The heat released when two molecules interact is often of interest. The origin of this energy can be worked out by an analysis of the terms in ENPART, but it is not easy to do. To understand why it is complicated, consider the stabilization energy arising from two water molecules hydrogen bonding together. The heat released when they bond is 4.9 kcal/mol. This is the difference in ΔHf of the separated molecules and the ΔHf of the hydrogen-bonded pair. (The data sets used here are at the bottom of this page.)
| Energy quantity |
Two isolated water molecules |
Water
dimer, hydrogen bonded |
Difference | ||
| ΔHf | -108.61 | -113.53 | -4.91 | ||
| Self-energy of first H2O | -7358.09 | -7354.93 | +3.16 | ||
| Self-energy of second H2O | -7358.09 | -7353.27 | +4.82 | ||
| Water-water interaction energy | 0.00 | -12.89 | -12.89 | ||
| Total energy of system | -14716.18 | -14721.09 | -4.91 |
(All energies in kcal/mol)
Question:
From ENPART, the energy of interaction of the two water molecules is 12.89 kcal/mol, much larger than the heat of dimerization, 4.9 kcal/mol Why is this?
Answer:
In an isolated water molecule, the energy is, by definition, a minimum. When a water molecule interacts with anything, even another water molecule, its geometry and electronic structure must change. Any change must result in an increase in energy. In this system, the effect of the second water molecule on the electronics and structure of the first water molecule is to cause its energy to rise by 3.2 kcal/mol, and the corresponding effect of the first water molecule on the second water is to cause its energy to increase by 4.8 kcal/mol. These increases in energy are much less than the energy of interaction, -12.9 kcal/mol, therefore there is a net stabilization of 4.9 kcal/mol.
The point here is that the energy of the hydrogen bond is not the energy of
interaction of the two water molecules, it is much less.
Data sets used here:
enpart(3,3) PM6 Two isolated water molecules O 0.00000000 +0 0.0000000 +0 0.0000000 +0 H 0.94888226 +1 0.0000000 +0 0.0000000 +0 1 0 0 H 0.94887671 +1 107.5510095 +1 0.0000000 +0 1 2 0 O 100.00000000 +0 134.3949691 +1 172.4547072 +1 1 2 3 H 0.94884149 +1 25.7258314 +1 -142.9814115 +1 4 1 2 H 0.94891219 +1 81.8463828 +1 -152.5832808 +1 4 1 3In the optimized hydrogen-bonded water dimer predicted by PM6, the O-O distance is 2.37 Å, much less than the correct 2.91Å given by G. S. Tschumper, M. L. Leininger, B. C. Hoffman, E. F. Valeev, H. F. Schaefer III, M. Quack, J. Chem. Phys. 116, 690 (2002). The potential energy surface of H2O dimer is very flat, and the energy of the correct structure is only slightly above that of the predicted structure. With the exception of the water dimer, PM6 predicts hydrogen-bonded structures with good accuracy.
enpart(3,3) PM6 Two water molecules hydrogen-bonded together, PM6 optimized geometry O 0.00000000 +0 0.0000000 +0 0.0000000 +0 H 0.94764900 +1 0.0000000 +0 0.0000000 +0 1 0 0 H 0.96476300 +1 108.1613840 +1 0.0000000 +0 1 2 0 O 2.05858800 +1 96.4475540 +1 179.9402340 +1 3 1 2 H 0.96087500 +1 84.7452660 +1 -52.9965190 +1 4 3 1 H 0.96083600 +1 84.9704820 +1 106.0583530 +1 4 3 5Here is the correct, fully optimized water dimer geometry:
enpart(3,3) 1scf PM6
Two water molecules hydrogen-bonded together, reference geometry from Tschumper, et.al.
O 0.000000 0 0.000000 0 0.000000 0 0 0 0
H 0.958071 1 0.000000 0 0.000000 0 1 0 0
H 0.965310 1 104.452397 1 0.000000 0 1 2 0
H 2.470416 1 154.448639 1 134.557884 1 3 1 2
H 1.518484 1 72.101385 1 132.496880 1 4 3 1
O 0.959705 1 47.110146 1 33.416060 1 4 3 5