I'm not too experienced w/ computational chemistry but in analyzing gas-phase IR data using an newer functional, I've found that the only way to get the appropriate scaling factor is to find an experimental data set and simply scale the calculated values to the most intense peaks. Many people doing infrared multiphoton dissociation (IRMPD) experiments just overlay the experimental and calculated spectra to get them to match correctly.

Since you have a complex in solvent you probably wont find a spectrum - but, If you can find gas-phase spectra of some kind of model molecule and find the scaling factors, you may be able to apply that scaling factor to your system.

For me, I specifically plot the experimental and calculated in excel. However instead of plotting the wavenumber values extracted from calculations, I multiply them by an arbitrary number and just start visually adjusting from there to get the best match. I've done a dipeptide system using wb97xd/6-311+g(d) and found a scaling factor to be 0.950.

Hi Patrick, thanks for you answer. It confirms a lot of what I suspected. I agree, the complex in an implicit solvent will change the frequency of bonds (I tested the difference earlier today). Also, I failed to mention that I am using IR (amongst other techniques) to detect hydrogen bonds. So not only am I not working in gas phase, but also every one of the published scaling factors (if you follow the link) explicitly states that they do not factor in non-bonded/weak interactions. Also, scaling an IR frequency for OH from water using the wb97xd/... chemistry model was approx 0.950, as you mentioned. 

At this stage, given that I am study water binding to my complex, I can simply use unscaled values to monitor red shift and explicitly state that no scaler factor has been published. 

Your point on comparing with experimental - that would be really good. It is something we are in the process of doing, however, synthesising our standard->HPLC->Mass Spec, is proving difficult. 

Many thanks. 

Mr. Nash,

Not, you can't! The value 3640 cm-1 is accepted as a value of the nOH stretching vibration of an isolated OH - group, meaning a value obtained my the matrix-isolation IR-technique. But you have computed your system in a aquatic-environment, meaning that your OH - group takes part into inter (and/or intra) molecular hydrogen bonds. For such as systems the nOH is usually about 3300 cm-

1, but thus value is also approximative, because of, generally, the X-H (X=N,O,S,P) vibrations are very sensitive towards any kind of intra/intermolecular interactions. In this content, they are maximum unsuitable for scaling, furthermore you can have experimentally other IR-effects such as for example Fermi-resonance and more, which can additionally perturb the position of the nOH band in the spectrum.

It is recommendable to use those scaling factor, which fit excellent to a frequency of X-Y type for example nC-C, ArC-C and related, than:

(i) you can predict the mode of nOH, using the last scaling factor, and;

(ii) to compare with the experimental nOH mode of your system, however determining the nOH position by the isotopic exchange approach.

(iii) When you have unambiguously determined nOH by deuterium exchange, than you can correct the corresponding theoretical scaling factor, via point (i) with a new one.

Usually any corrections of the theoretical IR-spectra based on the nOH/nNH modes have yielded to a significant deviations of the theoretical and experimental frequencies within 1400 - 1000 cm-1 (fingerprinting region).

Thanks for your comment Bojidarka. That was a lot of very useful information. 

Check this website

https://cccbdb.nist.gov/vibscalejust.asp

Hi Dewakar,

The answers above really cover the question, but just to give a slightly different spin on things I will add my two cents. The coffee cup is your system and the surrounding are not isolated from your system. It is the entropy of the universe (Ssys + Ssurr = Suniv) that is always increasing for an irreversible process. As stated above, independent of the path of the real system and real surroundings, the entropy is only defined for a reversible process that takes you from point A to point B. Point A is the coffee at Thi and the surroundings at Tlo, otherwise, the heat will not flow from the system to the surroundings. At point B, the system and the surroundings are at Tlo. Here I am assuming that the surroundings are so large that the low T of the surrounding does not change, but if your surroundings and the system are isolated from the rest of the complete universe, then your small universe will have the system and surroundings come to an equilibrium T which is somewhere between the original Thi and Tlo. Going with the large universe scenario, you would calculate the delta Ssys = Cp(sys)*ln(Tlo/Thi) (assuming Cp to be T independent), This is obviously a negative number. The delta Ssurr = Qrev(surr)/Tlo = -Q(lost by system)/Tlo) = [Cp(sys)*(Thi – Tlo)]/Tlo. I think you can convince yourself that the magnitude of the delta Ssys is always less that the magnitude of delta Ssurr, which means that delta Suniv is always positive. Obviously, this is a very heuristic proof of a very specific example, but if you try all of the variations of a small universe versus a large universe and temperature dependence of the heat capacity of the system, you finally see that these other scenerios do not make any difference in the second Law of Thermodynamics. Ultimately, it rests on the requirement of the first Law of Thermodynamics that Qrev(sys) = -Qrev(surr) and the only way for the spontaneous (irreversible) process to occur is if the Tsurr is lower than Tsys and they are in thermal contact. That means that Qrev(surr) is always positive and Qrev(sys) is always negative with their magnitudes equal. Since the Qrev(surr) is divided by a lower Kelvin temperature than the Qrev(sys), the delta Suniv is always positive. Hopefully, this will add another slightly different way of saying the same as the comments above.