The single-atom R1: a new optimization method to solve crystal structures.

A crystal structure with N atoms in its unit cell can be solved starting from a model with atoms 1 to j - 1 being located. To locate the next atom j, the method uses a modified definition of the traditional R1 factor where its dependencies on the locations of atoms j + 1 to N are removed. This modified R1 is called the single-atom R1 (sR1), because the locations of atoms 1 to j - 1 in sR1 are the known parameters, and only the location of atom j is unknown. Finding the correct position of atom j translates thus into the optimization of the sR1 function, with respect to its fractional coordinates, x, y, z. Using experimental data, it has been verified that an sR1 has a hole near each missing atom. Further, it has been verified that an algorithm based on sR1, hereby called the sR1 method, can solve crystal structures (with up to 156 non-hydrogen atoms in the unit cell). The strategy to carry out this calculation has also been optimized. The main feature of the sR1 method is that, starting from a single arbitrarily positioned atom, the structure is gradually revealed. With the user's help to delete poorly determined parts of the structure, the sR1 method can build the model to a high final quality. Thus, sR1 is a viable and useful tool for solving crystal structures.