How to predict the 31P NMR spectra?

Question

What can I predict about the $\ce{^{31}P}$ spectra of $\ce{TiP2O7}$?

To get the required information about the crystal structure of the compound

Here is a screenshot from the ICSD website:

Since there is only one oxidation state (+5) for $\ce{P}$, there will be only one peak. And from the Wyckoff symbol, 4c, the intensity of the signal is 4, i.e. 4 $\ce{P}$ atoms in the unit cell.

I can't go any further to complete the task and extract all the relevant information. I'm using SIMPSON software to simulate the spectra. Can somebody walk me step by step through this?

Answer 1

If the question you were asked to answer was literally "what can you predict about the $\ce{^31P}$ NMR spectrum of $\ce{TiP2O7}$ (from the crystal structure), then I believe you have vastly overcomplicated the problem.

This is a question about solid-state NMR (as $\ce{TiP2O7}$ is a solid).

In solid-state NMR of crystalline compounds, the chemical shift depends on the exact arrangement of atoms within the crystal unit cell. The number of signals (for each element) depends on how many non-equivalent atoms of a particular element there are within one unit cell.

From the screenshot, it says that "formula units per cell" = 4. As the formula is $\ce{TiP2O7}$, this indicates there are 4*2 = 8 different phosphorus atoms in the unit cell.

So the answer is: You expect to observe 8 phosphorus signals in the $\ce{^31P}$ NMR spectrum.

There is no need to simulate the NMR spectrum with simpson. In fact, it is not possible to simulate the spectrum using simpson with only the crystal unit cell parameters. In order to set up a simulation in simpson, you actually have to supply the chemical shift and the interactions between the sites. You can calculate the interaction between the sites from the distances specified in the unit cell, but there is no information about chemical shifts!