![]() The angle between the dipoles can be qualitatively explained by thinking of the tetrahedral geometry of oxygen’s two bonds and two lone pairs under sp³ hybridization. The lowest in energy had a hydrogen bond between the H of HCN and O of H₂O with an energy of -169.7358Ha the dipole of H₂O formed an angle of approximately 30° with the axis of HCN. ![]() ResultsĪll equilibria we found fell into one of three categories. ![]() Those interested in reproducing our results should note that, with our maximum step size of 0.3Å, in a few cases (namely, those in which H₂O was initially repulsed by dipole forces) this took slightly over 50 iterations to converge. Our minimization criterion was to have the energy and displacement between successive steps vary by less than, respectively, 10⁻⁵Ha and 0.002Ha/Å. Two examples are shown below in Figure 1.įigure 1 – Two example initial geometries with C of HCN as the origin, the upper H₂O is at 30° off the z-axis (measured as the angle O-C-N) with a dipole parallel to the x-axis and the lower H₂O is at 120° with a dipole antiparallel to the x-axis For each location one optimization began with the H₂O dipole either parallel or antiparallel to the x axis, with the plane defined by the three atoms of H₂O at a 45° angle to the xz plane. At a distance of 2-3Å from the carbon of HCN, H₂O was placed at approximately 30°, 60°, 90°, 120° and 150° from the z axis. With the bond lengths and angles fixed, we chose five initial positions for the water molecule, each with two orientations. We are left with four parameters for H20, two for each of its location and its orientation. Symmetry in reflection across the yz plane means we can further narrow the space to be considered to the portion of the xz plane with x>0. Furthermore, because HCN is linear, it is identical upon rotations about this axis and hence we can also take H₂O to be in the xz plane. This is immediately reduced by the fact that only the relative displacement and orientations of the molecules matter, and we exploit this freedom by choosing to place the carbon of HCN at the origin initially and align it with the z-axis. polar and azimuthal angles) of each molecule. three Cartesian coordinates) and two-variable orientations (e.g. Here we discuss our choice of initial geometries.Īs free parameters our we may choose the three-variable locations (e.g. Individual initial geometries must be chosen so that appreciable forces exist, and the set of initial geometries must be diverse enough to capture all local minima. Table 1: Geometry of isolated HCN and H₂Oīecause the geometry optimization algorithms proceed by using calculated forces to update initial atomic positions, it is critical that we choose judiciously the set of initial geometries we will optimize. Our calculations corroborate and are corroborated by the values reported in the literature, as may be seen in Table 1. This served a dual purpose, not only providing us with a suitable initial geometry for each of the molecules in our main calculation, but also giving us an idea the systematic errors implicit in our method. MethodsĪs a precursor to our main result, we performed geometry optimization for isolated H₂O and then isolated HCN and compared our results to values in the literature. The specific basis set used was DNP 3.5 (double numerical with polarization). ²⁾ using a basis set of atomic orbitals and the PBE⁽³⁾ functional for the exchange-correlation energy. ![]() We performed these calculations for all electrons within the framework of DMol³⁽¹ In this work we use density functional theory to find the preferred geometry of molecular pairs of hydrogen cyanide (HCN) and water (H₂0). ![]()
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