Hello, in order to calculate the change of vibration entropy after introducing defects into the system, I need to calculate the frequency of the defective system. In the process of calculation, I encountered three problems, as follows:
1)In the defect system, only the frequency of the atoms in region 1 can be output, but the number and position of the atoms in region 1 are different from that of the atoms in the supercell I construct, so there is a non-negligible error in the calculation of the difference. Is there a way to output the frequency of the same atoms as the supercell I construct when calculating the frequency of the defect system?
2) The calculated results of frequency of system with defects can only appear in out file, but the results in out file are not accurate enough (the accuracy is very high when output in a separate osc file or freq file. But only supercell results can be displayed).Is there a way to separately output the high precision frequency results of the defect system or modify the accuracy of the defect frequency in the out file?
3) Is the result of frequency calculation related to temperature?

Hello My_Name (shame your parents didn’t have a bit more imagination).
Here are some responses to your points:

Only frequencies for region 1 are computed in the Mott-Littleton method since region 2 is infinite and so it would be clearly impossible to compute the frequencies for this. The key point is that the results of M-L and supercell calculations won’t be the same except in the limit of a very large supercell. This is because the first method is simulating the limit of an isolated defect whereas the second is simulating a finite concentration. If you extrapolate the supercell results as a function of 1/L where L is the cell size then this should tend to the infinitely dilute case at 0. The M-L does have an issue in that at the region 1-2 boundary you have an interface between a vibrating and non-vibrating system. Therefore only the frequencies that are localised around the defect will be strictly correct.

I think you mean that they’re not precise enough, since the accuracy is determined by the quality of the model. It’s not clear why you need more that 2 decimal places of precision in the frequencies? It’s important to keep in mind that thermal energy is of the order of 207 cm^-1 at room temperature and so 0.01 cm^-1 is a negligible amount of energy and well below the accuracy of any theoretical method. If you really are set on having more decimal places then you can always edit the source code to print out as many as you like up to the limit of double precision.

Normal frequency calculations are temperature-independent (in terms of the frequency values themselves), though the properties of the vibrations include the effect of temperature via statistical mechanics formulae. If you want temperature-dependent frequencies then you need to read up about quasiharmonic free energy minimisation (or use molecular dynamics in the classical/anharmonic limit).