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For example, if I just take V''(R), leaving everything in atomic units, and plug in R (in bohrs), I get a number...but what units is it in? How would I convert that number to its SI equivalent, which is J/m^2?

Of course, V''(R) = d^2 V / dR^2 is

**supposed**to be a (harmonic) force constant, which in SI would be measured in J/m^2. But I've tried a number of different approaches to doing the right sort of conversions, but each one gives me a (wildly) different answer.