First, when the radicand is negative, we simply set it to zero. This is justified as follows. The reason why a formula like eq 4 or q 5 works is best appreciated by considering the nature of two potential curves near a locally avoided crossing. In a typical case the lower curve is concave, and the upper curve is convex, so the radicand is positive. Therefore, a situation where the radicand is negative is expected to occur only far from conical intersections where the NAC is small, so this should not cause a large error.