# Finding identities of diatomics from Spectroscopy and Mass Spec Data

Let's say I have a sample of 2 (assumingly different) diatomics A and B.

Through spectroscopy I found the data below:

For molecule A: \begin{align} B&\approx2.17690\ \mathrm{cm^{−1}}\\ D&\approx4.79000\times10^{-5}\ \mathrm{cm^{−1}}\\ I&=1.28590\times10^{-46}\ \mathrm{kg\ m^2}\\ \tilde ν_e&=928.15\ \mathrm{cm^{−1}} \end{align}

For molecule B:

\begin{align} B&\approx1.51695\ \mathrm{cm^{−1}}\\ D&\approx7.1049\times10^{-6}\ \mathrm{cm^{−1}}\\ I&=1.84533\times10^{-46}\ \mathrm{kg\ m^2}\\ \tilde ν_e&=1401.86\ \mathrm{cm^{−1}} \end{align}

Through Mass Spec, I found 2 strong spectral lines at $30.0077086\ \mathrm{g\ mol^{-1}}$ and $41.9766928\ \mathrm{g\ mol^{-1}}$. How do I deduce which is which and further, how do I determine the bond length. [FYI, I'm thinking the former mass is the molecule NO and the latter NaF just by guessing]

I'm thinking that the heavier molecule will have the larger inertia value. And from the inertia equation $I=\mu R^2$ I'll derive the bond length $R$. but how do I find the $\mu$ from the actually mass of the molecule from the mass spec data?

Is this problem conceptual, based on hypothetical data?

Through [m]ass [s]pec, I found 2 strong spectral lines at $$30.0077086\ \mathrm{g\ mol^{-1}}$$ and $$41.9766928\ \mathrm{g\ mol^{-1}}$$.

These mass-to-charge ratios or $$m/z$$ values are implausibly precise. The significant figures you show imply a precision of about 30 parts-per-billion (ppb) mass accuracy. That is well outside the specification of any commercial instrument I am aware of.

Also, if you are right about the first ion being, $$\ce{NO}$$, the value is inaccurate. The neutral $$\ce{^14N^16O}$$ molecule has a mass of 29.99799 Da. The positively charged ion formed by electron loss from the neutral species would have a mass of 29.9974 Da. This latter value is off from the value you quote by about 341 parts-per-million. So if the mass spectrometry data really is precise to within 30 parts-per-billion, and it is accurate, then the molecule can't be $$\ce{NO}$$.

In fact, with mass spectrometry data that precise (and accurate), we shouldn't need any other data to identify the diatomics, other than the fact that they are diatomics. We can add the mass of every possible nuclide to every other possible nuclide and see which give the right mass.

Here's how to do that using the R packages ecipex and dplyr.

require(ecipex)
require(dplyr)
nistiso %>%
mutate(foo = 1) %>%
left_join(., ., by='foo') %>%
filter(mass.x > mass.y) %>%
mutate(diatomic_mass = mass.x + mass.y) %>%
filter(diatomic_mass < 30.00771, diatomic_mass > 30.00770)


The result is that only the $$\ce{^11B^19F}$$ diatomic molecule has the requisite mass. Even if you loosen the mass tolerances to allow for e.g. for electron loss or gain, this is still the only possible diatomic with the right mass.

You can repeat this exercise for the other data point, and find that $$\ce{^40Ca^2H}$$ is the only possible ion consistent with the data. ($$\ce{^40Ar^2H}$$ is close in mass but is more than one electron's mass too light.)

I'll leave it to you to decide whether these ions are chemically meaningful or possible for you, and if they are consistent with the rotational spectra.