metho d， indicating that theσvalues in this study are c ompletely at the
DKH21evel． The details of the formulation are given in other report［2］．
−21一
1．3．3．Generalized UHF Method
We used generalized UHF（GUHF）wave ftmctions in order to describe correctly the spin−orbit interaction and the re sponse to external magnetic fields． A one−electron wave ft ncti on by
the UHF method，ψ（x）， is expressed as
ψ（x）＝／驚；： （17）
whereψ（x）is composed by multiplying the spatial orbital fUnction il and the spin fUnction｛a，fi｝．In UHF， different spatial fUnctions can be assigned to the alpha and beta spin fUhctions． On the other hand， a GUHF spin orbital is written as a linear combination of alpha and beta spin f㎞ctions，
namely，
ψ（x）＝φα（r）α（σ）＋φβ（r）β（σ）． ，（19）
The 1＞」electron GUHF wave fUnction is expressed as a Slater determinant of Eq．（19），
（1） GUHF（x1・x2…XN）＝ψ（Xl）q（x2）…，op（XN）・ （18）
For calculatio血s with the electron correlation， we employed the second−order M／ller−Plesset（MP2）
metho d who se reference fUnctions are the GUHF wave ft nctions．
1．3・4。 Basis sets
g
The basis sets were ［221211／212］ fbr F， ［22121111／31111］ fbr Cl，
［2312111111／3212111／41］fbr Br，［221211111111／311111111／3111］fbr I， and［721／41／1］fbr O，
respectively． For details， see Appendix G
一22一
1．4． Results and Discussions
Table l shows calculated values of X magnetic shielding constants fbr halides X and perhalides XO4− iXニF， Cl， Br，1）， The corresponding experimental values are available only for ClO4 and IO4 m12］． The calculated values show good agreement with the experimental ones except fbr Non−Relativistic（NR．）−MP2， indicating that these calculated values would be valid． The NR−MP2 value for ClO4 is considerably deviated from the experimental one， and it is attributed to overe stimation of the electron correlatioll e」ffect for the NR−MP2 calculati on．
Table 1． X Magnetic Shielding C onstants and Chemical Shifts（X＝F， Cl， Br and I）（ppm）
calculated by Generalized UHF（GUHF）， RHF， and MP2 methods with Non−Relativistic （NR） and Relativistic second−order D ouglas−Kroll−Hess DK且2 Hamiltonians．
NR−RHF DKH2−GUHF NR−MP2 DKH2−MP2 Exptl．b
F『
Cr
Br隅
1
484．5 1150．3 3128．5 5507．4
492．6 1201．6
35352
484．0 1150．3 3127．6
…FO4−
ClO4隅 BrO4 104圏
183．2
（967．1）a・
537．8 1614．6 3892．8a
256．8
（944．8）a 921．7 2961．7
3895．1a
一538．3
（1688．6）a l49．5
1289．6 4217．5a
492．2
12015
3534．1
＿＿．益｛i≦≦』豆＿＿＿一一一．、
530．6 2559．7 4295．3a
（1003±100）
4100土100 aValue s血parentheses are chemical shifts
δ（＝σ（x ）一σ（xo4−））．
b Experimental values are taken from Ref．［12］．
1．4．1．Relativistic Effect
We classify the relativistic effects in two cases；the case that electron correlation（EC）is
not considered，σ（DKH2−GUHF） 一 （s（NR−RHF）， and the case that EC is considered，
σ（Dllll2−MP2）一 6（NR−MP2）， The se results are…rized in Figure 1． B oth X−and XO4−show the same tendency， namely， the relativistic effects become large as the halogen atoms become
−23一
heavier irrespective of the EC effect．
We decompose the G values of r and IO4−in which the relativistic effect is very large
（Table 2）． The details of these values are given elsewhere［2］（also see Appendix B and C）， and we
here show their qualitative outline；
σdia Diamagnetic te㎜：eiectron density
σpa「a paramagnetic term：angular momentum σFc Fenni contact te㎜：electron spin density σsD Spin dipolar te㎜：electron spin density
SinceσFc is generated by introducing the spin−orbit interaction，σFc can l）e inteIpreted as a kind of the relativistic effects． Regardless of the electron correlation，σFc fbr r accoU血ts fbr ca．18％of the totalσvalue． Likewise， theσFc values with and without considering the electron correlation fbr IO4 account fbr ca．59％and 49％， respectivel）召The contril）ution ofσFc in the relativistic effbct is
more than 90％fbr both r and IO4 ．
00 14
00 2 1
00 0 1
0 0 8
0 0 6
O 4O
00 2
0
x：without EC o：with
F− C「 Br− 「
0 40 1
0 0 2 1
0 0 0 1
0 0 8
0 0 6
0 0 4
0 0 2
0
00 4 1
00 2 1
0 0 0 1
0 0 8
0 0 6
0 0 4
0 0 2
0
x：without EC o：with EC
XO4
FO4 @CIO4 BrO4−IO4『
Figure 1． Relativistic Effects in Magnetic Shielding C onstants of X ileft−hand side）
and XO4− iright−hand side）（X＝F， Cl， Br，1）without and with Electron Correlation
（EC）．
For X凹CσPa「a becomes zero within the Hartree−Fock theory because they have spherical and closed−shell electronic ground states． Therefbre， theirσPa「a values appear as an electron correlation effect With magnetically allowed excited configuration．s．
−24一
N．
n卜鑓
い．
｢N鴇
◎c．
｢トー
◎o．
求k gマ
卜．
｢ー
一一，卜寸雲
卜．
ﾐいいN
い．
｢N9
oO．
｢トー
い．
ﾐ℃笛寸−
い．
ﾐト寸い
（N角Σ−N霞O）o 罵斜ρ［
゜㌔
∩のb
§㌔
署b
Q国毫露
卜，
nい二
ゆ．
｢寸
O．
揩潤
い．
ζ，まN 一
卜．
艪｢三
ゆ．
｢寸
寸．
ﾐNひめー
ひ。
ﾐト寸い
（臣POぺ円旨）b
罵βH
Q㌔
゜°。り
§㌔
書b
Q国ぢo壱霞
O，
m寸9
マ．
mN⊆
卜．
m
寸。
ﾚUへ
O，
｢ー
ぢ名国o題亨慧τ出
一．
mOいい
O．
｢いooり
O．
n
寸，
md禦
卜o（回o
O。
n
寸．
y覧X
一，
mOいい い．
ﾂいい
寸．
ﾐ寸σへ一
卜．
揩Umq
◎Q，
ゆ，
ｴ⊆
ゆ．
（鑓Σ出乙b…
（鑓Σぺ＝】。）b
一εβ
゜㌔
o㌔
§㌔
帽㌔
Q国頚露
寸．
mO鴇
゜o．
閧｢゜QO
O，
n
卜．
pom⊆
●oo■ ，
（No
O．
n
O．
ﾊ§
寸．
mO鴇 oO．
ｨ鴇
（山臣出乙り
｝ヨβ
Q、
゜％
爵㌔
暑b
9国琶o転露
1．4．2．Electron Correlation Effect
We classifンthe electron correlation effects in two cases；the non−relativistic（NR）case，
σ（NR−MP2）−G（NR−RHF）， and the relativistic（Rel）case，σ（DKH2−MP2）一σ（DKH2−GUHF）．
500 400 300 200 100
0
−100
一300 ×：NR
×：NR −350
0：Rel o：Rel
−4°°…四 ｝…… 1匿…皿r、、財…
X−…・・−1−・1・一……i−一・…・一・ −45° …−XOガ
ー卿一…・ 珈
・550
F− Cl− Br− 1− FO4− CIO4・ BrO4− 104−
Atom Molecule
Electronic Correlation Effect of X ileft）and XO4−（right）（X自F， Cl， Br，1）
Figure 2．
with Non−Relativistic（NR）and Relativistic（Rel．）Hamiltonian．s
These results are s−ized in Figure 2． The electron co皿elation effects for X−are vanishingly small（＋05〜−2 ppm）both in the NR and Rel calculations． On the other hand， Electron correlation effects for XO4 are comparatively large， i．e．，−721〜−325 ppm fbr NR and−402〜e−391 ppm for Rel．
Broadly speaking， the electron correlation effect becomes smaller as X is heavier． However， it is larger fbr IO4闇than BrO4嘲in the Rel calculations， and this wi ll be discussed later．
Table 3 shows decomposed components of the shielding constants fbr BrO4−． Electron correlation effects mainly contribute toσPa「a both for NR and Rel． This indicates that the electron correlation af驚cts the magnetic field response of angular momenta rather than the electrqn density
in perspective of the magnetic shielding． For the Rel calculations， the electron correlation inf【uences theσFc t・an extent， as・well・as・the 6Para values．
一26一
O．
黷ﾐ゜h−
℃．
｢い
い．
黹}
Oo．
｢゜h寸
卜．
n
ぢ讃国Q国
卜．
Rひ ゆ．
n訟
寸．
m寸寸
O．
盾盾 ﾐ寸
翰．
ﾘ一−
oQ．
ﾌペー
N．
nひいN，
O．
閧mO6h−
卜．
黶揩盾n笛
寸．
m●QO笛
（山＝PO・N自∩）b
（N角Σ凶霞O）o 罵←ρ［
9㌔
ロ゜・b
§㌔
署b
電出
翰．
宦宦
◎6
?￨ O．O
．O
．ひ
Kon−
o．O
o名国Q国 oo．卜゜hい
い．ひ三
．O
．O
．O
．O
．寸
｢いN、
．等 ﾐ守
h．N ﾐO【h
．凶 ﾐOn
山臣−出−乙b N角Σ，出Z）b
桓β
㌔
のb
㌔
b
Z
1．4．3． Coupling Effect of Electron Correlation and RelatiVistic Theory
We discuss additivity between the relativistic and electron correlation effects in this section．
We define the following classification terms．
relativistic effect A（R）ニσ（DKH2−GUHF）一σ（NR−RHF）
electron correlation effect A（EC）＝・σ（NR−MP2）一σ（NR−RHF）
relativistic＆correlation effects A（R＋EC）＝σ（DKH2−MP2）一σ（NR−RHF）
coupling effect ∠（R＋EC）一（∠（R）＋∠（EC））
The coupling effects for X−and XO4°ate summarized in Table 4． For I O4 ， the relativistic effect
∠1（R）is 1347．1 ppm， and ．the electron correlation effect A（EC）is−325．O ppm． Therefbre， the simple s㎜of the楠e㊧cts are」（R）＋∠（EC）＝1022．1ppm． On the other hand， when the relativistic and electron correlation effect are simultaneously considered， the total effe ct is A（R＋EC）＝945．l ppm Obviously， the relativistic and the electron correlation effects in magnetic shielding constants do not satisfシadditivity， and the coupling effect is calculated to be−77．O ppm． This effect is indispensable fbr quantitative calculations．
As seen in the above section， the electron correlation effect becomes smaller as halogens are heavier for the NR・calcUlations， while， it tends to be larger fbr Rel in contrast． This tendency can
be interPreted as the coupling effect of the relativistic and electron correlation treatments． In other words， the re sults fbr Re1（open circles）in Figure 2 contain not only the electron correlation effect but also the coupling effect． The coupling effect for 104−is much larger than that fbr BrO4−in Table 4，and therefbre， the glectron correlation effect of IO4−seems to be larger than that of BrO4−in
consequence・ ．
Table 4． Coupling Effects b etWeen Relativistic Theory and Electron Correlation（ppm）
F C1 Br一 1一 FO4 ClO4 BrO4冒 104胃
Coupling Effect
0．0 一〇．1 一〇．3 一15 一2．7 一77．0
一28一
1．5．Acknowledgments
The calculation programs fbr nuclear magnetic shielding constants with the higher ordeI relativistic theory are developed by the author（M． H．）in collaboration with Prof Hiroshi Nakats吋i
（Kyoto University）． Dr． Ryoichi Fu㎞da（Kyoto University）gave us use血l advices． A p飢t of曲 work was supPorted by Grants−in−Aid fbr Scientific Research fヒom the Ministry of Education，
Cult皿e， Spo質s， S cienc e and Technology（Proj ect Number 14340179）．
一29一
1．6．References
［1］H．Nakats両i， H． Takashima， and M． Hada，αθ栩． P伽．五ett．，254，170（1996）．
［2］C．C． Ballard， M． Hada， H． Kaneko， and H． Nakatsuj i， Chem．」P伽． Lett．，254，170（1996）．
［3］1．Morishima， K． Endo， and T． Ybnezawa，」． Chem． P伽．，59，3356（1973）．
［4］M．Hada，旺Kaneko， and H． Nakats嘘， Chem． P1加． Letters，261，7（1996）．
［5］M．Hada， J． Wan， R． Fukuda， and H． Nakats両i，1． Comp． Chem．，22，1502（2001）．
［6】R．Fukuda， M Hada， Y Nakamura， and H． Nakatsuj i， Annua1、ideeting（）flapan Sociのプbr Molecular Science（Kobe），3PO93，2002．（written in Japanese）
［7］J．Gauss， J． F． Stanton，」〔Chem．1）hys．，103，3561（1995）．
［8］B．A．Hess，、P1加．」Rev．．4，32，756（1985）。
［9］RFukuda， M． Hada， and H． Nakats両i， J． Che〃2。」P1加118，1015（2003）．
［10］R．Fukuda， M． Hada， and H． Nakatsuji， Z Che〃2．」Phys．118，1027（2003）．
［11］R．Fukuda， M． Hada， and H． Nakats可i，、Rec． Adv． Co卯． Chem． 5，191（2004）
［12］J．Mason， Multinuclear NMR， PLENUM，447（1987）．
9
一30一
Chapter 2
Calculations and Electronic Analyses of 55Mn and i3C Nuclear Magnetic Shielding C onstants for
Mn（CO）5X（X＝H， F， C1， Br， 1， and CH3）and M（CO）（NH3）3 （M＝Cr2＋， Fe2＋， Cu＋， and Zn2＋）
一31一
Chapter 2． Calculati・ns and Electr・nic Analyses・f 55Mn and 3C
Nuclear Magnetic Shielding Constants for Mn（CO）5X（X＝H， F， Cl， Br，
1，and CH3）and M（CO）（NH3）3（M−Cr2＋， Fe2＋， Cu＋， and Zn25
2．1．Abstract
We calculated 55Mlr t and i 3 C magnetic shielding constants for Mn（CO）5X（X＝H， F， Cl， Br，
1，and CH3）and M（CO）（NH，）3（M＝Cr2＋， Fe2＋， Cu＋， and Zn2＋）， respectively． F or the first molecular
group， we compared the calculated 55Mn chemical shifts with the experimental ones， and clarified
effects of the basis sets． The calculated magnetic shielding constants using the second−order Douglas−Kroll−Hess（DKH2）metllod showed good agreement with the experimental ones．
According to the atomic orbital（AO）contribution analysis， the origin of the chemical shifts was
attributed to the d−d transitions of Mn． In particular， the 3dπorbital mainly contributed to the paramagnetic term of the Mn chemical shift． For the second molecular group， the 13C che血cal shifts were dependent on the metal ．atoms． When the metals of center were Cr2＋or Fe2＋， the lower field shifts were seen． When the metals of center were Cu＋or Zn2＋， the upper field shifts were
observed． These results were in good agreement with the experimental trends． The change of the paramagnetic term mainly depended on the d orbital configurations of the metal of centers， and the donation fヒom the metal d orbital to the CO anti−bondingπ＊orbitals is expected to affect the chemical shift．
一33一
