[Svarec]

Hello,

I've got set a certain oscillation (vibration) frequency f¹ at base level for HeH⁺ molecul (atoms are the most common isotopes). How do I calculate oscillation frequency f¹' for ³He²H⁺? Is it as simple as f¹/μ¹ = f¹'/μ² where μ is reduced mass or is it more complex than that? Frequncy of the original molecule is the only thing set.

Thanks for your help

[mjc123]

Well, what is the formula for the frequency of a harmonic oscillator? How does it depend on the reduced mass?

[Svarec]

I know its ω = (k/μ)^1/2 but can I just assume the "k" is the same for both cases?

[mjc123]

Yes, but you can't assume f¹/μ¹ = f^1'/μ² , can you?

[Svarec]

Yeah, I spewed that out without much thinking. I didn't know I could use that formula for frequency because I assumed "k" would change too. But I see it now. Thanks for help.

[mjc123]

Just a caution - the formula applies to the true harmonic frequency ω_e. Because of anharmonicity, the observed transition frequency ω₀ may be somewhat different, and an apparent k derived from this frequency will vary slightly between isotopomers. Check whether your data are ω₀ (observed) or ω_e (derived by applying anharmonicity correction).

[Irlanur]

I know its ω = (k/μ)1/2 but can I just assume the "k" is the same for both cases?

the k between different isotopes is the same withing the Born-Oppenheimer Approximation, meaning that the nuclear dynamics does not influence the electronic structure. in other words: there is no coupling between the electronic and the vibrational level. In other words: the vibrational frequencies are much lower than the electronic frequencies.