Strategies for Varying Multiple Parameters (variables) with Limited Observables

GULP
1

I am trying to find Interatomic potential (Buckingham potential) for different phases of NaYF₄ in GULP 6.2 (running via Cygwin on Windows 11).

How can I effectively vary multiple parameters (variables) when the number of available observables is limited?

Is it always necessary to have a greater number of observables (such as mechanical properties, structural parameters, static dielectric constant, or optical-phonon energy) to reliably explore variations of more variables?

I have attached snippet of my input file.

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Any guidance would be greatly appreciated.

Best regards,
Aravind

2

Think about simultaneous equations if you’re not familiar with least squares fitting. If you have 2 unknown variables, how many simultaneous equations do you need to find them? If you have only 1 then there are infinite number of possible values that satisfy the equation, and so the solution is ill-defined. Same is true for fitting.