This code is not entirely correct. On error, among others, is that the author misinterpreted Equation (39) of the original published document on the Standard Atmosphere of 1976. This involves the calculation of the Hydrogen number density. The author oversimplified the equation. Also, the temperature gradient in Equation (28) involves a constant "a" which the author had the wrong sign on.
Do you have an alternate source or correction for your value of Helium number density @86km? The value in Table 9 looks like 10^10 to me, but you have it in "atmo_compo.m" as 10^14.
Nice submission otherwise, there's a lot you could do to vectorize the computations though.