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The quantum chemistry community has developed analytic forces for approximate electronic excited states to enable walking on excited state potential energy surfaces (PES). One can thereby computationally characterize excited state minima and saddle points. Always implicit in using this machinery is the fact that an excited state PES only exists within the realm of the Born-Oppenheimer approximation, where the nuclear and electronic degrees of freedom separate. This work demonstrates through ab initio calculations and simple nonadiabatic dynamics that some excited state minimum structures are fantastical: they appear to exist as stable configurations only as a consequence of the PES construct, rather than being physically observable. Each fantastical structure exhibits an unphysically high predicted harmonic frequency and associated force constant. This fact can serve as a valuable diagnostic of when an optimized excited state structure is non-observable. The origin of this phenomenon can be attributed to the coupling between different electronic states. As PESs approach one another, the upper surface can form a minimum that is very close to a near-touching point. The force constant, evaluated at this minimum, relates to the strength of the electronic coupling rather than to any characteristic excited state vibration. Nonadiabatic dynamics results using a Landau-Zener model illustrate that fantastical excited state structures have extremely short lifetimes on the order of a few femtoseconds. Their appearance in a calculation signals the presence of a nearby conical intersection through which the system will rapidly cross to a lower surface. 

Sodium hydride (NaH) in the gas phase presents a seemingly simple electronic structure making it a potentially tractable system for the detailed investigation of nonadiabatic molecular dynamics from both computational and experimental standpoints. The single vibrational degree of freedom, as well as the strong nonadiabatic coupling that arises from the excited electronic states taking on considerable ionic character, provides a realistic chemical system to test the accuracy of quasi-classical methods to model population dynamics where the results are directly comparable against quantum mechanical benchmarks. Using a simulated pump–probe type experiment, this work presents computational predictions of population transfer through the avoided crossings of NaH via symmetric quasi-classical Meyer–Miller (SQC/MM), Ehrenfest, and exact quantum dynamics on realistic, ab initio potential energy surfaces. The main driving force for population transfer arises from the ground vibrational level of the D 1 Σ + adiabatic state that is embedded in the manifold of near-dissociation C 1 Σ + vibrational states. When coupled through a sharply localized first-order derivative coupling most of the population transfers between t = 15 and t = 30 fs depending on the initially excited vibronic wavepacket. While quantum mechanical effects are expected due to the reduced mass of NaH, predictions of the population dynamics from both the SQC/MM and Ehrenfest models perform remarkably well against the quantum dynamics benchmark. Additionally, an analysis of the vibronic structure in the nonadiabatically coupled regime is presented using a variational eigensolver methodology.