, a side-on exponential decay constant of b = 2.85 Å -1 , and a cosine period modulation of m = 0.91. When we visualized the dependence of ∆𝜈̅ 𝐻𝐵 (d, θ) in eq. 7 on d(C≡N---Owater/MeOH) and θ(C≡N---Owater/MeOH) as a 2D heat plot (Fig. ), we found a highly analogous profile to those in Fig. and Fig. with a similarly broad range of values adopted (-5 -50 cm -1 ), showing that eq. 7 can recapitulate the DFT HB blueshifts with high accuracy. A 2D heat plot of the residuals between ∆𝜈̅ 𝐻𝐵 (d, θ) (eq. 7) and ∆𝜈̅ 𝐻𝐵 obtained from DFT (Fig. ) has residual values ranging from just -3 to +3 (Fig. ; R 2 = 0.96), further indicating eq. 7 accurately describes the blueshift for many HB distance and angle combinations. Some of largest residuals are found for angles corresponding with side-on HBs, where the Buckingham potential slightly underestimates ∆𝜈̅ 𝐻𝐵 (Fig. ). Even though eq. 7 takes the form of a lengthy expression, only four parameters are needed to sufficiently tune the distance and angle dependence (Table ), and all of them carry physical meaning in terms of describing specific underlying intermolecular interactions.