# Why You May Want to Simulate a Spectrum

There's a point when an NMR spectrum gets too complex. The difference of chemical shifts between the coupled nuclei becomes too small, compared to the coupling constant. Multiplets become increasingly asymmetric. The practical consequence is that it's no more possible to derive the shifts and the couplings from the line frequencies.

The solution is to simulate a model spectrum with variable parameters (shifts and Js). When the model is sufficiently similar to the experimental spectrum, we conclude that their parameters are the same. Because the parameters of the model have been defined by ourselves, they are perfectly known.

iNMR can simulate plain (single-pulse) spectra of 1/2 spins, in the liquid phase or in partially oriented phases.

Don't save a simulation inside an experimental spectrum. Bruker and Varian data are common examples of spectra that are stored as folders. Never save a simulation into those folders.

## To Simulate a Spectrum:

The first 3 steps are pure planning. You can use paper and pencil or do everything mentally.

Count the spin systems.

A spin system is a set of nuclei that share no coupling with the nuclei of the outside world.

It's easy to simulate many systems simultaneously; it's difficult to simulate a single large system: the computing time grows exponentially with the size of a system. Working with a system of more than 10 nuclei can be painful. Factorize when possible.

Consider as different systems the component of an isotopic mixture. For example, a platinum compound is a mixture: 1/3 contains 195-Pt (spin 1/2 and shows couplings with 1-H); the rest doesn't couple.

Identify the relations that reduce the number of independent parameters. If you know that two parameters are always equal, you should define the first only.

In the Pt example above, the chemical shifts of the two isotopomers are the same.

Another case where the parameters are duplicated, is when the molecule is symmetrical.

Identify the groups of magnetically equivalent nuclei. Although it's possible to declare each nucleus independently, it's a source of confusion. Always declare magnetically equivalent nuclei in groups.

Here we go.

Choose Simulate > New Spectrum.

A new document is created; the dialog to define the systems appears. You can reopen the dialog (and redefine the systems) at any time with Simulate > Define Systems.

Define the first system.

Press add row until the number of rows equals the groups of magnetically equivalent nuclei.

For each group, enter the number of constituent nuclei in the second column (n).

In the third column, enter the tentative chemical shifts. If the same value is repeated inside the system, enter it the first time only. Look at the letter at the beginning of that row: use the same symbol (A, B, C...) to specify an identical shift elsewhere.

Enter, into the rest of the row, the coupling constants with the nuclei below. For example, the value of JAB goes into the row of A, not into the row of B. If a value appears more than once, refer to it with expressions like: JAB, JAC, JBC, etc...

Define the other systems, if they exist. You can either duplicate the current system or click the [+] button.

Use the population value to set the relative ratios of the systems. When the population is the same, refer to an already defined value with expressions like 1pop, 2pop, etc...

If the second spin system shares a parameter with the first one, enter expressions like: 1A, 1JAB, etc...

Close the dialog. To simulate a specific experimental spectrum, perform these additional steps:

Import the experimental spectrum (previously opened) as an overlay.

Choose Format > Overlay to open the Overlay Manager.

Check the row corresponding to the experimental spectrum.

Use contrasting colors for the two spectra. Close the Manager.

To copy Spectrometer Frequency and Intensity from the experimental spectrum:

Put a check mark near pop, into the sidebar, then click the large button fix at the top.

Reduce the frequency difference between corresponding peaks.

To change the chemical shifts, drag the colored labels under the plot.

To change a coupling constant, select it into the sidebar and click the little arrows at the top.

Optimize the Fit.

The mathematical treatment of the problem was reported in literature during the 60s-70s. iNMR has added many mechanisms for MANUAL fitting, which was obviously impossible before the advent of graphical user interfaces. Manual and automatic fitting complement each other quite well. The former is intuitive and, at the high fields in use today, often the faster one. The latter methods solve the most intricate problems, but must be learned and are not as automatic as their name says. The most ancient method, that only fits a selected number of lines, and only their frequencies, requires the assignment of each experimental line to a line of the theoretical spectrum. The alternative approach fits the total line shape of the spectrum, point by point. It eliminates the need of assignments but suffers when the experimental spectrum is not perfect. Not only it's necessary to correct the phase and baseline with accuracy, but it's desirable to have an homogeneous magnetic field, no impurities and a decent signal/noise ratio. Both automatic methods require a starting guess for the parameters to be adjusted. This is where manual fit comes into play: it brings the simulated spectrum near to the perfect fit, which is eventually obtained using the automated methods.

There's a division of tasks among the three components of the window: the sheet is required to define new parameters, the sidebar to change the values, the main area to monitor the simulation.

iNMR does not simulate multi-pulse sequences and solid state spectra. Many other special cases are handled, however, including chemical exchange.

### Related Topics

Spin Systems

Parameters and Controls to Manipulate a Simulated Spectrum

### Web Tutorials

How to Fit an Abstract Spin System

How to Fit a Real Spin System