JOURNAL OF MAGNETIC RESONANCE 129, 134–144 (1997) ARTICLE NO. MN971268 Technique for Importing Greater Evolution Resolution in Multidimensional NMR Spectrum Gary McGeorge, Jian Zhi Hu, Charles L. Mayne, D. W. Alderman, Ronald J. Pugmire, and David M. Grant 1 Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 Received July 9, 1997 A very simple and general procedure that extracts constant- Manassen et al. ( 5 ) first proposed in 1987 that information evolution-frequency data from a truncated multidimensional (2D, from 1D spectra could be transferred into the analysis of 2D 3D, 4D, etc.) FID is described, generalized, analyzed, and illus- data with linear least-squares procedures. In the meantime trated. The method replaces Fouriertransformation of the evolu- much attention has been focused on linear prediction ( 6 ) and tion dimension with a linear model created from a separate, high- maximum entropy ( 7 ) as a means of increasing resolution in quality 1D FID. The equivalent of high resolution in the evolution evolution dimensions, and the usefulness of the simple least- dimension can be achieved without obtaining an extensive multidi- squares alternative has not been appreciated. This paper re- mensional FID. The analysis of the 1D FID can also be used to examines, generalizes, and analyzes the linear least-squares predict the signal to noise ratio of the extracted slices that will procedure, and presents examples from solid state NMR that result from various evolution dimension sampling protocols, mak- ing it possible to develop a priori an optimal sampling strategy for illustrate its power. It is shown that closely spaced constant- the multidimensional FID. The evolution dimension need not be evolution-frequency slices can be extracted from a truncated sampled periodically. The procedure has a potential signal-to- multidimensional FID, here called the ‘‘main’’ FID, with noise ratio advantage because it extracts usable information from the aid of data from a separate 1D FID, called the ‘‘guide’’ a multidimensional FID at short evolution times before the magne- FID. The procedure may be thought of as exporting resolu- tization has decayed significantly.  1997 Academic Press tion from the guide FID, and importing it into the associated evolution dimension of the main FID. Thus our acronym, ‘‘TIGER,’’ is derived from technique for importing greater INTRODUCTION evolution resolution. TIGER can also be seen as a generaliza- tion of the 1D chemical shift modulated correlation spectros- Although multidimensional NMR spectroscopy is remark- copy ( 8 ) developed for single crystals. ably powerful, its application often suffers from the lengthy TIGER is applicable to any multidimensional spectros- experimental times required to acquire sufficient resolution copy with an evolution dimension for which an equivalent in indirectly detected evolution dimensions. This limitation high-resolution 1D FID can be obtained. It also requires that may be especially frustrating in those cases where an equiva- the main multidimensional FID be composed of sums of lent, well-resolved spectrum may be obtained relatively products of responses (see below). TIGER replaces Fourier quickly from a 1D direct-detection experiment. For example, transformation of the designated evolution dimension with in solid state NMR the slow-sample-turning 2D PHORMAT a linear model created from the guide FID. Applying the experiment ( 1, 2 ) displays an isotropic shift spectrum in the linear model to the truncated experimental main FID then evolution dimension, whereas this same spectral information directly extracts constant-evolution-frequency slices equiva- is readily available from a high-speed magic-angle-spinning lent to those that could be separated by Fourier transforma- (MAS) 1D experiment. Likewise, in the single-crystal 2D tion of a much-expanded evolution dimension FID. Thus, chemical shift correlation experiment ( 3, 4 ) the evolution the equivalent of high resolution in the evolution dimension dimension spectrum can be obtained directly by taking a 1D is achieved without obtaining an extensive main FID. TIGER spectrum with the crystal in its evolution position. In both accommodates any magnetization-decay function, as the cases it is much easier to obtain high resolution by fully character of the decay is observed directly in the correspond- sampling the 1D free induction decay (FID) than by ex- ing 1D guide FID. TIGER is thus more general than linear tending the 2D FID to long evolution times. prediction ( 6 ) , which requires exponential magnetization decay. TIGER automatically incorporates the matched filter that optimizes the signal-to-noise ratio ( S / N ) when Fourier 1 To whom correspondence should be addressed. 134 1090-7807/97 $25.00 Copyright  1997 by Academic Press All rights of reproduction in any form reserved.