Cartesian coordinates are ubiquitous and pervasive in science an engineering. In my work however, curvilinear coordinates will be used to locate the nuclei position. These natural coordinates devised by Marcus in 1966, allow the expression of a single Hamiltonian which continuously and accurately produces the dynamics throughout the whole reaction.
Below is a skewed coordinate system where the dotted line is the reaction coordinate. The small green circle is the transition state. The red line is the reaction path. The red dot shows that along the reaction coordinate you can project to another orthogonal coordinate.