**UPDATE:**Below is an accurate calculator, but it is impractically slow for large molecules. A practical AND accurate calculator is found here:http://verahill.blogspot.com.au/2012/10/isotopic-pattern-caculator-in-python.html

Use the post below to learn about the fundamental theory, but then look at the other post to understand how to implement it.

**Old post:**

Getting fast and accurate isotopic patterns can be tricky using tools available online, for download or which form part of commercial packages. A particular problem is that different tools give slightly different values -- so which one to trust?

The answer: the tool for which you know that the algorithm is sound.

The extreme conclusion of that way of thinking is to write your own calculator.

Below is the conceptual process of calculating the isotopic pattern of a molecule using GNU Octave.

You need the linear algebra package:

*sudo apt-get install octave octave-linear-algebra*

*b*is the isotopic distribution for an element, and

*bb*are the masses of those isotopes.

Once you've got a computational engine it's not too difficult to expand it for more general cases, account for charge, and instrument resolution.

**Molecule: Cl**

_{4}b=[0.7578,0.2422]; bb=[34.96885,36.96885]; e=prod(cartprod(b,b,b,b),2); ee=sum(cartprod(bb,bb,bb,bb),2); n=4; g=histc([ee e],linspace(min(ee),max(ee),n*(max(ee)-min(ee)+1)),2); h=linspace(min(ee),max(ee),n*(max(ee)-min(ee)+1)); distr=e'*g; plot(h,100.*distr/max(distr)) [h' (100.*distr/max(distr))']Here's the output for n=1:

139.87540 78.22048 140.87540 0.00000 141.87540 100.00000 142.87540 0.00000 143.87540 47.94141 144.87540 0.00000 145.87540 10.21502 146.87540 0.00000 147.87540 0.81620

And here's the output from Matt Monroe's calculator:

Isotopic Abundances for Cl4 Mass/Charge Fraction Intensity 139.87541 0.3297755 78.22 140.87541 0.0000000 0.00 141.87541 0.4215974 100.00 142.87541 0.0000000 0.00 143.87541 0.2021197 47.94 144.87541 0.0000000 0.00 145.87541 0.0430662 10.22 146.87541 0.0000000 0.00 147.87541 0.0034411 0.82

**Another molecule: Li2Cl2**

Here's the code:

a=[0.0759,0.9241]; aa=[6.01512,7.01512]; b=[0.7578,0.2422]; bb=[34.96885,36.96885]; e=prod(cartprod(a,a,b,b),2); ee=sum(cartprod(aa,aa,bb,bb),2); n=1; g=histc([ee e],linspace(min(ee),max(ee),n*(max(ee)-min(ee)+1)),2); h=linspace(min(ee),max(ee),n*(max(ee)-min(ee)+1)); distr=e'*g; plot(h,100.*distr/max(distr)) [h' (100.*distr/max(distr))']

ans = 81.96794 0.67170 82.96794 16.35626 83.96794 100.00000 84.96794 10.45523 85.96794 63.71604 86.96794 1.67079 87.96794 10.17116

vs Matt Monroe's calculator:

Isotopic Abundances for Li2Cl2 Mass/Charge Fraction Intensity 81.96795 0.0033082 0.67 82.96795 0.0805564 16.36 83.96795 0.4925109 100.00 84.96795 0.0514932 10.46 85.96795 0.3138084 63.72 86.96795 0.0082288 1.67 87.96795 0.0500941 10.17

We can then expand the code to allow for plotting

a=[0.0759,0.9241]; aa=[6.01512,7.01512]; b=[0.7578,0.2422]; bb=[34.96885,36.96885]; e=prod(cartprod(a,a,b,b),2); ee=sum(cartprod(aa,aa,bb,bb),2); n=1; g=histc([ee e],linspace(min(ee),max(ee),n*(max(ee)-min(ee)+1)),2); h=linspace(min(ee),max(ee),n*(max(ee)-min(ee)+1)); distr=e'*g; gauss= @(x,c,r,s) r.*1./(s.*sqrt(2*pi)).*exp(-0.5*((x-c)./s).^2); k=100.*distr/max(distr); npts=1000; resolution=0.25; x=linspace(min(ee)-1,max(ee)+1,npts); l=cumsum(gauss(x,h',k',resolution)); l=100*l./max(l(rows(l),:)); plot(x,l(rows(l),:))

which gives:

Compare with Matt Monroe's calculator: