Retrieving interaction potentials from the topology of the electron density distribution: The case of hydrogen bonds

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.