In frequency calculations in Gaussian09 using DFT-B3LYP and 6-311+G(d) functional and basis set, we know that scaling factor is applied to correct the obtained frequencies. But is there any printable error bar for frequency calculations?
No, at least not in an established manner. An error bar shows the precision of the calculation while the scaling factor affects the accuracy.
If you're not familiar with the difference between precision and accuracy, here's an analogy to an archer:
Precise archer: all arrows end up close to each other on the target, but not necessarily the desired center.
Accurate archer: the base point of the arrows is the center of the target, but they may be widespread.
Now, DFT calculations are ultraprecise with a given combination of basis set, functional and convergence criteria so there is no "statistical error bar" while the accuracy is only known from experience (aka benchmark calculations). Many theoreticians therefore reject the concept of error bars for their calculations completely for that reason.
A concept that has been brought up but is not established is that you can calculate values for a certain substance class and look how wide they spread around the true (= experimental) value with the right scaling factors. Note, however, that a new molecule may still be in an exceptional position and therefore the experiment-theory deviation therefore may be bigger than the "error bar" you generated with all those efforts.
And that is the major reason why you barely find error bars on DFT calculations.
No, at least not in an established manner. An error bar shows the precision of the calculation while the scaling factor affects the accuracy.
If you're not familiar with the difference between precision and accuracy, here's an analogy to an archer:
Precise archer: all arrows end up close to each other on the target, but not necessarily the desired center.
Accurate archer: the base point of the arrows is the center of the target, but they may be widespread.
Now, DFT calculations are ultraprecise with a given combination of basis set, functional and convergence criteria so there is no "statistical error bar" while the accuracy is only known from experience (aka benchmark calculations). Many theoreticians therefore reject the concept of error bars for their calculations completely for that reason.
A concept that has been brought up but is not established is that you can calculate values for a certain substance class and look how wide they spread around the true (= experimental) value with the right scaling factors. Note, however, that a new molecule may still be in an exceptional position and therefore the experiment-theory deviation therefore may be bigger than the "error bar" you generated with all those efforts.
And that is the major reason why you barely find error bars on DFT calculations.
If you are talking about the variability of the data, then none. You will get virtually the same values if you carry out the same calculations and parameters over many trials/tests.
If you are talking about the error against a known or true value, then the closest is against the experimental values or benchmarked values.
Actually we do not talk about any error bar in the DFT generated vibrational results. However, scaling factor is a different story. It is necessary to get values close to the experimental results and depends on the level (accuracy) of the adopted methodology i.e functional + basis set.
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