At a conical intersection point, the plane spanned by the gradient difference vector (${\mathit{x}}_{\mathbf{1}}$) and the gradient of the interstate coupling vector (${\mathit{x}}_{\mathbf{2}}$): $$x_1=\frac{\delta (E_2-E_1)}{\delta Q}\mathit{q}$$ $$x_2=<{\mathit{C}}_{\mathbf{1}}^t(\frac{\delta H}{\delta Q}){\mathit{C}}_{\mathbf{2}}>\mathit{q}$$ where ${\mathit{C}}_{\mathbf{1}}$ and ${\mathit{C}}_{\mathbf{2}}$ are the configuration interaction eigenvectors (i.e., the excited and ground-state adiabatic wavefunctions) in a conical intersection problem, $H$ is the conical intersection Hamiltonian, $\mathbf{\text{Q}}$ represents the nuclear configuration vector of the system, and thus $\mathbf{\text{q}}$ is a unit vector in the direction of vector $\mathbf{\text{q}}$. $E_1$ and $E_2$ are the energies of the lower and upper states, respectively.