Conical Intersections and Bound Molecular States Embedded in the Continuum

Nuclear dynamics on coupled potential surfaces can lead to bound states embedded in the continuum. For one type of conical intersection situation, an explicit proof is presented that such states exist. Non-Born-Oppenheimer effects are responsible for the binding of these states. Once the Born-Oppenheimer approximation is introduced, these states at best become resonances which decay via potential tunneling. The tunneling is completely suppressed by the coupling between the electronic states. A numerical example is given.

Figure 1

(a) A cut of the diabatic potentials $V_b$ and $V_c$ along $x$ at $y=0$. Shown also are the exact energy of the bound state in the continuum and its wave function components $|{\psi }_b{|}^2$ (dashed curve) and $|{\psi }_c{|}^2$ (dotted curve); the latter has been scaled by a factor of 10 relative to the former. Both components exponentially decay at large $x$. The energy window for bound states in the continuum is indicated: it is between the breakup channels $E_{0_y}$ and $E_{1_y}$. (b) A cut of the lower adiabatic potential along $x$ at $y=0$. The resonance state shown possesses a short lifetime due to tunneling; the resonance wave function oscillates at large $x$. The complex resonance energy is indicated; the horizontal thin dotted line indicates the resonance position and the horizontal thin solid lines indicate the width. Tunneling is completely suppressed by non-Born-Oppenheimer effects as seen in (a). The values of the potential parameters used are given in the text below Eq. (6). All of the wave functions are shown along $x$ at $y=1.2$ since ${\psi }_c$ has a node at $y=0$. Except for ${\psi }_c$, the wave functions shown are very similar in form to those for $y=0$.