for a total of 48 carbons of the different models were then used in a linear correlation,
and the results are summarized in Figure 2. In all cases, the isotropic 13C chemical
shift was obtained by subtracting the isotropic chemical shielding of the 13C atom to
the one found at the same theory level for the methyl carbons of the NMR reference
tetramethyl-silane (TMS).
Fitting of Raw ab initio Data. Isotropic 13C shifts for the anomeric carbons obtained
as described above were employed in the derivation of equations relating the
data was scaled and fitted to trigonometric series expansions of general form:
The data was fitted using Mathematica 3.0 (Wolfram Research, Inc.), using from
91 (i = k = 3, j = 2) to 325 (i = k = 6, j = 2) terms. The results are detailed below.
Si [ Sj [ Ai,j * sinj( i * f ) + Bi,j * sinj( i * y ) + Ci,j * cosj( i * f ) + Di,j * cosj( i * y ) ]
+ Sk [ Ai,k * sin( i * f ) * cos( k * y ) + Bi,k * cos( i * f ) * sin( k * y ) ] ] + Co
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