The dependence of the total electron energy density at the (3,−1) critical point (CP) of the H…O interaction against the interatomic distance (ECP) has been obtained by the addition of the local electron kinetic (GCP) and potential (VCP) energy densities dependences (ECP=GCP+VCP) for a set of 83 X-H…O hydrogen bonds (X=C, N, O). The ECP function has been related to the interaction potential by means of a proportionality relationship U=−υ⋅ECP, υ being a positive constant in volume units. Based on the GCP and VCP functionalities, the proposed H…O interaction potential has been successfully checked against several physical and chemical properties. The behavior of the U function has been compared to Morse and Buckingham-type potentials, leading to an almost perfect matching between all of them when they were constrained to have the same three parameters: the potential well depth U0, its position r0, and the curvature of the potential function at r0. The resulting U(r) function is simply described by the addition of two exponential terms: U(r)=49 100 exp(−3.6r)−11 800 exp(−2.73r), where U is in kJ/mol and r is the H…O distance in Å.

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A Raman study of ice VIII in the range 4000–50 cm−1 at T≈100 K and atmospheric pressure (Ref. 9) lead to a force constant of the hydrogen bond of k=22.7 N/m(dHB(O…O)=2.965 Å) for an experimental frequency value of ν̄=214.3 cm−1 (the strongest intermolecular translational mode). Unfortunately, the equilibrium distance r0100 K=d(H…O) is still unpublished to our knowledge. In order to estimate a value for r0100 K, we have used the experimental neutron data for ice VIII (D2O) at T=10 K and P=2.4 GPa (Ref. 10), and the theoretical crystal-orbital ab initio calculations carried out for ice VIII from P=0 to P=28 GPa (Ref. 11). In the whole range of pressures, the theoretical analysis shows very small variations of both the HB angle and the O–H covalent bond distance: 178.7°<α(O–H…O)<179.8° and 0.9509 Å<d(O–H)<0.9554 Å. In particular, the structural magnitudes obtained from this theoretical analysis, and corresponding to the unit-cell volumes of both experimental studies (Refs. 9 and 10) are: α(O–H…O)=179.4° and 179.6°, and d(H–O)=0.9516 and 0.9522 Å, for Vexp(P≈0 GPa,T=100 K)=161.0 Å3 and Vexp(P=2.4 GPa,T=10 K)=146.9 Å3, respectively (Refs. 11 and 12) (looking at the volumes, effects of both pressure and temperature are implicitly taken into account when results are transferred to experimental data, even if the theoretical analysis is carried out varying only the pressure). It means that experimental differences in dHB(O…O) values should be related (in a very good degree of approximation) to differences in d(H…O) distances. As the experimental data of Ref. 10 indicate dHB(O…O)=2.879 Å and d(D…O)=1.910 Å, the estimated hydrogen bond distance at P=0 GPa and T=100 K(r0100 K) should be close to d(H…O)=1.996 Å.
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Due to the dependence of F against U, the interaction is repulsive (F<0) when r<r0 and it is attractive (F>0) when r>r0, with a maximum value Fd at r=rd.
17.
This condition is mathematically reached when the involved entities are separated at an infinite distance.
18.
If a net charge has also been transferred between the interacting entities, |U0pol| should be changed by |U0pol+U0CT|, where |U0CT| is the work done in making the ions at the equilibrium distance r0.
19.
In general, r0(T) (and, of course, r0) should be a function of the external constraints, as for instance temperature and pressure. However, for clarity, we assume that those (except the temperature) are constant at their standard values in normal conditions.
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Defined as the difference between the crystal Hartree–Fock unit-cell energy divided by the number of molecules in the unit cell and the Hartree–Fock energy for an isolated molecule at the same geometry, using the same basis set.
22.
Using the estimated polarization energies obtained from the theoretical calculations (Ref. 13) of the dipolar moment of the water molecule in both ice VIII and the prototype structure I41md (5.9 and 9.0 kJ/mol, respectively), we observe U0=−19.9 and −16.8 kJ/mol, which are also in very good agreement with the reported result of Ref. 12.
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24.
If we calculate r0273 K using the theoretical value r0 reported in Ref. 12, which was obtained at the same experimental unit-cell volume found for ice VIII in Ref. 11 (i.e., r00 K=1.928 Å, and then V00 K=−48.37 kJ/a03mol), we obtain
r0273 K={−(1/D)ln[(2⋅a0−3⋅ΔU+V00 K)/C]=1.955 År00 K⋅ΔT⋅α=1.954 Å.
25.
Using the two other estimated |UH2Opol/2| values obtained from the theoretical calculations of Ref. 13 (5.9 and 9.0 kJ/mol), Eq. (28) leads to 13.5 and 10.4 kJ/mol, respectively.
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It is pointed out that neither Morse nor 6-exp potentials include angular dependence of the hydrogen bond energy. However, even if this contribution is usually believed to be very important, the angular dependence is implicitly taken into account when dealing with nonbonded interactions, as Kitaigorodsky pointed out in Ref. 3.
30.
In the case of the H…O closed-shell interaction: Δr=0.318 Å.
31.
The ratio between homologous parameters (belonging to attractive and repulsive contributions) gives a measure of their corresponding influence in the function and leads to the final behavior of the potential.
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