A sketch of the geometric definition of the two coordinates used to map the bending manifold . The stereographic projection is obtained by finding the intersection point between the line that originates at , passes through the point on the circle at , and the tangent line that lays perpendicular to the line between the center and .
The ratio as a function of the bending SPC. is the square root of the determinant of the metric in , mapped by center of mass, orientation, and all internal DF coordinates. is the square root of the determinant of the metric over the manifold. The units of the ratio are those of mass. is convenient for the fast computation of , the classical Jacobian in simulations.
The Riemann Cartan curvature scalar of the manifold as a function of the SPC [cf. Eq. (62)].
Graph of as a function of the SPC .
Value of in the manifold [classical (white circles), quantum (white squares) labeled as “rigid”] compared to the values of computed with the manifold [classical , quantum ]. The quantum values are obtained with in both cases.
Values of , the intramolecular potential along the bending coordinate computed at several temperatures for various values of .
Values of , the total energy computed at several temperatures for various values of .
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