programs to enumerate hydrogen bond topologies in ice, and generate graph invariants

Programs available on this page are the work of Chris Knight and Sherwin Singer. Corey Beck helped finish the programming, and found many bugs in the programs and in the manual.

what these programs do

In the study of order/disorder phenomena in ice, an enumeration of all possible symmetry-distinct hydrogen bond (H-bond) configurations is required. For example, exactly 16, symmetry-distinct H-bond configurations are possible ins a 12-water orthorhombic unit cell of ice Ih. It is pointless to perform expensive ab initio calculations on more structures, since that will only regenerate a previously found energy. Furthermore, we have shown that the energy, and other scalar physical properties, can be concisely linked to the H-bond configuration with the use of polynomials which are invariant to all symmetry group operations. We have called such polynomials first, second, third,... order graph invariants when they are linear, quadratic, cubic,... in the bond variables.Type I clathrate unit cell

The Pm3n unit cell of a type I ice clathrate, pictured on the right, contains 46 water molecules. These FORTRAN programs will tell you that exactly 17,151,190 symmetry distinct H-bond structures are possible. (Click here for the input files in a tar.gz archive, prepared by Corey Beck.) Sometimes Monte Carlo sampling of H-bond configurations is preferred. In other situations, it is very useful to have all possible hydrogen bond topologies in hand. You can also generate all first and second order graph invariants for this system.

Besides the manual that is part of the program package, and the two primary articles listed below, the applications presented in other journal articles may illustrate and clarify the techniques.

Currently, programs for periodic unit cells for ice are available. Eventually, we will make programs for finite water clusters available as well.

Production of these programs were made possible by support from the National Science Foundation.


some relevant publications