Performing DFT calculations of XH (X=O or N) stretching frequencies in hydrogen bonded sytems a number of decisions have to be made:  appropriate functional, basis set, harmonic vs. anharmonic approximation, computing time in relation to the size of the molecule. Examples of medium large and large molecules or systems see Fig.1.  A different type of large system is a binary alocohol + cyclohexane. ^[1]

Figure 1.   c From Ref. ^[2]

A recent paper has summarized the methods to calculate IR frequencies in general. ^[3]  In the regime of weak hydrogen bonds Futami et al.^[4] calculated the OH stretching frequencies of (R)-1,3-butanediol using the VPT2 approach ^[5] and the B3LYP/6-311++G(3df,3pd) functional and basis set.  

In the same frequency range Medel and Suhm ^[6] investigated a series of alcolhols as seen.  The frequency range is very narrow but very accurate predictions were obtained dividing the alcohols according to primary, ceconday and tertiary (see Figure 2).

Figure 2.  Plot of observed OH stretching frequencies vs. calculated (B3LYP-D3/may-cc-pVTZ) taken from Ref. 6 with permission from Royal Society of Chemistry.

Hansen, Hansen and Spanget-Larsen investigated two different types of hydrogen bonded systems either with OH or RNH groups as hydrogen bond donors. Refs. 7,8,9.

Fig. 3. Linear regression of observed OH stretching wavenumbers νOH (cm-1) on those predicted within the harmonic approximation, B3LYP/6-31G(d). Taken from Ref. 7 with permission from Elsevier.

The regression line of Figure 3 is: νOH{Obsd} = –757 + 1.171*νOH{Harm} (R = 0.985, SD = 74 cm-1).  Eq. 1

In case of the -NHR derivatives a non-linear relationship was found (see Figure 4). REF

Figure 4.  Plot of observed NH stretching frequencies vs. calculated (B3LYP/6-311++G(d,p).  Data from Ref. 9 with permission from MDPI.

However, performing the same calculation but with B3LYP/6-31G* gave a correlation:

P(harm) =3470-6.714 x 10(super7)  exp(-Harm/270.3).  R² = 0.965 and SD= 38.1 cm-¹.  Eq.2

Figure 5.  Plot of NH stretching frequencies calculated with basis setes. 6-311++G(d,p) vs. 6-31G(d).  Data from Ref. 9 with permission from MDPI.

This is very similar to the much higher basis set used in Fig.  5.  As a matter of fact, the two types of calculations can be correlated with R²=0.991 and SD = 15 cm-1.  Calculations were also performed with the B3PW91.  These were linearly correlated to  the B3LYP calculations with a R² = 0.9999 and and SD of 2.6 cm-1. 

Performing anharmoic calculations in case of the -OH stretching frequencies led to the plot seen in Fig. . A good correlatation is found between the harmonic and the anharmonic data as seen in Figure 6.

Figure 6. Linear regression of OH stretching wavenumbers νOH (cm-1) calculated in the PT2 anharmonic approximation on the corresponding harmonic wavenumbers, B3LYP/6-31G(d). The regression line is νOH{Anh} = –2791 + 1.732*νOH{Harm} (R = 0.99, SD = 88 cm-1). From Ref. 7 with permission from Elsevier.

In case of the NH stretching frequencies a similar plot is found:

Figure .  Plot of NH stretching frequencies anharmonic (VPT2 B3LYP/6-31G(d) vs. the harmonic one.  Taken from Ref. 9 with permission from MDPI.

A calculations doing a VPT2 calculation at molecule a in Fig. 1, but with the higher basis set 311++G(d,p) took 28 days using 8 processors and resulted in a predicted NH stretching frequency of 2930 cm-1 as compared to the experimental value of 2760 cm-1.

Considering the use of the simple basis set G(d).  A strongly hydrogen bonded example is the enol form of nitromalonamide.  PT2 calculations gave 1428 cm-1 ^[10], whereas the P(harm) prediction gave 1920 cm-1.  The latter result was confirmed by using Car-Parrinello and path integral molecular dynamics.  ^[11]

In designing a scheme for prediction of XH stretching frequencies in hydrogen bonded systems, it is important to include molecules with extensive conjugation, steric interations and a range of hydrogen bond strengths varying from very weak to very strong.  This has led to the simple equations 1 and 2, which can predict OH and NH stretching frequencies in even very large molecules.