GRADE: A code to determine clathrate hydrate structures

GRADE is an open-source software package that identifies clathrate hydrate structures given the atomic coordinates of oxygen atoms of water. These structures are commonly found in natural gases and they are relevant to understand antifreezing proteins as well as the hydrophobic effect. In this manuscript, we describe basic algorithms used by GRADE to determine 5^12, 6^2 5^12 and 6^4 5^12 water cages. These algorithms are based on the connectivity of five and six-folded rings made of first-neighbor water molecules. Schemes to speed up the calculation of these cages are discussed and implemented in the code. GRADE also computes the four-body order parameter F_4 commonly used to identify different phases of water. An example of how GRADE can be used to compute the spontaneous nucleation of methane clathrates is also provided.