Re: Accurate/Consistent Proton Integrations
G. Pearson (gpearson@blue.weeg.uiowa.edu)
Wed, 14 Jun 1995 18:30:16 -0500
Charlie Fry <fry@chem.wisc.edu> wrote:
> 3. You should use line broadening (I think) 5 times smaller than than the
> line width of the _narrow_ line to preserve quantitative results; a larger
> LB will reduce the narrow line integral more than for the broader line.
I'd like to make 2 points.
1. I would use more broadening. As much as 1/3 of the width of the broad
line. The integral in the spectrum is proportional to the value of the
envelope of the FID for that signal at ZERO time. Since apodization envelopes
cannot change the relative intensities of the envelopes of the various signals
in the FID at _ZERO_ time, apodization in principle cannot change relative
values of integrals.
2. A Gaussian apodization envelope works much better than an EM. For the
same full width at half height, a Gaussian will have _much_ narrower feet than
will a Lorenzian. The narrower feet mean that the "steps" in the integral
will be significantly sharper, so the _height_ of the steps will be much
better defined. Felix & Nuts (& presumably other off-line stuff) allow you to
multiply by a Gaussian _WITHOUT_ necessarily multiplying by an increasing
exponential at the same time, but the Bruker software incorrectly assumes that
no one ever has any good reason to do just a simple Gaussian apodization.
You can lie to DISNMR and DISMSL so as to use a combination of GM and EM
produce a desired Gaussian broadening, without any Lorenzian garbage. Basic
equations are in:
Gerald A. Pearson, "Optimization of Gaussian Resolution Enhancement",
J. Magn. Resonance 74, 541-545 (1987).
In particular, eq. 11 gives the height of the shifted gaussian produced by GM,
in terms of the intrinsic line width and the fractional sharpening which is
wanted.
Let's take an example. Say you wanted to do a GAUSSIAN broadening of 5 Hz,
and your acquisition time is 4.096 sec.
1. First, multiply by an envelope which will transform a 1-Hz Lorenzian
into a 5-Hz Gaussian. [The 1-Hz Lorenzian is arbitrary, and will eventually
cancel; you could use any other convenient LB.] By eq. 11
t_max = 2 ln2 / ( pi * 1 Hz * (5/1)^2 )
= 2 * .693 / (3.14 * 1 * 25)
= 0.0176 sec.
So you want to set
LB = -1.0 and
GB = (0.0176 / 4.096) = 0.00431
and then do a GM.
2. Now, get rid of the increasing exponential:
set LB = +1.0
and then do an EM.
Real round-about way of doing such a simple thing, isn't it? That's one of
the reasons why we routinely process stuff off line on a PC, using either
Felix for Windows or NUTS. It seems to be nearly impossible to get organic
chemistry grad students to use a scientific calculator.
-- Gerry
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Gerald A. Pearson INTERNET: gerald-pearson@uiowa.edu
Chem. Dept., Univ. of Iowa VOICE: 319-335-1336
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