Chapter 2
Modeling NMR Chemical Shifts in Polymers and Amorphous Matter 1
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Isao Ando, Shigeki Kuroki, Hiromichi Kurosu , Masahito Uchida , and Takeshi Yamanobe 3
Downloaded by UNIV OF CALIFORNIA SAN DIEGO on April 20, 2016 | http://pubs.acs.org Publication Date: August 20, 1999 | doi: 10.1021/bk-1999-0732.ch002
Department of Chemistry and Materials Science, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8552, Japan
Two theoretical approaches for calculating N M R chemical shift of polymers and its application to structural characterization have been described. One is that model molecules such as dimer, trimer, etc., as a local structure of polymer chains, are in the calculation by combining quantum chemistry and statistical mechanics. This approach has been applied to polymer systems in the solution, amorphous and solid states. Another approach is to employ the tight -binding molecular orbital theory to describe the N M R chemical shift and electronic structure of infinite polymer chains with periodic structure. This approach has been applied to polymer systems in the solid state. These approaches have been successfully applied to structural characterization of polymers
The chemical shift is one of most important NMR parameters^). The N M R chemical shifts provide detailed information on the structure and electronic structures of polymers in the crystalline state and amorphous state(2). A polymer chain has an enormous number of chemical bonds. For this, in the solution and amorphous states the NMR chemical shifts of polymers are often the averaged values for all of the possible conformations because of rapid interconversion by rotation about chemical bonds. In solids, however, chemical shifts are often characteristic of specific conformations because of strongly restricted rotation about the bonds. The NMR chemical shift is affected by a change of the electronic structure through the structural change(2). Solid state NMR chemical 1
Current address: Department of Textile and Apparel Science, Nara Women's University, Kita -Uoya Nishimachi, Nara 630-8263, Japan. Current address: Tokyo Research Center, Tosoh Company, Hayakawa, Ayase, Kanagawa 2521123, Japan. Current address: Department of Materials Engineering, Gunma University, Kiryu, Gunma 3768515, Japan. 2
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© 1999 American Chemical Society
Facelli and de Dios; Modeling NMR Chemical Shifts ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
Downloaded by UNIV OF CALIFORNIA SAN DIEGO on April 20, 2016 | http://pubs.acs.org Publication Date: August 20, 1999 | doi: 10.1021/bk-1999-0732.ch002
25 shifts, therefore, give useful information about the electronic structure of a polymer or polymers with a fixed structure. Further, the full chemical shift tensor components can be often determined. The complete chemical shift tensor provides information about the local symmetry of the electron cloud around the nucleus and so provides more detailed knowledge of the electronic structure of the polymer compared with the average chemical shift. In order to establish the relationship between the N M R chemical shift and the electronic structure of polymers, it is necessary to use a sophisticated theoretical method which can take into account the characteristics of polymers. Some methodologies for obtaining structures and electronic structures of polymers both in the solution, amorphous and solid states by a combination of the observation and calculation of N M R chemical shifts have been developed, and have been applied them to various polymer systems(3-12). Theoretical calculations of N M R chemical shifts for polymer systems have been performed mainly by two approaches. One is that model molecules such as dimer, trimer, etc., as a local structure of polymer chains, are used in the calculation by combining quantum chemistry and statistical mechanics. In particular, this approach has been applied to polymer systems in the solution and amorphous states(2). However, it sometimes has to be recognized that the results of quantum chemical calculations on model molecules are not readily applicable to polymers in the crystalline state because of the existence of long-range intrachain interactions and interchain interactions. Electrons are constrained to a finite region of space in small molecules whereas this is not necessarily the case for polymers, and thus some additional approaches are required. Another approach is to employ the tight-binding molecular orbital(TB MO) theory, which is well known in the field of solid state physics, to describe the electronic structure of linear polymers with periodic structure within the framework of the linear combination of atomic orbitals(LCAO) approximation for the electronic eigenfunctions(4-12). These approaches have led to the determination of the structure and/or electronic structure of polymer systems including polypeptides in the solution, amorphous and solid states. The essence of these two approaches will be described. APPROACH USING MODEL MOLECULES Origin of NMR Chemical Shift: The chemical shift of an atom depends upon its electronic and molecular environments(l). The chemical shift for atom A can be calculated by the sum of the following terms. d
p
a = o + o + o'
(1)
A
d
ρ
where a is the diamagnetic term, σ the paramagnetic term, and σ' the other term which comes from the magnetic anisotropy effect, polar effect and ring current effect. For nuclei with 2p electrons such as C , N,etc, the relative chemical shift is predominantly governed by the paramagnetic term, and for the H nucleus by the first and third terms. The paramagnetic term is expressed as a function of excitation energy, bond order, and electron density according to the sum-over-state(SOS) method in the simple form as follows. , 3
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l
Facelli and de Dios; Modeling NMR Chemical Shifts ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
26 a ^ - C K f S p i E ^ Q
(2)
where E - E is the singlet-singlet excitation energy of the wth occupied and the mth unoccupied orbitals, and Q is a factor including the bond order and electron density. The quantity
