We will introduce new nonadiabatic dynamics algorithms that utilize curvature of the energy gap to approximate the TDC and the effective 3N-dimensional NAC, and we will show how they can be used to develop new variants of tSE and tCSDM that we shall call curvaturedriven semiclassical Ehrenfest (κSE) and curvature-driven coherent switching with decay of mixing (κCSDM). Both κSE and κCSDM require only energy and gradient information from electronic structure theory. The curvature-approximated TDC introduced in the current work is an extension of the approximate NAC previously developed for one-dimensional systems by Baeck Perhaps most importantly of all, CSDM balances coherence in strong interaction regions with decoherence between them in a fashion consistent with the Liouville-von Neumann equation.