4 The Information Content of Two-Dimensional
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Fourier Spectroscopy R. R. ERNST Eidgenössische Technische Hochschule, Laboratorium für Physikalische Chemie, 8092 Zürich, Switzerland
This brief essay discusses two-dimensional (2D) spectroscopy (1-6) with regard to its information content. In particular, we would like to elaborate those occasions where the use of 2D spectroscopy in place of one-dimensional (1D) Fourier spectroscopy is justified by the increase of available information. The fundamentals for such a comparison of 1D and 2D spectroscopy are quite simple and straightforward. In 1D spectroscopy, a signal is represented as a function S(ω) of a single frequency variable. The frequency ω is a numerical coordinate which measures one particular feature, like the local magnetic field sensed through the chemical shielding, or the local electric field gradient through the nuclear quadrupole interaction. The single intensity S(ω) represents a measure for the probability density of occurence of the value ω . It measures, for example, the number of nuclei experiencing a certain local magnetic field. A system is fully describable by a 1D spectrum only when its Hamiltonian Η contains separate terms for each nucleus, each being characterized by a single parameter p (like the chemical shift or the quadrupolar coupling constant), k
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We have t o impose t h e a d d i t i o n a l r e s t r i c t i o n t h a t each term H ( p ) leads to a unique t r a n s i t i o n frequency. As soon as the n u c l e i e x p e r i e n c e s i m u l t a n e o u s l y d i f f e r e n t t y p e s o f i n t e r a c t i o n s o r when p a i r i n t e r a c t i o n s o c c u r , a 1D s p e c t r u m becomes ambiguous, and i t i s no l o n g e r p o s s i b l e t o uniquely r e l a t e apparent f e a t u r e s t o i n h e r e n t p a r a m e t e r v a l u e s . The most w e l l known ambiguous s i t u a t i o n i s h i g h - r e s o l u t i o n s p e c t r o s c o p y i n l i q u i d phase where s i m u l t a n e o u s l y c h e m i c a l s h i e l d i n g and s p i n - s p i n c o u p l i n g s a r e a c t i v e , l e a d i n g to c h e m i c a l l y s h i f t e d m u l t i p l e t s w h i c h may p o s s i b l y s e r i o u s l y overlap. An unequivocal a n a l y s i s o f such a spectrum i s no longer k
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In NMR Spectroscopy: New Methods and Applications; Levy, G.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982. Washington, 0. C. 20031
NMR
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p o s s i b l e . Three c h e m i c a l l y s h i f t e d l i n e s o f equal s e p a r a t i o n and r e l a t i v e i n t e n s i t i e s 1, 2, 1 may, f o r example, be m i s i n t e r p r e t e d as a s p i n - s p i n c o u p l i n g t r i p l e t . I n s u c h a s i t u a t i o n , an e x t e n s i o n t o 2D s p e c t r o s c o p y i s i n order. A 2D s p e c t r u m S(u^ ω ) i s capable of r e p r e s e n t i n g s i m u l t a n e o u s l y two i n d e p e n d e n t f e a t u r e s w i t h o u t l e a d i n g t o any ambiguity, f o r example r e p r e s e n t i n g m u l t i p l e t s p l i t t i n g s a l o n g ω- which are s h i f t e d by the p e r t i n e n t chemical s h i f t s i n the ωρ d i r e c t i o n . Such a r e p r e s e n t a t i o n i s r e a l i z e d i n 2D J - r e s o l v e a p r o t o n spectroscopy (Z). I n g e n e r a l , 2D s p e c t r o s c o p y i s r e q u i r e d t o r e m o v e a m b i g u i t i e s whenever the H a m i l t o n i a n c o n t a i n s two d i f f e r e n t k i n d s o f terms i n v o l v i n g the same n u c l e a r s p i n s I , w i t h the two s e t s of parameters p and q , 9
Downloaded by UNIV OF MICHIGAN ANN ARBOR on February 18, 2015 | http://pubs.acs.org Publication Date: July 9, 1982 | doi: 10.1021/bk-1982-0191.ch004
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