Within the Born–Oppenheimer approximation, a semi-classical model for the probability, $P$, of hopping from one electronic state to another of the same or different multiplicity $$P=\exp (-\frac{4{\pi }^2{\epsilon }_{12}^2}{h\nu |s_1-s_2|})$$ where $\text{Math input error}$ is the potential energy gap between the two electronic states at a surface crossing point, $|s_1-s_2|$ is the difference in slopes between the intersecting potential energy curves at this point and $\nu$ is the nuclear relative velocity with which the system passes the point of closest approach.