Energy natural orbital characterization of nonadiabatic electron wavepackets in the densely quasi-degenerate electronic state manifold.

Dynamics and energetic structure of largely fluctuating nonadiabatic electron wavepackets are studied in terms of Energy Natural Orbitals (ENOs) [K. Takatsuka and Y. Arasaki, J. Chem. Phys. 154, 094103 (2021)]. Such huge fluctuating states are sampled from the highly excited states of clusters of 12 boron atoms (B), which have densely quasi-degenerate electronic excited-state manifold, each adiabatic state of which gets promptly mixed with other states through the frequent and enduring nonadiabatic interactions within the manifold. Yet, the wavepacket states are expected to be of very long lifetimes. This excited-state electronic wavepacket dynamics is extremely interesting but very hard to analyze since they are usually represented in large time-dependent configuration interaction wavefunctions and/or in some other complicated forms. We have found that ENO gives an invariant energy orbital picture to characterize not only the static highly correlated electronic wavefunctions but also those time-dependent electronic wavefunctions. Hence, we first demonstrate how the ENO representation works for some general cases, choosing proton transfer in water dimer and electron-deficient multicenter chemical bonding in diborane in the ground state. We then penetrate with ENO deep into the analysis of the essential nature of nonadiabatic electron wavepacket dynamics in the excited states and show the mechanism of the coexistence of huge electronic fluctuation and rather strong chemical bonds under very random electron flows within the molecule. To quantify the intra-molecular energy flow associated with the huge electronic-state fluctuation, we define and numerically demonstrate what we call the electronic energy flux.